Plasmonics
https://doi.org/10.1007/s11468-023-02082-7
RESEARCH
Theoretical Study of Graphene Wrapped CdS, CdSe, ZnSe,
and Cu2 O@Au Core‑Bishell Nanoparticles Embedded in Water
for Applications in Medical Fields and as a Sensor
Teshome Senbeta1
Received: 12 September 2023 / Accepted: 27 September 2023
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023
Abstract
We studied the effect of core-semiconductor radius, Au-shell thickness, graphene chemical potential, and graphene layers
on the plasmonic resonance under quasi-static approximation. The core quantum dots used in the study are CdS, CdSe,
ZnTe, and Cu2 O. The core-semiconductors are coated with Au and then wrapped with graphene. We compared the absorbance peaks position, the width of the absorbance peaks (FWHM), and the enhancement of the peak intensity of each corebishell nanoparticles. We considered three fixed radii of the core semiconductors; r1 = 20, 30, and 35 nm. For each radius,
the thickness of the Au varied from 1 to 15 nm, and 𝜇 varied from 1.0 to 1.6 eV. For all samples, the first resonance peaks
are found in the visible region or in near-infrared region depending on the value of the chemical potential and the second
peaks found in the infrared or near-infrared region. The effect of the graphene layers is also studied. From the four samples,
Cu2 O@Au@graphene has better absorbance/extinction cross-section, with relatively large values of d for each value of 𝜇 and
r1. CdSAu@graphene has least absorption cross-section intensity that occurs relatively at small thickness of Au. The overall
combined effect of the four parameters is enhanced absorption/extinction surface plasmon resonance peaks accompanied by
blue shift of the graphene resonance. The obtained results can be used in medical applications that require sensitive imaging,
therapy, and as a sensor.
Keywords Graphene · Semiconductor · Plasmonic · Nanoparticles absorbance
Introduction
Different studies showed that as the size of the material
changed from bulk to nanoscale, the properties of the materials significantly altered, and these nanoscale materials show
unique properties that are not observed in the bulk systems.
The new properties observed in nanoscale size are due to
enhanced surface to volume ratio, quantum confinement effect,
and dynamical interactions in the electronic structure [1].
Plasmonic nanoparticles (NPs) that constitute noble metals gold and silver showed unique optical properties due
to decrease in size and because of the change in the morphology of the material. Gold and silver are the most used
plasmonic materials as they have better absorbance due to
* Teshome Senbeta
teshome.senbeta@aau.edu.et; teshomesenbeta@gmail.com
1
Department of Physics, Addis Ababa University,
Addis Ababa, Ethiopia
negative real refractive index. When light interacts with electrons at the surface of a metal, it results in surface plasmon
resonance (SPR). If the wavelength of the incoming light is
much greater than the size of the nanoparticles (NPs), the
electrons at the surface of the metal oscillate collectively.
Plasmonic nanoparticles are known for their strong absorbers, scatters of light, and high field enhancement [2]. Gold
nanoparticles are widely used in the field of medicine for
X-ray imaging, computed tomography, drug delivery, nanosensing, diagnostics, thermal therapy, photo-induced therapeutics, and theranostics [3–10] due to its biocompatible,
capable to fix in the desired functionalization, not easily damageable, and low toxicity. These classes of materials exhibit
size and shape-dependent optical and electronic properties.
Core-shell nanoparticles (CSNPs) have received significant attentions from researchers and technologists because
of their interesting unique properties observed in the composite system but are not seen in either core or shell parts.
Core-shell materials have applications in a diversified fields,
like in catalysis, energy storage, coating agents, biology,
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Plasmonics
materials chemistry, biomedical, sensors, and in construction industry [11–20].
Metal/metaloxide core-shell nanoparticles and metal/
metal chalcogenide semiconductor core-shell nanoparticles
are used for energy and environmental applications [21, 22].
The use of metal/metaloxide core-shell nanoparticles as a
gas sensor is reported in [23]. Au@Cu2 O hybrid core-shell
nanoparticles showed enhanced and expanded plasmonic
tunability [24]. In [25], it was reported that Au@Cu2 O
showed good performance in surface plasmon resonance
that are attributed to the pronounced electronic sensitization,
high thermal stability, and low screening effect of Au nanoparticles in which this core-shell nanoparticles can be used
as a gas sensor. This core-shell nanoparticles also demonstrated absorption and scattering of lights over a broad spectral range across the visible and near-infrared regions. As
reported in [24], Au@Cu2 O can be used to the optimization
of the overall performance of hybrid heteronanostructurebased materials and/or devices for photonic, electronic, and
optoelectronic applications. Due to enhanced visible-light
absorption and high separation rate of electron–hole pairs,
Au@Cu2 O showed a better photocatalytic property [26, 27].
Au@Chalcogenides core-shell nanoparticles have great
applications in different areas due to efficient charge
transport and separation. The common Au@Chalcogenids
core-shell nanoparticles include Au@CdS, Au@CdSe, and
Au@ZnTe.
Au@CdS nanoparticles demonstrate better photocatalistic activity as heterojunction interface between Au and CdS
facilitates the separation of electron–hole pairs and transfers electrons from CdS to Au-core [28, 29]. In [30], it was
reported that by probing photoelectrochemical processes in
Au@CdS core-shell nanoparticles, it is possible to develop
surface plasmon resonance sensor for acetylcholinesterase
inhibitors. Au@CdS is also used as highly selective biosensors
[31]. Experimental work by [29] showed that Au@CdS can be
utilized as photocatalysts for reduction and oxidation reactions
as well as materials for two-photon absorption applications.
Metal/metal chalcogenide semiconductors materials are
well known for their efficiency in the photocatalytic reaction
to generate energy or wastewater treatment. Au@CdSe coreshell nanoparticle is another kind of metal/metal chalcogenide semiconductor that is used in photocatalytic activity,
photovoltaic, nanoelectronic,and sensing devices [32–37].
One more metal/metal chalcogenide semiconductor material that we need to discuss in the paper is Au@ZnTe. Like
other core-shell nanoparticles discussed above, Au@ZnTe
core-shell nanoparticles have different applications. This
material is used to produce a water soluble, biocompatible nanomaterial which may be exploited for drug delivery applications, cancer therapy, bio-imaging, and optoelectronic applications [38, 38–41]. The experimental
13
study by [41] on Au@ZnTe showed that this material has
good biosafety, nontoxicity, non-biohazards, and better
bio-interactions.
The purpose of this study is to investigate theoretically
better core-bishell material that enables tuning the graphene
plasmonic effect from infrared to visible and near-infrared
region. The theoretical work in [42] showed that a small
change in the chemical potential of graphene results in an
increase in the plasmon energy that is accompanied by blue
shift and significant enhancement in plasmon absorption.
Similar theoretical investigation on simiconductor@metal
@graphen monolayer indicates that the absorption enhancement in graphene can be easily tuned over a wide range from
visible to near-infrared by varying the size of the semiconductor core and the metal shell [43]. This study suggested
that the use of this material for graphene-based photodetectors and imaging sensors. The effect of changing the graphene chemical potential in tuning the plasmon resonance on
Ag@SiO2 @graphen core-shell nanostructures was reported
in [44], and this study suggested the hope to use this material
in the design of practical plasmonic devices.
The effect of shell thickness and core radius, dielectric
function of the host medium, and graphene layer on absorption cross-section was studied in [45]. The results of this
study showed that the presence of graphene layer enhances
the absorption and extinction cross-sections accompanied
by red shift. The presence of the graphene layer assists additional plasmon-plasmon interaction at the metal nanoparticles. Moreover, it was suggested that the use of bimetallic core-shell rapped with graphene for biological sensor
and optical communication devices. The use of graphene
wrapped dielectric materials like silica, polystyrene, and
titanium dioxide for biosensing, photothermal, and in vivo
imaging was reported in [46, 47] due to enhanced plasmonic
resonance near-infrared and visible regions. The tuning of
the plasmon resonance can be controlled by varying the
aspect ratio and the graphene chemical potential. The recent
study by [48] on graphene-assisted core-bishell nanoparticle exhibits two localized surface plasmons in the visible
and near-infrared regions in which the first resonance peaks
attributed to the core-shell interaction, while the second resonance peaks found in the near-infrared region corresponds
to the graphene plasmon excitation at the outer interface.
The local surface plasmon resonance of graphene demonstrate too narrow resonance peaks that may have applications
in sensing devices. It is this unique property that motivates
us to study graphene-coated composite nanostructure that
constitutes core semiconductor and shell metal (gold).
In this work, we study CdS@Au@graphene, CdSe@Au@
graphene, ZnTe@Au@graphene, and Cu2 O@Au@graphene
core-shell nanostructures. The effect of gold thickness, the
dielectric function of the core semiconductor quantum dot, the
Plasmonics
chemical potential, and the number of graphene layers on the
local surface plasmon resonance of the composite nanostructures with the aim to obtain better nanostructure for practical
application for biological sensing devices and other applications is the central interest of this work.
The paper is organized as follows: all theoretical foundations needed for evaluating polarizability, absorbance, scattering, and extinction cross-sections are presented in the
“Theoretical model and method” section. The “Results and
discussions” section is devoted to the presentation and analysis of numerical results for absorbance and extinction crosssection that depends on the shell thickness, core radius, and
number of graphene layers and graphene Fermi energy. The
“Conclusions” section concludes the findings of the study.
Theoretical Model and Method
In this work, we report core-bishell NPs composed of
CdS, CdSe, ZnTe, and Cu2 O semiconductor materials as
a core and Au noble metal as inner shell and graphene as
outer shell embedded in host matrix, water. The radius
of the semiconductor core is represented by radius r1 ,
the gold shell is represented by radius r2 = r1 + d (with
d being the thickness of the gold shell), and the graphene shell is characterized by its thickness tg and radius
r3 = r2 + tg . In addition, the core semiconductor material
is characterized by its dielectric function 𝜀1, the dielectric
function of gold is 𝜀2 , the dielectric function of graphene
is 𝜀3 , and the dielectric function of the host medium is 𝜀4 .
Figure 1 illustrates the schematic diagram of the proposed
core-bishell NP structure embedded in host matrix, water.
The proposed particle size is much smaller than the
incoming radiation wavelength, and hence, we can employ
the electrostatic approximation ( a ≪ 𝜆 , a being the size
of the nanoparticle and 𝜆 is the wavelength of the incoming radiation) to calculate the induced potentials and the
fields in the region of interest. The advantage of employing electrostatic approximation for such structure is that in
this approximation, the curl of the electric field E vanishes
and that leads to the reduction of the Maxwell equations
to simple form. We apply the necessary boundary condition to solve the Laplace equation. Note that for small size
particle, the polarization vector has the same direction as
applied electric field. As we will show soon, this approach
enables us to calculate the polarization of the media, a
quantity that is important in discussing absorbance and
extinction cross-sections in terms of the dielectric functions of the mediums.
Au
CdS, CdSe,
ZnTe, or Cu2O
r1
r2
r3
r
d
Fig. 1 Schematic representation of the model NPs. Here, the core is
the semiconductor material either CdS, CdSe, ZnTe, or Cu2 O with
dielectric function 𝜀1 and radius r1 . The first shell is the noble metal
gold with thickness d, radius r2, and dielectric function 𝜀2. The second shell is the graphene layer with thickness tg, radius r3, and dielectric function 𝜀3 . The host matrix is water with dielectric function 𝜀4
and radius r
Determination of Polarizability
For a plane wave of wavelength 𝜆 (𝜆 ≫ a), the quasi-static
approach enables us to solve the Laplace equation ∇2 Φ = 0.
For the modeled NPs structure, we have four potentials, Φ1 at
the core, Φ2 within the gold shell, Φ3 in the graphene shell,
and Φ4 at the host matrix with their solutions in compact form
are given by [48–50].
{
( )}
Bj
Φj = Aj r +
cos 𝜃
(1)
r2
where j = 1, 2, 3, 4 represent core semiconductor, gold shell,
graphene shell, and host matrix, respectively. The corresponding electric fields can be obtained from the gradient
of these potentials by imposing the necessary boundary conditions. Hence,
𝜕Φj
𝜕𝜃
|r=rj =
𝜕Φj
𝜀j
𝜕𝜃
𝜕Φj+1
𝜕𝜃
|r=rj = 𝜀j+1
(2)
|r=rj ,
𝜕Φj+1
𝜕𝜃
|r=rj ,
(3)
Performing the gradient operation given by Eqs. (2) and
(3) on Eq. (1) gives
Aj rj +
Bj
rj2
= Aj+1 rj +
Bj+1
rj2
,
(4)
13
Plasmonics
]
]
[
[
Bj+1
Bj
𝜀j Aj − 2 3 = 𝜀j+1 Aj+1 − 2 3 .
rj
rj
(5)
The potential of the electric field at the center of the core
is finite, and this demands B1 = 0. Moreover, the potential in
region 4 (at the host matrix) far from the graphene layer can be
approximated by the first term of Eq. (1). That is,
(6)
Φ4 = A4 r cos 𝜃,
where A4 = −E0 , E0 is the applied external field. Substituting Eqs. (4) and (5) back into Eq. (1) and then performing
the gradient operation gives the electric field at each region
as [48, 50]
{
}
{
}
Bj
Bj
̂
Ej = 2 3 − Aj cos 𝜃̂r +
+ Aj sin 𝜃 𝜃,
(7)
r
r3
where
A1 = A2 +
B2
r13
B2 = A4 𝜓r23
A3 =
A4 r23
(r23
B3 = A4
, B1 = 0, A2 =
B2 𝜑
𝜓
− A4 ,
𝜁
r3 𝜁
2
(𝜀1 − 𝜀2 )
r23 𝜁(𝜀1
+ 2𝜀2 ) + (𝜀1 − 𝜀2 )𝜑r13
(
)
B
A2
𝜅
+ 23 − 3 , ,
A
− 𝜉)
A4 r2 r2
4
(
)
A3
𝜅− 𝜉 ,
A4
r13 ,
𝜓=
𝜀3 𝜅
r23
(
2(r23 − 𝜉) + (r23 + 2𝜉)
(r23 − 𝜉)
)
.
From Eq. 7, the induced electric field in region 4 or at the
host matrix is
)
(
)
(
B4
B4
̂
+ A4 sin 𝜃 𝜃.
E4 = 2 − A4 cos 𝜃̂r +
r3
r3
With the help of B4 = A3 r33 + B3 − A4 r33 , E4 gives
)
( [
]( 3 )
r3
A3
B3
+ 1 E0 cos 𝜃̂r
E4 = 2 1 −
−
A4 r3 A4
r3
3
)
([
]( 3 )
r3
A3
B3
̂
− 1 E0 sin 𝜃 𝜃.
+ 1−
−
3
A4 r3 A4
r
3
The induced field outside the graphene shell or at the
host matrix is the same as a dipole field with effective dipole
moment given by p = 𝜀4 𝛼E0 . The polarizability 𝛼 is related to
the terms in the square brackets in Eq. (8) by
]
[
B
A
𝛼 = 4𝜋𝜖0 r33 1 − 3 − 3 3 ,
(9)
A4 r A4
3
where 𝜖0 = 8.85 × 10−12 Fm−1 is the permittivity of free
space. For a small particle as compared to the plane wavelength (𝜆 ≫ a, a size of the particle), the scattering and the
absorption cross-sections are given by [49]
𝜎abs =
1 4 2
k
Im(𝛼), 𝜎sca =
k |𝛼| ,
𝜖0
6𝜋𝜖02
(10)
A4 = −E0 , B4 = A3 r33 + B3 − A4 r33 ,
𝜎ext = 𝜎abs + 𝜎sca ,
with
√
where the wave number k = 2𝜋 𝜀4 ∕𝜆.
𝜅=
Dielectric Function
𝜀4
3
r3 ,
2 (𝜀4 − 𝜀3 ) 3
It is well known that the local surface plasmon of core-shell
nanoparticles highly depends on the dielectric function of the
constituent materials. As our proposed model consists of core,
bishell, and the embedding medium, it is necessary to provide
the dielectric function of each materials.
The dielectric function of the gold metal is given by the
modified Drude-Lorentz model that includes the size-dependent
dielectric function [49]
1 (2𝜀4 + 𝜀3 ) 3
r ,
𝜉=
2 (𝜀4 − 𝜀3 ) 3
𝜁=
𝜑=
𝜀2 (r23 − 𝜉) − (r23 + 2𝜉)𝜀3
(r23 − 𝜉)
,
2𝜀2 (r23 − 𝜉) + 𝜀3 (r23 + 2𝜉)
13
(r23
− 𝜉)
(8)
,
𝜀(a, 𝜔) = 𝜀(𝜔)exp +
𝜔2p
𝜔2 + i𝜔Γ0
−
𝜔2p
𝜔2 + i𝜔Γ
,
(11)
Plasmonics
where 𝜔p is the plasma frequency, Γ0 is damping constant,
and Γ is size-dependent of the bulk collision frequency
given by [49]
Γ = Γ0 + A
vf
a
(12)
.
Here, vf is the fermi velocity, A is a parameter that
depends on the geometry of the material, and we can set
A = 1 for simple Drude theory and isotropic scattering.
a is the reduced mean free path of electrons that can be
equated to r2 − r1 = d , d being the shell thickness of gold
for our case. 𝜀(𝜔)exp is the experimental bulk dielectric
function that consists of a contribution from both intraband and interband. The intraband contribution is from
free electron, and the interband contribution was arises
partly by polarizability and partly by interband transition.
𝜀(𝜔)exp is given by [48, 51]
𝜀(𝜔)exp = 1 −
Ω2p
𝜔2 + i𝜔Γ0
+
p
∑
j=1
fj 𝜔2p
𝜔2j − 𝜔2 − i𝜔Γj
.
(13)
√
with Ωp = f0 𝜔p is the plasma frequency associated to the
intraband transition with oscillator strength f0 and damping
constant Γ0 . p is the number of oscillator with frequency 𝜔p
and oscillator strength fj and lifetime 1∕Γj . The values of the
parameters indicated in Eqs. (11), (12), and (13) are used
according to [51].
The dielectric functions of the semiconductors used in
this study can be obtained from the dispersion√formula of
refractive index n(𝜆) through the relation n = 𝜀(𝜔) with
𝜔 = (2𝜋c)∕𝜆. c is speed of light. The dispersion formulas
for CdS and CdSe are given by [52, 53]
n2CdS = 5.1792 +
0.036927
0.23504
,
+
𝜆2 − 0.083591 𝜆2 − 0.23504
1.7680𝜆2
3.1200𝜆2
.
+ 2
− 0.2270 𝜆 − 3380
n2CdSe = 4.2243 +
𝜆2
(14)
3.01𝜆2
.
− 0.142
𝜆2
𝜀(a, 𝜔) = 5.5 + i
𝜎tot
,
𝜖0 𝜔tg
(17)
where 𝜎tot is the total optical conductivity that contains the
contribution from intraband and interband transitions, and tg is
the shell thickness of graphene with a value equals to 0.34 nm
for single layer and N × 0.34 × 10−9 m for N number of graphene layers. The total optical conductivity 𝜎tot depends on
the temperature of the sample T, the angular frequency 𝜔,
and the Fermi energy or the chemical potential 𝜇, which is
expressed as [42]
𝜎tot = 𝜎real (𝜔) + i𝜎imag (𝜔),
(18)
[
(
)
(
)]
𝜎0 H
ℏ𝜔 + 2𝜇
ℏ𝜔 − 2𝜇
tanh
+ tanh
𝜎real (𝜔) =
,
2
4kB T
4kB T
(19)
(
(
)
)
H𝜎0
4𝜇𝜎0
|ℏ𝜔 + 2𝜇|
2𝜇2
1− 2 −
log
.
𝜎imag (𝜔) =
ℏ𝜔𝜋
𝜋
|ℏ𝜔 − 2𝜇|
9t
(20)
Here, 𝜎0 = e2 ∕(4ℏ), H = 1 + (ℏ𝜔)2 ∕(36t2 ) with e is elementary charge of electron, ℏ is reduced Planck constant, T
is the temperature, t is the hopping parameter with a value of
2.7 eV at a temperature of 300 K [42], and kB is Boltzmann
constant. The appearance of the chemical potential (𝜇) in
Eqs. (18) to (20) show the possibility of tuning the graphene
dielectric function and in turn the plasmonic effect of the
core-shell nanostructure.
Before concluding this section, it is important to note the
dielectric function of the host matrix. The host matrix is
water with a dielectric function of 𝜀4 = 1.77.
(15)
According to [52], the incoming photon wavelength to
apply Eq. (14) is from 510 to 1400 nm and to use Eq. (15) is
from 101 to 22, 000 nm.
Similar expression can be unitized to obtain a wavelength-dependent dispersion formula for ZnTe [54]
n2ZnTe = 4.27 +
is negligible in the low energy ranges up to 2.6 eV [55–58]
and our work is in the visible and in the infrared regions.
The size and frequency-dependent dielectric function of
graphene is given by [42]
(16)
The incoming photon wavelength to use Eq. (16) is from
580 to 2500 nm.
The dielectric function of Cu2 O is set to the experimental
value of 7.5 in this study. The reason we decide to use this
constant value is because of the fact that the optical absorption
Results and Discussions
In this section, we present the effect of gold shell thickness
(d), the core radius (r1), the chemical potential (𝜇) of the graphene layer, and the number of graphene layers (N) have on
the surface plasmon resonance of the selected semiconductor
@Au@@graphene core-bishell composite NPs embedded in
host matrix, water. In other words, we discuss the absorbance,
and the extinction cross-sections are graphs plotted using
Eq. (10) that consists of the dielectric function expressions
through the expression of polarizability 𝛼. For simulating the
graphs of absorption and extinction cross-sections, we used
Mathematica 9.1 Software. In simulating the graphs, we use
13
Plasmonics
𝜀1 for the dielectric functions of the semiconductors. That is,
𝜀1 equals the square root of Eq. (14) for CdS core or square
root of Eq. (15) for CdSe or square root of Eq. (16) for ZnTe
and equals 7.5 for Cu2 O . Moreover, 𝜀2 equals the expression given by Eq. (11), and 𝜀3 equals the graphene dielectric
function given by Eq. (18). All constants like the plasma
frequency (𝜔p), damping constant (Γ0), oscillator strength ( f0
and fj ), and lifetime(1∕Γj ) are adopted from [51].
Figure 2a and b and Fig. 3a and b depict the absorption
cross-section as a function of the incoming radiation wavelength for CdS@Au@graphene, CdSe@Au@graphene,
ZnTe@Au@graphne, and Cu2 O@Au@graphene , respectively, embedded in host matrix, water. For each figure,
the core radius is fixed at 20 nm, the graphene chemical
potential 𝜇 = 1.0 eV , the graphene layer tg = 0.34 nm , and
the thickness of the metal shell is varied from 4 to 9 nm.
For all cases, the first resonance peak position shifts from
a longer wavelength to a low wavelength as the thickness
of the gold shell increases, but resonance peak positions
are different. For CdS@Au@graphene, the first peak position is located around 744 nm for the gold shell thickness
Fig. 3 Absorption cross-section as a function of radiation wavelength
for different values of gold shell thickness. The core radius is fixed
at 20 nm, tg = 0.34 nm, and 𝜇 = 1.0 eV . a ZnTe@Au@graphen and b
Cu2 O@Au@graphen embedded in host matrix water
Fig. 2 Absorption cross-section as a function of radiation wavelength
for different values of gold shell thickness. The core radius is fixed
at 20 nm, tg = 0.34 nm, and 𝜇 = 1.0 eV . a CdS@Au@graphen and b
CdSe@Au@graphen embedded in host matrix water
13
of 4 nm, and the resonance peak position is shifted to the
left at 621 nm for gold shell thickness of 9 nm. Similarly,
for CdSe@Au@graphene, the first resonance peak position is found around 820 nm for d = 4 nm and shifted to
the left at 655 nm for d = 9 nm . The first peak position of
ZnTe@Au@graphene that was found at 822 nm for the gold
shell thickness of 4 nm is shifted to the left at 620.5 nm
as the gold shell thickness increases to 9 nm. The trend is
almost the same for Cu2 O@Au@graphen with the first peak
position appeared at 924 for d = 4 nm and at 715 nm for
d = 9 nm. The amplitudes of these peaks are also different.
The second peaks position that arises due to the coupling
of electromagnetic radiation with the surface electrons at
the interface between the graphene layer and the gold shell
occurs at the same wavelength, around 997.2 nm for all
cases. The first set of resonance peaks is too wide, while
the second set of resonance peaks is too narrow with diminished in amplitudes. One of the objectives of this study is to
find the absorption peaks where the second peak dominates
over the first with a narrow width. Accordingly, a close look
into Figs. 2 and 3 shows the second peaks dominate over the
Plasmonics
first for the small values of gold shell thickness provided that
the chemical potential is small, 𝜇 = 1.0 eV. This situation is
illustrated in Figs. 4 and 5.
Figures 4 and 5 clearly show the effect of gold shell
thickness on the surface plasmon resonance of the selected
NPs. Even though we used the same parameters in Figs. 2
and 3, the value of the gold shell thickness that gives us a
better second peak resonance is different depending on the
core material. From Fig. 4a, the width of the second peak
for CdS@Au@graphene core-bishell is 1 nm and the corresponding gold shell thickness is 4, and from Fig. 4b, the
second peak width of CdSe@Au@graphene core-bishell NP
is 2 nm with gold shell thickness of 5 nm.
Similarly, from Fig. 5a, the width of the second peak for
ZnSe@Au@graphene core-bishell is 2.1 nm and the corresponding gold shell thickness is 5, and from Fig. 5b, the
second peak width of Cu2 O@Au@graphene core-bishell NP
is 1.8 nm with gold shell thickness of 7 nm.
The width and the position of the peaks for the first
resonance peaks are 153.7 nm with peak position at
Fig. 5 Absorption cross-section as a function of radiation wavelength
for a gold shell thickness of 5 nm for CdS@Au@graphen and b gold
shell thickness of 7 nm for CdSe@Au@graphen. The core radius is
fixed at 20 nm, tg = 0.34 nm, and 𝜇 = 1.0 eV . Host matrix is water
Fig. 4 Absorption cross-section as a function of radiation wavelength
for a gold shell thickness of 4 nm for CdS@Au@graphen and b gold
shell thickness of 5 nm for CdSe@Au@graphen. The core radius is
fixed at 20 nm, tg = 0.34 nm, and 𝜇 = 1.0 eV . Host matrix is water
744 nm for CdS@Au@graphene, 136.6 nm with peak
position at 761.8 nm for CdSe@Au@graphene, 136.5 nm
with peak position at 762.5 nm for ZnSe@Au@graphene,
and 110 nm with peak position at 767.7 nm for
Cu2 O@Au@graphene. These values are almost the same for
CdSe/ZnTe@Au@graphene NPs. Relatively, the amplitude
of Cu2 O@Au@graphene is better. The variation in peaks
position, peaks width at half maxima, and peaks amplitude
is due to the difference in the dielectric functions of the core
material. As the dielectric function increases, the plasmon
resonance peaks demonstrate red shift [47]. The results in
Figs. 4 and 5 justify this fact.
It is also necessary to discuss the effect of core radius on the
plasmonic effect of core-bishell materials under consideration.
Figures 6, 7, 8 and 9 illustrate the effect of core radius of
the semiconductor materials on the surface plasmon resonance
of the core-bishell materials. We changed the core radius of
Figs. 2 and 3 from 20 to 30 nm and to 35 nm. As clearly seen
from Figs. 6, 7, 8, and 9, the first resonance peaks position
shifts toward the longer wavelength regions, and at the same
time, the extinction cross-section amplitudes increase.
13
Plasmonics
Fig. 6 Extinction cross-section of CdS@Au@graphen as a function
of radiation wavelength for gold shell thickness of 5 nm when a the
core radius is fixed at 30 nm and b core radius is fixed at 35 nm. For
both cases, 𝜇 = 1.0 eV, tg = 0.34 nm, and the host matrix is water
For CdS@Au@graphene, the extinction cross-section
peaks for r1 = 20 nm occur at 748 nm and at 621 nm for
d = 4 nm and d = 9 nm, respectively. However, as illustrated
in Fig. 6, for r1 = 30 nm , the first peaks position is shifted
to the higher wavelength side to around 848 nm and 670 nm
for d = 4nm and d = 9 nm, respectively. Further increase
in the core radius to r1 = 35 nm results in the shift of the
first resonance peaks positions to 892 nm for d = 4 nm and
697 nm for d = 9 nm. Another point that can be noticed from
Fig. 6a and b is that the amplitude of the extinction crosssection increases as the result of the increase in the core
radius. Particularly, the ratio of the extinction cross-section
peaks intensity for r1 = 30 to r1 = 20 nm approximately
gives 2.67 and 3.5 for d = 4 nm and d = 9 nm, respectively.
And this cross-sections amplitude ratio is 3.9 and 5.8 for
r1 = 35 nm for d = 4 nm and d = 9 nm , respectively. The
increase in the resonance absorption and extinction crosssection peaks as the thickness of the Au shell increases is
attributed to the increase in the conduction electrons at the
Au shell surfaces. The second peaks position does not show
any significant shift due to the change in the core radius as
13
Fig. 7 Extinction cross-section of CdSe@Au@graphen as a function
of radiation wavelength for gold shell thickness of 5 nm when a the
core radius is fixed at 30 nm and b core radius is fixed at 35 nm. For
both cases, 𝜇 = 1.0 eV, tg = 0.34 nm, and the host matrix is water
well as the change in the thickness of the gold shell. As we
see soon, the second peak will shift to the left or the high
energy, low wavelength region, as the chemical potential of
graphene increases.
The extinction cross-section peaks for r1 = 20 nm of
CdSe@Au@graphene occur at around 820 nm and at 657 nm
for d = 4 nm and d = 9 nm , respectively. However, as illustrated in Fig. 7, for r1 = 30 nm , the first peaks position are
shifted to higher wavelength side to around 939 nm and
723 nm for d = 4nm and d = 9 nm, respectively. Further
increase in the core radius to r1 = 35 nm results in the shift
of the first resonance peaks positions to 974 nm for d = 4 nm
and at 756 nm for d = 9 nm. The ratio of the extinction crosssection intensity for r1 = 30 to r1 = 20 nm approximately
gives 2.4 and 3. for d = 4 nm and d = 9 nm, respectively.
And this ratio gives 3.2 when d = 4 nm and 4.6 for d = 9 nm
and r1 = 35 nm.
Changing the core radius from r1 = 20 to 30 nm and
then to 35 nm for ZnTe@Au@graphene core-bishell NPs
almost has similar results with the extinction cross-section
intensity of CdSe@Au@graphene core-bishell structure.
That is the first peak position for ZnTe@Au@graphene
Plasmonics
Fig. 8 Extinction cross-section of ZnTe@Au@graphen as a function
of radiation wavelength for gold shell thickness of 5 nm when a the
core radius is fixed at 30 nm and b core radius is fixed at 35 nm. For
both cases, 𝜇 = 1.0 eV, tg = 0.34 nm, and the host matrix is water
Fig. 9 Extinction cross-section of Cu2 O@Au@graphene as a function
of radiation wavelength for gold shell thickness of 5 nm when a the
core radius is fixed at 30 nm and b core radius is fixed at 35 nm. For
both cases, 𝜇 = 1.0 eV, tg = 0.34 nm, and the host matrix is water
when r1 = 20 nm occurs at around 822 nm and at 657 nm
for d = 4 nm and d = 9 nm, respectively. As can be deduced
from Fig. 8, for r1 = 30 nm , the first peaks positions are
shifted to higher wavelength side to around 944 nm and
723 nm for d = 4nm and d = 9 nm, respectively. Similarly,
for r1 = 35 nm, the first resonance peaks positions occurred
at 975 nm for d = 4 nm and at 757 nm for d = 9 nm. The
extinction cross-section intensities ratio for r1 = 30 to
r1 = 20 nm is approximately 2.41 and 3 for d = 4 nm and
d = 9 nm, respectively. And the extinctions cross-section
intensities ratio of r1 = 35 nm to r1 = 20 nm gives 2.93 when
d = 4 nm and 4.61 for d = 9 nm. As in other cases discussed
above, there is no shift in the second peaks position; for
samples under study, the second peaks are found around
997.2 nm. The ratio of the highest peak for r1 = 30 nm to
r1 = 20 nm gives 2.29, 2.4, 2.42, and 2.63 and the ratio of the
highest peak at r1 = 35 nm to r1 = 20 nm is 3.75, 3.9, 3.83,
and 4.27 for CdS, CdSe, ZnTe, andCu2 O@Au@graphene ,
respectively. Note that these highest peaks are found for different values of d as the core radius r1 are different.
The result of changing r1 from 20 to 30 nm and then to
35 nm for Cu2 O@Au@graphene is illustrated in Fig. 9.
What makes this case different from the other three materials discussed is that for d = 4 nm , the first peaks totally
disappeared or merged with the second peak at a wavelength
value of 997.2 nm. For gold shell thickness of 9 nm, the
first extinction cross-sections resonance peaks appeared at
a wavelength of 804 nm for r1 = 30 nm and at 846.6 nm for
r1 = 35 nm. The cross-sections amplitude ratios are relatively small for Cu2 O@Au@graphene in comparison to the
three materials discussed here. One of the reason, as we see
below, is that Cu2 O@Au@graphene needs relatively higher
chemical potentials for peaks to be split, and for chemical
potential of 𝜇 = 1.4 and 𝜇 = 1.6 , it shows better enhancement of the resonance of surface plasmons. As noted in [45],
increasing the core radius allows more electrons to lie in the
core surface, and the plasmon-plasmon interaction in the
interface region increases that result in the enhancement of
the surface plasmon resonance.
Figures 10 and 11 demonstrate the effect of graphene
chemical potential on the surface plasmon resonance of
the selected core-bishell nanoparticles. Figure 10 depicts
the absorption cross-section as a function of the incoming radiation wavelength for (a) CdS@Au@graphene and
13
Plasmonics
Fig. 10 Absorption cross-section as a function of graphene chemical potential for a CdS@Au@graphene with d = 3 nm and b
CdSe@Au@graphene with d = 4 nm. For both graphs, the core radius
is fixed at 20 nm, tg = 0.34 nm, and the host matrix is water
(b)CdSe@Au@graphene when the core radius is fixed at
20 nm. From Fig. 10a, a very narrow peak was formed at a
wavelength of 997.2 nm for 𝜇 = 1.0 eV that corresponds to a
gold shell thickness of d = 3 nm. A wide and too wide peaks
appeared at 𝜆 = 881.5 nm and at 810.5 nm for 𝜇 = 1.2 eV
and 𝜇 = 1.4 eV, respectively. Similar pattern is observed
for CdSe@Au@graphene as shown in Fig. 10b, but with
d = 4 nm. For CdSe@Au@graphene, the narrow peak
appeared at 𝜆 = 997.2 nm for 𝜇 = 1.0 eV , a wide peak at
𝜆 = 879.4 nm for 𝜇 = 1.2 eV , and too wide absorption peak
at 𝜆 = 812.5 nm for 𝜆 = 1.4 eV.
We further studied the effect of graphene chemical potentials on the plasmon resonance of ZnTe@Au@graphene
and Cu2 O@Au@graphene core-bishell NPs embedded in water as depicted in Fig. 11a and b, respectively.
For ZnTe@Au@graphen, the peaks positions and the
cross-sections amplitudes are almost the same as that for
CdSe@Au@graphene cases. For Cu2 O@Au@graphene ,
the peaks positions for 𝜇 = 1.0 eV and 𝜇 = 1.2 eV are
again similar to the other three cases, but for 𝜇 = 1.4 eV ,
there is a significant shift in comparison to others that is
13
the peak position occurs at 𝜆 = 852.5 nm while for others
around 812 nm. Here, for Cu2 O@Au@graphene, we did not
found significant resonance peaks splitting for d = 3 nm
and d = 4 nm. From the four figures indicated in Figs. 10
and 11, one can deduce that increasing the chemical potential shifts the absorption resonance peaks to the left, to the
higher energy direction, and the peaks amplitude reduced
in good agreement with the reports in [44, 47, 48]. It is also
noteworthy to mention the local surface plasmon resonance
due to graphene approaches or overlaps to the metal local
surface plasmon region as the graphene chemical potential
increases further.
To see the combined effect of the shell thickness, the core
radius, and the graphene chemical potentials that give better
enhanced local surface plasmons, we tabulated the results
in Table 1.
Table 1 shows the combined effect of the core radius, the
metal gold shell thickness, and the graphene chemical potential on the absorption cross-section resonance peaks. The
first column of the table shows the core-bishell materials
we studied with the notation ′ gra′ used for graphene in the
table, and the last column represents the width of the second
peaks of full width at half maxima (FWHM). The study carried out for a gold shell thickness of 1 nm to 15 nm and for
𝜇 = 1.0, 1.2, 1.4, and 1.6 eV except the last row of the table
where we extend the gold shell thickness up to d = 18 nm for
Cu2 O@Au@graphene that corresponds to 𝜇 = 1.6 eV. The
values of gold shell thickness d given in the third column are
those values that able to produce better narrow absorption
cross-section resonace peaks for the given core radius and
graphene potential. Note that in each case, the graphene shell
thickness is about 0.34 nm.
The increase in the radius of the core has two effects on
the surface plasmon resonance peaks; the first is it increases
the intensity of the absorption cross-section, and the second is it produce a red shift of the first resonance peaks
and has no any effect in shifting the second peaks position.
The effect of increasing the chemical potential is to shift
both resonance peaks to the lower wavelength region and
reducing the peaks intensity. On the other hand, the effect
of increasing the gold shell thickness is to shift the first
resonance peaks to the higher energy side of the incoming
radiation with an increase in the intensity of the first peaks
is that accompanied by an irregular change in the intensity
of the second peaks without change in the peaks position.
Therefore, the overall combined effect is enhanced intensity that is accompanied by blue shift of the second peaks
position. The first peaks position depends on the amount of
the change we made in r1, because significant change in r1
resulted in significant red shift of the first peaks position.
The narrow width of the second resonance peaks can be
obtained by careful selection of the three quantities (d, 𝜇 ,
and r1) together with the dielectric function of the core
Plasmonics
Table 1 Combined effect
of core radius, metal shell
thickness, and graphene
chemical potential on the
plasmon resonance peaks
position, intensity, and width
of the resonance peaks. For all
cases, tg = 0.34 nm
Material
r1/nm
d/nm
𝜇/eV
𝜆1 ∕nm
𝜆2 ∕nm
FWHM(𝜆2)
CdS@Au@gra
CdSe@Au@gra
ZnTe@Au@gra
Cu2 O@Au@gra
CdS@Au@gra
CdSe@Au@gra
ZnTe@Au@gra
Cu2 O@Au@gra
CdS@Au@gra
CdSe@Au@gra
ZnTe@Au@gra
Cu2 O@Au@gra
CdS@Au@gra
CdSe@Au@gra
ZnTe@Au@gra
Cu2 O@Au@gra
CdS@Au@gra
CdSe@Au@gra
ZnTe@Au@gra
Cu2 O@Au@gra
CdS@Au@gra
CdSe@Au@gra
ZnTe@Au@gra
Cu2 O@Au@gra
CdS@Au@gra
CdSe@Au@gra
ZnTe@Au@gra
Cu2 O@Au@gra
CdS@Au@gra
CdSe@Au@gra
ZnTe@Au@gra
Cu2 O@Au@gra
CdS@Au@gra
CdSe@Au@gra
ZnTe@Au@gra
Cu2 O@Au@gra
CdS@Au@gra
CdSe@Au@gra
ZnTe@Au@gra
Cu2 O@Au@gra
CdS@Au@gra
CdSe@Au@gra
ZnTe@Au@gra
Cu2 O@Au@gra
CdS@Au@gra
CdSe@Au@gra
ZnTe@Au@gra
Cu2 O@Au@gra
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
35
4
5
5
7
5
6
6
8
6
8
8
10
8
10
11
13
4
5
5
7
5
7
7
9
7
9
9
12
9
11
9
15
4
6
6
8
6
7
7
10
8
10
10
13
10
12
13
18
1
1
1
1
1.2
1.2
1.2
1.2
1.4
1.4
1.4
1.4
1.6
1.6
1.6
1.6
1
1
1
1
1.2
1.2
1.2
1.2
1.4
1.4
1.4
1.4
1.6
1.6
1.6
1.6
1
1
1
1
1.2
1.2
1.2
1.2
1.4
1.4
1.4
1.4
1.6
1.6
1.6
1.6
744
761.8
762.5
767.7
696.6
719.5
721
736.1
664
666
667.7
692.3
621.9
633.6
622.5
650.4
842.9
865.6
868
874.2
780
773.3
775.5
802.3
706.3
719.2
717.9
733.6
661.2
678.9
678.9
689.5
886.3
858.7
860
880.3
774.5
812
813
814.3
710.5
726.5
728.5
784.9
668.9
689.1
678
687
997.2
997.2
997.2
997.2
877.8
877
877
876.1
791.8
791.6
791.4
791.2
728.1
728.4
727.9
728.9
998
996.9
997.4
997
877.9
876.7
877
877
791.9
791.7
791.9
791.6
728.9
729
729.1
729
998.3
997
996.7
997
877.3
878
877.9
876.8
791.9
792
791.9
791.6
728.9
729.3
729.1
728.8
1
2
2.1
1.8
2.7
1.9
2.7
2.3
3.4
3.2
3
3.4
3.0
3
3.6
3.8
5
4.3
4.1
3.1
4.6
3.9
4.6
4.2
5.2
5
5.1
4.3
4.7
6.1
5.3
6
8.9
3.3
3
3.1
5
4.3
7.2
5.2
5.2
4.8
5.3
6.3
6.7
7.8
54
4.7
13
Plasmonics
Fig. 11 Absorption cross-section as a function of graphene chemical potential for a ZnTe@Au@graphene with d = 4 nm and b CdSe@
Au@graphene with d = 5 nm.For both graphs, the core radius is
fixed at 20 nm, tg = 0.34 nm , and the host matrix is water
Fig. 12 Absorption cross-section as a function of radiation wavelength for a gold shell thickness of 8 nm for CdS@Au@graphen and
b gold shell thickness of 10 nm for CdSe@Au@graphen. The core
radius is fixed at 35 nm, tg = 0.34 nm and 𝜇 = 1.4 eV , and the host
matrix is water
semiconductor materials. To support this idea, we can take
one example for each material from Table 1.
If we change the three parameters of CdS@Au@graphene
that is if r1 = 20 nm → r1 = 30 nm , d = 4 nm → d = 7 nm ,
and 𝜇 = 1.0 eV → 𝜇 = 1.4 eV , the first resonance peak
shifted from 𝜆1 = 744 nm to 𝜆1 = 706.3 nm and the second resonance peak position shifted from 𝜆2 = 997.2 nm
to 𝜆2 = 791.9 nm. For CdSe@Au@graphene, if the three
parameters changed according to r1 = 20 nm → r1 = 35 nm,
d = 6 nm → d = 10 nm , and 𝜇 = 1.2 eV → 𝜇 = 1.4 eV ,
the first resonance peak shifted from 𝜆1 = 719.5 nm to
𝜆1 = 726.5 nm and the second peak position shifted from
𝜆2 = 877 nm to 𝜆2 = 792 nm. Here, as the change in r1 is
significant, the first peak is red shift in contrary to the case
of CdSe@Au@graphene. If r1 = 30 nm → r1 = 35 nm ,
d = 9 nm → d = 13 nm , and 𝜇 = 1.4 eV → 𝜇 = 1.6 eV ,
the first resonance peak shifted from 𝜆1 = 717.9 nm
to 𝜆1 = 678 nm and the second resonance peak position shifted from 𝜆2 = 991.9 nm to 𝜆2 = 729.1 nm for
ZnTe@Au@graphene. Similarly, for Cu2 O@Au@graphene,
changing r1 = 20 nm → r1 = 30 nm, d = 7 nm → d = 9 nm,
and 𝜇 = 1.0 eV → 𝜇 = 1.2 eV , the first resonance peak
shifted from 𝜆1 = 767.7 nm to 𝜆1 = 802.3 nm and the second resonance peak position shifted from 𝜆2 = 997.2 nm
to 𝜆2 = 877 nm. Note that the FWHM presented in the last
column of Table 1 are the best narrow width from the available simulated graphs. That is from 15 graphs plotted for a
shell thickness of d = 1 nm to d = 15 nm for each values of
r1 and 𝜇. Hence, we select the graph that has small width at
FWHM and the graph that its second peak dominates over
the first or relatively equals in intensity.
From Table 1, it is not possible to see the enhanced intensity of the absorption cross-section. To show this enhancement, we present Figs. 12 and 13, and these figures can be
compared with Figs. 4 and 5.
Figures 12 and 13 depict the absorption cross-section as
a function of incoming radiation wavelength for r1 = 35 nm,
𝜇 = 1.4 eV of the four sample materials under study. Hence,
because of the reasons discussed above, their gold metal shell
thickness is different. Comparing Figs. 4a and 12a, as we
change r1 = 20 nm → r1 = 35 nm , d = 4 nm → d = 8 nm ,
13
Plasmonics
Fig. 13 Absorption cross-section as a function of radiation wavelength for a gold shell thickness of 10 nm for ZnTe@Au@graphen
and b gold shell thickness of 12 nm for Cu2 O@Au@graphen. The
core radius is fixed at 35 nm, tg = 0.34 nm and 𝜇 = 1.4 eV , and the
host matrix is water
Fig. 14 Absorption cross-section as a function of radiation wavelength
for different values of graphene shell layers a CdS@Au@graphen of
gold shell thickness of 8 nm and b for CdSe@Au@graphen of gold
shell thickness of 10 nm. For both figures, the core radius is fixed at 35
nm, and the graphene chemical potential is 𝜇 = 1.4 eV embedded in
host matrix water
and 𝜇 = 1.0 eV → 𝜇 = 1.4 eV , the intensity of the second
peak increased from 4.12 to 31.22 which is about 7.6 folds
and even this is about 9.5 folds for the same radius but with
𝜇 = 1.6 eV and d = 10 nm for CdS@Au@graphene. Similar comparison between Figs. 4b and 12b gives enhanced
intensity of about 7.5 times for CdSe@Au@graphene when
the core radius increased from 20 to 35 nm, the chemical
potential increased from 1.0 to 1.4 eV, and the gold shell
thickness increased from 5 to 10 nm. Here, the enhancement
is about 9.4 folds for 𝜇 = 1.6 eV and d = 12, while keeping
the r1 at 35 nm.
To demonstrate the combined effect of the three parameters (d, 𝜇, andr1) on the intensity of the absorption crosssection of ZnTe@Au@graphene and Cu2 O@Au@graphene,
we simulated Fig. 13. Comparing Figs. 5a and 13a, we
observe that there is 7.5 folds in the intensity of the
absorption cross-section when r1 = 20 nm → r1 = 35 nm ,
d = 5 nm → d = 10 nm , and 𝜇 = 1.0 eV → 𝜇 = 1.4 eV for
ZnTe@Au@graphene. This enhancement is about 9.53 if
r1 = 20 nm → r1 = 35 nm , d = 4 nm → d = 13 nm , and
𝜇 = 1.0 eV → 𝜇 = 1.6 eV. Finally, for Cu2 O@Au@graphene,
the peak height at r1 = 20 nm , d = 7 nm , and 𝜇 = 1.0 eV of
Fig. 5b is about 7.07, and the peak height at r1 = 35 nm ,
d = 13 nm , and 𝜇 = 1.4 eV of Fig. 13b is about 50.38.
Similarly, the peak height at r1 = 35 nm , d = 18 nm , and
𝜇 = 1.6 eV is 65.4 (figure not shown here). The ratio
of these heights gives 7.13 and 9.25 for 𝜇 = 1.4 eV and
𝜇 = 1.6 eV, respectively.
The other property that we studied in the present
work is the effect of number of graphene layers on the
absorption, scattering, and extinction cross-section of the
selected core-bishell NPs embedded in host matrix. The
increase in the number of graphene layers that wrapped
over the gold metal significantly increases the absorption
or the extinction cross-section of the core-bishell materials considered in this study. We investigated the effect of
changing the graphene layer for N = 1, 2, 3, and 4 for each
materials with different radii as discussed above.
From Figs. 14 and 15, the increase in the number of graphene layers results in considerable increase in the intensity
13
Plasmonics
of the absorption cross-section. In addition to the increase
in absorption cross-section, the increase in number graphene
layers shows a red shift in the position of the second set
of resonance peaks that is associated to the plasmon resonance at the interface between gold shell and the graphene
layer. As one can infer from Figs. 14 and 15, the increase in
graphene layer from N = 1 to N = 3 doubles the absorption
peaks for samples under studied nearly.
The other feature of the increase in the number of graphene layers is the chance to tune the resonance peaks from
far infrared window to the near infrared window by adjusting
the chemical potential, which is very important in medical therapy. To tune the resonance peaks from far infrared
to infrared and near-infrared regions that correspond to the
two windows of medical applications, the graphene chemical
potentials has to be increased, say from 1.0 to 1.4 eV. Even
the shift and the enhancement is very better for 𝜇 = 1.6 eV.
We a l s o c h e ck e d w h e t h e r o u r p r o p o s e d
Semiconductor@Au@graphene were enhanced in relation
to Semicondutor@Au core-shell NPs embedded in the same
host matrix (graphs not shown here). The results show that
for single-layer graphene ( tg = 0.34 nm ), there is a slight
decrease of the first resonance absorption cross-section peaks
for materials we studied. As an example, the absorption peak
intensity for graphene unwrapped of CdS@Au core-shell NP
embedded in host matrix water is about 30.46 × 10−15 m2
when r1 = 30 nm, d = 7 nm with the peaks position located
at 706.7 nm. But for graphene wrapped CdS@Au@graphene,
the first peak intensity of the absorption cross-section is about
20.13 × 10−15 m2 r1 = 30 nm , d = 7 nm , and 𝜇 = 1.4eV ,
with the peaks position located at 706.7 nm. Similar calculations give us the absorption cross-section peaks intensity of
30.46 × 10−15 m2 (d = 9 nm), 31.14 × 10−15 m2 (d = 9 nm),
and 32.74 × 10−15 m2 (d = 12 nm) for CdSe@Au, ZnTe@Au,
and Cu2 O@Au, respectively, when r1 = 30 nm. For graphene
wrapped case, the absorption cross-section peaks intensity are
21.24 × 10−15 m2 (d = 9 nm), 20.92 × 10−15 m2 (d = 9 nm),
and 28.74 × 10−15 m2 (d = 12 nm) for CdSe@Au@graphen,
ZnTe@Au@graphene, and Cu2 O@Au@graphen , respectively, when r1 = 30 nm and 𝜇 = 1.4 eV. The decrease in the
absorption cross-section is attributed to the effect of graphene
chemical potentials. However, as discussed above, when we
increase the number of graphene layers, there is significant
increase in the absorption cross-section intensities.
Conclusions
Fig. 15 Absorption cross-section as a function of radiation wavelength for
different values of graphene shell layers a ZnTe@Au@graphen of gold
shell thickness of 10 nm and b for Cu2 O@Au@graphen of gold shell
thickness of 13 nm. For both figures, the core radius is fixed at 35 nm,
and the graphene chemical potential is 𝜇 = 1.4 eV embedded in host
matrix water
13
With the help of a quasi-static approximation, we calculated
the expression for optical polarizability of the three layered
core-bishell NPs embedded in host matrix, water. With the
aim to find better materials that may be used for sensor and
medical therapy in the visible, near-infrared, and in the infrared regions, we proposed four different materials consisting
of the semiconductor core (CdS, CdSe, ZnTe, andCu2 O), inner
shell Au, and outer shell graphene embedded in water. As the
dielectric functions of the four materials are different, the
optical absorption, extinction, and scattering cross-section
are also different. In addition to varying the dielectric functions of the materials considered in this study, we used four
parameters: radius of the core semiconductor (r1 ), the thickness of the inner gold shell (d), the chemical potential of
graphene (𝜇), and the number of graphene layers (N).
Our results show that as the shell thickness of gold metal
increased, the first resonance peak position shifted to the
lower wavelength region and accompanied by an increase
in the intensity of the absorption cross-section, but no shift
in the second peaks position with an irregular change in the
peaks amplitude. As the radius of the core-semiconductor
material increased, the first absorbance peak position
shifted to a larger wave length side accompanied with an
increase in the intensity of the absorbance peaks. The effect
of increasing graphene chemical potential is shifting both
Plasmonics
peaks position to the low wavelength region and decreasing
the intensity of the peaks. Moreover, our study of the effect
of the number of graphene layers shows that increasing the
number of the graphene layer gives significant increment
in the intensity of the absorption/extinction cross-section
and red shift in the peaks positions. The overall combined
effect is enhanced absorption/extinction cross-sections in
the desired window of the wavelength region that can be
utilized in different applications. Our findings are in good
agreement with other studies carried out for different materials as reported in [41, 44, 45, 47, 48, 59]. Form the four
selected core-bishell NPs, Cu2 O@Au@graphene shows
better absorbance cross-section when the chemical potential is large and when thickness of gold shell is also large.
From the other side, when the chemical potential and the
shell thickness of gold shell are small, CdS@Au@graphene
shows better absorption cross-section intensity spectra. The
absorption cross-section spectra of CdSe@Au@graphene
and ZnTe@Au@graphene are almost similar, and no significant difference observed. This is may be due to very
close dielectric functions of the two materials.
Finally, the obtained results can be utilized in the fabrication of sensors that needs very narrow width of the absorption
peaks. Similarly, as we able to tune the graphene resonance
absorbance peaks to the near-infrared and infrared regions,
the obtained results can be used for medical imaging that
needs very sensitive absorbance and thermal therapy.
Author Contributions As this work is a solo work, all tasks of research
problem formulation, manuscript writing, data analysis, discussion, and
writing the final version of the manuscript were prepared by Teshome
Senbeta Debela.
Data Availability This work is a theoretical work, and I used Mathematica 9.1 software to generate all numerical results and graphs. The
programs used, the procedures followed, and the data generated for
this work can be available on request from the author at email address
indicated at the first page of this manuscript.
Declarations
Competing Interests The author declares no competing interests.
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13
Photonics and Nanostructures - Fundamentals and Applications xxx (xxxx) xxx
Contents lists available at ScienceDirect
Photonics and Nanostructures - Fundamentals
and Applications
journal homepage: www.elsevier.com/locate/photonics
Enhanced magneto-optical properties of Fe3O4@Au nanoparticles and its
reverse core-shell nanostructure embedded in host matrix SiO2
Teshome Senbeta
Department of Physics, Addis Ababa University, Addis Ababa, Ethiopia
A R T I C L E I N F O
A B S T R A C T
Keywords:
Core-shell
Dielectric function
Polarizability
Absorbance
We studied the effect of electric and magnetic polarizability of Fe3O4@Au and the reverse structure Au@Fe3O4
core-shell spherical nanostructures embedded in SiO2. Employing electrostatic approximation and MaxwellGarnett effective medium theory, we evaluate the electric and magnetic polarizability, the refractive index
and absorbance as a function of radiation energy. The modified Drude-Lorentz form and Lorentz model used to
evaluate ϵ(ω) and μ(ω), respectively. For fixefd r2 = 30 nm, β = 0.875, εh = 3.9 and f = 0.001 maximum
absorbance obtained at E = 2.742 eV for Au@Fe3O4 core-shell and at E = 2.937 eV for the reverse structure with
β = 0.578. The ratio of the maximum absorbance peak of Au@Fe3O4 core-shell to Fe3O4@Au core-shell gives 3.5.
Both graphs of n2 and absorbance possess three sets of peaks. All sets of resonance peaks of Fe3O4@Au found in
the visible region. For the revers structure the first two sets of resonance peaks found in the visible region and the
third set of resonance peaks in UV region. The peaks arise due to the coupling between the surface plasmon of the
gold metal with Fe3O4∕SiO2 interfaces and the interaction of incident radiation with magnetic dipole moment of
the magnetic semiconducting nanoparticles. The findings may be used in applications that require the combined
plasmonic and magnetic effects such as drug delivery.
1. Introduction
Nanoscience as a field of study of the nanoscale structures and
molecules shows significant development in the last few decades. The
technology that applies the nonoscience is defined as nanotechnology
[1]. The nanotechnology activities include both manufacturing and
manipulating nanomaterials in the atomic scale. Those materials engi­
neered through nanotechnology used for different applications. Of
course, nowadays nanotechnology used in every fields and to mention
some common areas where we use them are sunscreen, adhesive,
coating and painting industries, in sport materials like tennis ball rac­
quets fabrication, in the furniture and cloth industries, computer chips,
in medicine field for both diagnoses and treatment of diseases, in the
field of environmental protections, biosensing devices and so on [2–5,6,
7].
As the size of material reduced from bulk to nanoscale it shows
unique properties that are not observed in the bulk states. These unique
properties may be attributed to large value of surface to volume ratio,
quantum effect as the result of size reduction, and electrodynamical
interactions in the material [8].
Nanoparticles (NPs) composed of noble metals such as gold, silver
and platinum demonstrate unique optical properties due to their size
and shape. These metals are also the most utilized as plasmonic mate­
rials. Plasmonic materials exhibit plasmon resonance, a resonance
occurred due to the interaction of light and electrons at the surface of
metals. This kind of resonance is called Surface Plasmon Resonance
(SPR). If the size of the nanoparticles much smaller than the wavelength
of the incoming light, the surface electrons collectively oscillate with the
light propagation. Such kind of oscillation occurs being on the frequency
match between the frequency of incoming light and the frequency of free
electrons.
Plasmonic nanoparticles are characterized by strong absorbers,
scatters of light and high field enhancement [9]. These plasmonic NPs
have a wide range of applications. Spherical gold nanoparticles (AuNPs)
have shown different properties like good optoelectric related to
changes in size- and shape, large surface-to-volume ratio, excellent
biocompatibility, and low toxicity [10]. Gold nanoparticles attracted
great attention in the field of medicine. It is used in X-ray imaging,
computed tomography, drug and gen delivery, photothermal therapy
and photodynamic therapy, diagnosis and theranostic systems[11–13].
Core-shell nanoparticles (CSNPs) are a class of nanostructured ma­
terials that are composed of two or more materials. The core-shell
E-mail addresses: teshome.senbeta@aau.edu.et, teshomesenbeta@gmail.com.
https://doi.org/10.1016/j.photonics.2023.101182
Received 19 May 2023; Received in revised form 9 July 2023; Accepted 18 August 2023
Available online 25 August 2023
1569-4410/© 2023 Elsevier B.V. All rights reserved.
Please
cite
this
article
as:
Teshome
https://doi.org/10.1016/j.photonics.2023.101182
Senbeta,
Photonics
and
Nanostructures
-
Fundamentals
and
Applications,
T. Senbeta
Photonics and Nanostructures - Fundamentals and Applications xxx (xxxx) xxx
nanoparticles consist of a core (the inner material) and a shell (the outer
layered material). The core-shell materials exist in different form of
combinations like inorganic/inorganic, inorganic/organic, organic/
inorganic, and organic/organic materials [14,15]. The choice of these
combinations depends on the intended end use or applications. CSNPs
have attracted attention from different groups because of their inter­
esting properties that are not seen in either core nor shell materials and
because of their applications in a diversified fields, like in catalysis,
biology, materials chemistry, biomedical and sensors [14–17,18]. The
observed unique properties can be easily achieved by tuning the core or
the shell or both materials size and shape.
The main advantages of inorganic nanoparticles are non-toxicity,
hydrophilic, biocompatible and highly stable compared to organic ma­
terials [19]. These properties are very useful in drug delivery systems.
One common and intensively studied inorganic semiconductor nano­
material is magnetite (Fe3O4) nanoparticles. Magnetite nanoparticles get
great attentions from many researchers as they have many applications
because of their intrinsic magnetic properties, nano-scale size, and
definite surface morphology [20]. Magnetite (Fe3O4) nanoparticles show
superior magnetic properties, electronic conductivity (which shows
half-metallic nature and exhibits better conductivity than other mag­
netic oxides, Fe2O3) and it is used in removing heavy metals from
wastewater, used in solar cells, photocatalysis, medical imaging, for
diagnostic and laser repair cartilages, drug delivery, chemotherapy, in
light emitting diodes, blocking ultraviolet and as sensors [21–24,25].
The direct band gap nature of Fe3O4 and its high optoelectronic effi­
ciency relative to the indirect band gap group-IV crystals, makes it a
reliable candidate material for visible and near-ultraviolet applications.
Most of the applications discussed above can be successully managed
by combining magnetite with noble metals like gold and silver in the
form of host matrix and core-shell NPs. Combining iron oxide nano­
particles (Fe3O4 NPs) and gold nanoparticles (Au NPs) as one nano­
structure is an assuring method for various applications. Fe3O4@Au
core-shell NPs were successfully synthesized and the composite prop­
erties from the synthesized samples were analyzed in different studies
[26–29]. The engineered Fe3O4@Au NPs has uses in magnetic resonance
imaging (MRI), magnetic guiding and near infra red (NIR) photothermal
therapy [29,30].
In general, what we can understand from the above discussion is that
Au NPs, Fe3O4 NPs, and Au coated Fe3O4 NPs are used in broad spectrum
of applications such as in biomedical, drug delivery, cancer treatment,
thermotherapy, in wastewater treatment, MRI, and so on. With thus
applications in mind we proposed to study the Fe3O4@Au core-shell and
reverse structure for different applications. More specifically to study its
magneto-optical properties that it highly important in biomedical
applications.
The paper is arranged as follows: all the mathematical foundations
needed for evaluating effective permittivity and permeability of the
theoretically modeled material, effective polarizability, refractive index
for modeled magnetic-semiconductor/metal core-shell spherical NP
embedded in a dielectric host matrix are presented in Section 2. Section
3 devoted to the presentation and analysis of numerical results that are
the magneto-optical responses of Fe3O4@Au core-shell NPs, and the
reverse structure (Au@Fe3O4 core-shell) dielectric function, perme­
ability, polarizability, refractive index, and absorbance. Section 4 con­
cludes the findings of the study.
Fig. 1. Schematic representation of the model NPs. Here the core is the semi­
conductor Fe3O4 with permittivity ε1 and permeability μ1. The shell is the noble
metal gold with permittivity ε2, and permeability μ2. The host matrix is SiO2
with permittivity εh and permeability μh. The radius vectors r1, r2 are the radii
of the core and the shell, respectively, while r is the distance from the center of
the NP to an observation point.
is assumed to have frequency dependent permeability and constant
dielectric function. On the other hand, the shell material (in this case Au)
is characterized by its frequency dependent dielectric function and
constant magnetic permeability. The complete description of the
magneto-optical properties of this composite structure needs a complete
determination of both effective permittivity εeff and permeability μeff.
Hence, the εeff and μeff are calculated based on electrostatic approxi­
mation and the Maxwell-Garnett effective medium theory.
The electrostatic approximation is valid when the wavelength of the
incident radiation (λ) is much much greater than the size of the nano­
particle (a) and this approximation demands the vanishing of curl of
electric field E. This reduces the Maxwell equations to simple form from
which the potential can be solved using Laplace equation by applying
appropriate boundary conditions. Moreover, as the size of the particle is
small the polarization vector will have the same direction as the applied
electric field. Hence, this approximation leads to the polarizability
expression in terms of the dielectric functions of different medium. The
obtained polarizability expression can be easily related to ClausiusMossotti relation. In addition, the advantage of employing the
Maxwell Garnett theory is that it provides simple relation between the
effective permittivity of the composite inclusions in terms of two pa­
rameters; the inclusion permittivity relative to host matrix and the
volume fraction of inclusions, f, provided that f is small.
Therefore, the two theories enables us to evaluate the relevant
magneto-optical parameters like electric and magnetic polarizability,
the refractive index, and the absorbance of the modeled core-shell NPs.
2.1. Permittivity
Shining electromagnetic radiation on the model core-shell nano­
particles induce electric field in the composite NPs system as the result of
electric polarization. In the electrostatic approximation (when λ ≫ a,
where λ is the wavelength of the incident electromagnetic radiation and
a is a size of the NPs) the induced potential in the three regions (inside
the core, inside the shell and beyond the core-shell system) of interest
are given by [31].
2. The model
Φ1 (r, θ) = − E0 a1 rcosθ;
In this paper, we study core-shell NPs composed of Fe3O4 semi­
conductor material as a core and Au noble metal as a shell and also the
reverse structure (Au as a core material and Fe3O4 as a shell) NPs
structure embedded in host matrix, SiO2. Our sample has radius r1 for
the core (Fe3O4) and radius r2 for the core-shell structure as illustrated in
Fig. 1. The core material is characterized by its dielectric ε1 and mag­
netic permeability μ1(ω). That is the magnetic semiconducting material
2
(1)
r < r1 ,
(
)
b2
Φ2 (r, θ) = − E0 a2 − 3 rcosθ;
r
r1 < r < r2 ,
(2)
(
)
b3
Φ3 (r, θ) = − E0 a3 − 3 rcosθ;
r
r > r2 .
(3)
T. Senbeta
Photonics and Nanostructures - Fundamentals and Applications xxx (xxxx) xxx
Eqs.(1), (2), (3), represent the electrostatic potentials inside the core,
shell and the host matrix, respectively. E0 is the magnitude of applied
electric field. The symbols a1, b2, a2, a3, and b3 are constants that can be
determined from the electrostatic boundary conditions.
The optical response of the system is related to the induced potential
outside the concentric sphere and this potential is obtained from the
second term of Eq. (3). Hence,
Φind
b3 E0
= 2 cosθ.
r
a = − E0 ∕M11
̂ =
M
(4)
b
)cosθ.
r2
(
2b1
R3
)
⎛
2
2
1⎜
⎜ r2
= ⎜
9⎝
r22
⎛
⎜
̂
S n (R) = ⎜
⎝
R
εn
( )
)
a1
a2
, φ2 =
, and
b1
b2
⎞
1
2 ⎟
R ⎟
.
2εn ⎠
− 3
R
M21 =
2
1
⎞⎛
⎜ r1
ε2 ⎟
⎟⎜
⎟⎜
− r31 ⎠⎝ ε
ε2
1
⎞
1
2 ⎟
r1 ⎟
⎟.
− 2ε1 ⎠
r31
]
[(
r3
2ε2 + ε1 )(εh − ε2 ) + 13 (ε2 − ε1 )(εh + 2ε2 )
9ε2 εh
r2
r32
(14)
⎛
1
⎞
εn ⎟
⎟
−
⎟.
R3 ⎠
M21
.
M11
(15)
where νf = (r1 ∕r2 )3 .
For core-shell NPs embedded in host matrix of dielectric constant εh,
the effective dielectric function εcs of the core-shell system is given in
terms of electric polarizability by the Clausius-Mossotti [32–35] relation
as
where
(7)
α = 4πr32
εn
εcs − εh
.
εcs + 2εh
(17)
Combining Eqs. (16) and (17), one can derive the effective permit­
tivity of the core-shell spherical nanoinclusion as
Comparing Eq. (1) and (5) together with b1 = 0, we see that a = − E0a1.
This modifies the potential equation given by Eq. (5) for outer region as
(
)
b
Φout = − E0 r + 2 cosθ,
(8)
r
and
(
)
( )
(
− E0
̂ 1 = a M11
= aM
b
0
M21
εh
⎞⎛
1
2
2 ⎟⎜ 2
r2 ⎟⎜ r1
⎟⎜
− 2ε2 ⎠⎝ 2
r1
r32
Using Eqs. (13) and (14) in (15), we obtain the complete expression for α
as
[
]
(ε1 + 2ε2 )(ε2 − εh ) + νf (ε1 − ε2 )(2ε2 + εh ) 3
α = 4π
(16)
r ,
(ε1 + 2ε2 )(ε2 + 2εh ) + 2νf (ε1 − ε2 )(ε2 − εh ) 2
̂ 1,
φ2 = S−2 1 (R)̂
S 1 (R)φ1 = Mφ
S−n 1
⎟⎜
− r32 ⎠⎝ ε
α = − 4π
With this φ2 can be expressed as
and
⎞⎛
The electric polarizability α of the core-shell NPs embedded in the host
matrix is defined as
Here n = 1 for core, n = 2 for shell and n = 3 for host matrix. The po­
tential of the electric field at the center of the core nanoparticle is finite,
( )
( )
1
a1
φ1 =
.
= a1
0
0
̂ = S− 1 (R)̂
M
S 1 (R),
2
1
⎜ r2
εh ⎟
⎟⎜
(11)
The complete evaluation of the matrices product indicated in Eq. (11)
gives the values of M11 and M21 as follow
]
[(
1
2r3
M11 =
(13)
2ε2 + ε1 )(2εh + ε2 ) + 31 (εh − ε2 )(ε2 − ε1 )
9ε2 εh
r2
(6)
2
1⎜
⎜R
= ⎜
3⎝ 2
R
(10)
It is clear that the final results of the above matrix product will give
2 × 2 matrices of the form
(
)
̂ = M11 M12 .
M
(12)
m21 M22
(
)
b2
= ε2 a2 − 2 3 .
R
(
− 1
̂
S n+1 (rn )̂
S n (rn )
− 1
− 1
̂ =̂
M
S 3 (r2 )̂
S 2 (r2 )̂
S 2 (r1 )̂
S 1 (r1 ),
These two equations can be written in a matrix form as
where φ1 =
N
∏
Our model NPs consists of two concentric spherical layers; core and shell
embedded in host matrix as illustrated in Fig. 1 and hence the number of
layers are n = 2. For n = 2 Eq. (10) takes the following form
(5)
Ŝ1 (R)φ1 = Ŝ2 (R)φ2 ,
M21
,
M11
n=1
→
→
Using the boundary conditions for tangential of E and normal of D
fields at r = R, one can obtain
(
)
b1
b2
a1 R + 2 = a2 R + 2 ,
R
R
ε1 a1 −
b = aM21 = − E0
where b describes the amplitude of the scattered field.
The above matrix representation can be generalized to multiple
layers of NPs as follow:
We may use the transfer matrices method for the spherical layers to
obtain the expressions of the constants used in Eq. (1), (2), (3). It is
better to start with a single layer expression of transfer matrices and then
the result can be generalized for multiple layers. For a single layer
spherical nanoparticle embedded in host matrix the potential
Φ = (ar +
and
εcs = ε2
(ε1 + 2ε2 )r32 + 2(ε1 − ε2 )r31
.
(ε1 + 2ε2 )r32 − (ε1 − ε2 )r31
(18)
Defining the volume fraction, β, of core-shell NP system as
M12
M22
)( )
1
.
0
β = 1−
(9)
r31
= 1 − νf .
r32
(19)
Substituting Eq. (19) in to Eq. (18), we can rewrite the expression of εcs
as
Performing the product operation in equation (9) gives
3
T. Senbeta
εcs = ε2
ε1 (3∕β − 2) + 2ε2
.
ε1 + ε2 (3∕β − 1)
Photonics and Nanostructures - Fundamentals and Applications xxx (xxxx) xxx
gives
(20)
μcs = μ2
For fixed number N of the core-shell nanoparticles that are homo­
genously distributed in a host matrix as shown in Fig. 1, the effective
permittivity and the electric polarizability of the system can be
described by combining Maxwell-Garnett mixing theory and ClausiusMossotti relation. That is the electric polarizability and the effective
permittivity are related by [31,34].
Nα
εeff − εh
.
=
3
εeff + 2εh
Furthermore, for N NPs uniformly dispersed in the host matrix as
shown in Fig. 1, applying Clausius-Mossotti relation and the MaxwellGarnett mixing theory together gives us the relation between the mag­
netic polarizability and permeability as follow [31,32,34,36].
(21)
μeff − μh
Nκ
=
.
3
μeff + 2μh
(23)
The dimensionless effective electric polarizability of the inclusion ηe =
where ηm = κ∕(4πr32 ) is the dimensionless magnetic polarizability that is
defined in terms of μcs and μh as follow
α∕(4π r32 ) can be given in terms of εcs by
ηe =
εcs − εh
.
εcs + 2εh
(24)
ηm =
For magnetized sphere the scalar magnetic potentials can be deter­
mined in similar fashion as that of scalar electric potentials calculated in
→
Section 2.1. One may start with Maxwell-Ampere equation ∇ × H =
→
→ ∂D
→
→
J + ∂t . For magnetostatics, this relation is reduced to ∇ × H = J .
→
→
Moreover, for source free media, J = 0, then ∇ × H = 0. If the curl of
the vector vanishes, the vector itself can be expressed as the gradient of
some scalar function. Hence, it is possible to introduce a magnetic scalar
→
potential ΦM such that H = − ∇ΦM . Moreover, for isotropic perme­
→
ability μ, and from ∇⋅ B = 0 we can construct the Laplace equation for
magnetic scalar potential as
(25)
ε2 (ω) = ε∞ −
ω2p
,
ω(ω + iγ)
(33)
where ε∞ is the permittivity at high frequencies, ωp is the plasma fre­
quency, γ is the damping parameter, and ω is the frequency of the
incident radiation. It is clear that Eq. (33) can be decomposed into real
and imaginary parts which may be expressed as
(34)
ε2 = ε′2 + iε″2 .
From Eq. (24) two independent equations can be obtained; one for real
ε′2 and the other for imaginary ε″2 as follow
Applying the Clausius-Mossotti relation allow us to relate the coreshell permeability (μcs) with the magnetic susceptibility (κ) [32,36] as
follow
μcs − μh
κ = 4π
.
μcs + 2μh
(32)
This section is devoted to the derivation of optical properties
(refractive index and polarizability) of Fe3O4@Au core-shell nano­
particles embedded in silica (SiO2) host matrix. Here first we derive the
expression for frequency dependent dielectric function of the shell ma­
terial (Au) and frequency dependent permeability of the core (Fe3O4).
The host matrix has both constant dielectric function and magnetic
permeability. Moreover, we assumed the magnetic permeability of the
Au is constant, independent of the frequency of the electromagnetic
wave (EMW) and the permittivity of the core material Fe3O4 is assumed
as independent of frequency of propagation of EMW.
For uncoated metallic Au shell, the response to the incoming EMW is
described by frequency dependent dielectric function. As stated above
the permeability of the gold (Au) is constant and set to (μ2 = 1). Hence,
we can use the frequency dependent complex dielectric function
described by the modified Drude-Lorenz form [37] as
When an electromagnetic radiation shone on the system of NPs as the
one illustrated in Fig. 1, the radiation induces both electric and magnetic
fields. These fields are responsible for the resulting electric and magnetic
polarizations. The procedures to obtain expressions for magnetic po­
tentials in the three regions of interest are the same as the procedures we
employed to find the expressions for electrostatic potentials. Hence, we
present here only the final results of magnetic polarizability (magnetic
susceptibility) and the effective permeability of the NP composite sys­
tem. Accordingly, the magnetic polarizability κ of the core-shell NP
embedded in the host matrix with permeability μh is given by
[
]
(μ1 + 2μ2 )(μ2 − μh ) + νf (2μ2 + μh )(μ1 − μ2 ) 3
κ = 4π
r .
(26)
(μ1 + 2μ2 )(μ2 + 2μh ) + 2νf (μ1 − μ2 )(μ2 − μh 2
r32
μcs − μh
.
μcs + 2μh
2.3. Frequency Dependent Permittivity and Permeability of Fe3O4@Au
NPs
2.2. Permeability
∇2 Φm = 0.
(30)
Here, μeff and κ are the effective magnetic permeability and the magnetic
polarizability, respectively.
The effective magnetic permeability (μeff) may be written in terms of
the effective magnetic polarizability (ηm) and the filling factor f (Eq.
(23)) by combining Eqs. (29) and (30) as follow
(
)
1 + 2f ηm
,
(31)
μeff = μh
1 − f ηm
Here f is the filling factor of the core-shell NPs defined as
4π r32
N.
3
(28)
With the definition of β given by Eq. (19), we may express μcs as
[
]
μ (3∕β − 2) + 2μ2
μcs = μ2 1
.
(29)
μ1 + μ2 (3∕β − 1)
Here α is the electric polarizability given by Eq. (17) and εeff is the
effective dielectric function of the core-shell NPs structure. Inserting
Eqs. (16) into (21) and carrying out the necessary calculations and
rearranging the result is
(
)
1 + 2f ηe
.
(22)
εeff = εh
1 − f ηe
f =
[
]
(μ1 + 2μ2 ) + 2νf (μ1 − μ2 )
.
(μ1 + 2μ2 ) + νf (μ2 − μ1 )
ε′2 (ω) = ε∞ −
(27)
and
Using Eqs. (27) into (26) and carrying out the necessary calculation will
4
ω2p
ω2 + γ 2
,
(35)
T. Senbeta
ε″2 (ω) =
Photonics and Nanostructures - Fundamentals and Applications xxx (xxxx) xxx
γω2p
.
ω(ω2 + γ2 )
(36)
ηm = η′m + η″m ,
where η′m and η″m are the real and imaginary parts of the effective mag­
netic polarizability, respectively.
In this study we are keen to include the frequency dependent magnetic
permeability in the optical properties of the core-shell NPs. Of course, it
is well known that the variation of the dielectric function of the noble
metal is large in comparison with the variation of the magnetic
permeability of the magnetic semiconductor materials and often the
relative permeability of metals and dielectric materials assigned a value
of unity. However, for composite materials the contribution of the
magnetic permeability and polarizability cannot be ignored as it is
possible to tune the structures properties that give large imaginary
component. In turn this large imaginary component has significant
contribution in refractive index of the media that may have different
applications in magneto-optical devices ranging from visible to UV re­
gions. Hence, in Fe3O4 core-shell NPs, the core material (Fe3O4) can be
described by constant dielectric function ε1 and frequency dependent
permeability μ1(ω). Accordingly, we can use a Lorentz model for mag­
netic permeability given by [38–41].
Fm ω2pm
μ1 (ω) = 1 + 2
,
ω0m − ω2 + iΓm ω
2.5. Effective Refractive Index
The optical properties of the composite NPs can be deduced from the
complex refractive index n(ω). This complex refractive index can be
defined in terms of the effective permittivity (εeff) given by Eq. (22) and
the effective magnetic permeability (μeff) given by Eq. (31) for the sys­
tem of spherical core-shell composite NSs embedded in a host matrix.
√̅̅̅̅̅̅̅̅̅̅̅̅̅
n(ω) = εeff μeff = n1 + in2 ,
(45)
where n1 and n2 are the real and imaginary parts of the refractive index.
Rewriting effective permittivity Eq. (22) and effective permeability
Eq. (31) as
εeff = ε′eff + iε″eff ,
(37)
μeff = μ′eff + iμ″eff .
(47)
Substituting Eqs. (46) and (47) back into Eq. (45) one can obtain
1
n1 = √̅̅̅[(ξ2 + ψ 2 )1∕2 + ξ]1∕2 ,
2
(38)
(48)
and
with
μ′1 = 1 +
(
)
Fm ω2pm ω20m − ω2
2
0m
(ω
− ω
2 )2
+
Γ2m
ω
2
,
1
n2 = √̅̅̅[(ξ2 + ψ 2 )1∕2 − ξ]1∕2 ,
2
(39)
Fm ω2pm ωΓm
″
2
(ω20m − ω2 ) + Γ2m ω2
ξ = ε′eff μ′eff − ε″eff μ″eff ,
.
(40)
and
ψ = ε′eff μ″eff + ε″ef μ′eff .
2.4. Effective electric and magnetic polarizabilities
In the next Section we exploit Eqs. (48) and (49) together with other
fundamental equations derived in Sections 2.1 to 2.5 to discuss
magneto-optical properties of the model composite nanostructure. It is
also necessary to mention that all the mathematical tools derived
through Sections 2.1 to 2.5 are for Fe3O4@Au core-shell nanoparticles
embedded in host matrix. For the reveres structures the mathematical
tools can be obtained by changing the role of electric permittivity and
magnetic permeability. That is for Au@Fe3O4 core-shell nanoparticles
composite structure ε1 → ε2, ε2 → ε1, μ1 → μ2, and μ2 → μ1.
In this section we present the expressions for effective electric and
magnetic polarizability based on the results obtained in Sections 2.1 and
2.2. We use these results to carry out numerical analysis that will be soon
presented in Section 3.
Now we substitute Eqs. (20) into (24) to get
]
[
3
εh (ε1 + ε2 (3∕β − 1))
ηe = 1 −
.
(41)
2
2 εh (ε1 + ε2 (3∕β − 1)) + ε1 ε2 [3∕(2β) − 1] + ε2
Note that Eq. (41) contains ε2 which is a complex quantity as it is given
by Eq. (34) and so that the effective electric polarizability is a complex
quantity which is presented as
ηe = η′e + η″e ,
(49)
with
and
μ1 = −
(46)
and
where ωpm, ω0m, Γm and Fm are magnetic plasma frequency, magnetic
resonance frequency, magnetic damping coefficient and oscillator
strength, respectively. The frequency dependent permeability μ1 can be
decomposed in to its real (μ′1 ) and imaginary (μ″1 ) parts that are given by
μ1 = μ′1 + iμ″1 ,
(44)
3. Numerical analysis
In this Section, we present the numerical analysis of the magnetooptical response of the theoretically modeled spherical Fe3O4@Au
core-shell NPs embedded in a dielectric host matrix, silica. In particular
we discuss the electric and magnetic polarizabilities, the effective
permittivity and permeability, the refractive index, and the absorbance
under different conditions (i.e., varying β, f and εh) as a function of
incident radiation energy. The parameter values used are ε∞ = 9.84, ωp
= 1.37 × 1016 rad∕s, μ2(μAu) = 1 and γ = 1.1 × 1014 rad∕s [37,42–45]
for the Fe3O3@Au core-shell; ε1 = 5.85, ωpm≤ 0.5ωp [37,45] and we set
ωpm = 8.65 × 1015 rad∕s, γm = 2.73 × 1013 rad∕s, ω0m = 0.2ωp
= 2.74 × 1015rad∕s, and Γ=1 [38,39,41,45] for Au@Fe3O4 core-shell.
The host matrix silica (SiO2) have εh = 3.9 and μh = 1.
(42)
where η′e and η″e are the real and imaginary parts of the effective electric
polarizability, respectively.
Similarly, employing Eqs. (29) and (32), the effective magnetic
polarizability (ηm) is equals to
]
[
3
μh (μ1 + μ2 (3∕β − 1))
.
(43)
ηm = 1 −
2 μh (μ1 + μ2 (3∕β − 1)) + μ1 μ2 [3∕(2β) − 1] + μ22
Here, again Eq. (43) contains μ1 which is a complex quantity as it is
given by Eq. (38) and so that the effective magnetic polarizability is a
complex quantity given by
5
T. Senbeta
Photonics and Nanostructures - Fundamentals and Applications xxx (xxxx) xxx
3.1. Electric Polarizability and Effective Permittivity
carried out numerical analysis of the effect that εh has on the electric
polarizability of Fe3O4@Au core-shell NPs structure. With the help of Eq.
(41) we plot the graph of η′e and η″e as a function of the incident radiation
energy (graphs not included here) for εh = 1, 1.55, 1.77, 2 and 3.9. The
Figure 2 depicts (a) the real and (b) the imaginary parts of the
dimensionless electric polarizabilities (η′e and η″e , respectively) of the
spherical Fe3O4@Au core-shell nanocomposite as a function of the en­
ergy of the incident light for different values of β. Other parameters used
to plot the graphs are those listed above and the size of Fe3O4@Au
quantumdot is fixed at r2 = 30 nm. Both graphs possess two sets of
resonance peaks in the visible regions. The first set of resonance peaks
for η′e are found in the range of 1.5 eV (corresponding to r1 = 0.75r2 or
shell thickness of 7.5 nm) to 1.9 eV (corresponding to r1 = 0.5r2 or shell
thickness of 15 nm). For η″e the first set of resonance peaks occurs in the
range of 1.533 eV (corresponding to r1 = 0.75r2) to 1.943 eV (corre­
sponding to r1 = 0.5r2). For both η′e and η″e the first set of resonance
peaks are blue shift and the amplitude of the polarizabilities increases
with increasing the value of β, (increasing the shell thickness). The
second set of resonance peaks are diminished in amplitude as compared
with the first set of resonance peaks and found in the range of 2.604 eV
to 2.785 eV for η′e and in the range of 2.629 eV to 2.757 eV for η″e. These
second sets of resonance peaks are red shift and the amplitudes of the
polarizabilities still increase with increase in the values of β (increases
with increasing the shell thickness).
The first peaks are related to the coupling of the surface plasmon
oscillations of Au with the energy gaps of the host matrix (Au∕SiO2) at
outer interface and the second is due to the coupling of the surface
plasmons of the Au with the inner semiconducting nanoparticles
(Fe3O4∕Au) interfaces.
The values of the first set of resonance peaks are more pronounced
than the second set. This is due to the surface area of Au∕SiO2 is greater
than the corresponding surface area of Fe3O4∕Au that accounts for more
carries availability in the outer interface than the inner interface.
Figure 3((a) and (b)) illustrates the real and imaginary parts of the
electric polarizability (η′e and η″e , respectively) of Au@Fe3O4 core-shell
nanostructure (that is Au core and Fe3O4 shell) as a function of the
incident light energy. An unlike Fig. 2, here there is only one set of
resonance peaks in the energy range of 1.941 eV to 2.074 eV for η′e and
in the energy range of 1.974 eV to 2.038 eV for η″e. The peaks position
shows slight red shift and decreases in intensity as the value of β in­
creases (as the thickness of Fe3O4 increases). The absence of the second
set of resonance peaks may be explained by the fact that the incoming
radiation could not able to overcome the energy band gap of the shell
material (Fe3O4) to induce electric field at the inner interface of Fe3O4
and Au. Even the polarization at the outer interface of this structure is
relatively small in comparison to Fe3O4@Au core-shell NPs embedded in
host matrix, SiO2.
We also studied the effect of dielectric function of the host matrix εh
and the feeling factor f on the polarizability of the electric field. We
results show that there is significant dependence of both η′e and η″e on εh.
That is as the value of εh increases the first set of resonance peaks in­
tensity largely pronounced and accompanied by red shift. The second set
of the resonance peaks intensity diminished and red shift with the same
trend. It is shown that for Fe3O4@Au core-shell composite nano­
structures embedded in SiO2 host matrix, for all values of f ranging from
f = 0.001 to f = 0.006 in steps of 0.001, there are two sets resonance
peaks for all values of f at the same position showing that ηe is inde­
pendent of f, (see Eq. (41)). The first set of resonance peaks of the real
part of the electric polarizability found in the vicinity of 2.1 eV and the
second set of resonance peaks found around 2.81 eV. The amplitude of
the first set of resonance peaks is almost 3.3 times the amplitude of the
second set of resonance peaks. Similarly, it is observed that the imagi­
nary parts of the electric polarizability provides two set of resonance
peaks at E = 2.1 eV and at E = 2.8 eV. In this case the amplitude of the
first set of resonance peaks is about 3.38 times the amplitude of the
second set of resonance peaks.
For the reverse structure, that is for Au@Fe2O4 core-shell NPs
structure, the dependence of η′e and η″e on εh and f are similar to the case
of Fe3O4@Au core-shell NPs structure. But, for Au@Fe3O4 core-shell NPs
structure there is only one set of resonance peaks. The magnitude of the
resonance peaks are much smaller for Au@Fe3O4 core-shell NPs
structure.
Figure 4 depicts the effective dielectric function as a function of the
incoming energy for Fe3O4@Au core-shell composite NPs embedded in
SiO2 host matrix. The graphs are plotted by employing Eq. (22) for the
same parameters that were used in Fig. 2 and Fig. 3. Fig. 4(a) is the real
part and Fig. 4(b) represents the corresponding imaginary part. Just like
Fig. 2, the dielectric function possesses two set of resonance peaks with a
little shift in the energy ranges. That is the first resonance peak for real
part of dielectric function occurred around E = 1.504 eV for β = 0.578
(shell thickness of 7.5 nm) and in the vicinity of E = 1.908. eV for
β = 0.875 (shell thickness of 15 nm). The resonance peaks position shift
to higher energy region as the values of β increases (as the shell thickness
of Au increases) and at the same time the intensity of the resonance
peaks is also increase with increasing β (with increase in Au shell
thickness). The second set of resonance peaks position starts in the vi­
cinity of E = 2.602 eV for β = 0.875 ( for shell thickness of 15 nm) and
extends to E = 2.724 eV for β = 0.578 (shell thickness of 7.5 nm). The
second resonance peaks increases and companied by red shift as the
values of β increases (or as shell thickness of Au increases.
Fig. 4(b) depicts the imaginary part of the effective dielectric func­
tion of Fe3O4@Au core-shell structure and the graph possesses two sets
Fig. 2. The real (a) and imaginary (b) parts of the electric polarizability versus energy of the incident light for different values of β; with εh = 3.9 and r2 = 30 nm fixed
constant, when Au used as a shell and Fe3O4 used as a core.
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Fig. 3. The real (a) and imaginary (b) parts of the electric polarizability versus energy of the incident light for different values of β; with εh = 3.9 and r2 = 30 nm fixed
constant, when Au used as a core and Fe3O4 used as shell.
Fig. 4. The real (a) and imaginary (b) parts of the effective dielectric function versus energy of the incident radiation for different values of β; with εh = 3.9 and r2
= 30 nm fixed constant. Fe3O4@Au core-shell composite NPs.
of resonance peaks. Comparing Fig. 2(b) with Fig. 4(b) shows that the
imaginary part of electric polarizability is almost 86 time the corre­
sponding effective dielectric function.
Similar to Fig. 3, the graph of the dielectric function of the reverse
structure (Fig. 5) exhibits only single set of resonance peaks. As stated
above, the reason for these sets of peaks is due to the coupling of the
surface plasmon oscillations of Fe3O4 with the host matrix (SiO2) inter­
face. Comparison between the first set of resonance peaks of Fig. 4(b)
and that of Fig. 5(b) show that the amplitudes of Fe3O4@Au core-shell
are 2–5 times the amplitudes of Au@Fe3O4 core-shell. Moreover, the
peaks position for the later case shift with very small energy values.
Before concluding this section, we present the graphical analysis of
on εh and f as illustrated in Fig. 6. From Fig. 6(a) one can see that there
are two sets of resonance peaks corresponding to the coupling of the
surface plasmon oscillations with inner semiconductor Fe3O4 and the
outer surface host matrix of Au. The amplitude of the peaks of the
effective dielectric function of the Fe3O4@Au composite nanoparticles
embedded in SiO2 increases and accompanied by red shift as the value εh
increases. As we see soon, the study of the dependence effective
refractive index on the dielectric function of the host matrix is very
important for different applications, like in drug delivery as it needs the
dielectric match between the dielectric function of the plasma/blood
with the host matrix. For example, from Fig. 6(a) the dielectric function
of the host matrix εh = 3.9 corresponds to SiO2 and εh = 1.77 is for water.
The resonance peak for SiO2 host matrix appeared at E = 1.944 eV and
the imaginary part of the effective dielectric function (ε″eff ) dependence
Fig. 5. The real (a) and imaginary (b) parts of the effective dielectric function versus energy of the incident radiation for different values of β; with εh = 3.9 and r2
= 30 nm fixed constant, the case of Au@Fe3O4 core-shell composite NPs.
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Fig. 6. The imaginary part of the effective dielectric function Fe3O4@Au core-shell composite NPs versus energy of incident radiation (a) for different values of εh; f
= 0.001, β = 0.875 and (b) for different values of f; with β = 0.875, f = 0.001. r2 = 30 nm fixed constant for both (a) and (b).
for water at E = 2.173 eV. That means the resonance peak position for
water needs more energetic incident radiation than that of SiO2. At the
same time the amplitude of the resonance peak of the effective dielectric
function of SiO2 is 3 times that of water. In turns large value of ε″eff results
peaks of the real part of magnetic polarizability appear at E = 2.928 eV
and the resonance peaks of the imaginary part occurred at E = 2.937 eV.
The energy values at which both resonances appeared are almost near
the upper limit of visible light. These energy values are completely
different and have higher energy values in comparison with the two sets
of resonance peaks that result due to electric polarizability (see Fig. 2).
The amplitude of resonance peaks of the imaginary part of the magnetic
polarizability is large and negative, which will contribute lots for
refractive index and optical absorbance as we discuss in Section 3.3 and
3.4, respectively.
The other feature of the magnetic polarizability for Fe3O4@Au coreshell composite NPs embedded at SiO2 is that there is only single set of
resonance peaks that are related to the induced magnetic field at the
inner interface between Fe3O4 and shell, Au. As the value β decreases
(deacrease of the shell thickness) for Fe3O4@Au core-shell composite
NPs, the intensity of the resonance peaks increases. Here, decreasing the
values of β means that increasing the radius r1 (decreasing the thickness
of the gold shell). As the thickness of the gold shell decreases light
(EMW) can easily penetrates into the semiconductor Fe3O4 and so that
light interacts with the magnetic dipoles of the semiconducting Fe3O4
and then results in significant magnetic polarization.
Figure 8 depicts the magnetic polarizability ((a) real and (b) imagi­
nary parts) as a function of incident radiation energy for the reverse
structure of Fe3O4@Au core-shell that is for Au core and Fe3O4 shell
composite NPs embedded in SiO2 host matrix. All the parameters used
are the same as those stated in the beginning of Section 3. The graphs
reveal that there is significant differences having Au as shell (Fig. 7) or as
core Fig. 8 that forms composite structure with Fe3O4. The first differ­
ence observed is that when Au is used as a core there are two sets of
resonance peaks for magnetic polarizability; the first set of resonance
in the large value of refractive index and the corresponding absorbance
as we will see in the next two sections.
Figure 6(b) describes the dependence of the imaginary part of the
dielectric function on the feeling factor f. It is clearly seen from the graph
that there are two sets of resonance peaks related to the outer and inner
interfaces. The first set of resonance peaks occurred around E = 2.07 eV
with very slight variation in resonance peaks positions. The amplitude of
resonance peak increases with increasing the value of f. The second set
of resonance peaks which corresponds to the inner coupling at the inner
interface appeared around E = 2.80 eV without change in resonance
peaks positions. The inset graphs of Fig. 6(b) shows the width of the
resonance peaks and it enables us to compare the amplitudes of the first
set of resonance peaks and amplitudes of the second set of resonance
peaks. Hence, the amplitudes of the first set of resonance peaks are about
8 times the amplitude of the second set of resonance peaks. The result
reflects that no more light penetrates the shell material (Fe3O4) to reach
the core metal (Au)in which the induced charges due to electric polar­
izabilty at the core-shell interface produces weak coulomb interaction.
3.2. Magnetic polarizability and effective permeability
Figure 7 illustrates ((a) real and (b) imaginary parts) of the magnetic
polarizability of the Fe3O4@Au core-shell NPs as a function of the inci­
dent radiation energy for different values of β. We used Eq. (43) to plot
these graphs. From the graphs we can see that there is no shift in the
resonance peaks position as the values of β changes. The resonance
Fig. 7. The real (a) and imaginary (b) parts of the magnetic polarizability versus energy of incident light for different values of β; with εh = 3.9, f = 0.001 and r2
= 30 nm fixed constant for Fe3O4@Au core-shell NPs structure.
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Fig. 8. The real (a) and imaginary (b) parts of the magnetic polarizability versus energy of incident light for different values of β; with εh = 3.9, f = 0.001 and r2
= 30 nm fixed constant for Au@Fe3O4 core-shell NPs structure.
peaks in the visible region and the second set of resonance peaks in UV
region. Here the shell material (Fe3O4), which is a magnetic NP, have
two interfaces with the outer host matrix SiO2 and with the core Au.
Hence, the first set of resonance peaks is due to the induced magnetic
field at the interface between the shell(Fe3O4) and the host media (SiO4),
while the second set of resonance peaks related to the induced magnetic
field at the interface between core Au and the shell (Fe3O4).
One more differences between Figs. 7 and 8 is that in the latter case
the positions of the resonance peaks for both real and imaginary parts of
the magnetic polarizability is blue shift for the first set of resonance
peaks and red shift for the second set of resonance peaks in relation to
increases in β, but there is no shift in the peaks position for the former
with changes in the values of β. From Figs. 7 and 8 one can notice that
the intensity of the first set of resonance peaks of Fig. 8 is almost twice
the intensity of the first set of resonance peaks of Fig. 7. Even the second
set of resonance peaks of Fig. 8 which is in the UV region is comparable
with the corresponding electric polarizability given by Fig. 3. The insets
in Fig. 8 enables us to understand the energy ranges at which the reso­
nance peaks occurs and the order of magnitude of the intensity of
polaizability in arbitrary units.
When Fe3O4 is used as a core there is shielding from shell Au NPs so
that the incoming radiation may not able to produce sufficient magnetic
polarization and the magnetization of Fe3O4@Au core-shell NPs is less
than the magnetization of uncoated Fe3O4. But, as one can see from
Figs. 7 and 8 the magnetic polarizability of Au@Fe3O4 core-shell NPs is
greater than the magnetic polarizability of Fe3O4@Au core-shell. This is
may be due to the large inter particle distance that prevents the inter­
action of magnetic domains for Au@Fe3O4 core-shell case.
Figures 9 and 10 illustrates the effective permeability ((μ′eff ) real and
(μ″eff) imaginary parts) for Fe3O4@Au core-shell and the reverse
structure, respectively. As μeff related to ηm through equation (31), the
pattern of μ′eff is similar to η′m and the pattern of μ″eff is similar to η″m
except that the magnitude is highly diminished because of the fact that
we have a factor f in the expression of μeff. The intensity of the first set of
resonance peaks of Fig. 10(a) is almost twice the intensity of the reso­
nance peaks of Fig. 9(a). Similarly, the intensity of the first set of reso­
nance peaks of Fig. 10(b) is double the intensity of the resonance peaks
of Fig. 10(b).
As the refractive index of the medium is governed by the combined
effect of the effective dielectric function and effective permeability, it is
necessary to make comparison between the effective dielectric function
(Fig. 4) with effective permeability (Fig. 9) for Fe3O4@Au core-shell
composite NPs structure. And similar comparison can be done for
effective dielectric function (Fig. 5) with effective permeability (Fig. 10)
for the reverse structure. Hence, the first point one can noticed from
Figs. 4 and 9 is that the energy of the incident radiation is different for
the real part of the effective dielectric function (ε′eff ) and effective
permeability (μ′eff ) and also for the corresponding (ε″eff) and (μ″eff). Thus
un-overlapping energy ranges implies that we expect three resonance
peaks in the refractive index, as we see soon. The second difference
between the two graphs is the intensity (amplitude) of (ε′eff ) and (μ′eff ).
To the left of the resonance peaks of μ′eff , the value of μ′eff is constant and
equals unity. But, to the right of the second set of resonance peaks for
ε′eff , the value of ε′eff is nearly constant and takes a value of 3.9. These
two values will highly determine the value of n1.
From the comparisons between Figs. 4(b) and 9(b), we can see that
μ″eff have negative values that play a great role in the magnitude of
refractive index and the corresponding optical absorbance of the system.
Furthermore, we may analyses the relations between Figs. 5 and 10.
As this is the case of reverse structure of Figs. 4 and 9, 5 has one set of
Fig. 9. The real (a) and imaginary (b) parts of the effective permeability versus energy of incident light for different values of β; with εh = 3.9, f = 0.001 and r2
= 30 nm fixed constant, for Fe3O4@Au core-shell NPs structure.
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Fig. 10. The real (a) and imaginary (b) parts of the effective permeability versus energy of incident light for different values of β; with εh = 3.9, f = 0.001 and r2
= 30 nm fixed constant, for Au@Fe3O4 core-shell NPs structure.
resonance peaks due to effective dielectric function and Fig. 10 has two
sets of resonance peaks due to effective magnetic permeability for both
real and imaginary parts. Here also the range of energies at which the
resonance peaks occurred for both real and imaginary parts of the
reverse structure of Fe3O4@Au core-shell composite NPs structure do not
overlap and this leads to the appearance of three sets of resonance peaks
in refractive index. The real part of the effective permeability (μ′eff ) have
constant value unity that equals to the permeability of the host matrix
(μh) in the left side of the first set of resonance peaks. Moreover, the real
part of the effective dielectric function (ε′eff ) have a constant value 3.9
that equals to the value of the host matrix (εh) in the right side of the
resonance peaks.
Among different parametres that affects the optical properties of the
medium are the dielectric function of the host matrix and (εh) and the
feeling factor f. Here we discuss the dependence of the effective mag­
netic permeability of the reverse structure (Au@Fe3O4) core-shell com­
posite NPs embedded in SiO2 on the dielectric function εh and the feeling
factor f. Accordingly, Fig. 11 depicts μ″eff as a function of the incoming
radiation energy for different values of εh (Fig. 11(a)) and for different
values of f (Fig. 11(b)). From Fig. 11(a) one can deduce that the effective
permeability does not depend on εh (see Eq. (31) But, from Fig. 11(b) one
can see that as the feeling factor f increases, the effective permeability of
the medium also increases without shifting the position of the peaks.
This is because of the fact that the change in the feeling factor does not
associated to the variation in thickness of the shell that mainly deter­
mine the shift in the position of the resonance peaks.
Fe3O4@Au core-shell spherical nanoinclusions and its reverse structure
based on the equations developed in Section 2. We analyzed the real and
imaginary parts of the refractive index using Eqs. (48) and (49). For the
simulation of the graphs the parameters listed at the start of Section 3
are used.
Figure 12(a) depicts the graphs of the real (n1(E)) and (b) the
imaginary (n2(E)) parts of the refractive index of Fe3O4@Au core-shell
composite NPs as a function of the energy of the incident radiation for
different values of β. Both graphs ( n1(E) and n2(E)) possess three sets of
resonance peaks in the visible region. The first and the second sets of
resonance peaks are due to the dominance effect of the electric polar­
izability, while the third set of resonance peaks related to the dominance
effect of magnetic polrizability at that specified energy ranges. The first
set of peaks arise due to absorption of the light at the interface between
Au∕SiO2 (outer interface) and the second set of resonance peaks are due
to the dispersion of light at the interface between Au∕Fe3O4 (inner
interface). The third set of resonance peaks arises again at the inner
interface between magnetic semiconducting core Fe3O4 and the shell Au
as the result magnetic polarization.
From Fig. 12 one can notice that as the metal fraction β increases
(equivalently decreasing radius r1 or increasing the shell thickness) re­
sults in increasing the magnitude of the first and second sets of reso­
nance peaks for both n1(E) and n2(E). The first set of resonance peaks
position are accompanied by blue shift and the second set of resonance
peaks position are accompanied by red shift. Form Fig. 12(a) and (b) the
amplitude of the third set of peaks deceases when the values of β in­
creases, without any shift in peaks position. The reason for decrease in
the amplitude of n1(E) and n2(E) as β increases is related to the decrease
in the radius r1) which is equivalent to decreasing the volume fraction of
the magnetic semiconductor that contributes to the magnetic
3.3. Refractive index
This Section is focused on the discussion of refractive index of
Fig. 11. Both (a) and (b) are the imaginary parts of the effective permeability versus the energy of the incident radiation (a) for different values of εh and (b) for
different values of f for Au@Fe3O4 core-shell composite NPs embedded in host matrix, SiO2. In each case, r2 = 30 nm, and β = 0.875.
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Fig. 12. The real (a) and imaginary (b) parts of the refractive index versus energy of the incident light for different values of β, f = 0.001, r2 = 30 nm, and εh = 3.9,
for Fe3O4@Au core-shell structure. (c) the imaginary part of Fe3O4@Au for μ1 = 5.
polarizabilitity or increasing the shell thickness of the plasmonic Au, and
this result in decrease of the effective permeability and then the
refractive index of the medium. On the contrary, decreasing the values
of β means increasing r1 or equivalently increasing the thickness of
magnetized semiconductor Fe3O4 quantumdots.
Fig. 12(c) illustrates the imaginary part of refractive index n2 ac­
cording to Eq. (49) for the same parameters used to plot Fig. 12(b)
except that the frequency dependent permeability Eq. (37) is replaced by
a constant value equals to 5, magnetic permeability of Fe3O4. Compar­
ison between Fig. 12(b) and (c) clearly shows that the absence of the
third set of resonance peaks of Fig. 12(c) is due to the absence of fre­
quency dependent magnetic permeability μ1, Eq. (37). This is evidence
that the third peak of Fe3O4@Au core-shell structure is due to a contri­
bution from the frequency dependent magnetic polarizability/perme­
ability. Note that for the first two sets of resonance peaks of Fig. 12(b)
the amplitude, the position of the peaks and the direction in which the
peaks position shift as β increases (as the thickness of the shell increases)
is the same as Fig. 12(c).
The amplitude of the third resonance peak of n2 for β = 0.875 is
almost equals to the amplitude of the first resonance peak, and six times
the amplitude of second resonance peak for the same β value. However,
for β = 0.578 the amplitude of the third resonance peak is nearly 3 times
the first resonance peak and 26 times the second peak for the same β
value. This shows that if one is interested to use the Fe3O4@Au CoreShell composite NPs for application in the high energy region, it is
necessary to have thin Au thickness and thick core of Fe3O4.
The refractive index of the reverse structure of Fe3O4@Au core-shell
composite nanonstructure is depicted in Fig. 13. Fig. 13 shows (a) the
real and (b) the imaginary parts of the refractive index of Au@Fe3O4
core-shell composite NPs structure (the reverse structure of Fe3O4@Au).
From the figures of n1 and n2 it is clearly seen that there are three set of
resonance peaks. The first set of the resonance peaks are related to the
dominance of electric polarizability and the second and third sets of the
resonance peaks related to dominance of the magnetic polarizability as
we already discussed in Sections 3.1 and 3.2. The first and the second
sets of the resonance peaks of refractive index for both n1 and n2 are in
the visible region and the third set of the resonance peaks are in the UV
region. The first set of the resonance peaks are very weak in comparison
to the other two sets of peaks, indicating that the magnetic polarizability
dominates over the electric polarizability in the reverse structure of
Fe3O4@Au nanoinclusions.
Fig. 13(c) depicts the imaginary part of the refractive index n2 of
Au@Fe3O4 core-shell nanoinclusion embedded in SiO2 according to Eq.
(49). Here, the permeability expression given by Eq. (37) is assumed to
be independent of the frequency of the incoming radiation and we set μ2
= 5. Other parameters used to plot the graph are the same as those used
for Fig. 13(b). As one can see from the graph the second and the third
sets of the resonance peaks observed in Fig. 13(a) and (b) disappeared.
This is a confirmation that these two sets of the resonance peaks are due
to the frequency dependent magnetic permeability that contributes to
frequency dependent magnetic polarizability.
For Fig. 13(b) we have calculated the ratio of the intensity of the
second resonance peak to the first resonance peak for β = 0.875(r1 =
0.5r2 or shell thickness of 15 nm) and also the ratio of the intensity of the
second resonance peak to the third resonance peak. Fig. 13(b). The
obtained results are about 27.5 and 8.3, respectively. For β = 0.578(r1
= 0.75r2) these ratios are 5.7 and 4.9, respectively. As we increase the
value of β which is equivalent to increasing the thickness of the magnetic
semiconducting Fe3O4, the intensity of the first set of resonance peaks
decreases and shows red shift, but the intensity of the second set of
resonance peaks increases and accompanied by blue shift. The third set
of resonance peaks are red shift with no significant change in the
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Fig. 13. The real (a) and imaginary (b) parts of the refractive index versus energy of the incident light for different values of β, f = 0.001, r2 = 30 nm, and εh = 3.9.
Au core and Fe3O4 shell. (c) the imaginary part of Fe3O4@Au for μ1 = 5.
amplitude as the value of β increases. Note that increasing the thickness
of Fe3O4 means that increasing the surface area of the magnetic material
in the expense of decrease in volume fraction of the plasmonic gold.
Hence, as discussed above the appearance of the second and third
resonance peaks for the reverse structure is related the contribution from
magnetic polarizability and the increase in the intensity of the second set
of resonance peaks is expected.
We have calculated the ratio of the intensity of the second resonance
peak to the first resonance peak for β = 0.875(r1 = 0.5r2) and also the
ratio of the resonance peak to the third resonance peak for n2; and the
results are about 27.5 and 8.3, respectively. For β = 0.578 (r1 = 0.75r2)
these ratios are 5.7 and 4.9, respectively. As we increase the value of β,
the intensity of the first set of resonance peaks decreases and shows red
shift, but the intensity of the second set of resonance peaks increases and
accompanied by blue shift. The third set of resonance peaks are red shift
with no significant change in the amplitude associated with increase in
β.
A close look into Figs. 12(b) and 13(b) shows that the intensity of the
second resonance peak for β = 0.875(r1 = 0.5r2) of Fig. 13(b) is almost
twice the third peak of Fig. 12(b) for β = 0.578(r1 = 0.75r2), at the
incoming radiation energy of E = 2.742 eV and E = 2.937 eV, respec­
tively. Note that as the two figures are the reverse structure of each other
and the second set of resonance peaks of Fig. 13(b) and the third set of
resonance peaks of Fig. 12(b) are due to the dominance of magnetic
polarizability, it is reasonable to have large β value for Fig. 13(b) and
small β value for Fig. 12(b). Moreover, this result shows that thick shell
of Fe3O4 is has great effect on the magnetic polarizability than thick shell
of Au.
We also have studied the effect of increasing εh that may have impact
on n2 values of Fe3O4@Au core-shell composite structure and its reverse
structure (figures not presented here). As εh increases the first set of
resonance peaks of n2 for Fe3O4@Au core-shell structure increases and
accompanied by red shift. The corresponding second set of resonance
peaks are also red shift but the amplitude increases for some values of β
and then decreases for other values of β. The third set of resonance peaks
do not show any shift in peaks position but the resonance amplitudes of
n2 is more pronounced than the first and second set of resonance peaks.
For reverse structure (Au@Fe3O4) core-shell composite structure, the
first set of resonance peaks is red shift, while the second and the third set
of resonance peaks do not show any shift in peaks position. For all cases
the value of n2 increases with increasing in εh. Finally, changing the
value of f does not have any effect in the resonance peaks position of n2
for both structures. However, increasing f results in increasing the
amplitude of the resonance peaks of n2. This is a reasonable result as an
increase in f values is related to increasing the number of nanoparticles
(N) that each particle contributes to polarizability.
3.4. Optical absorbance
Absorbance also called optical density is one of the major parameter
used to distinguish the optical properties of optical materials. For an
electromagnet wave polarized in certain direction (say along the posi­
tive x-axis), the amount of the wave intensity I(x) passing through a
sample of thickness x is given by [46,47].
I(x) = I(0)e−
αx
,
(50)
where I(0) is the intensity of incident light just falling on the surface
(x = 0) and α is called the absorption coefficient of the sample material
that is given by
12
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α=
Photonics and Nanostructures - Fundamentals and Applications xxx (xxxx) xxx
4πn2 4πn2 E
,
=
ch
λ
peaks increases with increase in β values that are accompanied by blue
shift. Here, as the second set of peaks are related to dominant magnetic
polarization, it is true that increasing the volume fraction of the mag­
netic shell contribute a lot to the peaks intensity. Unlike Fe3O4@Au coreshell composite nanostructure that do not show shifts in position posi­
tion for the set of the third peaks, the peaks position for the set of third
resonance peaks of Au@Fe3O4 core-shell shift to the low energy side (red
shift) and the intensity of the resonance peaks increases with increase in
β (increase with shell thickness). Comparison between Fig. 14(a) and (b)
shows that the ratio of the maximum intensity of Fig. 14(b) from second
set of peaks at E = 2.742 eV (β = 0.875, for Fe3O4 shell thickness of
15 nm) to the maximum intensity from the third set of resonance peaks
at E = 2.937 eV (β = 0.578, for gold shell thickness of 7.5 nm) is about
3.5.
In each case of the two figures shown in Fig. 14 the absorption peaks
of the first set arise at the low energy regions are due to near band edge
absorption of the free exciton recombination. But, the absorption at
higher energy values, second set of resonance peaks of Fe3O4 core-shell
related to the deep level emissions which are attributed to the surface
plasmon resonance of gold shell. However the emission of the third set of
resonance peaks of Fe3O4 core (Fig. 14(a)) and the second and third sets
of resonance peaks of Fe3O4 shell of Fig. 14(b) are due to the dominant
magnetic polarizability at the interface between Fe3O4 and Au or SiO2.
Fig. 15 illustrates the absorbance of (a) Fe3O4@Au core-shell, and (b)
Au@Fe3O4 core-shell nanoinclusions embedded in silica when the fre­
quency dependent magnetic permeability given by Eq. (47) is set to
constant with a value equals to 5. These two figures are just presented to
highlight the contribution of frequency dependent magnetic perme­
ability in the optical properties of magnetic NPs. As discussed in Section
3.3 for Fe3O4@Au core-shell structure the third set of resonance peaks
are due to dominant magnetic polarizability. Similarly for Au@Fe3O4
core-shell NPs the second and the third set of resonance peaks are due to
dominant magnetic polarizability. Hence, the absence of the third peak
in Fig. 15(a) and the absence of the second and the third set of resonance
peaks in Fig. 15(b) are because of the fact that we make μ(ω) constant.
Finally, before concluding this section we want to highlight clearly
the effect of the shell thickness for both structures. Fig. 16(a) and (b)
illustrates the absorbance as a function of the incident radiation for
Fe3O4@Au and Au@Fe3O4 core-shell embedded in SiO2 when the shell
thickness of both materials is 3 nm, respectively. Now let make a com­
parison between Figs. 14(a) and 16(a). In Fig. 14(a) we have seen that as
the shell thickness decreases the first set of the resonance peaks are red
shift and the magnitude of the peaks decreases. So, as we decrease the
shell thickness of the gold from 15 nm (β = 0.875) to 3 nm (β = 0.271),
the amplitude of the first peak is diminished by a factor of 14. Moreover,
the peaks position shifted to the left from the energy value of
E = 1.948 eV to the energy value of E = 1.041 eV, a shift from visible
(51)
where E is the energy of the incident radiation, c is the speed of light, h is
Planck’s constant and n2 is the imaginary part of the refractive index
given by Eq. (49).
The absorbance A of the system is the product of the absorption
coefficient and the thickness of the sample through which the light
propagates. It is simply the logarithm of Eq. (50).
A(E) = ln(I(x)∕I(0) ) = αx =
4πn2 E
x.
ch
(52)
Here x = r2 − r1 is the thickness of the Au shell for Fe3O4@Au core-shell
structure and it is the thickness of the Fe3O4 shell for reverse structure.
Figure 14(a) illustrates the optical absorbance of Fe3O4@Au coreshell nanoinclusion embedded in host matrix (SiO2) and Fig. 14(b) is
the absorbance for the corresponding reverse structure. Both figures are
plotted for shell thickness ranging from 7.5 nm to 15 nm in steps of
1.5 nm. That is a thickness of 15 nm corresponds to β = 0.875 and a
thickness of 7.5 nm corresponds to β = 0.578.
Both figures possess three sets of resonance peaks. In Fig. 14(a) the
first and the second sets of the resonance peaks are as the result of the
dominance of the effective permittivity and the third set of resonance
peaks arise due to the dominance of effective magnetic permeability. In
the case of Fig. 14(b) the first set of the resonance peaks are a contri­
bution from the dominant imaginary part of the electric polarizability or
effective permittivity, and the second and the third sets of resonance
peaks are due to a contribution from the dominant imaginary part of the
magnetic polarizability or effective magnetic permeability through n2.
Note that all the three sets of absorbance peaks for Fe3O4@Au core-shell
nanoinclusions are in the visible region and for the reverse structure the
third set of resonance peaks are in the UV region.
For Fe3O4@Au core-shell the intensity of the first set of resonance
peaks increases and accompanied by blue shift with increasing β (or
decreasing r1). Similarly, the intensity of the second set of resonance
peaks increases with increase in β values but accompanied by red shift.
As β values increases (or as the thickness of the gold shell increases), the
intensity of the third set of the resonance peaks decreases and do not
show any shift in peaks position. The decrease in peaks intensity may be
explained in terms of the increase in the thickness of the gold shell; that
is as the gold shell thickness increases the incident radiation may not
enough to reach the core material to excite electrons that couples with
the surface plasmon of gold shell.
For Au@Fe3O4 core-shell (reverse structure) the intensity of the first
set of resonance peaks decreases and accompanied by red shift with
increase in β values (equivalent to decreasing r1 or increasing the
thickness of Fe3O4 shell). The intensity of the second set of resonance
Fig. 14. The absorbance a) Fe3O4@Au core-shell (b) Au@Fe3O4 core-shellns NPs embedded in silica εh = 3.9 as a function of energy for different values of β, with r2
= 30 nm and f = 0.001.
13
T. Senbeta
Photonics and Nanostructures - Fundamentals and Applications xxx (xxxx) xxx
Fig. 15. The absorbance (a) Fe3O4@Au core-shell (b) Au@Fe3O4 core-shell NPs embedded in silica εh = 3.9 as a function of energy for different values of β, with r2
= 30 nm and f = 0.001 with the magnetic permeability of Fe3O4 equals 5.
Fig. 16. The absorbance vs energy of the incident radiation for (a) Fe3O4@Au core-shell (b) Au@Fe3O4 core-shell when the shell thickness is 3 nm in each case. The
other parameters is the same as Fig. 14.
14
T. Senbeta
Photonics and Nanostructures - Fundamentals and Applications xxx (xxxx) xxx
region to infrared region. The second set of resonance peaks of Fig. 14(a)
is almost disappeared, that is the intensity of the second peak for gold
thickness of 15 nm decreased by a factor of 30.4 when its thickness
decreased down to 3 nm. The other feature of the second peak of Fig. 16
(a) is that it is blue shift and almost overlaps with the third peak. For the
third set of the resonance peaks there is no shift in the resonance peak
position associated to the decrease in thickness, but the amplitude of the
resonance peak increases by a factor of 1.2 showing that thin gold shell
is more favorable than thick gold shell at this particular energy.
Similarly, comparison between Figs. 14(b) and 16(b) shows that as
the shell thickness of the Fe3O4 decreases from 15 nm (β = 0.875) to
3 nm (β = 0.271), the first set of resonance peaks of Fig. 14(b) increases
with amplitude that are accompanied by blue shift and Fig. 16(b) is just
the confirmation of this fact. That is for shell thickness of 15 nm
(β = 0.875), the first resonance peak of Fig. 14(b) occurs at the incident
energy of E = 1.977 eV. But for Fig. 16(b) when the shell thickness of
Fe3O4 is 3 nm (β = 0.271), the first resonance peaks occurs at
E = 2.081 eV. The ratio of the amplitude of the first resonance peaks of
Fig. 16(b) to that of Fig. 14(b) gives 2.1. From Fig. 14(b) for the shell
thickness of Fe3O4 is 3 nm (equivalently as the value of β decreases) the
second set of the resonance peaks decreases in amplitude and accom­
panied by red shift. Hence, the narrow gap between (nearly overlapping)
the first peak and the second peak of Fig. 16(b) is due to the first and the
second peaks position are shifted in opposite direction. The second peak
shifted from E = 2.741 eV to E = 2.015 eV. The amplitude of the second
resonance peak of Fig. 16(b) (for shell thickness of 3 nm) is smaller than
the amplitude of Fig. 14(b) when the shell thickness 15 nm. From Fig. 14
(b) the third set of the resonance peaks diminished in magnitude and the
peaks positions are blue shifted when the value of β decreases or the
thickness of the shell is decreased. The resonance peak position at
E = 3.886 eV for shell thickness of 15 nm is shifted to E = 4.279 eV and
the amplitude of the third resonance peak is diminished by a factor of
7.5.
effect of electric polarzability observed only at the interface of the host
matrix and the shell (SiO2∕Fe3O4 interface). Moreover, when β is
increased, the first set of resonance peaks in the UV region are red shift
which is mainly attributed to the decrease of the size of the semi­
conducting Fe3O4 core, while the second set of resonance peaks are blue
shift with an increase of β values, as the result of increase in the thick­
ness of the metallic shell.
The graphs of the real and imaginary parts of the refractive index and
absorbance as a function of incident radiation energy for different values
of β possess three sets of resonance peaks for both structures. The first
and the second set of the resonance peaks of the imaginary part of the
refractive index (n2) of Fe3O4@Au core-shell are blue and red shift,
respectively while the third set of the resonance peaks do not show any
shift in peaks position as β increases. Note that all sets of resonance
peaks appear in the visible region. For the reverse structure, the first and
the third sets of resonance peaks are red shift with decrease in intensity
as β increases. But, the second set of the resonance peaks is blue shift and
accompanied by increase in the peaks intensity. The resonance peaks of
absorbance follow similar trend of the corresponding n2.
For both structures our results show that the absorbance due to
magnetic polarizability dominates over the electric part for the second
and third set of resonance peaks. By comparing the graphs of n2 and
absorbance we may suggest that the Fe3O4@Au core-shell structure is
best at high frequency values of visible region and can be used in the
application of sensor as the width of the resonance peaks are too narrow
(sensitive) and large. However, the maximum absorbance of Au@Fe3O4
core-shell occurs relatively in low energy regions, and so that its appli­
cation is more appropriate for medical applications that needs the
effective combination of plasmonic and magnetic properties of material.
Declaration of Competing Interest
I did not received any financial and (or) material supports from my
institution as well as from other institution. I did this research while I am
on sabbatical leave without traveling to abroad or other institutions.
4. Conclusions
Based on the proposed nanoparticles structure, we studied the effects
of changing the metal fraction β, dielectric function of the host matrix
(εh), and filling fraction (f) on the magneto-optical properties of com­
posite spherical Fe3O4@Au core/shell nanoparticles embedded in a
dielectric matrix silica and its reverse structure.
With the help of the equations developed in Section 2, we plotted the
graphs of real and imaginary parts of both the electric and magnetic
polarizability, effective permittivity, effective permeability, refractive
index and the optical absorbance for both Fe3O4@Au embedded in SiO2
and the reverse structure for different values of β, εh and f as a function of
the incident radiation energy.
For Fe3O4@Au core-shell nanoparticle structure, the graphs of real
and imaginary parts of the electric polarizability and effective dielectric
function possess two sets of resonance peaks in the visible region and
one set of resonance peaks for magnetic polarizbility and effective
permeability near the end of visible region. The intensity of the peaks
due to magnetic polarizability dominates over the counter electric part.
For the reverse structure the results show one set of resonance peaks for
electric polarizability and effective permittivity in the visible region and
two sets of resonance peaks for magnetic polarizability and effective
permeability in the visible and UV region in which the intensity of the
graphs due to magnetic polarizability in the visible region dominates the
other two.
These sets of resonance peaks arise due to the coupling of the surface
plasmon oscillations of gold with the energy gaps of Fe3O4 at the inner
and the coupling of the surface plasmons of gold with SiO2 at the outer
interfaces, for electric polarizability and the interaction of light with
magnetic dipoles in the inner interface (Fe3O4∕Au). For reverse struc­
ture, the effect of interacting light with the magnetic semiconducting
Fe3O4 have effect at both inner and the outer interface, whereas the
Data Availability
No data was used for the research described in the article.
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RESEARCH ARTICLE | JULY 13 2023
Dependence of quantum dot solar cell parameters on the
number of quantum dot layers 
Tewodros Adaro Gatissa 
; Teshome Senbeta Debela
; Belayneh Mesfin Ali
AIP Advances 13, 075215 (2023)
https://doi.org/10.1063/5.0145361
 
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Online
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Export
Citation
14 July 2023 06:08:32
AIP Advances
ARTICLE
pubs.aip.org/aip/adv
Dependence of quantum dot solar cell
parameters on the number of quantum dot layers
Cite as: AIP Advances 13, 075215 (2023); doi: 10.1063/5.0145361
Submitted: 9 February 2023 • Accepted: 22 June 2023 •
Published Online: 13 July 2023
Tewodros Adaro Gatissa,a)
Teshome Senbeta Debela,
and Belayneh Mesfin Ali
AFFILIATIONS
Department of Physics, Addis Ababa University, P.O. Box 1176, Addis Ababa, Ethiopia
a)
Author to whom correspondence should be addressed: tewodros.adaro@gmail.com
ABSTRACT
© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license
(http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0145361
I. INTRODUCTION
The sun energy is one of the most promising renewable energy
sources.1 A solar cell can convert the sun energy into electrical
energy. Conventional solar cells have a big loss of energy because
of the spectral mismatch between the bandgap of a semiconductor material and the energy distribution of photons in the solar
spectrum.2 Photons with energies lower than the energy bandgap
of the absorber material are not absorbed and cannot generate
electron–hole pairs.1 This loss of energy caused by spectral mismatch can be minimized by using the intermediate band solar cell
(IBSC) concept.3 The idea of IBSC photovoltaic is exciting electrons
by two-step over a semiconductor bandgap with the help of intermediate band.4 Using low-energy photons with the concept of the
intermediate band method enhances the maximum detailed balance
efficiency from 40.7% to 63.1%.3 To obtain the operating principles
of IBSC, a confined levels of quantum dot (QD) was proposed.5,6
The proof of obtaining three distinct quasi-Fermi levels7,8 and the
generation of photocurrent by absorption of photons lying under
the semiconductor bandgap,5,7–9 which are the pillars of IBSC principles, has attracted the interest of many researchers in the field of
quantum dot solar cells (QDSC).
Previous experimental reports10 of quantum well solar cells
revealed that embedding up to 50 InGaAs quantum wells in the
AIP Advances 13, 075215 (2023); doi: 10.1063/5.0145361
© Author(s) 2023
i-region of a p-i-n GaAs cell structure increases photocurrent and
cell efficiency but decreases the open circuit voltage. However, in
Ref. 11, it was reported that increasing the number of wells from
50 to 65 leads in a drop in cell efficiency. Another experimental
report12 revealed that the inclusion of ten stacks of GaSb QDs in the
i-region of GaAs-based solar cells significantly improves the spectral response. This cell has a higher short circuit current and a lower
open circuit voltage than the cell without QDs. Ganesan13 experimentally showed the influence of the thickness of the absorber layer
on the efficiency of PbS QD solar cell. It was found that a device
with absorber layers 240 nm thick performed the best, with increasing thickness leading to a reduction in efficiency. Sugaya et al.14
also reported that increasing the number of stacked layers to 150
increases the external quantum efficiency (EQE) and short circuit
current density of multi-stacked In0.4 Ga0.6 As QD solar cells. Similarly, an experimental report15 using In0.4 Ga0.6 As/GaAs QD solar
cells reveals that increasing the number of QD layers from 10 to 30
and 50 results in an increase in short circuit current density and a
decrease in open circuit voltage and efficiency.
Quantum dot solar cells’ short circuit current density, open
circuit voltage, and efficiency are highly dependent on the dot
parameters, QDs areal density, QDs volume density,16,17 and number of QD layers.18 Experiments to determine the influence of the
number of QD layers on the cell efficiency are currently under
13, 075215-1
14 July 2023 06:08:32
We report the theoretical results of improved solar cell efficiency form InAs quantum dots (QDs) embedded in the intrinsic region of
n-i-p GaAs structure. The effect of QD layers on the QD solar cell parameters is explained in detail. For QD layers of 250, we obtained a
maximum efficiency of 27.4%. Increasing the number of layers beyond the optimum value resulted in the decrease of efficiency. The presence
of InAs QD layers in the cell structure results in a significant rise of the short circuit current density from 33.4 mA/cm2 without InAs QD to
45.4 mA/cm2 in the presence of InAs QD. At the same time, the efficiency of the cell increased from 20.5% without InAs QD to 27.4% with
InAs QD.
AIP Advances
ARTICLE
way. Here, we focus on brief theoretical analysis of the dependency of QDSC reverse saturation current, short-circuit current,
open-circuit voltage, fill factor (FF), and efficiency on the number of QD layers. Previous theoretical model18 used different-sized
QDs in different layers of the structure, but each layer has the
same-sized QDs. The present study uses periodically distributed
same-sized QDs in all layers in order to maintain only one electron confined state in all QD layers. Furthermore, our theoretical
model presents the effect of the number of quantum dot layers on
the solar cell parameters in a more simplified and general form than
other models,18 which use the carrier emission and capturing process in the multilayer QD region, requiring complicated numerical
calculations.
Our theoretical model of QDSC is presented in Sec. II. In this
section, we discuss the photocurrent generated and collected in the
device, and then the efficiency of quantum dot solar cell. By means
of equations derived in Sec. II, the detail analysis of the impact of the
number of quantum dot layers on QDSC parameters are presented
in Sec. III. Section IV concludes our findings.
II. MODEL
For 1 Sun, 1.5 AM condition, the spectral distribution of the
solar flux is given by20
⎤
⎡
⎥
E2
2π ⎢
⎥
⎢
⎥,
ϕ(E) = fs 3 2 ⎢
⎥
⎢
E
h c ⎢ exp (
)
−
1
⎥
K
T
B
s
⎦
⎣
where f s = 1/46 050 is the Sun solid angle, c is the speed of light,
T s = 5760 K is the sun temperature, K B is the Boltzmann constant,
and h is the Planck’s constant.
The hole photocurrent generated by n-type as a function of
photon energy is calculated as
Jp (E) = [
qϕ(E)[1 − R]ap
]
ap 2 − 1
p
×[
(bp + ap ) − β1 exp (−αx j )
− ap exp (−αx j )],
p
β2
(3)
where q is the absolute value of the electronic charge, ap
S L
x
x
x
p
p
= αLp , bp = Dp pp , β1 = bp cosh [ Lpj ] + sinh [ Lpj ], β2 = bp sinh [ Lpj ]
√
x
+ cosh [ Lpj ], Lp = Dp τp is diffusion length of holes, Sp is surface
recombination velocity of holes, Dp is diffusion constant of holes, τ p
is minority carrier lifetime of holes, and xj is n-region width.
The total hole photocurrent collected from the n-region is
equal to
Jpn = ∫
∞
Eg
A. Photocurrent
For the semiconductor sample indicted as Fig. 1, the generation
rate of electron–hole pairs at a distance x from the semiconductor
surface is given by19
(2)
Jp (E)dE.
(4)
The electron photocurrent generated in the p-type as a function
of photon energy is calculated as
qϕ(E)[1 − R]an
] exp (−α[x j + WD ])
an 2 − 1
βn1 + (an − bn ) exp (−αH ′ )
× [an −
],
βn2
Jn (E) = [
G(λ, E) = α(E)ϕ(E)[1 − R(E)] exp [−α(E)x],
(1)
where E is photon energy, ϕ(E) is the photon flux, R(E) is the fraction of these photons reflected from the surface, and α(E) is the
absorption coefficient.
βn1 = bn cosh [ HLn ] + sinh [ HLn ], βn2
√
′
′
= bn sinh [ HLn ] + cosh [ HLn ], Ln = Dn τn is diffusion length of
where
an = αLn ,
bn =
(5)
Sn Ln
,
Dn
′
′
FIG. 1. QDSC model.
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In this section, we employed the model developed by Aroutiounian et al.19 as presented in Fig. 1. In this model, InAs quantum dot
multi-layers are inserted in the i-region of a GaAs n+ − i − p+ cell
structure for low-energy photon absorption to improve photocurrent generation in the i-region. The numerical values for different
parameters were used from Ref. 19.
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electrons, Sn is surface recombination velocity of electrons, Dn is
diffusion constant of electrons, τ n is minority carrier lifetime of
electrons, and H ′ is p-region width.
The total electron photocurrent collected from the p-region is
equal to
p
Jn
∞
=∫
Eg
Jn (E)dE.
(6)
Evaluating Eq. (14) gives
jB (E) = qϕ(E)[1 − R(E)] exp [−α(E)x j ]
× [1 − exp [−(1 − nD VD )α(E)WD ]],
(7)
where αD (E) is the QDs ensemble absorption coefficient.
The quantum dot photocurrent generation as a function of
photon energy is calculated from
x j +nl ao
jD (E) = q∫
xj
GD (E, x)dx.
(8)
The integral in Eq. (8) gives
jD (E) = qϕ(E)[1 − R(E)][1 − exp [−αD (E)nl ao ]],
(9)
where nl is the number of QD layers and ao is size of single QD.
The total photocurrent collected from the quantum dot is given
by
JD = ∫
EQD
jD (E)dE,
(11)
The barrier photocurrent generated inside the i-region as a
function of photon energy is
x j +WD
GB (E, x)dx.
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ji (E) = jB (E) + jD (E).
(17)
From Eqs. (10) and (16), total photocurrent collected from the
i-region is given by
Ji = ∫
∞
Eg
jB (E)dE + ∫
Eg
EQD
jD (E)dE.
(18)
From Eqs. (4), (6), and (18), the short-circuit current density of
the cell is written as
p
Jsc = Jpn + Ji + Jn.
(19)
The behavior of a solar cell is modeled by using the standard superposition approximation of an ideal diode equation. The
current density is expressed as21
J(V) = Jsc − Jo [exp (
qV
) − 1],
KB Tc
(20)
where J o is total reverse saturated current, T c is solar cell temperature
in degrees Kelvin, and K B is Boltzmann’s constant.
J o in Eq. (20) has two parts. The first part is due to minority
carrier diffusion at the depletion layer edges (J s1 ) and it is given by19
Js1 = A exp (−
EgB
),
νKB Tc
(21)
D
GB (E, x) = ϕ(E)[1 − R(E)] exp [−α(E)xj ][(1 − nD VD )α(E)]
× exp [−(1 − nD VD )α(E)(x − xj )].
(13)
xj
(16)
For trap free i-region, the photocurrent generated by light of
a given photon energy in the i-region equals the sum of Eqs. (9)
and (15)
(12)
Therefore, the fraction of the i-region volume not occupied by
barrier
QDs becomes VVi−region
= 1 − nD VD . The generation rate in the barrier
region is written by taking into account the attenuation of light in the
n-region and the fraction of the i-region not occupied by quantum
dots (1 − nD V D )19
jB (E) = q∫
jB (E)dE.
B. Efficiency calculation of QDSCs
where V i-region is the total volume of the i-region, V barrier is the volume of the i-region without QDs, and N QD is the total number of
QDs in the i-region. The volume density of QDs can be defined as
NQD
nD = Vi−region
.
Dividing both sides of Eq. (11) by V i-region gives
V
1 = nD VD + barrier .
Vi−region
∞
Eg
(10)
where EQD is QD energy bandgap and E g is bulk energy bandgap.
Now, let us consider the volume of single QD is V D and the
volume density of QDs is nD (number of QDs per volume of the
i-region). The total volume of the i-region can be written as
Vi−region = NQD VD + Vbarrier ,
JB = ∫
(14)
where A = eNc Nv ( ND pLp + NDA nLn ). Here, N v and N c represent the
valance and conduction band effective density of state in bulk,
respectively. While N A and N D represent the acceptor and donor
concentrations in the p- and n-type regions, respectively.
The second part of J o in Eq. (20) is the contribution due to
thermal excitation inside the i-region (J s2 ) and it is given by19
js2 = Aeff exp (−
Eeff
).
νKB Tc
(22)
2
2
Here, ν is the ideality factor, Aeff = 4πqnh3 cK2 B Tc Eeff
, n is the i-region
average index of refraction, and Eeff is the effective bandgap of the
i-region and approximated by19
E ff = (1 − nD VD )EgB + (nD VD )EgD ,
(23)
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Eg
(15)
where W D is the width of the i-region.
The total photocurrent can be harvested from the barrier region
is
To calculate the photocurrent generated and collected from the
QD ensembles, we can write the generation term as19
GD (E, x) = αD (E)ϕ(E)[1 − R(E)] exp [−αD (E)(x − xj )],
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where Po is the incident solar power (Po = 116 mW/cm2 for 1 Sun,
1.5 AM condition).
where E gD is the bandgap of QD and it is given by22
EgD = Eg (InAs) +
π2 h̵2
,
2μR 2
(24)
III. RESULTS AND DISCUSSION
where μ is effective mass of electron–hole pair, Eg (InAs) is the band
gap of bulk InAs and R is the average radius of spherical QDs.
When the net current density in Eq. (20) is zero and the voltage
produced is the open-circuit voltage,23 the open circuit voltage (V oc )
can be calculated as
Voc =
KB Tc
Jsc
ln ( + 1).
q
Jo
We use parameters in Table I for theoretical analysis of the
dependency of quantum dot solar cell J sc , V oc , FF, and η on nl .
The absorption coefficient of bulk GaAs is calculated by25
πq2 h̵
2∣pcv ∣2
)
(
mo
̵
2εr εo mo hωc
√
̵ − Eg )1/2 2
2(m∗r )3/2 (hω
×[
]( )
2 ̵3
3
π h
√
̵
5.1 hω − Eg
=
,
̵
hω
̵ =
α(hω)
(25)
The fill factor (FF) of a solar cell is defined by
FF =
Vmax Jmax
,
Voc Jsc
(26)
where V max and J max are the voltage and current density of the solar
cell at the maximum power point, respectively. The fill factor can be
expressed as a function of an open circuit voltage V oc using a semiempirical formula, assuming that the solar cell behaves as an ideal
diode
FF =
νoc − ln [νoc + 0.72]
,
νoc + 1
(27)
Vmax Jmax FFVoc Jsc
=
,
Po
Po
(28)
1
2
(29)
where εr = 12.9 is relative permittivity of GaAs,24 m∗r = 0.058 mo
is the reduced mass of electron–hole pair (me = 0.067 mo ,
mh = 0.45 mo ),25 the momentum matrix of bulk GaAs is approxi2
mated as 2∣pmcvo ∣ = 25.7 eV,25 E g is the bandgap of bulk GaAs, and hω
is the photon’s energy. Here, units of E g and hω are in eV and the
̵ is 1/μm.
unit of α(hω)
The average refractive index of the i-region is 4.16,26 effective
density of state of GaAs in valance band (N v ), and conduction band
(N c ) are given by N v = 9.0 × 1018 cm−3 and N c = 4.7 × 1017 cm−3 ,
respectively.24
TABLE I. The physical parameters used in calculations are obtained from Eqs. (24), (30), and (31) and Refs. 19 and 24 .
Parameters
Electron surface recombination velocity (Sn )
Hole surface recombination velocity (Sp )
Electrons diffusion length of (Ln )
Holes diffusion length of holes (Lp )
Electron diffusion constant of (Dn )
Holes diffusion constant (Dp )
Average radius of QD (R)
Number of QD layers (nl )
Volume of QD (V D )
Areal density of QDs (AD )
Volume density of QDs (nD )
Surface reflection coefficient (R)
Bandgap of bulk GaAs (E gB )
Bandgap of bulk InAs [E g (InAs)]
Bandgap of InAs QDs (E gD )
Acceptor concentration (N A )
Donor concentration (N D )
n-region width (xj )
p-region width (H ′ )
i-region width (W D )
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Unit of measure
cm/s
cm/s
μm
μm
cm2 /s
cm2 /s
nm
cm3
cm−2
cm−3
eV
eV
eV
cm−3
cm−3
μm
μm
μm
Value
6 × 103
6 × 103
2
3
200
10
3.1
1–484
1.25 × 10−19
4.43 × 107 –2.5 × 1012
1.47 × 1011 –4.2 × 1018
0.1
1.424
0.354
1.0532
1.4 × 1018
1.7 × 1017
0.8
2.0
3.0
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14 July 2023 06:08:32
where νoc = νKqB Tc Voc is a normalized voltage.
Finally, the cell power conversion efficiency is calculated using
η=
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Quantum dot areal density per layer (AD ) can be approximated
by
AD =
1
2,
(30)
(2R + XB )
where R is average radius of QD and X B is barrier width between
QDs.
Quantum dot volume density (nD ) in terms of nl can be
written as27
nD =
nl AD
.
WD
(31)
⎛ ( kxnl
s
2
− 1) ⎞
⎟,
2ξ 2
⎠
(2l + 1)
̵ = ( 3πβ )∑
αQD (hω)
exp ⎜
(n,l)
4R
ξk2nl
⎝
(32)
where (2l + 1) is the degeneracy. In these equations, knl refers to the
zeros of the spherical Bessel functions with index n and order l, β is
a dimensionless constant defined by Eq. (34),
ξ is Gaussian function
√
relative standard deviation defined as ξ =
reduced photon energy given by
xs2 =
̵ − Eg
hω
̵
h2
2μR 2
,
⟨(R−R )2 ⟩
R
, and xs is the
(33)
where hω is the photon energy and E g is the bandgap energy of the
semiconductor material.
The constant β is given by
Aμ
1
β = √ ( 2 ̵2 ),
2π π h
(34)
where A is defined as28
A=
2πq2 ∣pcv ∣2
1/2
m2o εr εo cω
,
(35)
where μ is the reduced mass, pcv is the momentum matrix element, ω
is the photon frequency, c is the speed of light, εr is the permittivity
of the host material, εo is the permittivity of free space, and mo is the
electron mass. The electron effective mass in bulk GaAs (0.067 mo )
and the vertical heavy hole effective mass in bulk InAs (0.34 mo ) are
considered to be the most acceptable values for the electron and hole
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effective mass in InAs/GaAs quantum dots, respectively.29 For completely filled valance band and completely empty conduction band,
2
the momentum matrix element is approximated by 2∣pmcvo ∣ = mμo EgD ,30
where μ = 0.056 mo . The bandgap of QD is defined by Eq. (24) and
has a value E gD = 1.0532 eV for spherical InAs QD of R = 3.1 nm;
thus,
2∣pcv ∣2
mo
≈ 18.8 eV.
A. Effect of the number of QD layers (nl )
on the reverse saturated current density
Figure 2(a) illustrates the effect of the number of QDs layers
on the reverse saturated current density caused by thermal excitation in the interior of the i-region; plotted according to Eq. (22). It is
observed from the graph that the reverse saturated current density
increases when the number of QD layers increases. In particular,
J s2 starts to increases very rapidly just after ∼350 QD layers of the
QDSC. The possible reason for this can be analyzed by combining Eqs. (22) and (23), i.e., the combination of the two equations
indicates that as the number of quantum dot layers increases, the
effective bandgap decreases whereas the reverse saturated current
density increases. The decreases in the effective bandgap is attributed
to an increase in the recombination of carriers at the QD/barrier
interface. Therefore, it can be concluded that an increase in number of QDs layers increases the thermal recombination process in
the intrinsic region.
B. Effect of nl on the total reverse saturated
current density
The total reverse saturation current can be written by combining Eqs. (22) and (21). It is given by
Jo = Js1 + Js2.
(36)
It is worth noting that the reverse saturation current do not
depend on the number of QD layers and has a calculated value of
Js1 = 7.9 × 10−16 mA/cm2 . Figure 2(b) shows the effect of the number of QD layers on the total reverse saturation current drawn using
Eq. (36). The total reverse saturation current [Fig. 2(b)] shows the
same characteristics as the reverse saturated current due to thermal excitation [Fig. 2(a)]. Both the reverse saturation current due to
thermal excitation and the total reverse saturation current increases
from Js2 = 2.5 × 10−13 mA/cm2 at nl = 0 to Js2 ∼ 1.0 × 10−10 mA/cm2
at nl = 484. Form the aforementioned values of J s1 and J s2 , we see
that the total reverse saturation current of quantum dot solar cell is
dominated by thermal excitation. That is the reason why Figs. 2(a)
and 2(b) are identical. Experimental report of InGaAs/GaAs quantum dot solar cell shows that as the number of QD layers is increased,
so did the dark saturation current.14 This demonstrates increased
carrier recombination in the depletion region with an increase in the
QD layers.
C. Dark current density–voltage characteristics curve
In the dark, most solar cells behave like diodes.21 The dark
current density J dark (V) of ideal diodes is given by
Jdark (V) = Jo [exp (
qV
) − 1].
KB Tc
(37)
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If we have nl number of QD layers in a fixed width W D of the
i-region, then we will have nl + 1 barrier width for a periodically distributed QDs. The width of the i-region can be written as
WD = nl (2R) + (nl + 1)XB . Therefore, the number of QD layers
D −XB
becomes nl = W
. Hence, the variation of the number of QD
2R+XB
layers is due to the variation of barrier width. From this equation,
we can see that the barrier width has to decrease to increase the
number of QD layers inserted in the i-region. The maximum possible number of QD layers inserted in the i-region is achieved when
the QDs touch each other or X B = 0. For R = 3.1 nm, X B = 0 and
W D = 3.0 μm, and the maximum number of QD layers inserted in
the i-region becomes 484.
A spherical quantum dot optical absorption coefficient has
previously been studied in detail,28 and it is given by
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FIG. 2. (a) The dependency of reverse saturated current density due thermal excitation (Js2 ) on the number of QD layers (nl ) using Eq. (22). (b) The dependency of total
reverse saturated current density (Jo ) on the number of QD layers (nl ) using Eq. (36).
D. Effect of n l on the quantum dot
photocurrent density
Figure 4(a) illustrates the effect of number of QD layers on the
QD photocurrent density drawn according to Eq. (10). Figure 4(a)
shows that the quantum dot photocurrent density increases when
the number of QD layers increases and reach the maximum value
of JD = 14.2 mA/cm2 at nl = 484. This figure shows the slope of the
QD photocurrent density becomes sharp from nl = 0 to ∼200, but
the slope slowdowns after nl ∼ 200. This is due to the attenuation
of the light with increasing number of QD layers. When the number of QD layers increases beyond a certain limit, the generation of
electron–hole pairs in QD ensembles decreases. As a result, for QD
layers greater than ∼200, a small improvement in QD photocurrent
density is observed. The observed increase in QD photocurrent density with the number of quantum dot layers is in good agreement
with the experimental report of InAs/GaAs quantum dot solar cell.31
In this experimental report, it is found that the external quantum
efficiency (EQE) at all QD-related transitions increases as the number of QD layers increases; which asserts that QD-related absorption
processes are responsible for the generation of a part of the QDSC’s
short circuit current density.
FIG. 3. The dark current density–voltage characteristics curve plotted using Eq. (37).
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Figure 3 depicts the effect of the number of QD layers on
the dark current, plotted according to Eq. (37). It is seen from the
figure that the cut-in voltage of the J dark vs voltage (V) curve is
determined by the number of QDs layers, i.e., the cut-in voltage
decreases as the number of layers increases. In particular, J dark is
almost the same for QD layers of nl = 0, 50 and 90 (as can be seen
overlapped in Fig. 3), while J dark has the largest value for nl = 484
compared to the others. As it is discussed above, the recombination
current in QDSC increases as the number of QD layers increases.
This results in a decrease in the open-circuit voltage (V oc ) due to
carrier recombination.
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E. Effect of n l on the barrier photocurrent density
The effect of the number of QD layers on the barrier photocurrent density is shown in Fig. 4(b), plotted according to Eq. (16). It
shows that the barrier photocurrent density decreases with increasing number of QD layers for a fixed width of the i-region, reaching
a minimum of 7.9 mA/cm2 at nl = 484. Small degradation of the
barrier photocurrent density is observed up to ∼300 number of QD
layers. However, above ∼300 number of QD layers, the degradation
of barrier photocurrent density increases with increasing number of
QD layers. When the number of QD layers inserted in the intrinsic
region increases, then the fractional volume of the i-region occupied by QDs increases. Therefore, the photocurrent generated by the
barrier region decreases. The decrease in the barrier photocurrent
density is related to the decrease in fractional volume of the barrier region. The relation between the barrier photocurrent density
and the number of QD layers may be explained using the spectral response curve of InAs/GaAs quantum dot solar cell reported
in Ref. 31. In this experimental report, as the number of QD layers increases, the spectral response decreases for wavelengths less
than the GaAs band edge while it increases for wavelengths greater
than the GaAs band edge. This result confirms that the decrease
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in barrier photocurrent density and the increase in QD photocurrent is due to the increase in the number of QD layers. Therefore,
increasing the number of QD layers improves the QD photocurrent
by absorbing lower energy photons and decreases the barrier photocurrent density by decreasing the volume fraction of the barrier
region.
F. Effect of n l on the total photocurrent
in the i-region
Figure 4(c) shows the effect of the number of QD layers
on the total photocurrent of the i-region, drawn using Eq. (18).
The total photocurrent collected from the i-region is the sum of
QD photocurrent density and barrier photocurrent density, and
it is also dependent on the number of layers of the quantum
dots. The figure shows that the total photocurrent in the i-region
increases with an increase in the number of layers and reach a maximum value of Ji = 22.35 mA/cm2 at nl = 429 and then decreases to
Ji = 22.1 mA/cm2 when the number of QD layers increases to 484.
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FIG. 4. The dependence of (a) the QD photocurrent density (JD ), (b) the barrier photocurrent density (JB ), (c) the total photocurrent density in the i-region (Ji ), and (d) the
short circuit current density (Jsc ) on the number of QD layers (nl ), plotted using Eqs. (10), (16), (18), and (19), respectively.
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The observed variation of the i-region photocurrent density with
the number of QD layers is in good agreement with the theoretical model of Inx Ga1−x N/GaN quantum dot solar cell reported in
Ref. 18.
G. Effect of n l on the short circuit current density
The short circuit current density is the sum of the photocurrent
densities from the n-, p-, and i-regions. The minority hole photocurrent density (Jpn ) from the emitter is defined by Eq. (4) and
is calculated to be Jpn = 24.23 mA/cm2 . The minority electron phop
tocurrent density (Jn ) from the base is defined by Eq. (6) and is
p
calculated to be Jn = 0.22 mA/cm2 . Figure 4(d) illustrates the effect
of the number of QD layers (nl ) on the short circuit current density plotted according to Eq. (19). It is found that J sc increases as
nl increases and reach its maximum value of Jsc = 46.8 mA/cm2 at
nl = 429 and then decreases to Jsc = 46.6 mA/cm2 when nl increases
to 484, as shown in Fig. 4(d). Hence, the insertion of large number
of QD layers has greatly enhanced the photogenerated current density J sc of the theoretically modeled device. This model’s improved
short-circuit current density with an increase in QD layers is in good
agreement with the experimental and theoretical results reported in
Refs. 10, 12–14, 18, and 31–32.
Figure 5(a) shows the effect of the number of QD layers on the
open circuit voltage drawn according to Eq. (25). The effect of nl on
the V oc of QDSC can be related through the dependence of V oc on
both J sc and J o . Figure 5(a) shows that a small open circuit improvement is observed up to nl = 180. Maximum V oc = 0.85 V is obtained
at nl = 90. Above nl = 180, the open circuit voltage decreases very
rapidly. The increase in V oc associated with a fast increase in J sc for
the number of QD layers less than ∼180 [Fig. 4(d)], whereas a very
slow increase in total reverse saturated current density is observed
for the number of QD layers less than ∼180 [Fig. 2(b)]. A fast degradation in open circuit voltage is the result of a fast increase in J o
above nl ∼ 350 [Fig. 2(b)] and a small J sc improvement above nl ∼ 200
[Fig. 4(d)]. The degradation in open circuit voltage with the increase
in the number of QD layers in this model agrees with experimental
and theoretical results reported in Refs. 14 and 18, respectively.
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I. Effect of n l on the fill factor
Figure 5(b) depicts the effect of the number of QD layers on
the fill factor, plotted according to Eq. (27). It shows that a small
fill factor improvement is observed up to QD layers of nl = 180.
The maximum fill factor, i.e., FF = 84.7% is obtained at nl = 90. The
slight increase in the fill factor may be attributed to improved carrier
transport through the intrinsic and emitter regions. Above nl = 180,
the fill factor decreases very rapidly. This decrease in fill factor with
an increase in the number of QDs layers (beyond nl = 180) can be
related to a decrease in carrier transport through the intrinsic and
emitter regions and an increase in the recombination current with
increasing number of QDs layers. Our result is in good agreement
with the experimental result reported in Ref. 14.
J. Current density–voltage characteristic curves
Figure 6 depicts the current density–voltage (J-V) characteristic
curves of InAs/GaAs QDSC structure, drawn according to Eq. (20).
The J-V characteristic curves show that when the number of QD
layers increases, the short circuit current increases and the open circuit voltage decreases. However, the increase in J sc above nl = 250 is
small, while the decrease in V oc becomes more pronounced, indicating that a further increase in the QD layers above nl = 250 results
in a decrease in the efficiency of the QDSC structure. This theoretical model shows that using quantum dots as an intermediate band
will improve the J sc of the solar cell as well as its efficiency. However, there is an optimum value (about ∼nl = 250) of the number
of QD layers that results to the maximum possible efficiency of the
theoretically modeled QDSC. It is worth noting that the obtained
current density–voltage (J-V) characteristics curve agrees with the
experimental result studied in Ref. 14.
K. Effect of n l on the efficiency
Figure 7 illustrates the dependence of quantum dot solar cell
efficiency on the number of QD layers, plotted according to Eq. (28).
It shows that there is an optimum number of QDs layer to get maximum efficiency, which is in good agreement with the experimental
reports in Refs. 10, 12–14, 31, and 33 and theoretical model of quantum dot solar cells studied in Refs. 18, 34, and 35. The efficiency
of QDSC is found to be maximum at nl = 250, and increasing the
number of QD layers above this value reduces the cell’s efficiency.
The increase in efficiency up to 250 QD layers is due to a greater
FIG. 5. The dependence of (a) the open circuit voltage (V oc ) and (b) the fill factor (FF) on the number of QD layers (nl ), plotted using Eqs. (25) and (27), respectively.
AIP Advances 13, 075215 (2023); doi: 10.1063/5.0145361
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H. Effect of n l on the open circuit voltage
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FIG. 6. The effect of the number of QD layers (nl ) on the current density–voltage (J-V) curve, plotted using Eq. (20).
more rapidly. We can say that the decrease in efficiency above 250
QD layers is caused by an increase in short circuit current density, which is less significant than a decrease in open circuit voltage
and fill factor. Finally, we deduce that 250 layers of QD are optimal for maximum efficiency. The calculated value of J sc , V oc , FF,
and η is given in Table II along with the same configuration of
solar cell without QDs. Table III shows the comparison between
our theoretical model of the InAs/GaAs QD solar cell and published theoretical and experimental reports of the InAs/GaAs QD
solar cell.
FIG. 7. The dependence of efficiency (η) on the number of QD layers (nl ), obtained using Eq. (28).
AIP Advances 13, 075215 (2023); doi: 10.1063/5.0145361
© Author(s) 2023
13, 075215-9
14 July 2023 06:08:32
increase in short circuit current density than a decrease in the open
circuit voltage and fill factor. When the number of layers exceeds
250, the slope of short circuit current density slows because the
slope of QD photocurrent density starts to slow and the negative
slope of barrier photocurrent density begins to rise as a direct result
of the attenuation of light and increasing volume fraction of QDs.
Similarly, as the number of QD layers exceeds 250, the reverse saturation current due to thermal excitation increases as a result of
a decrease in effective bandgap. Thus, short circuit current density
improved slowly while open circuit voltage and fill factor degraded
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TABLE II. The calculated value of Jsc , V oc , FF, and η of solar cell with and without
QDs.
Solar cell
Without QD
max
QDSC (Voc
)
QDSC (ηmax )
QDSC (Jscmax )
nl
J sc (mA/cm2 )
Voc (V)
FF (%)
η (%)
0
90
250
249
33.4
40.7
45.4
46.8
0.84
0.85
0.83
0.74
84.6
84.7
84.4
83.1
20.5
25.1
27.4
24.9
pubs.aip.org/aip/adv
Belayneh Mesfin Ali: Supervision (equal); Validation (equal);
Writing – original draft (equal); Writing – review & editing (equal).
DATA AVAILABILITY
The data that support the findings of this study are available
within the article.
REFERENCES
1
TABLE III. Jsc , V oc , FF, and η comparison for InAs/GaAs quantum dot solar cell. NA
stands for “not available.”
Solar cell
This model
Theoretical19
Theoretical31
Expt.32
nl
J sc (mA/cm2 )
Voc (V)
FF (%)
η (%)
250
NA
20
40
45.4
45.2
25.0
23.8
0.83
0.75
0.9
0.99
84.4
NA
75.0
82.3
27.4
25.0
12.4
14.3
IV. CONCLUSION
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Tewodros Adaro Gatissa: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Writing – original draft (equal).
Teshome Senbeta Debela: Supervision (equal); Validation (equal);
Writing – original draft (equal); Writing – review & editing (equal).
AIP Advances 13, 075215 (2023); doi: 10.1063/5.0145361
© Author(s) 2023
13, 075215-10
14 July 2023 06:08:32
We investigated the dependence of quantum dot solar cell
parameters on the number of quantum dot layers. In particular,
a theoretically modeled InAs/GaAs n-i-p SC is considered. The
results indicate that inserting InAs multilayer QDs into the intrinsic region of GaAs significantly improves the conversion efficiency
of the n-i-p structure. The short circuit current density increased
from 33.4 mA/cm2 (without QDs) to 45.4 mA/cm2 (with QDs),
a relative enhancement of 35.9%. The conversion efficiency of the
solar cell device improved from 20.5% without QDs to 27.4% with
QDs, which a relative enhancement of 33.7%. However, the efficiency of QDSC is determined by the number of QD layers. This
theoretical model shows that there is an optimum number of quantum dot layers (nl = 250) to get maximum efficiency (ηmax = 27.4%).
Above the optimum number of QD layers, the efficiency decreases.
The result obtained in this theoretical model of InAs/GaAs quantum dot solar cell can be used for experimental study of QDSCs
as well in the design and fabrication of better performance solar
cell panels.
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and M. Mazzer, “Spectral response and I-V characteristics of large well number
multi quantum well solar cells,” J. Mater. Sci. 40(6), 1445–1449 (2005).
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and D. L. Huffaker, “GaSb/GaAs type II quantum dot solar cells for enhanced
infrared spectral response,” Appl. Phys. Lett. 90(17), 173125 (2007).
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films,” M.S. thesis, Delft University of Technology, 2018.
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T. Sugaya, O. Numakami, R. Oshima, S. Furue, H. Komaki, T. Amano, K. Matsubara, Y. Okano, and S. Niki, “Ultra-high stacks of InGaAs/GaAs quantum dots
for high efficiency solar cells,” Energy Environ. Sci. 5(3), 6233–6237 (2012).
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T. Sugaya, S. Furue, H. Komaki, T. Amano, M. Mori, K. Komori, S. Niki,
O. Numakami, and Y. Okano, “Highly stacked and well-aligned In0.4 Ga0.6 As
quantum dot solar cells with In0.2 Ga0.8 As cap layer,” Appl. Phys. Lett. 97, 183104
(2010).
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H. L. Weng, H. Y. Ueng, and C. P. Lee, “Efficiency of quantum dot solar cell
enhanced by improving quantum dots performance,” Phys. Status Solidi A 212(2),
369–375 (2014).
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H. Movla, F. Sohrabi, J. Fathi, A. Nikniazi, H. Babaei, K. Khalili, and N. E. Gorji,
“Photocurrent and surface recombination mechanisms in the Inx Ga1-x N/GaN
different-sized quantum dot solar cells,” Turk. J. Phys. 34(4), 97–106 (2010).
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N. Es’haghi Gorji, H. Movla, F. Sohrabi, A. Hosseinpour, M. Rezaei, and
H. Babaei, “The effects of recombination lifetime on efficiency and J–V characteristics of Inx Ga1−x N/GaN quantum dot intermediate band solar cell,” Physica E
42(9), 2353–2357 (2010).
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solar cells,” J. Appl. Phys. 89(4), 2268 (2001).
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incorporating carrier transport and recombination,” J. Appl. Phys. 105(6), 064512
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21
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effect on energy gap of CdSe, ZnS and GaAs quantum dots using particle in a box
model,” Chalcogenide Lett. 14(2), 49–54 (2017).
23
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(McGraw-Hill, 2012).
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25
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(UIT Cambridge, 2003).
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“Optical properties of InAs/GaAs quantum dot superlattice structures,” Results
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27
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Quantum Dot Structures (Wiley, 2011).
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on the absorption spectrum of semiconductor quantum dots,” Nanotechnology
15(8), 975–981 (2004).
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self-assembled quantum dots,” Eur. Phys. J. B 68(2), 233–236 (2009).
30
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Institute of Technology, 2001), Vol. 2.
31
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M. Bennett, D. V. Forbes, and R. Raffaelle, “InAs quantum dot enhancement of GaAs solar cells,” in 35th Photovoltaic Specialists Conference (IEEE,
2010).
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the quantum dot solar cells,” Sol. Energy 86(3), 935–940 (2012).
14 July 2023 06:08:32
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RESEARCH ARTICLE | MARCH 23 2023
Effects of shape on the optical properties of CdSe@Au coreshell nanocomposites
Garoma Dhaba Bergaga  ; Belayneh Mesfin Ali ; Teshome Senbeta Debela
AIP Advances 13, 035331 (2023)
https://doi.org/10.1063/5.0138456
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Some Considerations on Luminescent Fiber Chambers and Intensifier Screens
Rev Sci Instrum (December 2004)
Dipole moment analysis of excited van der Waals vibrational states of ArH35Cl
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Effects of shape on the optical properties
of CdSe@Au core-shell nanocomposites
Cite as: AIP Advances 13, 035331 (2023); doi: 10.1063/5.0138456
Submitted: 12 December 2022 • Accepted: 6 March 2023 •
Published Online: 23 March 2023
Garoma Dhaba Bergaga,1,2,a)
Belayneh Mesfin Ali,1
and Teshome Senbeta Debela1
AFFILIATIONS
2
Department of Physics, Addis Ababa University, P.O. Box: 1176, Addis Ababa, Ethiopia
Department of Physics, Sebeta Special Needs Education Teachers College, P.O. Box: 195, Sebeta, Addis Ababa, Ethiopia
a)
Author to whom correspondence should be addressed: garoma.dhaba@gmail.com
ABSTRACT
We studied the local field enhancement factor (LFEF), absorption, and extinction cross sections of spherical, cylindrical, oblate, and prolate
core–shell nanocomposites (NCs) theoretically and numerically using the quasi-static approach. By solving Laplace’s equations, we obtained
expressions for the LFEF, polarizability, absorption, and scattering cross sections for each of the core–shell NCs. We found that the LFEF,
absorption, and extinction cross section of spherical and cylindrical core–shell NCs possess two peaks whereas oblate and prolate spheroids
show three observable peaks. Moreover, the prolate core–shell spheroid shows greater tunability and larger intensity of the LFEF than its corresponding oblate structure. Furthermore, spherical nanoshells are characterized by the higher LFEF than cylindrical and spheroidal core–shells
of the same size and composition. When compared, even the smallest value of the LFEF of the spherical core–shell is 11.42 and 10.09 times
larger than the biggest values of oblate and prolate core-shells, respectively. The study also indicated that for spherical and cylindrical NCs,
the first two peaks of the LFEF and extinction cross sections are achieved at the same corresponding frequencies. Furthermore, all peaks of the
extinction cross sections of the prolate spheroid are found to be the lowest while those of the cylindrical peaks are the highest. Where there
are an equal number of peaks of different shapes, the peak values are different, showing that shapes of core–shell NCs determine the intensity,
the number, and the positions of peaks of the LFEF and optical cross sections. Such NCs are promising for applications in optical sensing,
bio-sensing, and electronic devices. Especially, gold coated core–shell spheroids have good potential applications in multi-channel sensing.
© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license
(http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0138456
I. INTRODUCTION
Nowadays, the optical properties of nanoparticles are central
to many applications in the areas of light-emitting diodes, photocatalysis, biochemical sensing, solar energy conversions, bio-sensors,
degradation of harmful chemicals, and medical diagnostics.1–4 In
studying these nanoparticle structures, metallo-dielectric core–shell
nanoparticles, composed of a dielectric core and a metal shell, have
attracted a great amount of interest in plasmonics due to the wide
tunability of the plasmon resonance.5 As the plasmon resonance
of core–shell nanoparticles is sensitive to their geometry,6 the optical properties of such nanocomposites (NCs) can be controlled and
modified as desired.7 As a result of this, core–shell NCs with different shapes are currently one of the leading active research fields.8
Several research studies have been conducted experimentally, computationally, and theoretically regarding the effect of shape on the
optical properties of core–shell NCs such as SiO2 @Au,9 Si@SiO2 ,10
AIP Advances 13, 035331 (2023); doi: 10.1063/5.0138456
© Author(s) 2023
Ag@SiO2 ,11 Fe2 O3 @SiO2 ,12 Au–Ag@TiO2 ,13 CdSe@Al2 O3 @Ag,14
CdSe@Ag,15 ZnO@Au,16 and so on.
Among many core–shell nanoparticles, CdSe quantum dots
have been studied intensively owing to the size-dependent photoemission.17 It was reported that higher emission efficiency and
desired emission wavelength can be obtained from CdSe based
quantum dots.18,19 When noble metals such as silver and gold are
used as a shell and coated over the CdSe core, it was indicated that
CdSe based core–shell nanoparticles showed high electromagnetic
field enhancement.20
However, many of these studies were carried out by varying the
sizes of the quantum dot and not the shapes. Even where shapes were
considered, many of the systems studied so far have been spherical,
cylindrical, spheroidal, or, at most, two of the shapes at a time. To the
best of our knowledge, the optical properties of CdSe@Au core–shell
NCs have not been studied by changing their shapes alternately as
spherical, cylindrical, oblate, and prolate spheroids. Thus, in the
13, 035331-1
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1
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present study, we theoretically and numerically investigated the local
field enhancement factor, absorption, and extinction cross sections
of spherical, cylindrical, oblate, and prolate shaped core–shell NCs
each consisting of cadmium selenide (CdSe) as a dielectric core and
gold (Au) as a metallic shell with the whole system embedded in a
SiO2 host medium.
II. THEORETICAL MODELS AND CALCULATIONS
The coefficient of E0 in Eq. (4) is called the local field enhancement
factor (LFEF), and A can be given by
A=
′′2
81ε23
ε′2
2 + ε2
2 ( ′2
′′2
′
′ 2 ).
4p (ε2 − ε2 + qε2 + ε1 ε3 )2 + ε′′2
2 (q + 2ε2 )
When electromagnetic radiation interacts with matter (in our case,
spherical core–shell nanocomposites), the scattering and absorption phenomena arise, which are in turn determined by electrostatic polarizability, α. For the core–shell nanosphere geometry, the
polarizability is given by24
α = 4πr23 [
(ε2 − ε3 )(ε1 + 2ε2 ) + f (ε1 − ε2 )(ε3 + 2ε2 )
].
(ε2 + 2ε3 )(ε1 + 2ε2 ) + 2 f (ε1 − ε2 )(ε2 − ε3 )
3
3
− 1)ε1 + ( − 1)ε3 ,
2p
p
(2)
p = 1 − f.
(3)
Hence, Eq. (1) can be written as
E1 =
9ε2 ε3
E0.
2pΔ
(4)
FIG. 1. Schematic of the spherical core–shell nanocomposite embedded in a host
matrix.
AIP Advances 13, 035331 (2023); doi: 10.1063/5.0138456
© Author(s) 2023
(8)
From this, the scattering and absorption cross sections can be given
by25
Cscat =
q=(
(7)
where k =
2π √
ε3
λ
k4 2
∣α∣ ,
6π
Cabs = kIm[α],
(9)
is the wavevector in the medium.
B. Cylindrical core–shell nanocomposite
Recently, investigating the optical properties of coated NCs
associated with their shapes has been given significant attention.26
Based on this ample interest, let us consider a coated cylindrical
core–shell nanoparticle embedded in a host medium, as shown in
Fig. 2. In this scheme, we assumed that the cylinder is infinitely
extended along the z−axis.
Based on the quasistatic approximation and by solving
Laplace’s equation, the electric field in the core, the shell, and the
host medium can be obtained as follows:27
A1 Ð
Ð
→
→
E1 = (1 −
)E0 ,
E0
(10)
A2 Ð
Ð
→
→ B2
)E0 + 2 (cos φêr + sin φêφ ),
E2 = (1 −
E0
r
(11)
Ð
→ Ð
→ B3
E3 = E0 + 2 (cos φêr + sin φêφ ),
r
(12)
where r denotes the position vector of the observation point and φ is
the included angle the incident field makes with the position vector
r. êr and êφ are unit vectors in the r and φ directions, respectively.
13, 035331-2
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∣A∣2 =
where
Δ = ε22 + qε2 + ε1 ε3 ,
(6)
where ε′2 and ε′′2 are the real and imaginary parts, respectively. Now,
substituting Eqs. (3) and (6) into Eq. (5) and taking its modulus
square, the LFEF in the dielectric core, as briefly detailed in previous
study,23 is given by
(1)
where f = (r1 /r2 )3 . For the sake of simplicity, let’s represent the
denominator in Eq. (1) by
2pΔ,
(5)
ε2 = ε′2 + iε′′2 ,
Changing the shapes of core–shell NCs can help control their
optical properties that determine the effectiveness of the nanostructure. In this section, we considered a spherical core–shell
nanocomposite, which is shown in Fig. 1. The dielectric core (CdSe)
has a radius r1 with a dielectric function ε1 . The metallic shell (Au)
has a radius r2 and a frequency dependent dielectric function ε2 ,
with the whole nanocomposite embedded in a dielectric host matrix
(SiO2 ) of a dielectric function ε3 .
When an electromagnetic wave with electric field intensity
E0 is incident on this core–shell nanoparticle along the z−axis,
the local electric field in the dielectric core under the quasi-static
approximation can be written as21,22
9ε2 ε3
E0 ,
(ε1 + 2ε2 )(ε2 + 2ε3 ) + 2 f (ε1 − ε2 )(ε2 − ε3 )
E1 9ε2 ε3
=
.
E0
2pΔ
In Eq. (5), ε2 is the complex frequency dependent electric permittivity of the metal shell, and it can be written as
A. Spherical core–shell nanocomposite
E1 =
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Considering the modulus squared of the enhancement factor, we get
∣F∣2 = ∣
E1 2 16ε22 ε23
∣ = 2 2 .
E0
pΔ
(20)
In Eq. (20), ε2 (of gold) is a complex function with real (ε′2 )
and imaginary (ε′′2 ) parts, as given by Eq. (6). Using the Drude–
Sommerfeld model,29 this dielectric function can be written as
ε′2 = ε∞ −
The coefficients A1 , A2 , B2 , and B3 can be given by28
A1 =
ε2 (ε2 − 3ε3 ) + ε1 (ε2 + ε3 ) + f [(ε1 − ε2 )(ε2 − ε3 )]
E0 ,
(ε1 + ε2 )(ε2 + ε3 ) + f (ε1 − ε2 )(ε2 − ε3 )
B2 =
2ε3 (ε1 − ε2 )r12
E0 ,
(ε1 + ε2 )(ε2 + ε3 ) + f (ε1 − ε2 )(ε2 − ε3 )
(15)
4ε2 ε3
E0.
(ε1 − ε2 )(ε2 − ε3 ) + f (ε1 + ε2 )(ε2 + ε3 )
4ε2 ε3
E0.
pΔ
AIP Advances 13, 035331 (2023); doi: 10.1063/5.0138456
© Author(s) 2023
reff
(23)
Throughout this study, we used v F = 1.4 × 106 m/s, γ0 = 4.6
× 10 Hz, ωp = 1.37 × 1016 Hz, and ϵ∞ = 9.84 for gold.32 By substituting the complex dielectric function of gold ε2 with its real (ε′2 ) and
imaginary (ε′′2 ) parts into Eq. (20), the enhancement factor of the
local field for the coated cylindrical nanocomposite in the dielectric
core can be given by
∣F∣2 =
′′2
16ε23
ε′2
2 + ε2
(
′′2
′
2
′′2
′ 2 ).
p2 (ε′2
2 − ε2 + qε2 + ε1 ε3 ) + ε2 (q + 2ε2 )
(24)
In investigating the optical resonance of nanoshells, it is
important to consider its polarizability. Thus, the polarizability of
cylindrical concentric nanoshells is defined as follows:33
(18)
(19)
[(r2 − r1 )(r22 − r12 )] 3
=
.
2
13
(17)
From this, the enhancement factor (F) in the dielectric core can be
obtained as
E1 4ε2 ε3
F=
=
.
E0
pΔ
(22)
where γ0 is the damping constant for the bulk material, v F is the
electron velocity at the Fermi surface, A is a parameter related to the
details of the scattering process, and reff is the effective mean free
path of the collision and can be calculated as31
(16)
If we let the denominator of Eq. (17) be pΔ, where p = 1 − f ,
Δ = ε22 + qε2 + ε1 ε3 , q = (2/p − 1)ε1 + (2/p − 1)ε3 , we can represent
the local field of the dielectric core of the inclusion in a simple
expression as follows:
E1 =
vF
,
reff
1
where f = (r1 /r2 )2 . By substituting these coefficients A1 , A2 , B2 , and
B3 into Eqs. (10)–(12), the electric field in the core, the shell, and the
surrounding medium can be calculated. If we insert the expression
of A1 into Eq. (10) and simplify it, the local field enhancement in the
dielectric core of the composite becomes
E1 =
(21)
where ε∞ , ω, ωp , and γ are the contribution of the bound electrons to polarizability, the frequency of the incident electromagnetic
wave, the bulk plasma frequency of the silver metal, and the collision
frequency of free electrons, respectively.
Decreasing the size of the nanoparticle will eventually cause the
thickness to become less than the bulk mean free path, and electron scattering from the surfaces of the particle will have the effect
of decreasing and broadening its plasmon resonance peak(s). There
is a correlation available for the case of nanoshells, and in this case,
γ can be modified according to Ref. 30,
γ = γ0 + A
(14)
(ε1 − ε2 )(ε2 + ε3 )r12 + (ε1 + ε2 )(ε2 − ε3 )r22
E0 ,
B3 =
(ε1 + ε2 )(ε2 + ε3 ) + f (ε1 − ε2 )(ε2 − ε3 )
ω2p γ
,
ω + γ2
2
(13)
(ε2 − ε3 )[(ε2 − ε1 ) f − (ε2 + ε3 )]
E0 ,
(ε1 + ε2 )(ε2 + ε3 ) + f (ε1 − ε2 )(ε2 − ε3 )
A2 = −
ε′′2 =
α = 4π
(ε1 − ε2 )(ε2 + ε3 ) f + (ε1 + ε2 ) + (ε2 − ε3 )
.
(ε1 − ε2 )(ε2 − ε3 ) f + (ε1 + ε2 )(ε2 + ε3 )
(25)
From the optical absorption and scattering theories, the absorption
and scattering cross sections for a single shell nanoparticle34 can be
written as in Eq. (9).
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FIG. 2. Schematic of the cylindrical core–shell nanocomposite embedded in a host
matrix.
ω2p
,
ω + γ2
2
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ARTICLE
φ0 = −E0 z = −E0 F1 (ξ)G(η, ζ),
C. Ellipsoidal core–shell nanocomposite
Let us consider a core–shell ellipsoid shown in Fig. 3 with principal semiaxes a1 , b1 , and c1 for the core surface and a2 , b2 , and c2
for the outer shell surface. Using the ellipsoidal coordinates (ξ, η, ζ),
the confocal ellipsoidal surfaces can be expressed by35
x2
y2
z2
+ 2
+ 2
= 1,
a1 + ξ b1 + ξ c1 + ξ
2
x
2
a1 + η
2
+
y
2
b1 + η
2
2
2
+
z
2
c1 + η
2
= 1,
2
y
z
x
+
= 1,
+
a1 2 + ζ b1 2 + ζ c1 2 + ζ
−c12 < ξ < ∞,
−b21 < η < −c12 ,
−a21 < ζ < −b21.
(26)
where
F1 (ξ) = (c12 + ξ)1/2 ,
(27)
(28)
(b21 + ξ)(b21 + η)(b21 + ζ)
,
(a21 − b21 )(c12 − b21 )
(c2 + ξ)(c2 + η)(c2 + ζ)
z = 1 2 21 2 12
.
(a1 − c1 )(b1 − c1 )
1/2
.
(c2 + ξ)(c2 + η)(c2 + ζ)
]
(a2 − c2 )(b2 − c2 )
1/2
.
Under the quasi-static approximation, the distribution of electric
potentials in the dielectric core, in the metal shell, and in the
embedding dielectric matrix can be given by36
−c2 < ξ < 0,
φ1 = D1 F1 (ξ)G(η, ζ),
(29)
φ2 = [D2 F1 (ξ) + D3 F2 (ξ)]G(η, ζ),
0 ≤ ξ < t,
(30)
φ3 = [−E0 F1 (ξ) + D4 F2 (ξ)]G(η, ζ),
t ≤ ξ < ∞,
(31)
where
F2 (ξ) = F1 (ξ)∫
ξ
∞
dq
,
(c12 + q) f 1 (q)
f 1 (q) = [(a21 + q)(b21 + q)(c12 + q)]1/2.
The coefficients D1 , D2 , D3 , and D4 are unknown constants to
be determined using the following boundary conditions. For electric
potentials, the boundary conditions can be found from continuity
conditions as
φ1 = φ2 ,
φ2 = φ3 ,
2
The potential due to the applied field, which we take to be parallel to
the z axis, is
(c12 + η)(c12 + ζ)
]
(a21 − c12 )(b21 − c12 )
at ξ = 0,
at ξ = t,
(32)
and the normal components of the electric displacement vector can
be found as
∂φ2
∂φ1
= ε2
, at ξ = 0,
∂ξ
∂ξ
∂φ2
∂φ3
ε2
= ε3
, at ξ = t.
∂ξ
∂ξ
ε1
(33)
where ε1 , ε2 , and, ε3 are the electric permittivities of the dielectric core, the metallic shell, and the host medium, respectively.
By substituting Eqs. (29)–(31) into Eqs. (32) and (33) and solving
simultaneously, the unknown coefficients D1 , D2 , D3 , and D4 can be
obtained and are given by
D1 = −
ε2 ε3
E0 ,
Q
(1)
D2 = −
FIG. 3. Schematic representation of (a) oblate and (b) prolate spheroidal
core–shell NCs.
AIP Advances 13, 035331 (2023); doi: 10.1063/5.0138456
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[ε3 (ε1 − ε2 )Lz
Q
D3 =
(34)
+ ε2 ]
E0 ,
a1 b1 c1 ε3 (ε1 − ε2 )
E0 ,
2Q
(35)
(36)
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(a2 + ξ)(a21 + η)(a21 + ζ)
x2 = 1 2
,
(b1 − a21 )(c12 − a21 )
G(η, ζ) = [
That is to say,
φ0 = −E0 [
The coordinate ξ is normal to the surface. The variables η and ζ are
the parameters of confocal hyperboloids and as such serve to measure the position on any ellipsoid (ξ = constant). In other words,
each ellipsoidal surface is defined by a constant ξ. Therefore, ξ = 0
is the equation of the surface of the inner ellipsoid, and ξ = t is
that of the surface of the outer ellipsoid, where a21 + t = a22 , b21 + t
= b22 , c12 + t = c22 .
For a given (x, y, z), if we assume x > 0, y > 0, z > 0, there is a
one to one correspondence between (x, y, z) and the three largest
roots (ξ, η, ζ). Solving for x, y, and z, we obtain the following
expressions:
y2 =
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D4 = −
ARTICLE
a2 b2 c2
(2)
{ f (ε1 − ε2 )[Lz (ε2 − ε3 ) − ε2 ]
2Q
For a prolate spheroid (ai = bi < ci ),
(1)
− (ε2 − ε3 )[Lz (ε1 − ε2 ) + ε2 ]}E0 ,
(i)
(2)
(1)
⎡
L − Lz ⎤
⎢
⎥
⎥ − qε2 + ε1 ε3.
Δ = ⎢1 + z
⎢
⎥
p
⎣
⎦
(38)
1 − e2i
1
1 + ei
(−1 + 2 ln
),
1 − ei
2e2i
2ei
1
(i)
(i)
(i)
Lx = Ly = (1 − Lz ),
2
Lz =
(37)
where Q = pΔ and
e2i = 1 −
(1)
(2)
q = [1 − Lz /p]ε1 + {[Lz
− 1]/p + 1}ε3
(1)
(1)
(2)
− 1] − Lz [Lz
− 1],
f = a1 b1 c1 /a2 b2 c2.
(i)
Lz =
E1 = −∇φ1 = K1 E0 ,
(2)
The variables Lz and Lz are the geometrical factors for the inner
and outer confocal ellipsoids, respectively.
Spheroids are a special class of ellipsoids, which have two
axes of equal length. Hence, only one of the geometrical factors
is independent.35,37 Oblate spheroids are generated by rotating an
ellipse about its minor axis, whereas prolate spheroids are generated
by rotating an ellipse about its major axis.
For an oblate spheroid (ai = bi > ci ),
g 2 (ei )
g(ei ) π
−1
,
2 [ − tan g(ei )] −
2
2ei 2
1
(i)
(i)
(i)
Lx = Ly = (1 − Lz ),
2
(39)
where
¿
Á 1 − e2i
À
g(ei ) = Á
,
e2i
e2i = 1 −
ci2
.
a2i
⎡
⎢
ε23 ⎢
⎢
∣K1 ∣ = 2 ⎢
p ⎢
⎢ ((ε′2 − ε′′2 )(1 +
2
2
⎢
⎣
2
where K 1 is the factor that relates the local field in the dielectric core
with the external incident electric field. Comparing Eq. (34) with
Eq. (41), the coefficient of E0 , called the enhancement factor (K 1 ),
is given by
K1 =
ε2 ε3
.
Q
(42)
In this expression, ε2 is the dielectric permittivity of gold. From
the Drude–Sommerfeld model,38 it can be seen that this dielectric
permittivity is complex and is given by Eq. (21). By employing the
correction of the bulk damping rate of the nanoparticle formula,
the size dependent damping parameter γ for the nanospheroid39 can
also be given by Eq. (22), where its effective radius, reff , is written
by40
reff = [(a2 − a1 )(b2 − b1 )(c2 − c1 )]1/3.
i = 1, 2 where 1 is for the inner spheroid and 2 for the outer spheroid.
(41)
(43)
Substituting Eq. (21) into Eq. (42) and considering the real quantity,
the local field enhancement factor is given by
⎤
⎥
⎥
⎥
.
2
2⎥
(2)
(2)
(1)
(1)
⎥
Lz −Lz
Lz −Lz
′
′′2
′
⎥
)
−
qε
+
ε
ε
)
+
ε
(2ε
(1
+
)
−
q)
1 3
2
2
2
⎥
p
p
⎦
′′2
ε′2
2 + ε2
(44)
In our analysis, the nanostructure size is much smaller than the wavelength of the incident field. Hence, the spheroidal nanocomposite
is subjected to an almost uniform field. The particle then oscillates like a simple dipole with the polarization proportional to the incident
field. Therefore, the quasi-static approximation can be employed in the calculation. In this dipole approximation, the polarizabilities along
the principal axes of the spheroids are given by41
(1)
α1 = α2 = V
(1)
(2)
(2)
(1)
(2)
,
(45)
(2)
{(ε2 − ε3 )[ε2 + (ε1 − ε2 )(L3 − f L3 )] + f ε2 (ε1 − ε2 )}
(2)
(2)
{[ε2 + (ε1 − ε2 )(L3 − f L3 )][ε3 + (ε2 − ε3 )L3 ] + f L3 ε2 (ε1 − ε2 )}
AIP Advances 13, 035331 (2023); doi: 10.1063/5.0138456
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(2)
{[ε2 + (ε1 − ε2 )(L1 − f L1 )][ε3 + (ε2 − ε3 )L1 ] + f L1 ε2 (ε1 − ε2 )}
(1)
α3 = V
(2)
{(ε2 − ε3 )[ε2 + (ε1 − ε2 )(L1 − f L1 )] + f ε2 (ε1 − ε2 )}
,
(46)
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(2)
a2i
.
ci2
Assuming that a uniform parallel electric field E0 is directed
along the z-axis, the local field in the dielectric core of the nanocomposite can be obtained with the help of Ei = −∇φi . Using this
relation, the local field in the dielectric core can be given by
and
(2)
(40)
where
In this expression,
p = f Lz [Lz
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ARTICLE
where V = 4πa2 b2 c2 /3 is the total nanocomposite particle volume.
From the polarizability, the scattering and absorption cross sections of a coated nanoellipsoid under quasi-static approximation can
be expressed as42
Cscat =
k4
[2∣α1 ∣2 + ∣α3 ∣2 ],
18π
where k is the wavenumber in the medium that strongly depends on
the shape of the nanostructure, which is given by39
k=
TABLE I. LFEF of spherical, cylindrical, oblate, and prolate core–shell NCs.
Peak 1
Shape
k
Cabs = Im[2(α1 ) + (α3 )], (47)
3
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Spherical
Cylindrical
Oblate
Prolate
Peak 2
Peak 3
Shell thickness
(nm)
(nm) Peak (nm) Peak (nm) Peak
8
8
8
8
482 2775
467 397
481
34
480
42
552 7878
600 2445
547 227
548 137
–
–
579
606
–
–
243
275
2π(a2 b2 c2 )1/3
,
λ
and λ is the wavelength of the incident light.
In this study, all the four core–shell NCs (spherical, cylindrical, oblate, and prolate spheroids) consist of the same core (CdSe)
and the same shell (Au) material. On top of this, all of them were
placed in the same host medium (SiO2 ) with the dielectric constant
ϵ3 = 2.5. Moreover, their corresponding radii are set to the same
values (for sphere, cylinder, and oblate spheroids, r1 = a1 = b1
= 4 nm and r2 = a2 = b2 = 12 nm; for the prolate spheroid,
c1 = 4 nm and c2 = 12 nm). Then, their optical properties were investigated according to their shapes, and the results were discussed as
follows:
A. Local field enhancement factor of core–shell
nanocomposites
With a uniform shell thickness of 8 nm, the local field enhancements of spherical and cylindrical core–shell NCs have two peaks
while those of oblate and prolate spheroids show three peaks, all in
the visible range of spectrum [Figs. 4(a) and 4(b)]. From the same
figure, it could be observed that all the enhancement peaks have
different intensities and wavelengths. Comparing the first (counting from the short to the long wavelength) peaks of electric field
FIG. 4. LFEF of (a) spherical and cylindrical and (b) oblate and prolate core–shell NCs.
AIP Advances 13, 035331 (2023); doi: 10.1063/5.0138456
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III. RESULTS AND DISCUSSIONS
enhancements with the four of them (Fig. 4), that of the cylindrical
core–shell relatively occurs at the shortest wavelength (λ = 467 nm)
while that of the sphere is achieved at the longest wavelength
(λ = 483 nm).
When the highest intense resonance of electric field enhancement is required, the spherical core–shell nanocomposite is preferred to cylindrical and spheroidal core-shells of the same size
and composition. For the considered sizes and parameters, even the
smallest value (2775) of the LFEF of the spherical core–shell is 11.42
and 10.09 times larger than the biggest values of oblate (243) and
prolate (275) core-shells, respectively (Table I).
It can also be seen that the last two peaks of the field enhancements are closer to each other for the oblate spheroid (Δλ = 32 nm)
than its corresponding prolate shape (Δλ = 58 nm), showing
that the prolate core–shell spheroid can be tuned over a wider
range of the spectrum [Fig. 4(b)]. Thus, the core–shell prolate
spheroid nanocomposite shows greater structural tunability and
larger intensity of local field enhancements than its corresponding oblate nanocomposite. This finding agrees with the previously
reported study that emphasized the tunability of the dielectric
core-metallic shell prolate spheroid more than any dielectric–metal
nanostructures.43
When peaks of the LFEF of the two forms of the spheroids are
compared [Fig. 4(b)], nearly at λ = 547 nm, the intensity is larger for
the oblate spheroid (≈227) than that of the prolate shape (≈137).
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ARTICLE
This result agrees with the previous study that showed a bigger magnitude of the field enhancement factor for the oblate form than the
prolate form.44 Moreover, another similarity is also observed with
the former study that for both the oblate and prolate forms, larger
values of field enhancements were achieved near the wavelength of
600 nm. In the present study, larger field enhancement values were
observed at λ ≈ 579 nm and λ ≈ 606 nm for oblate and prolate forms,
respectively (Table I). From all these findings, it can be said that the
shape of NCs affects properties such as peak intensity, resonance
wavelength, and the number of peaks of nanostructures, which were
also indicated in previous studies.45
B. Absorption cross sections of core–shell
nanocomposites
highest. Especially, the first peak of the cylindrical shape is relatively
achieved at the shortest wavelength (λ ≈ 467 nm), whereas that
of the corresponding wavelengths of the spherical, the oblate, and
the prolate core–shell nanoparticles is about 482, 484, and 485 nm,
respectively.
The study also shows that the number of peaks of the absorption cross sections also varies with the shapes of the NCs, that is,
spherical and cylindrical shapes have two peaks while there are three
peaks in oblate and prolate spheroidal NCs. Regarding the number
of peaks and patterns of absorption cross sections, this result is in
agreement with previous findings.46 Where the peaks are the same in
number in different shape nanostructures, they are different in magnitudes, showing that the shape of core–shell NCs affects the number
and the magnitudes of peaks of the absorption cross sections.
Out of three observable peaks in the absorption spectrum of
spheroidal NCs [Fig. 5(c)], the first peaks are attributed to the transverse resonance from the outer gold metal surface while the last two
peaks are attributed to the longitudinal resonance from the inner
and the outer surfaces of the same metallic shell. Similar results
were also shown in previous research findings too.47 Such gold
coated three localized surface plasmon resonance peaks, which are
intense and are clearly separate, have good potential application in
multi-channel sensing.
FIG. 5. Absorption cross sections of (a) spherical, (b) cylindrical, and (c) oblate and prolate core–shell NCs.
AIP Advances 13, 035331 (2023); doi: 10.1063/5.0138456
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For the same composition and the same material parameters,
all the three absorption peaks of the prolate spheroid are lower than
those of its corresponding oblate form. Out of these peaks, the first
and the third (counting from the short to the long wavelength) peaks
of the prolate are relatively red shifted compared to the oblate one
[Fig. 5(c)]. Even when peaks of all the absorption cross sections of
the four different shapes of the NCs are compared (Fig. 5), that of the
prolate spheroid is the lowest while that of the cylindrical shape is the
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C. Extinction cross sections of core–shell
nanocomposites
In this study, we have also investigated the extinction cross sections of the same NCs [Figs. 6(a)–6(c)]. For the same composition,
core radii, shell thickness, and embedding medium, the extinction
spectra show different numbers of peaks, peak values, and positions
for spherical, cylindrical, oblate, and prolate core–shell nanoparticles. The peak values and the wavelengths at which those peaks are
achieved are shown in Table II for all the considered core–shell NCs.
It seems interesting to note that for spherical and cylindrical NCs,
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peaks 1 and 2 of the LFEF are achieved at the same frequencies with
the corresponding peaks of extinction cross sections (Tables I and
II). While investigating the extinction spectra, we have also seen the
scattering cross sections for those NCs. However, the peak values are
so small compared to the absorption peak values and have no significant effect on the extinction peak magnitudes. This in turn indicates
that smaller nanoparticles are mainly absorptive than scatterers.
Among all the different nanostructures presented, the cylindrical core–shell nanocomposite shows the largest extinction peak
values in the visible range of the electromagnetic spectrum, whereas
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FIG. 6. Extinction cross sections of (a) spherical, (b) cylindrical, and (c) oblate and prolate core–shell NCs.
TABLE II. Extinction cross sections of spherical, cylindrical, oblate, and prolate core–shell NCs.
Peak 1
Shape
Spherical
Cylindrical
Oblate
Prolate
Peak 3
Shell thickness
(nm)
(nm)
Peak
(nm)
Peak
(nm)
Peak
8
8
8
8
482
467
484
485
0.000 15
1.02
5.98 × 10−8
4.51 × 10−8
552
600
548
546
0.0006
1.9
16.3 × 10−8
8.77 × 10−8
–
–
546
582
–
–
13.3 × 10−8
8.77 × 10−8
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© Author(s) 2023
Peak 2
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IV. CONCLUSIONS
We studied core-shell (CdSe@Au) spherical, cylindrical, oblate,
and prolate NCs embedded in a host medium (SiO2 ). Then, we
investigated their LFEF and optical cross sections theoretically and
numerically using quasistatic approximation. The results show that
additional peaks are observed in the LFEF, absorption, and extinction cross sections in oblate and prolate core–shell spheroids compared to spherical and cylindrical core–shell nanoparticles. Where
the number of peaks is the same for different shapes, the values
(intensities) are found to be different. From the three peaks of the
LFEF of the spheroids, it can be seen that the last two of them are
closer to each other for the oblate spheroid than its corresponding prolate shape, indicating that the prolate core–shell spheroid
can show greater structural tunability. Moreover, two out of the
three peaks of the LFEF of the prolate spheroid show larger intensity
than its corresponding oblate nanocomposite in the electromagnetic
spectrum. We also found that the spherical core–shell nanocomposite is characterized by the higher LFEF than cylindrical and
spheroidal core–shell NCs of the same size and compositions. Under
these considerations, even the smallest value of the LFEF of the
spherical core–shell is 11.42 and 10.09 times larger than the biggest
values of oblate and prolate core-shells, respectively. Another finding of our study shows that for spherical and cylindrical NCs,
the first two peaks of the LFEF and extinction cross-sections are
achieved at the same corresponding frequencies.
The study further indicated that for the same compositions and
the same material parameters, the absorption peaks of the prolate
spheroid are lower than and relatively red shifted than its corresponding oblate form. Among all the different nanostructures
presented, the cylindrical core–shell shows the largest extinction
peak values in the visible range of the electromagnetic spectrum,
whereas the smallest peak value is observed for the prolate spheroid.
In the present study, we showed the possibility of controlling the
optical properties of core–shell nanoparticles by altering their shapes
without changing their sizes and compositions. As the intensities
and positions of plasmonic resonance peaks of core–shell NCs can
be tuned by altering their shapes, they are appropriate alternatives
AIP Advances 13, 035331 (2023); doi: 10.1063/5.0138456
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for various applications in many optical devices. Especially, gold
coated surface plasmon resonance peaks observed in the core–shell
spheroids have good potential applications in multi-channel
sensing.
ACKNOWLEDGMENTS
This work was supported financially by Addis Ababa University
and Oromia Education Bureau.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Garoma Dhaba Bergaga: Conceptualization (lead); Data curation
(lead); Formal analysis (lead); Investigation (lead); Methodology
(lead); Software (lead); Writing – original draft (lead); Writing –
review & editing (lead). Belayneh Mesfin Ali: Supervision (lead);
Writing – review & editing (supporting). Teshome Senbeta Debela:
Supervision (lead); Writing – review & editing (supporting).
DATA AVAILABILITY
The data that support the findings of this study are available
within this article.
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the smallest peak value is observed for the prolate spheroid. Moreover, peaks 2 and 3 of the prolate shape show the same values, which
were not observed in the remaining three shapes. Whatever the
number and the values of the extinction spectra are, all of them lie
in the visible range of the electromagnetic spectrum for the different
shapes indicated in Fig. 6.
The result also reveals that the resonance position of peak 1 is
slightly red shifted as the shape of core–shell nanoparticles changes
from cylindrical to spherical and oblate and prolate, while blue shift
is observed as the shapes change in the reverse order. These shifts
cause peaks 1 and 2 to come closer to each other in the prolate
spheroid than any other shapes investigated in this study. Previous
investigations also support our study that there are two extinction
peaks of dielectric core-metallic shell spherical nanoparticles.48
Here, it is interesting to note that the extinction cross sections
behave differently for different shapes of core–shell NCs. Hence, it
can be said that the shape of core–shell nanoparticles controls the
resonance frequencies of its plasmon modes and hence its optical
properties.
ARTICLE
AIP Advances
18
AIP Advances 13, 035331 (2023); doi: 10.1063/5.0138456
© Author(s) 2023
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ARTICLE
Materials Research Express
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Mater. Res. Express 9 (2022) 045001
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PAPER
OPEN ACCESS
Size dependent local field enhancement factor of CdSe based
core@shell spherical nanoparticles
RECEIVED
22 January 2022
REVISED
13 March 2022
ACCEPTED FOR PUBLICATION
Garoma Dhaba Bergaga1,2 , Belayneh Mesfin Ali1 and Teshome Senbeta Debela1
1
2
Department of Physics, Addis Ababa University, Addis Ababa, P.O. Box:1176, Addis Ababa, Ethiopia
Department of Physics, Sebeta Special Needs Education Teachers College, Addis Ababa P.O. Box:195, Sebeta, Addis Ababa, Ethiopia
24 March 2022
E-mail: garoma.dhaba@gmail.com
PUBLISHED
Keywords: local field enhancement factor, plasmons, core, spacer, shell, host matrix
6 April 2022
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Abstract
We investigated the size dependent local field enhancement factor (LFEF) of CdSe@Ag and
CdSe@ZnSe@Ag core/shell spherical nanoparticles theoretically and numerically within the framework of quasi-static approximation. From the potential distributions in the core, shell(s), and host
medium, and using the modified Drude-Sommerfeld model, we separately obtained the expressions
for LFEF of core/shell and core/spacer/shell nanocomposites. By changing the sizes of each of the
components of the nanocomposites in these expressions, we found that the LFEF of CdSe@Ag
increases with a decrease in the size of the core. At the same time, the resonance peaks are red shifted in
the inner interface and blue shifted in the outer interface of the shell. The result also reveals that
whether the shell radius is kept constant or decreased, increasing the core size produces a lower field
enhancement factor showing that the core size is a crucial parameter to change the field enhancement
factor of the dielectric core and metal shell nanoparticle (NP). When the spacer (ZnSe) is placed
between the core (CdSe) and the shell (Ag), the resonance peaks increased with increase in the size of
the core which was not observed in the case of the two layered core/shell nanocomposites having the
same core and shell sizes. We also found that placing the spacer and varying the sizes of the core, the
spacer, and the shell show different effects on the LFEF of the nanocomposite. The possibility of
obtaining size dependent LFEF by adjusting the sizes of nanoparticles makes these nanocomposites
attractive for applications in nonlinear optics, photocatalysis, and optoelectronics.
1. Introduction
Recent studies show that core/shell nanocomposites have attracted increasing research interest due to their
outstanding properties such as versatility, tunability, and stability [1, 2]. A core/shell nanocomposite consists an
inner core and outer shell(s) that is composed of different materials. The combination of different material
properties in a single core–shell system leads to several novel properties for potential applications in various
fields such as electronics, optics, biomedicine, environmental science, materials, energy, magnetism, and
catalysis [3, 4]. Moreover, the properties of these core/shell materials can be easily tuned by varying the size,
shape, morphology as well as the type of the core, shell, and embeding medium [5–7].
Among the widely studied core–shell nanocomposites is the CdSe-based quantum dots (QDs). In particular,
the emission intensity of CdSe QDs can be increased several times when it is capped with a ZnS shell to form a
CdSe/ZnS core–shell structure [8]. In addition, CdSe nanocrystals are considered as the most promising
emitting materials in the visible spectral region because their emission color can dramatically be adjusted from
blue to red. Wide band gap semiconductors such as ZnS, CdS, and ZnSe can be used as the shell material [9] to
cap a CdSe core. But, among these semiconductors, ZnSe over coated CdSe nanoparticles have shown
advantages that not only the bandgap of ZnSe (2.72 eV ) is larger than that of CdSe (1.76 eV ), but also it has
shown low toxicity as compared to CdS and ZnS [10]. Moreover, its lattice parameter and binding energy are
5.67 Å and 20 meV, respectively, while the band gap alignment is of type I, where both electrons and holes are
© 2022 The Author(s). Published by IOP Publishing Ltd
Mater. Res. Express 9 (2022) 045001
G D Bergaga et al
Figure 1. Schematics of core and single shell spherical nanoparticle embedded in host matrix.
confined in the CdSe core [11–13]. The lattice parameter mismatch of ZnSe relative to the CdSe core (6.3%) is
significantly smaller when compared with the most commonly used ZnS shell (10.6 %) material [14, 15]. All
these material parameters makes ZnSe an excellent shell material to cap a CdSe core in a core–shell
nanocomposite.
In support of this, experimental studies show that when CdSe is covered with ZnSe, the optical properties of
the combination is enhanced [16]. It was also reported that CdSe@ZnSe core/shell quantum dot are novel
materials incorporating CdSe core in a ZnSe shell [17]. For instance, the photoluminescence intensity of a
CdSe@ZnSe core–shell nanocomposites can be significantly enhanced by coating (capping) the CdSe core with a
few layers of ZnSe shell [18]. But, to the best of our knowledge, few or no theoretical and numerical studies were
carried out to support those many experimental works. Moreover, as the heterostructures formed with metal
and semiconductor composite nanostructures provide another efficient opportunity for tuning the unique
optical properties of nanoparticles [19], the plasmonic effects are also found to be interesting. For CdSe based
core/shell nanocomposites, the effect of the sizes of the core, the shell (metal), and the spacer (semiconductor)
on the local field enhancement factor (LFEF) were not further studied yet. Hence, this study focuses on the
theoretical and numerical investigations of the size dependent LFEF of CdSe@Ag and CdSe@ZnSe@Ag core/
shell spherical nanoparticle embedded in the host matrix, SiO2.
2. Theoretical models and calculations
2.1. Core and single shell spherical nanoparticles
When the size of a particle is much smaller than the wavelength of the incident electromagnetic radiation [20],
the electric field may be considered to be spatially uniform over the whole range of the particle [21].
Consequently, the particle may be represented by an oscillating dipole and this is known as the quasi-static
approximation [22, 23]. This approximation is important for a qualitative understanding of the interaction of
light with nanoparticles as it considerably simplifies the mathematical analysis.
In this paper, we considered a model of spherical core@shell nanoparticle in the quasi-static limit. In this
approach, the electrostatic solution can easily be calculated by solving the Laplace’s equation. In our model, we
separately considered CdSe@Ag and CdSe@ZnSe@Ag both embedded in a dielectric material. As shown in
figure 1, the radius of the core is r1 and its dielectric permittivity is e1. The shell is characterized by the radius r2
and dielectric permittivity e2 (where r1 < r2). The embedding material (SiO2) has an electric permittivity e3. The
expressions needed to calculate the electric potential in the system under the quasi-static approach is given by
[24, 25]. Accordingly, the electric potential in the dielectric core, the shell, and the surrounding medium can be
written as
j1 (r, q ) = - E o A1rcosq , (r  r1)
2
(1)
Mater. Res. Express 9 (2022) 045001
G D Bergaga et al
B
j2 (r, q ) = - E o ⎛A2r - 22 ⎞ cos q , (r1  r  r2)
r ⎠
⎝
B
j3 (r, q ) = - E o ⎛r - 23 ⎞ cos q , (r  r2)
r ⎠
⎝
(2)
(3)
where, j1 (r , q ), j2 (r , q ), and j3 (r, q ) are the electric potentials in the dielectric core, metallic shell, and
embedding medium, respectively. E 0 is the incident electric field (chosen along the z-axis), r and q are the
spherical coordinates of the observation point. The unknown coefficients A1, A2 , B2, and B3 are to be calculated
from the continuity conditions of the potential and the displacement vector at the interfaces of the dielectric
core/metal and metal/embedding medium.
The local electric field E1 induced in the dielectric core of the nanocomposite is related to the incident electric
field, E 0, by the following equation [26]:
E1 = A1 E 0.
In this equation (E1 = A1 E 0 ), the coefficient A1 can be shown to be given by
A1 =
Qe2 e3
,
pD
(4)
where Q = n2/ (n - 1) and p = 1 - (r1 /r2)3 is the volume fraction of the metal coated particle. Also, n
represents the dimension of the problem, which for a spherical nanoinclusion is 3. In equation (4), D is given by
D = e 22 + qe2 + e1 e3 ,
(5)
where
3
3
q = ⎛⎜
- 1⎞⎟ e1 + ⎛⎜ - 1⎞⎟ e3.
2
p
⎝
⎠
⎝p
⎠
In this study, we used silver metal as a shell material. From the Drude-Sommerfeld model, the electric
permittivity of metals is given by [27]:
e2 = e¥ -
w 2p
w (w + ig )
,
(6)
where e¥ is the phenomenological parameter that represents the contribution of bound electrons to
polarizability, wp is the bulk electron plasma frequency, and g is a parameter associated with damping in the
bulk material. Clearly, equation (6) has real and imaginary parts which can be rewritten as
e2 = e¢2 + ie 2 ,
(7)
where
e¢2 = e¥ -
w 2p
w2 + g
, e 2 =
2
w 2p g
w2 + g 2
.
Now, substituting equations (5) and (7) into equation (4), we find that A1 becomes a complex function. Rather, it
would be convenient to deal with the real quantity ∣A1∣2 , which is called the enhancement factor. It can be
presented as [28]:
∣ A1 ∣2 =
e¢22 + e 2 2
81e32 ⎛
⎞.
⎜
⎟
4p 2 ⎝ (e¢22 - e 2 2 + qe¢2 + e1 e3)2 + e 2 2 (q + 2e¢2)2 ⎠
(8)
2.2. Triple layer spherical nanoparticles
Here, let’s first consider a concentric n-layer nanocomposite that consists of multiple nanoscale layers of
controllable thickness. The electrostatic potential for each of the regions (layers) satisfy the Laplace’s equation
which is given by 2ji = 0, where ji is the electric potential associated with the electric field induced inside and
outside the nanocomposite, ji is the region where electric potential is to be determined. Let, the dielectric
function of the ith region be represented by ei.
The potential distribution in the different regions of the n-layered nanocomposite is obtained by solving the
Laplace’s equation. Accordingly, the potential ji in each region is given by [29]:
B
ji (r , q ) = ⎛A i r + 2i ⎞ cos q ,
r ⎠
⎝
where Ai and Bi are the coefficients that corresponds to the electric monopole and dipole terms, respectively.
These coefficients, Ai and Bi are to be determined by employing the appropriate boundary conditions for the
3
(9)
Mater. Res. Express 9 (2022) 045001
G D Bergaga et al
Figure 2. Triple layer spherical nanostructure embedded in host matrix.
continuities of the tangential and normal components of the electric field and the displacement vector,
respectively [30]. In our case, the spherical coordinates (r, q ) are used, where r is the radial distance andq is the
polar angle, while the direction of the applied field E 0 is chosen along the z-axis. Then, the electric field E in the
i th region for the concentric spherical n-layered nanocomposite is obtained using the equation Ei = -(
i r, q ) ,
where Fi (r, q ) is given by equation (9) [31]. Hence, the field takes the following form:


E i = A i ( - cos qeˆr + sin qeˆq ) + Bi r -3 (2 cos qeˆr + sin qeˆq ) ,
(10)
where i = 1, 2,...,n with n being the number of layers and ê r and êq are the unit vectors in the r and q directions,
respectively.
Next, we consider a triple layered (n = 3) core/shell nanostructure shown in figure 2, in which region one
with i = 1 is a semiconductor core (CdSe) of dielectric function e1, while the outer region is the embedding
medium (SiO2) with real dielectric constant en + 1 = e4. The dielectric functions of the spacer (ZnSe) and metallic
shell (Ag) are e2 and e3, respectively. Similarly, the radii of the dielectric core, spacer, and metallic shell are
denoted by r1, r2, and r3, respectively.
For triple layered nanocomposite, there are four regions [32]. Thus, by extending equation (10) to the
spherical nanocomposite, we find the electric fields in each of the four regions to be:


E1 = A1 ( - cos qeˆr + sin qeˆq ) + B1 r -3 (2 cos qeˆr + sin qeˆq ) ,
(11)

E2 = A2 ( - cos qeˆr + sin qeˆq ) + B2 r -3 (2 cos qeˆr + sin qeˆq ) ,
(12)

E3 = A3 ( - cos qeˆr + sin qeˆq ) + B3 r -3 (2 cos qeˆr + sin qeˆq ) ,
(13)

E4 = A 4 ( - cos qeˆr + sin qeˆq ) + B4 r -3 (2 cos qeˆr + sin qeˆq ) ,
(14)
where A4 = -E 0 and A1, A2 , A3 , B2, B3, and B4 are unknowns to be determined by imposing the appropriate
boundary conditions. In particular, the coefficient B1 = 0, since the magnitude of the electric field in the
dielectric core is constant.
To investigate the LFEF inside the concentric sphere, it is suffice to determine the electric field induced inside
the dielectric core. This means that (since B1 = 0), we only need to determine the coefficient A1 found in
equation (11). Hence, employing the relevant boundary condition at the interfaces, this coefficient can be shown
to have the following form:
4
Mater. Res. Express 9 (2022) 045001
G D Bergaga et al
A1 =
27 e2 e3 e4
E 0,
2 f2 M
(15)
where
M = y1 e3 2 + y2 e3 + y3 ,
3
r
f2 = 1 - ⎛ 2 ⎞
⎝ r3 ⎠
y1 = f1 (e1 - e2) + 3e3 ,
⎜
⎟
2e
3
e
y2 = ⎛⎜ - 1⎞⎟ ⎡3⎛ 1 + 4 ⎞ e2 + f1 (e1 - e2)(e4 - e2) ⎤
3 ⎠
⎦
⎝ f2
⎠⎣ ⎝ 2
3
+ e2 ⎛f1 (e1 - e2) - e4 - e2⎞ ,
2 ⎠
⎝
y3 = e2 e4 (3e1 + 2f1 (e2 - e1)) ,
where
3
r
f1 = 1 - ⎛ 1 ⎞ .
⎝ r2 ⎠
⎜
⎟
Substituting equation (15) into equation (11), the magnitude of induced field inside the dielectric core is
found to be
E1 =
27 e2 e3 e4
E 0.
2 f2 M
(16)
The coefficient of E 0 in equation (15) is the local field enhancement factor (F). That is,
E
27 e2 e3 e4
F=
=
,
Eo
2 f2 M
(17)
and the modulus square of the LFEF becomes:
∣F∣2 =
27 e2 e3 e4
2 f2 M
2
.
(18)
The optical properties of metals can be described by the Drude-Sommerfeld model of the frequency-dependent
dielectric function, e (w ) [33]. In our case (i.e., equation (18)), e3 represents the dielectric permittivty of the
metallic shell (silver) and can be written as
e3 = e¥ -
w 2p
w (w + ig )
.
(19)
For silver, wp = 1.37 ´ 1016 Hz , e¥ = 9.01eV , and w = 2pc /l is the angular frequency of the applied
electromagnetic field, c is the speed of electromagnetic wave [34] and g is a parameter associated with damping
[35]. If the mean free path of electron in the nanostructre depends on size of the nanocomposites, then its
damping parameter differs from its bulk counterpart, and hence g in equation (19) can be modified to [36]:
v
g = gbulk + A F ,
(20)
reff
where gbulk is the damping constant of the bulk material (for Ag: gbulk = 3.23 ´ 1013 Hz ), vF is the velocity of an
electron at the Fermi surface (vF = 1.4 ´ 106 m/s for silver), A is an empirical parameter, usually set to be
unity, reff is the effective mean free path of electrons and is calculated using the following equation [37]:
1
reff =
((r3 - r2)(r32 - r22 )) 3
.
2
(21)
3. Results and discussions
3.1. Core and single shell nanoparticles
In this section, we investigated the local field enhancement factor for the core and single shell CdSe@Ag
nanoparticles. Figures 3 and 4 depict the graphs of the enhancement factor for different core, shell, and QD sizes
as a function of wavelength plotted using equation (8).
5
Mater. Res. Express 9 (2022) 045001
G D Bergaga et al
Figure 3. LFEF of CdSe@Ag: (a) when the size of the QD size is fixed at 20 nm as the size of the core decreases and (b) when the size of
the core is fixed at 10 nm as the shell thickness increases.
Figure 4. LFEF of CdSe@Ag Quantum Dot: (a) when core and the NP sizes are both increasing and (b) when core size is increasing and
the shell thickness is decreasing.
From figure 3(a), it is observed that as the size (r1) of the core (CdSe) of the nanocomposite is reduced from
10 nm to 2 nm for a fixed radius (r2 = 20 nm ) of the silver (Ag) metal, the peaks of the resonances are increased
by 18.2 folds (increased from about 1, 743 at 452 nm to 31, 760 at 478 nm ) at the interface between CdSe@Ag.
This is observed when the core radius is relatively the smallest (2 nm ) and the metal shell thickness is the largest
(18 nm ), where 18 nm is the difference of the two radii (20 nm - 2 nm = 18 nm). From this, one can see that
when the core radius decreases and the shell thickness increases simultaneously at constant shell radius (20 nm),
the local field is enhanced and the surface plasmon peaks shift to the higher energy. This result agrees with other
research findings that when the core size is made smaller, the resonance peaks are enhanced [28, 37]. This may be
explained with the fact that as the shell thickness increases, the hybridization between the two plasmon
frequencies of the inner and outer surfaces decrease, leading to the blue shift. Moreover, the metal content of the
particle increases with decrease in the core radius so that there are more electrons to participate in the oscillation.
As a result, the coupling of localized surface plasmon resonance becomes stronger and leads to the enhancement
of the local field. Our findings are in good agreement with the previous findings [36, 38, 39]. For the same core/
shell nanoparticle parameters, the field enhancement factor has increased by about 6.3 times (nearly increased
from 8, 558 at 579 nm to 53, 960 at 514 nm ) at the interface between the shell (Ag) and the host matrix (SiO2 ).
From figure 3(a), it is observed that the resonance peaks shift towards the longer wavelength (red shift) of the
visible region of electromagnetic spectrum at the inner interface of CdSe@Ag, and towards the shorter
wavelength at its outer interface. Taking the ratio of the magnitudes of the resonance peaks of the outer interface
to the inner interface of CdSe@Ag, the local electric field is enhanced by about 1.7 factor (from 53, 960 to
31, 760). Moreover, the result also reveal that the local field enhancement factor of the CdSe@Ag has been
increased with the decrease in the core size.
Furthermore, figure 3(b) shows that keeping the core size constant (r1 = 10 nm ) and increasing the QD size
from 20 nm to 24 nm enhanced the LFEF from about 8, 434 to 12, 270. This enhancement is accompanied
with a blue shift of the enhancement peaks from 579 nm to 555 nm in the outer interface of silver (Ag@ SiO2).
Note that comparison of figures 3(a) and (b) shows that the LFEF is higher when the size of the core is reduced
6
Mater. Res. Express 9 (2022) 045001
G D Bergaga et al
Figure 5. LFEF of CdSe@ZnSe@Ag: (a) when core and the shell sizes are increasing and spacer thickness is decreasing and (b) when
spacer size is increasing at fixed core and shell sizes.
than when the thickness of the shell is increased. This might indicate that the quantum confinement is more
significant than the plasmonic effect for the local field enhancement.
However, when both the core and the shell radii increase simultaneously (r1 = 5 nm to 9 nm and
r2 = 12 nm to 16 nm ), the resonance peaks are significantly lowered from about 12, 270 at 555 nm to 6, 550 at
about 603 nm at the interface of Ag@SiO2 (figure 4(a)). Also, when the sizes of both the core and the shell
changes simultaneously by equal amounts (i.e., Dr = 4 nm ), the amplitudes of the resonance peaks are reduced
from 3, 316 at 460 nm to about 918 at 446 nm at the interface of CdSe@Ag region.
For the nanoparticle considered under this section, the simultaneous increase in the radii of the core and the
shell could not help to increase the local enhancement factor for the core/shell nanoparticle. This can be
attributed to the fact that, when the shell size increases, charge separation distance also increases, leading to the
decrease in the electric field inside the nanoparticle. In the other case, when the radius of the core is increased
from 3 nm to 7 nm, while reducing the size of the shell from 17 nm to 13 nm, the local field enhancement factor
is reduced from 42, 660 to 7, 237 (figure 4(b)). Whether the shell size is constant or decreased, increasing the
core size led to lower field enhancement factor for the material under the study. Hence, it is observed that the
core size of the nanoparticle is a crucial parameter to increase or decrease the field enhancement factor for the
core and single shell CdSe@Ag spherical nanoparticle. All these results show that the LFEF of CdSe@Ag
nanoparticle becomes controllable by carefully altering the size of the core radius.
3.2. Triple layered core@shell nanoparticle
In the second part of this study, ZnSe was placed as a spacer between the CdSe core and Ag shell and the local
electric field enhancement was analyzed using equation (18). The size of ZnSe (r2 = 10 nm ) is fixed and the sizes
of the core (r1) and the QD (r3) were varied (figure 5(a)). As the core and the QD sizes increase (r1 = 5 nm to
9 nm; r3 = 12 nm to 16 nm ), two sets of resonance peaks were observed. The two resonances are associated with
the inner and outer interfaces of silver shell, respectively.
In the absence of the ZnSe spacer, the intensities of the local field enhancements decrease with increase in the
core and the QD sizes (i.e., figure 4(a)). However, when the spacer was placed in between CdSe and Ag, the
magnitudes of the resonance peaks showed increasing effect for the same increase in the core size and for the
same size of the whole NP (figure 5(a)). This result reveals that the spacer has an increasing effect on the LFEF of
core/shell nanoparticle even when the core size is increasing. Previous researches show that the thickness of the
dielectric spacer controls the plasmonic response of the three-layered nanoparticles [40, 41]. Thus, one of the
reasons for the increase in the local field enhancement in this study might be due to the decrease in the thickness
of the spacer layer (ZnSe). As illustrated in figure 5(a), when the core radius and the shell thickness are
increasing, the spacer layer is decreasing from 5 nm to 1 nm. That is, the decrease in the thickness of the spacer
layer provides a platform for strong plasmonic coupling between the core and the outer metal shell nanomaterial
leading to the enhancement of the local field. For all the dimensions indicated in figure 5(a), the second set of the
resonance peaks show a blue shift within the visible range of electromagnetic spectrum.
In figure 5(b), the core and the QD sizes were fixed and the size of ZnSe was varied from r2 = 10 nm to
10.8 nm. In this process, still two peaks were observed but the resonance peaks were found to decrease with an
increase in the size of the spacer.
Among all the size combinations, comparatively the largest peak is obtained when the spacer size is the
thinnest. Previous experimental studies show that when thin layer of ZnSe is deposited on CdSe, its emission
efficiency increases [11]. When it becomes thicker, the defects on the ZnSe surface may induce the nonradiative
7
Mater. Res. Express 9 (2022) 045001
G D Bergaga et al
Figure 6. LFEF of CdSe@ZnSe@Ag: (a) when shell size is increasing at fixed sizes of the core and spacer and (b) when core size is
increasing and spacer thickness is decreasing at fixed NP size.
Figure 7. LFEF of CdSe@ZnSe@Ag: (a) when core size is decreasing and spacer thickness is increasing at fixed size of NP and (b) when
spacer and shell thicknesses are increasing at fixed core size.
transitions, thereby decreasing the emission intensity [18]. Our theoretical and numerical analysis also show
similar results that when relatively the thinnest ZnSe is used as spacer on the CdSe core, the LFEF increases.
However, when the spacer thickness increases, the resonance peaks decreases and are red shifted (figure 5(b)).
Comparison of figures 5(a) and (b) shows that the core and the spacer sizes have different effects on the field
enhancement factor of core/shell spherical NPs.
In figure 6(a), the radii of the core (r1 = 10 nm ) and the spacer (r2 = 14 nm ) are fixed and the shell size was
increased from r3 = 20 nm to 24 nm. The result shows that the field enhancement factor increases with an
increase in the metallic shell size which might be related to the surface plasmon resonance [31, 33].
This is similar to figure 3(b) in all aspects except the presence of the spacer (ZnSe). For the two layer NP
(figure (3b)), the resonance peaks are higher and are achieved at shorter wavelenghs whereas in the triple layer
case (figure (6a)), the peaks are lower and are located at relatively longer wavelengths. When the core size
increases and the spacer thickness decreases with constant NP (core+shell) size (r2 = 20 nm ), the field
enhancement factor decreases (figure 6(b)). In this process, the resonance peaks in the outer interface of the
metal shell were red shifted. Although the amplitudes were not the same, the peak positions of results in
figure 6(a) were nearly reversed in figure 6(b).
In figure 7(a), the spacer and the metal shell thickness sizes are increasing with decreasing core size. This
results in increased field enhancement factor.
In the two layer NP, a blue shifted and significantly enhanced local field can be obtained in the visible range
of the spectrum by decreasing the core size (figure 3(a)). However, in the presence of spacer between the core and
the metal shell of the same NP size, relatively smaller field enhancement is observed with significant blue shift
from infra-red (IR) to the visible spectral region (figure 7(a)). Keeping the core size fixed and simultaneously
increasing the spacer and the metal shell thicknesses also show enhancement of the LFEF with the blue shift of
the resonance peaks (figure 7(b)). Nevertheless, the magnitudes of the peaks were more pronounced in the
latter case.
8
Mater. Res. Express 9 (2022) 045001
G D Bergaga et al
Comparing the results of double and triple layered nanoparticles explored in this study, LFEF was enhanced
with increasing the core size in the presence of spacer (ZnSe). But this was not observed in the core and single
shell nanostructure. Increasing the metallic shell radius (keeping others constant) show increased LFEF both in
the double (figure 3(b)) and the triple (figure 6(a)) layered nanostructures except that the increment was larger
for two layered NP than the triple layered NP by the factor of about 15.3 (i.e., 12, 270 to 800 ). When the core and
the NP sizes increase simultaneously for double layered NP (figure 4(a)), the LFEF decreases accompanied with
red shift while the LFEF increases and are blue shifted for the triple layered one (figure 5(a)). This indicates that
in triple layered core/shell spherical nanoaprticle, the enhancement of the local field can be achieved at higher
energy.
4. Conclusions
In this study, the local field enhancement factor of CdSe@Ag and CdSe@ZnSe@Ag core/shell nanoparticles were
studied theoretically and numerically by changing the sizes of each components. For a fixed size of the NP, the
local field enhancement factor of CdSe@Ag was increased with the decrease in the size of the core. Moreover, the
resonance peaks were red shifted and blue shifted, respectively, in the inner and outer interfaces. By increasing
the size of metallic shell while keeping the core size constant, similar patterns of resonance peaks were obtained
except that the degree of enhancements were larger in the former case. Increasing the core size produces lower
field enhancement factor whether the shell thickness is constant or decreased in size. This may indicate that the
core size is a crucial parameter to change the field enhancement factor of the dielectric core and metallic shell
nanoparticle.
For triple layered spherical core/shell nanopartile, setting the ZnSe radius constant, the resonance peak
increases with an increase in the size of the core which was not observed in the case of two layered core/shell
nanocomposites having the same core and NP sizes. In triple layered core/shell spherical nanoparticle, an
increase in the size of the spacer led to a decrease in the field enhancement factor of the nanocomposite. For fixed
sizes of the core and the NP, the lower the size of the spacer produces the higher the field enhancement factor. On
the other hand, increasing the thickness of the shell size increases the magnitude of the resonance peaks.
Similarly, increasing the thicknesses of both the spacer and the shell sizes also increased the field enhancement
factor. In conclusion, the sizes of the core, the spacer, and the shell has vigorous effect on the local field
enhancement factor of core/shell nanoparticles. The possibility of obtaining size dependent LFEF by adjusting
the sizes of nanoparticles make these nanocomposites attractive for applications in optoelectronics and
nonlinear optics.
Acknowledgments
This work is supported financially by Addis Ababa University and Oromia Education Bureau.
Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).
Conflict of Interest
The authors have no conflicts to declare.
ORCID iDs
Garoma Dhaba Bergaga
https://orcid.org/0000-0001-6827-5447
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SINET:
Ethiop. J. Sci., 45(2): 132–142, 2022
ISSN: 0379–2897 (PRINT)
© College of Natural and Computational Sciences, Addis Ababa University, 2022
eISSN: 2520–7997
Date received: January 31, 2022; Date revised: August 03, 2022; Date accepted: August 05, 2022
DOI: https://dx.doi.org/10.4314/sinet.v45i2.2
The effect of surface plasmonic resonances on magneto-plasmonic
spherical core-shell nanocomposites
Kinde Yeneayehu*, Teshome Senbeta and Belayneh Mesfin
Department of Physics, Addis Ababa University, Addis Ababa, Ethiopia. E-mail:
kinde.yeneayehu@aau.edu.et
ABSTRACT: In this study, the effect of plasmon resonance on magneto-plasmonic
spherical core-shell nanocomposite enclosed in a dielectric host medium is theoretically
investigated by applying electrostatic approximation (ESA) and Maxwell-Garnet effective medium
theories to obtain magneto-optical parameters such as; effective electric permittivity and magnetic
permeability as well as the corresponding extinction cross-sections. Likewise, for a fixed size of
QDs (of radius
nm) numerical analysis was performed to determine the plasmonic
resonance effect by varying the parameters such as the metal fraction (β) and the dielectrics (εh) of
the host medium on the magneto-plasmonic nanostructures (NSs). The results depict that graphs of
absorption, scattering, and extinction cross-sections as a function of wavelength have two positions
of resonance peaks. The first set of peaks are in the ultraviolet (UV) and the second located in visible
regions. These peaks originated from the strong coupling between a regular periodic vibrations of
surface plasmons of silver (Ag) with the excitonic state of the dielectric/semiconductor at the
internal (
) and external (Ag/host) interfaces. As β increases, the absorption and
scattering cross-sections are blue-shifted in the first peak and red shifted the second set of peaks.
Similarly, as εh increases or as β decreases, the sets of resonance peaks for extinction cross-section
gets enhanced; while keeping one of these parametric quantities fixed at once. The resulting surface
plasmon resonance effect might be utilized in a variety of applications that combines both the
plasmonic and magnetic core-shell nanostructures ranging from UV to Visible spectral regions.
Keywords/phrases: Core-shell, Dielectric Function, Extinction Cross-section, Surface Plasmon
Resonance
INTRODUCTION
A great attention has been given to the
development of nanomaterials as they exhibit
unique material properties as compared to their
bulk counterpart. These unique properties
include optical, magnetic, specific heat, melting
point, surface activities, chemical and biological
properties (Chingsungnoen and Dasri, 2017).
Nanomaterials form heterogeneous structures
composed of a noble metal and a semiconductor.
These peculiar type of systems offer to design
materials with novel and unique physical and
chemical properties. As isolated systems, the
optical properties of semiconductor quantum
dots (QDs) and noble metal nanoparticles (NPs)
are characterized by excitons and plasmons,
respectively. In both cases, the required
wavelengths to produce such excitations are
governed mainly by the nanoparticle nature,
size, shape, and local environment (Ezequiel, et
al., 2013).
_____________________
*Author
to whom correspondence should be addressed.
As an important class of nanomaterials, coreshell nanoparticles (NPs) that integrate two
dissimilar materials with distinct functionalities
have attracted more and more attention, since
they have emerged at the frontier between
materials chemistry and many other fields, such
as biomedical, optics, catalysis. Because coreshell NPs enable the synergistic coupling of the
two constituents, they could offer the modified
properties by changing either the constituting
materials or the core to shell ratio. Therefore, this
nanostructure can meet the diverse application
requirements. Among various core-shell NPs,
magnetic/noble metal hybrid NPs have been
widely studied as they possess intriguing
magnetic/plasmonic and magnetic/catalytic
properties, and they can be used in many fields,
for example optical devices, chemical reactions
as magnetically recyclable catalysts, bioimaging,
targeted drug delivery. Ag-based magnetic
hybrid NPs play an important role in specialty
chemistry, physics and material science. By
varying the size of the
cores and Ag shell,
SINET: ETHIOP. J. SCI., 45(2), 2022
the optical properties of nano-hybrids can be
tuned in a broad spectral ranges (Fan,et al. 2019).
Magnetic and/or plasmonic nanostructures
demonstrate multiple properties not present in
individual nanomaterials. Such materials offer
the advantage of being manipulated by an
external magnetic field, showing tunable optical
properties being adjustable in accordance with
modifying shell thickness. Experimental and
computational studies by (Kheradmand, et al.,
2020) shows that the higher the magnetization in
magnetic core nanoparticles, the more is the
suitable response toward the exposed magnetic
field and the higher the effectiveness in nanomedical diagnostics. Magnetic-plasmonic core
shell NPs possess dual magnetic and plasmonic
properties and have widespread applications in
biomedical fields. The magnetic cores such as
iron-oxide (IO) are greatly desired for
applications such as magnetic separation,
magnetic resonance imaging or magnetic guided
drug delivery. The IO-cores can be chemically
stabilized by coating them with noble metals,
which not only provides a chemically inert
surface, but also introduces interesting
plasmonic properties which can be utilized for
sensing, imaging, and photothermal therapy
(Shweta et al., 2019).
The possibility of building new nanostructures
by mixing noble metals Ag and magnetic
nanoparticles (NPs) opens up a wide spectrum of
desirable synergistic and complementary effects.
One of the challenges is the conjunction of these
two dissimilar materials in a controlled way.
Thus, great efforts have been made on synthetic
routes to command the bonding of the
heteroparticle (Ahmad, et al., 2015). The plasmon
resonance
wavelength,
light
scattering,
absorption and extinction cross-section of coreshell are affected by shell thickness, core
diameter, electronic properties of shell and
surrounding environment at outer interface
between the surface and incident light, and inner
interface between metal and semiconductor.
Localized surface plasmon resonance gives rise
to an enhancement of electric field, localization
of energy at nanometer scale, and strongly
enhanced absorption and scattering of light.
Magnetic nanoparticles with a core-shell
structure promises for many applications due to
their multi-functionality including optical,
electronic, and magnetic properties (Poedji
Loekitowati Hariani, et al., 2013). In particular,
these
core-shell NPs combine the
magnetic and optical properties of
and
Ag together, exhibiting great potential in the
fields of bio-related separation, ultrasensitive
133
detection and cellular imaging (Fan, 2019).
(Magnetite) is one of the magnetic
nanoparticles.
Different
reports
are
demonstrating that magnetic
can be used
for waste water purification, such as to adsorb
arsenite, arsenate, cadmium, nickel (Luciano, et
al., 2013; Ana, et al., 2019) used to remove
alkalinity
and
hardness,
desalination,
decolourization of pulp mill effluent and
removal of natural organic compounds. After
adsorption,
can be separated from the
medium by a simple magnetic process (Poedji, et
al., 2013).
Noble metals nanoparticles, such as Ag and
Au, strongly absorb light in the visible region
due to coherent oscillations of the metal
conduction band electrons in strong resonance
with visible frequencies of light. This
phenomenon is known as surface Plasmon
resonance (SPR) and is highly dependent on NPs
size, shape, surface, and dielectric properties of
the surrounding medium. Light absorbed by
nanoparticles is readily dissipated as heat. Due
to their large absorption cross sections,
plasmonic NPs can generate a significant amount
of heat and increase temperatures in their
vicinities (Ana, et al., 2019; Kerker, 1969;
Papavassiliou, 1979; Huffman, 1998; Vollmer,
1995).
Silver NPs have been applied as a broad
spectrum and highly effective bactericide. The
antibacterial mechanism is associated to the
release of silver ions. For medical applications,
an
core-shell structure allows one to
add a magnetic functionality to silver properties.
Such nanostructure could lead to interesting
advances to solve the lack of bio-compatibility of
silver, eliminating its contact with tissues (ironoxide can be considered biocompatible, at least
up to the mg/ml range). However, an intriguing
behavior was observed on
NPs: its
bactericidal
efficiency
is
stronger
than
hetero-dimers or plain Ag (Maria,
et al., 2014; Morones, et al., 2005; Xu, et al., 2009).
Surface plasmon absorption has been observed
for silver particles in various media, including
aqueous solutions, gelatin and glass. Size effects
exhibited by nearly spherical silver particles are
similar to those for gold. While, extinction is the
attenuation of an electromagnetic wave by
scattering and absorption as it traverses a
particulate medium. In homogeneous media the
dominant attenuation mechanism is usually
absorption. Comparison of extinction spectra for
small particles of various sizes with absorption
134
Kinde Yeneayehu et al.
spectra for the bulk parent material reveals both
similarities and differences (Bohren, 1998).
To investigate the optical properties and
response (absorption and scattering) of NPs with
light (electromagnetic radiation) interaction, one
has to measure the effective dielectrics,
, and
permeability,
, (Challa, 2013). In this paper,
we studied the effect of plasmon resonance on
the theoretically modelled spherical
core-shell NPs. Silver nanoparticle was selected
as a shell on magnetite nanospheres, due to its
nontoxic, strong absorption in the UV and visible
spectrum (Vladimir, et al., 2013) and surface
plasmon resonance (SPR) which plays a great role
in determining the optical response of
nanoparticles.
The paper is structured as follow: In Section 2,
the effective dielectrics and permeability of the
theoretically
modelled
magneticsemiconductor/metal core-shell spherical NPs
embedded in a dielectric host matrix are derived.
In Section 3, equations for the effective
polarizabilities, absorption cross-section and
scattering cross-section are derived. The
numerical results are presented and discussed in
Section 4. Detailed analysis of the effect of
plasmonic resonance on
core-shell
NPs, namely the absorption cross-section,
scattering cross-section and extinction crosssection are presented. Finally, concluding
remarks are presented in Section 5.
Theoretical model
Interaction of electromagnetic radiation with
particles is well studied. Theoretical studies on
the optical properties of multilayer spherical
nanoparticles are reported in lots of literatures.
In particular, for our general discussion, in this
section we expose the basic concepts of the
theory for scattering of electromagnetic waves by
core-shell materials following the considerations
of a model of
spherical core-shell
NPs, which is composed of magnetic-half metallic
iron (III) oxide (
) core of radius ac and an
outer metallic (Ag) shell of radius as embedded in
a dielectric host matrix as shown in Fig. 1, where
. Because of the core material is
magnetic
with
permeability,
,
the
magneto-optical properties of the system
requires determination of its effective dielectrics
and permeability
. Based on
electrostatic approximation and the MaxwellGarnet effective medium theory, theoretical
analysis have been done to derive
and
.
Moreover,
using
these
theoretically
determined values, calculations has been done
on the magneto-optical parameters such, as the
electric polarizability, absorption, and scattering
cross-sections.
Effective Dielectric Function and Magnetic
Permeability
The effective dielectric function of the coreshell composite material given by (Kinde, et al.,
2021; Gashaw, et al., 2019; Leta, et al., 2015):
(1)
where
is the volume fraction of the
metal coated spherical core-shell nanoparticle,
and
.
Here, we consider a system composed of a finite
number of core-shell NPs uniformly dispersed in
a host matrix, as shown in Fig. 1.
Figure 1. Schematic of a core-shell spherical NPs embedded in a matrix. The dielectrics and permeabilities are
the core,
,
for the shell, and,
and the shell,
observation point.
,
for the host matrix, respectively. Also,
,
for
are the radii of the core
is the diameter of core-shell, and a is the distance from the center of the NP to an
SINET: ETHIOP. J. SCI., 45(2), 2022
135
Suppose N is the density number of the
inclusions (NPs) in the system, then the effective
polarizability and permittivity of the system can
be described by using the Clausius-Mossotti
relation together with the Maxwell-Garnet
mixing formula. Accordingly, the electric
polarizability and the effective dielectrics are
related by (Starodubtcev, et al., 2013),
(2)
Rearranging
and
carrying
out
some
mathematical
manipulation,
the
effective
dielectric function
of the system and
polarizability are given by
(3)
where is the filling factor of the core-shell NPs
defined by
(4)
and
the dimensionless effective electric
polarizability of the inclusion given by
(5)
In the same analogy of effective dielectric
function, the effective magnetic permeability of
composite material and the dimensionless
magnetic polarizability is given by (Kinde, et al.,
2021; Liao, 2011):
(6)
Using the Clausius-Mossotti relation and the
Maxwell-Garnet mixing theory, the magnetic
polarizability and permeability are related by
(Starodubtcev, et al., 2013; Jackson, 1999; Liao,
2011)
Optical Responses of
Nanocomposites
Core-Shell
In this Section, we present the equations for the
optical parameters, i.e., the absorption,
scattering, and extinction cross-sections with the
help of the polarizability equations for a system
composed of
core-shell NPs
embedded in a liquid/water medium. Hence, in
order to get an explicit expression for the
absorption and scattering cross-sections, we
must fix the dielectrics and effective electric and
magnetic polarizabilities of the system that
consists of the magnetic core, metallic shell, and
host matrix.
The response of ‘bare’ metallic (Ag) shell to
incident electromagnetic wave (EMW) is solely
described by the dielectric function (permittivity)
with the permeability being equal to unity
(
). Therefore, we choose the frequency
dependent complex dielectric function of the
metallic (Ag) shell to have the Drude form given
by
(10)
where the constant
frequencies,
is the permittivity at high
is the plasma frequency,
is the
damping parameter, and  is the frequency of
the incident radiation. Further, separating the
real and imaginary parts of Eq. (10), i.e.,
, we obtain the following:
(11)
and
(12)
(7)
where
is
the
effective
magnetic
permeability of the ensemble. After some
manipulation, we obtained
(8)
where
the core-shell NPs and
is the filling factor of
the dimensionless
magnetic polarizability which is given by
(9)
where
and
, respectively, are the
real and imaginary parts of
.
It was well understood that the dielectric
function of metals, specifically that of noble and
alkali metals, vary significantly as a function of
the frequency of the incident light in the visible
spectral region, but that of magnetite is constant
or vary very little. Hence, we assumed that both
the permittivity ( ) and permeability ( ) of
magnetite as well as the permittivity of the host
( ) to be real constants independent of
frequency.
136
Kinde Yeneayehu et al.
Effective Electric and Magnetic Polarizabilities
In particular, for the case where
The
effective
(dimensionless)
electric
polarizability of the system is given by (Kinde, et
al., 2021; Gashaw, et al., 2019; Leta, et al., 2015)
constant and
find that Eq. (18) for
polarizability reduces to
is a real
(nonmagnetic), we
the dimensionless
(13)
(19)
where,
and the corresponding magnetic polarizability
becomes
(20)
Note that both
and the corresponding electric polarizability
becomes
(14)
Because
for the system is complex, the
effective electric polarizability
, defined by
Eq. (13) is also complex, which may be written as
and
of Eqs. (19) and (20)
are real constants.
Absorption, Scattering, and Extinction CrossSections
The absorption cross-section,
, of the
system consisting of spherical core-shell
composite NPs embedded in a host matrix is
given by (Leta, et al., 2015):
(15)
where
and
(21)
are its real and imaginary
parts, respectively. Substituting
into Eq. (13), we get
where
Note that
is a real
constant.
In addition, we consider that the loss of
electromagnetic wave upon propagation through
the spherical nano-inclusions results by means of
the generation of heat and scattering. The
scattering cross-section,
of the system can be
(16)
and
(17)
shown to have the following form:
where
(22)
Furthermore, the extinction cross-section,
of the system is given by
,
(23)
where
and
(22), respectively.
are given by Eqs. (21) and
RESULTS AND DISCUSSION
Similarly, substituting Eq. (6) into (9), we find the
effective magnetic polarizability to be
(18)
Next, we numerically analyzed the polarizability
as well as the absorption, scattering, and
extinction cross-sections of the theoretically
modelled spherical
core-shell NPs
where
embedded in a dielectric host matrix. These
optical parameters are analyzed by varying the
material parameters
and
). For the
and
numerical evaluations, we used Mathematica
version 10 software. The following parameter
values
are
used
in
the
simulation:
and
SINET: ETHIOP. J. SCI., 45(2), 2022
137
for the silver shell;
and
and
for magnetite.
Absorption Cross-Section
The absorption cross-section of
core-shell
spherical
nanoinclusions
are
numerically analyzed using Eq. (21) together
with the corresponding expressions for
and
, i.e., Eqs. (14) and (20). The absorption crosssection (
) of the spherical nano-inclusions as
a function of the wavelength of the incident EMW
for different values of and
at a fixed value
of NPs size
as shown in the Figs.
2a) and 2b). The graphs possess two sets of
resonance peaks – the first set of peaks in both
cases are located in the vicinity of
nm
in the UV region which are attributed to the
interaction at the inner (
) interface.
increases (or equivalently as core radius ac
decreases), the two sets of peaks gets far apart
from each other accompanied with a spectral
shift towards lower wavelengths in the first set
of peaks and shifted to the higher wavelengths in
the second set of peaks (see Fig. 2a)). The peak
values of
are found to be more pronounced
in the second set of peaks than the first set of
peaks.
As it seen from the graphs, the effect of a rapid
onset of strong absorption, occurring in the UV
regions for all dielectric medium/host
, is
dependent on the particles size. That is, when the
value of
is increased, the absorption peaks
sharply drops (less intense) for both the first and
second peaks (see Fig. 2a) for a constant
. On the other hand, for a particular
value of
, the absorption cross-section
The second set of peaks are found above the
for both the first and second sets of peaks
sharply increases as
increases and red-shifted
wavelength of
as shown in Fig. 2b.
nm all in the visible
spectral region, which corresponds to the
resonances at the outer (Ag/host) interface. As
138
Kinde Yeneayehu et al.
Figure 1. The absorption cross-section versus wavelength a) for different values of
with
and
Scattering Cross-Section
Figures 3a and 3b depicts the size dependent
scattering cross-section (
) of the spherical
Fe3O4@Ag nano inclusions as a function of the
wavelength of the incident electromagnetic
waves (EMWs) for different values of
and
and a fixed value of QD size as = 10 nm. In each
figures there are two sets of resonance peaks.
The first set of resonance peaks positioned near
to
nm in the UV region and is
associated with the inner (magnetite/Ag)
interface. The second set of peaks which are
connected to Ag/host interface are located above
the wavelength of
and b) for different values of
;
nm.
nm all in the visible
spectral region. Figure (3a) illustrate that,
scattering of light is sharply increased (more
scattering takes place) in the first set of peaks
than the second set of peaks and gets sharply
decreased as
increases. Furthermore, the two
sets of peaks increases as
increases as shown
in the Fig. 3b. From both Figs. 3a and 3b, it is
observed that the first resonance peaks are more
pronounced than the second set of peaks. As the
size of the system of core-shell nanoparticles gets
smaller and smaller, the metal fraction,
, is also
decreased. This leads to the decrease in the
scattering cross-sections.
SINET: ETHIOP. J. SCI., 45(2), 2022
139
Figure 2. The scattering cross-section as a function of wavelength a) for different values of
; with fixed values of
and
In Fig. 3a, the two sets of resonances gets closer
each other as
decreases accompanied by the
shift towards the higher energy in the second
peaks and emission spectral shift to lower energy
in the first peaks. Both sets of resonance peaks
are red-shifted (see Figs. 3) as
increased. For
both figures 3a and 3b there are no noticeable
peaks found in the first sets of peaks at particular
values
and at
. This may
be due to the fact that, the absorption is more
likely to dominate over scattering processes at
and b) for different values of
nm.
the particular values of
and at
. On the other hand, the dielectric
medium at the value of
in the host
matrix may affect the propagation of the incident
electromagnetic wave.
Extinction Cross-Section
Figures 4 depict the graphs of extinction crosssection,
as a function of wavelength for
different values of
and
for the spherical
140
Kinde Yeneayehu et al.
nanoinclusions. As it is seen from the graphs, the
extinction cross-section possess two sets of
resonance peaks. The first set of peaks for Figs.
4a and 4b, the resonance peaks are located close
to
nm in the UV region and the first set
of peaks are due to resonances at the inner
(magnetite/Ag) interface. The second set of
peaks are those found above the wave length of
about
nm all in the visible spectral
region.
Figure 3. The extinction cross-section versus wavelength for different values of a)
and
and b)
; with fixed values of
nm.
As Fig. 4a) depicts, the two sets of resonances
gets closer to each other as
is decreased and
the spectra shift towards lower frequencies in the
first set of peaks, and shift toward higher
frequencies for the second set of peaks. Both sets
of resonance peaks are red-shifted (see Fig. 4b) as
is increased.
SINET: ETHIOP. J. SCI., 45(2), 2022
141
The extinction cross-section depends on the
chemical composition of the particles, their size,
shape, orientation, the surrounding medium, the
number of particles, and the polarization state
and frequency of the incident EMWs (Bohren,
1998). The system of spherical core-shell
nanoparticles that is considered in this study is
composed of two chemically dissimilar
nanoparticles - one as the semiconducting core
and the other as a plasmonic shell. We found that
the extinction cross-section is dependent on the
size and chemical composition of the
semiconducting core or the metallic shell.
As the results depict in Fig. 2 and Fig. 3, the
absorption cross–section dominates over the
scattering cross–section. Since the extinction
cross–section is the combined effect of both
absorption and scattering cross–sections, the two
sets of resonance peaks gets more pronounced
(see Fig. 4.).
CONCLUSIONS
In this study, we investigated the effects of
varying parameters like the metal fraction and
host matrix on the systems of spherical core-shell
nanoparticles embedded in a
dielectric host matrix. It is found that the
absorption cross-section, scattering cross-section
as well as the extinction cross-section of the
system plotted for different values of
and
as a function of wavelength possess two sets of
resonance peaks in the UV (in the vicinity of
nm) and visible (above
nm)
spectral regions. These sets of peaks arise due to
the coupling of the surface plasmon oscillations
of silver with the energy gap of the
semiconducting core at the inner (
interface and at the outer metal/dielectric
(Ag/host matrix) interface. Moreover, when is
increased, the first set of peaks in the UV region
are which is mainly attributed the decrease of the
size of the semiconducting
core, while
the second set of peaks are in the visible regions
with an increase of
due to an increase in the
thickness of the metallic Ag shell. For the graphs
of absorption and scattering cross-sections the
first set of resonance peaks are shifted towards
higher frequencies as increases.
Furthermore, the graphs of the absorption and
scattering cross-sections for different values of
the metal fraction
and at a constant dielectric
function of the host matrix (for fixed
)
possess two set of peaks - the first in the UV
(around
nm) and the second in the
visible (above
nm) spectral regions.
Both sets of resonance peaks are enhanced
accompanied with a red and blue shift. In the
same manner, it is found that with an increase in
the permittivity
of the host, the resonance
peaks are enhanced accompanied with a red
shift. In this case, both sets of peaks are shifted to
higher wavelength with an increase in .
Finally, the enhancement of the optical
properties of the system (spherical core-shell
nanoparticles embedded in a
dielectric host matrix) is because of the strong
coupling of the surface plasma oscillations of the
silver shell with the energy gap of the magnetic
semiconducting
) nano-core. It
means that the silver nanoshell strongly modifies
the optical properties of
nanoparticles
which correspondingly modify its potential
applications. The results obtained may be
utilized in device fabrication and applications
that integrates the plasmonic effects of noble
metals with magnetic semiconductors such as
in core-shell nanostructures.
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Physica E 134 (2021) 114822
Contents lists available at ScienceDirect
Physica E: Low-dimensional Systems and Nanostructures
journal homepage: www.elsevier.com/locate/physe
Enhancement of the optical response of Fe3 O4 @Ag core-shell nanoparticles
Kinde Yeneayehu *, Teshome Senbeta, Belayneh Mesfin
Department of Physics, Addis Ababa University, Addis Ababa, Ethiopia
A R T I C L E I N F O
A B S T R A C T
Keywords:
Core-shell
Dielectric function
Polarizability
Absorbance
In this work, the optical properties of Fe3 O4 @Ag core/shell spherical nanostructures embedded in a dielectric
host matrix are investigated theoretically. The theoretical analysis is carried out based on the electrostatic
approximation and Maxwell-Garnet effective medium theory to obtain the effective electric permittivity and
magnetic permeability, as well as the corresponding refractive index and absorbance. Moreover, for a fixed size
of NPs (of radius r2 = 30 nm) numerical analysis is carried out to see the effect of varying the metal fraction (the
volume fraction of the metallic shell) (β), the filling fraction (the volume fraction of inclusions in the composite)
(f), and the permittivity (εh ) of the host matrix on the optical properties of the nanostructures. The results show
that graphs of real and imaginary parts of polarizability, refractive index and absorbance as a function of
wavelength possess two sets of resonance peaks in the UV and visible regions. These sets of peaks arise due to the
strong coupling/interactions of the surface plasmon oscillations of silver with the semiconductor/dielectric at the
inner (Fe3 O4 /Ag) and outer (Ag/host) interfaces and/or to near-field inter-particle interaction. Moreover, the
two set of resonance peaks are found to be enhanced with an increase of β, f , or εh ; keeping two of these pa­
rameters constant at a time. The results obtained can be used in applications that are designed to integrate
plasmonic effects of noble metals with magnetic semiconductors in a core/shell nanostructure.
1. Introduction
Nanoscience and nanotechnology are recent revolutionary de­
velopments of science and technology that are evolving at a very fast
pace in the last few decades. Materials in the nanometer size regime
show behavior which are intermediate between that of a macroscopic
solid and an atomic or molecular system because of high surface to
volume ratio, quantum size effect, and electrodynamical interactions
[1]. Nanoparticles (NPs) made of noble metals like Au and Ag exhibit
surface plasmonic resonance (SPR) [2,3]. Plasmonic effects enhance
absorbance and scattering in the vicinity of the plasmon resonances.
Moreover, the intensity and position of plasmon resonance in absorption
spectra depend on the shape, size, and the embedding medium. SPR has
been used for biosensing, photothermal, and therapy applications [4,5].
Core-shell nanoparticles are heterogeneous NPs composed of two or
more materials [6]. A wide range of organic and inorganic nanomaterial
can be used for forming both, the core and the shell comprising core
shell NP [7]. Core/shell composite nanostructures (NSs) have attracted
much attention in recent years [8–13], which exhibit diverse unique
material properties [10], not shown by the core or the shell materials
alone, including mono-dispersion, core/shell operability, stability, and
self-assembly. Moreover, because of the strong exciton coupling effect
between the surface plasmon resonance (SPR) of the noble metal and the
excitons of semiconductor [12,14], the noble metal/semiconductor
core/shell composite nanostructure has been one of the most promising
composite for various applications.
Among the various inorganic semiconductor nanomaterials,
magnetite (Fe3 O4 ) nanoparticles have attracted great attention due to
the promising combination of size dependent electronic, optical,
photochemical, and luminescent properties combined with the avail­
ability, a great variety of attainable geometries of nano-assemblies, and
low toxicity [15,16]. The broad spectrum of applications of Fe3 O4 NPs,
such as sensors, solar cells, bioimaging, photocatalysis, UV-shielding,
LEDs put forth rigorous requirements for chemical, thermal, and
photochemical stability of Fe3 O4 NPs, versatility of surface chemistry,
control of the Fe3 O4 NP size and compatibility of Fe3 O4 NPs with water
based bio-environments. Many of these issues can be successfully
addressed by combining magnetite with noble metals in the form of host
composites and core/shell NPs. Indeed, magnetite/noble metal core/­
shell nanocomposites find broad potential applications because they
cannot only combine the unique properties of metals and semi­
conductors, but also generate novel electrical, optical, and, catalytic
* Corresponding author.
E-mail addresses: kindeyene@gmail.com, kinde.yeneayehu@aau.edu.et (K. Yeneayehu).
https://doi.org/10.1016/j.physe.2021.114822
Received 26 June 2020; Received in revised form 24 March 2021; Accepted 17 May 2021
Available online 26 May 2021
1386-9477/© 2021 Elsevier B.V. All rights reserved.
K. Yeneayehu et al.
Physica E: Low-dimensional Systems and Nanostructures 134 (2021) 114822
Ag core/shell NPs, namely the dielectric function, permeability, polar­
izability, refractive index, and absorbance. Finally, concluding remarks
are presented.
2. The model
In this study, we considered a system of core-shell spherical nano­
particle composed of a magnetic semiconducting core (Fe3 O4 ) of radius
r1 and an outer metallic (Ag) shell of radius r2 embedded in a dielectric
host matrix as shown in Fig. 1. Because of the magnetite (Fe3 O4 ) core
with permeability, μ≫1, a complete description of the optical properties
of the system requires the accurate determination of its effective
permittivity εeff and permeability μeff . Accordingly, theoretical analysis
is carried out based on electrostatic approximation and the MaxwellGarnet effective medium theory to obtain εeff andμeff . Moreover, using
these theoretically determined values, we calculated the relevant optical
parameters such as the refractive index, the electric and magnetic
polarizability, and the absorbance of the modeled core-shell NPs.
Fig. 1. Schematic of a core-shell spherical NPs embedded in a matrix. The
permittivities and permeabilities are ε1 , μ1 for the core, ε2 , μ2 for the shell, and,
εh , μh for the host matrix, respectively. Also, r1 , r2 are the radii of the core and
the shell, and r is the distance from the center of the NP to an observation point.
2.1. Permittivity
properties due to the synergetic interaction between the metal and the
semiconductor components [17–22]. Due to its high optoelectronic ef­
ficiency relative to the indirect band gap group-IV crystals, it is
considered as a reliable material for visible and near-ultraviolet
applications.
Silver-coated Fe3 O4 nanohybrids have been used in a broad range of
applications including chemical and biological sensing [23], drug de­
livery [24,25], catalytic reduction and are promising for water treat­
ment (cleaning) and food preservation [26]. In addition, the as-prepared
Fe3 O4 @Ag nanocomposites exhibit a self-sterilizing property that avoids
the formation of biofilms which are the most dangerous source capable
of spreading toxic bacteria into the environment [27], and hence has
great application in catalysis and agriculture [28], improving contrast of
IMR in cancer detection [29], for biosensor and ultra-high Raman
spectroscopy [30,31], in diagnostic and therapeutic applications [32].
Many works have attempted to combine Fe3 O4 and Ag challenges on
the core/shell Fe3 O4 @Ag due to surface enhanced Raman scattering
(SERS) effect, localized surface plasmon resonance (LSPR), where col­
lective oscillations of free conduction electrons in restricted curvature of
metallic nanoparticles (MNPs) when illuminated with incident light
cause strong optical responses at the plasmon resonance wavelength of
MNPs as a non-propagating plasmon. An effective approach for con­
trolling and understanding the phenomena is as follows: shell thickness,
core diameter, electronic properties of shell and surrounding environ­
ment at two different interfaces (outer interface between the surface and
incident light, and inner interface between metal and semiconductor),
affect the plasmon resonance wavelength, light scattering, absorption
and extinction cross section of core/shell. LSPR causes some suitable
characteristics such as enhancement of electric field, localization of
energy at nanometer scale, and strongly enhanced absorption and
scattering [33].
Analysis of the optical response of nanoparticles thus requires
measuring the effective permittivity, εeff , and permeability, μeff [34]. In
this paper, we studied the optical response of the theoretically modeled
Fe3 O4 @Ag core-shell nanoparticles. Silver nanoparticle was selected as a
shell on magnetite nanospheres, due to its nontoxic, strong absorption in
the UV and visible spectrum [35] and surface plasmon resonance (SPR)
which plays a great role in determining the optical response of
nanoparticles.
The paper is organized as follows: The effective permittivity and
permeability of the theoretically modeled magnetic-semiconductor/
metal core/shell spherical NP embedded in a dielectric host matrix are
derived. Firstly, the equations for the effective polarizability, and the
refractive index are derived. Then, the numerical results are presented
and discussed. Specifically, we analyzed the optical responses of Fe3 O4 @
When the composite core-shell NP is irradiated with an electro­
magnetic radiation, electric field is induced in the system due to po­
larization. The distribution of the electrostatic potential Φ associated
with the induced field inside and outside of the NP can be obtained by
solving the Laplace equation, ∇2 Φ = 0 in spherical coordinates. Assume
that the incident radiation is polarized along the positive z-axis and
there is an azimuthal symmetry. Then, in the electrostatic approxima­
tion, i.e., the wavelength of the incident electromagnetic wave is much
greater than a typical size of the NPs, the distribution of the electric
potential in the system may be described by the following expressions:
Φ1 (r, θ) = − Eh Ar cos θ;
r < r1 ;
(
)
C
Φ2 (r, θ) = − Eh B − 3 r cos θ;
r
r1 < r < r2 ;
(
)
F
Φh (r, θ) = − Eh D − 3 r cos θ. r > r2
r
(1)
(2)
(3)
Here Φ1 , Φ2 , and Φh are the electric potentials in the core, metal shell,
and the host matrix, respectively. Eh is the magnitude of the applied field
directed along the z-axis, θ is the zenith angle, and r is the distance from
the center of the NP to an observation point. Also, the coefficients A; B;
C; D and F are unknown constants that can be determined using
appropriate boundary conditions at the core/shell and shell/host in­
terfaces. At this point it is worth noting that the second term on the rightside of Eq. (3) represents the induced potential outside the core-shell NP.
The total induced field outside the concentric spheres represents the
optical response of the system. Equivalently, the induced potential
outside the concentric spheres is given by
Φind =
FEh
cos θ;
r2
(4)
where the coefficient, F, determined using the boundary condition is
found to be:
[
]
(ε1 + 2ε2 )(ε2 − εh ) + νf (ε1 − ε2 )(2ε2 + εh )
F=
(5)
Dr23 ;
(ε1 + 2ε2 )(ε2 + 2εh ) + 2νf (ε1 − ε2 )(ε2 − εh )
where νf =
( )3
r1
r2
.
Note that Φind describes the superposition of the applied field and
that of a dipole located at the center of the NP. Introducing the dipole
moment p, we may rewrite Φind as
2
K. Yeneayehu et al.
Φind =
Physica E: Low-dimensional Systems and Nanostructures 134 (2021) 114822
p cos θ
;
4πεh r2
(6)
2.2. Permeability
where p is the magnitude of the electric dipole moment. Using Eqs. (4)
and (6), we find that the dipole moment of the system to be p =
4πεh F Eh , or
→ →
→
From magnetostatics, we have ∇ × H = J , where H is the field
→
→
→
strength and J is the current density. If J = 0, then ∇ × H = 0, so that
→
we may introduce a magnetic scalar potential ΦM such that H = −
∇ΦM , similar to that in electrostatics. Further, if μ is spatial indepen­
→
dent, then ∇⋅ B = 0 results to
(7)
p = εh αDEh ;
where α is the polarizability of the core-shell plus host matrix composite
system given by
[
]
(ε1 + 2ε2 )(ε2 − εh ) + νf (ε1 − ε2 )(2ε2 + εh ) 3
α = 4π
(8)
r .
(ε1 + 2ε2 )(ε2 + 2εh ) + 2νf (ε1 − ε2 )(ε2 − εh ) 2
That means that the magnetic scalar potential ΦM satisfies the Laplace
equation. Now, consider the system of core-shell spherical NPs with a
magnetic core and a nobel metallic shell uniformly dispersed in a
dielectric host matrix (see Fig. 1). For such systems, an electromagnetic
wave incident on the system induces not only an electric polarization but
also magnetization. Then, similar to that employed for the electrostatic
fields the solution of the Laplace equation for the scalar potential, Φm , in
the various regions may be assumed to be given by the following
equations [37]:
Note that here we are using the concept of internal homogenization
of which the polarizability of the equivalent sphere is equated to that of
a core-shell in the electrostatic approximation. Accordingly, the effec­
tive dielectric function εcs for a core-shell NP embedded in a host matrix
of dielectric function εh is related to its polarizability α by the ClausiusMossotti relation as [36,38,40].
α = 4πr23
(εcs − εh )
.
εcs + 2εh
(9)
Φm1 (r, φ) = − Hy A1m r cos φ;
In view of Eqs. (8) and (9), we note that the effective permittivity of
the core-shell spherical nanoinclusion is given by
εcs = ε2
3
2 )r2 +
3
)r
2 2 −
(ε1 + 2ε
(ε1 + 2ε
3
2 )r1
.
3
)r
2 1
2(ε1 − ε
(ε1 − ε
(17)
∇2 Φm = 0.
(10)
Furthermore, introducing the volume fraction, β, of the metal coated
spherical core-shell nanoparticle as
(18)
r < r1
(
)
B1m
Φm2 (r, φ) = − Hy A2m − 3 r cos φ;
r
r1 < r < r2 ;
(19)
(
)
B2m
Φmh (r, φ) = − Hy A3m − 3 r cos φ;
r
r > r2
(20)
Now, consider the system composed of a finite number of core-shell
NPs uniformly dispersed in a host matrix as shown in Fig. 1. Suppose N is
the density number of the inclusions (NPs) in the system. Then, the
polarizability and the effective permittivity of the system can be
described by using the Clausius-Mossotti relation together with the
Maxwell-Garnet mixing theory. Accordingly, the electric polarizability
and the effective permittivity are related by [36].
where Φm1 , Φm2 , and Φmh are the magnetic potentials in the magnetic
semiconductor core, the metallic shell, and the host matrix, respectively.
Hy is the magnitude of the applied field (with Hy directed along the
positive y-axis), φ is an ‘azimuthal’ angle measured with respect to the
+y-axis, r is the distance from the center of the NP to an observation
point. A1m , A2m , A3m , B1m , and B2m are unknown coefficients that need to
be determined using the boundary conditions for the H-field. Note that
the second term on the right-side of Eq. (20) represents the magnetic
scalar potential outside the core-shell NP due to the induced magnetic
dipole. Note that the system’s response due to the magnetic component
of the applied field is described by the induced field outside the
concentric spheres. Hence, we need to find only the coefficient B2m , i.e.,
imposing the appropriate boundary condition, it is found to have the
form:
[
]
(μ1 + 2μ2 )μ2h + νf (2μ2 + μh )μ12
B2m =
(21)
A3m r23 ;
(μ1 + 2μ2 )(μ2 + 2μh ) + 2νf μ12 μ2h
N α εeff − εh
;
=
3 εeff + 2εh
where νf =
(11)
β = 1 − νf ;
Eq. (10) for the effective dielectric function of the core shell com­
posite material takes the form:
)
(
ε1 β3 − 2 + 2ε2
) .
(
εcs = ε2
(12)
ε1 + ε2 β3 − 1
(13)
Φmi =
(15)
Φmi =
α/(4πr23 )
and αeff =
is the dimensionless effective electric polarizability
of the inclusion given by
αeff =
εcs − εh
.
εcs + 2εh
, and introduced the following notations μ12 = μ1 − μ2 ,
Hy B2m
cos φ;
r2
(22)
where the coefficient, B2m is given by Eq. (21).
Note that Φmi describes the superposition of the applied field and that
of a magnetic dipole located at the center of the NP. But, the scalar
potential outside the NP may be given by [37].
where f is the filling factor (the volume fraction of inclusions in the
composite) of the core-shell NPs defined by
4πr23
N;
3
r1
r2
and μ2h = μ2 − μh .
Hence, the induced magnetic scalar field, Φmi , outside the core-shell
NP becomes
where εeff is the effective dielectric function of the system and α is the
polarizability defined by Eq. (9). Further, substituting Eq. (8) into (13)
and manipulating, we get
(
)
1 + 2f αeff
εeff = εh
;
(14)
1 − f αeff
f=
( )3
m
cos φ;
4π r 2
(23)
where m is the magnitude of the magnetic dipole moment. Then,
combining Eqs. (22) and (23), we get m = 4π B2m Hy ̂
y , or
(16)
y;
m = κm A3m Hy ̂
3
(24)
K. Yeneayehu et al.
Physica E: Low-dimensional Systems and Nanostructures 134 (2021) 114822
of Eq. (32), i.e., ε2 = ε2 + iε′′2 , we obtain the following:
′
where κm is the magnetic susceptibility of the core-shell NP embedded in
the host with permeability μh given by
[
]
(μ1 + 2μ2 )μ2h + νf (2μ2 + μh )μ12 3
κm = 4π
r .
(25)
(μ1 + 2μ2 )(μ2 + 2μh ) + 2νf μ12 μ2h 2
μcs − μh
;
μcs + 2μh
ε′′2 (ω) =
γω2p
;
ω(ω2 + γ2 )
The effective electric polarizability of the system may be obtained by
substituting Eq. (12) into (16), i.e.,
)
(
⎞
⎛
3
ε
1 εh + ε2 εh β − 1
⎟
3⎜
⎟;
(
[
)
]
(35)
αeff = 1 − ⎜
⎠
2⎝
3
3
2
ε1 εh + ε2 εh β − 1 + ε1 ε2 (2β) − 1 + ε2
Because εeff for the system is complex, the effective electric polariz­
ability αeff , defined by Eq. (35) is also complex, which may be written as
(29)
where αeff and α′′eff are its real and imaginary parts, respectively.
′
Substituting ε2 = ε2 + iε′′2 into (35), we get
( ′ ′
) ′ (
′)
3 [ ε2 φ + ε1 εh ϕ + ε′′2 φ ψ ]
′
;
αeff = 1 −
′
2
ϕ 2 + ψ2
′
where f = 4πNr23 /3 is the filling factor (the volume fraction of inclusions
in the composite) of the core-shell NPs defined by Eq. (15) and κeff = κm /
(4πr23 ) is the dimensionless magnetic polarizability which is given by
(37)
and
α′′eff =
(31)
( ′ ′
)
(
′) ′
3 [ ε2 φ + ε1 εh ψ + ε′′2 φ ϕ ]
;
′2
2
ϕ + ψ2
(
where φ = εh
′
3. Optical properties of Fe3 O4 @Ag NPS
3
β−
(38)
(
)
)
′
′
′ 2
′
3
1 ; η = φ + ε1 2β
− 1 ; ϕ = (ε2 ) − (ε′′2 )2 + ε2 η +
ε1 εh , ψ = 2ε’2 ε’’2 + ε’’2 η.
Similarly, substituting Eq. (28) into (31), we find the effective
magnetic polarizability to be:
)
(
3
μ1 μh + μ2 Δ
κeff = 1 −
(39)
2 μ1 μh + μ2 Δ + μ1 φ + μ22
In this section, we derive the equations for the optical parameters, i.
e., the refractive index and the polarizability of a system composed of
Fe3 O4 @Ag core-shell NPs embedded in a liquid/water. Hence, in order
to get an explicit expression for the refractive index (n), we must fix the
permittivities and permeabilities of the constituents (i.e., the magnetic
core, metallic shell, and host matrix).
Now we consider the ‘bare’ metallic (Ag) shell. Note that its response
to incident electromagnetic wave (EMW) is solely described by the
dielectric function (permittivity) with the permeability being equal to
unity (μ2 = 1). Therefore, we choose the frequency dependent complex
dielectric function of the metallic (Ag) to have the Drude form given by
ω2p
;
ω(ω + iγ)
(36)
′
αeff = αeff + iα′′eff ;
where μeff is the effective magnetic permeability of the ensemble and κm
is the magnetic polarizability defined by Eq. (26). Further, substituting
Eq. (26) into (29) and manipulating, we get
(
)
1 + 2f κeff
μeff = μh
;
(30)
1 − f κeff
ε2 (ω) = ε∞ −
(34)
3.1. Effective electric and magnetic polarizabilities
Now, consider the ensemble that is composed of the core-shell NPs
homogeneously embedded in the host matrix (see Fig. 1). Suppose N is
the density numbers the inclusions (NPs) in the system. Then, using the
Clausius-Mossotti relation and the Maxwell-Garnet mixing theory, the
magnetic polarizability and permeability are related by [36–38].
κeff
(33)
′
Further, using β = 1 − νf which is the volume fraction of the metal
coated spherical core-shell NP defined by Eq. (11), Eq. (27) for the
effective magnetic permeability of the composite material becomes
)
⎡ (
⎤
3
⎢μ1 β − 2 + 2μ2 ⎥
) ⎥
(
(28)
μcs = μ2 ⎢
⎣
⎦
μ1 + μ2 3β − 1
μ − μh
= cs
.
μcs + 2μh
;
where ε2 (ω) and ε′′2 (ω), respectively, are the real and imaginary parts of
ε2 .
It is worth noting that the dielectric function of metals, in particular
the noble and alkali metals, vary significantly as a function of the fre­
quency of the incident light in the visible spectral region. However, in
the same spectral region the dielectric function for magnetite varies very
little with frequency compared with that of the metal. Hence, without
loss of generality we assumed both the permittivity (ε1 ) and perme­
ability (μ1 ) of magnetite as well as the permittivity of the host (εh ) to be
real constants independent of frequency.
(26)
Substituting Eq. (25) into (26) and simplifying, we obtain the
effective permeability of the core-shell spherical NP to be
[
]
(μ + 2μ2 ) + 2νf (μ1 − μ2 )
μcs = μ2 1
(27)
(μ1 + 2μ2 ) + νf (μ2 − μ1 )
Nκm μeff − μh
;
=
3
μeff + 2μh
ω + γ2
2
and
The effective permeability μcs for a core-shell NP embedded in the
host matrix of permeability μh may be related to its susceptibility κm by
the Clausius-Mossotti relation as
κm = 4πr23
ω2p
′
ε2 (ω) = ε∞ −
(
where Δ = μh
3
β−
)
)
(
3
1 ; φ = μ2 2β
− 1 ;
In particular, for the case where μ1 is a real constant and μ2 = μh =
1 : 0 (nonmagnetic), we find that Eq. (39) reduces to:
[
]
3 + β(μ1 − 1)
κeff = 1 −
;
(40)
μ1 + 2
(32)
and the corresponding effective permeability, Eq. (30), becomes
where the constant ε∞ is the permittivity at high frequencies, ωp is the
plasma frequency, γ is the damping parameter, and ω is the frequency of
the incident radiation. Further, separating the real and imaginary parts
μeff = 1 −
3f (β − 1)(μ1 − 1)
.
(μ1 + 2) + f (β − 1)(μ1 − 1)
(41)
Note that both κeff and μeff of Eqs. (40) and (41) are real constants.
4
K. Yeneayehu et al.
Physica E: Low-dimensional Systems and Nanostructures 134 (2021) 114822
]12
[ (
)1
1
’’2 2
’
+
ε
−
ε
μ
.
n2 = √̅̅̅ μeff ε’2
eff
eff
eff eff
2
(47)
It is worth noting that the phase velocity of the wave propagating in
the medium is described by real part of refractive index, n1 , and the
attenuation of the wave as it propagates through the medium is deter­
mined by its imaginary part, n2 [37].
4. Numerical analysis
In this Section, we present the numerical analysis performed to
characterize the optical response of the theoretically modeled spherical
Fe3 O4 @Ag core-shell NPs embedded in a dielectric host matrix. We used
Wolfram Mathematica Software codes for numerical evaluation, opti­
mization and visualization of a very wide range of numerical functions.
In particular, the electric and magnetic polarizabilities, the refractive
index, and the absorbance under different conditions (i.e., varying β, f
and εh ) will be simulated. The parameter values used are ε∞ = 4.5, ωp =
1.46 × 1016 rad/s and γ = 1.67 × 1013 rad/s for the silver shell; and ε1 =
5.85 and μ1 = 9.0 for magnetite.
4.1. Electric polarizability
The real and imaginary parts of the dimensionless electric polariz­
′
abilities (αeff and α′′eff , respectively) of the spherical Fe3 O4 @Ag nano­
inclusions as a function of the wavelength of the incident radiation for
different values of the metal fraction (the volume fraction of the metal
coated), β, and constant values of εh = 1.77 and NPs size r2 = 30 nm are
′
depicted in Fig. 2. Both the graphs of αeff and α′′eff shows that, it possess
Fig. 2. The real (a) and imaginary (b) parts of the electric polarizability versus
wavelength for different values of β; with εh = 1.77 and r2 = 30 nm
fixed constant.
3.2. Effective refractive index
The complex refractive index ̃
n of the system consisting of spherical
core-shell composite NSs embedded in a matrix may be defined as
√̅̅̅̅̅̅̅̅̅̅̅̅̅
̃
n(ω) = εeff μeff ;
(42)
where εeff and μeff are the effective permittivity and permeability of the
system given by Eqs. (14) and (30), respectively. Now, using εeff = εeff +
′
iε′′eff
and μeff = const, Eq. (42) may be written as
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
(
) (
)̅
̃
n=
ε′eff μeff + i ε′′eff μeff ;
(43)
Further, introducing
̃
n = n1 + in2 ;
(44)
where n1 and n2 are the real and imaginary parts, respectively. Then,
squaring Eq. (44), we get
)
(
̃
n2 = n21 − n22 + i(2n1 n2 )
(45)
Also, squaring Eq. (43), equating with Eq. (45), and manipulating,
we find that the real and imaginary parts of the refractive index takes the
form
]12
[
( ′
)12
1
′
n1 = √̅̅̅ μeff εeff2 + ε′′2
+
ε
μ
;
eff
eff eff
2
(46)
and
Fig. 3. The real (a) and imaginary (b) parts of the refractive index versus
wavelength for different values of β. Also, f = 0.001, r2 = 30 nm, and εh =
1.77.
5
K. Yeneayehu et al.
Physica E: Low-dimensional Systems and Nanostructures 134 (2021) 114822
two set of resonance peaks - the first in the UV region in the vicinity of
the wavelength λ = 300 nm and the second peaks in the visible spectral
region above the wavelength of λ = 420 nm. The first and second sets of
peaks arise due to the coupling/interactions of the surface plasmon os­
cillations of silver with the semiconductor/dielectric at the inner
(Fe3 O4 /Ag) and outer (Ag/host) interfaces and/or to near-field interparticle interaction, respectively.
′
Moreover, it is found that the polarizabilities, αeff and α′′eff , increases
as the value of the metal fraction β is increased (or equivalently as the
core radius r1 is decreased). Moreover, the second set of peaks are more
pronounced than the first set. This may be explained with the fact that
the surface area of the outer surface (Ag/host interface) of the Ag shell is
larger than that of the inner surface area (magnetite/Ag interface), and
hence large number of carriers available at the outer interface than the
inner.
The analysis also shows that when β is increased, the first set of peaks
in the UV region are red-shifted which is mainly attributed the decrease
of the size of the NPs, i.e., the semiconducting Fe3 O4 core. On the other
hand, the second set of peaks are blue-shifted with an increase of β, due
to an increase in the thickness of the metallic shell. Indeed, the two
resonance peaks corresponding to each NPs become closer and closer to
each other as β is increased indicating that the metallic shell plays the
dominant role in determining both the real and imaginary parts of the
electric polarizability.
4.2. Refractive index
In this Section, the real and imaginary parts of the refractive index of
Fe3 O4 @Ag core-shell spherical nanoinclusions are numerically analyzed
using Eqs. (46) and (47) together with the corresponding expressions for
εeff and μeff , i.e., Eqs. (14) and (30). The following parameter values are
used: and ε1 = 5.85 and μ1 = 9.0 for Fe3 O4 with the other parameters
being the same as that used in Section 4.1.
Fig. 3 depicts the graphs of the real (n1 (λ)) and imaginary (n2 (λ))
parts of the refractive index of the spherical nanoinclusions as a function
of the wavelength of the incident radiation for different values of β. As
the Figures show, there are two sets of resonance peaks. The first set of
peaks for both n1 and n2 are located around λ = 300 nm in the UV region
and is linked to the dispersion/absorption at the inner (magnetite/ Ag)
interface. The second set of peaks are those found above the wavelength
of λ = 420 nm all in the visible spectral region, which are connected to
Ag/host interface. As it is seen from the graphs, propagation of light/
photon is more pronounced in the second set of peaks than the first set of
peaks.
As it can be clearly seen from Fig. 3, the effect of decreasing the
radius of the core, i.e., increasing β, results in a decrease of the refractive
index; accompanied with a slight blue shift in the first set of peaks and
red shift in the second set of peaks. In addition, the resonances for each
NPs gets more closer to each other, when the metal fraction β is
increased.
For Fe3 O4 @Ag nanostructure, the Fermi level of Ag is near ‘weak’
energy levels ofFe3 O4 ; therefore, electrons can be transferred readily
from the Ag weak energy levels to the Fermi level of Fe3 O4 , where these
electrons are excited by incident ray. The energy level of these excited
electrons is near the conduction band of Ag; therefore, these excited
electrons are transferred to the conduction band of Ag where they
become a part of the electron/hole recombination process, increasing
the near band edge emission. As a consequence of the electrons transfer,
the visible emission will be reduced and will be enhanced which is in
agreement to that reported in Ref. [39]. Due to this maximum value of
refractive index used for medical application in nanofields like cancer
treatment, cancer detection.
In addition to the metal fraction β, the refractive index of the system
depends on other factors such as the surrounding medium (the dielectric
function εh of the host matrix) and the filling factor. The effect of the
Fig. 4. The real (a) and imaginary (b) parts of the refractive index as a function
of wavelength for different values of the dielectric function of the host, εh ; with
β = 0 : 65, r2 = 30 nm and f = 0.001.
dielectric function εh on the real and imaginary parts of the refractive
index of an ensemble of spherical Fe3 O4 @Ag NPs embedded in a host
matrix as a function of the wavelength of the incident radiation is shown
in Fig. 4. It is shown that as εh is increased from 1.00 – 2.25 in steps of
0.25 the resonance peaks of both n1 (λ) and n2 (λ) increase with the peaks
of the second set located above λ = 460 nm more pronounced than the
first set of peaks located around λ = 300 nm. Both set of peaks shift
toward high wavelength regions (red shift) with an increase in εh .
Moreover, for each values of εh the “reference” value of the real part of
√̅̅̅̅̅
the refractive index, which is given by n1 = εh , shifts upward along the
n1 -axis as the value of εh is increased.
Fig. 5 shows the dependence of the real and imaginary parts of the
refractive index of the system on the filling fraction (the volume fraction
of inclusions in the composite) f; versus wavelength for fixed values of β,
r2 , and εh . The Figure depicts that there are two sets of resonance peaks
for both the n1 (λ) and n1 (λ), located on either sides of λ = 300 nm (first
sets shown as insets) and λ = 506 nm (second peaks). It is seen that all
the peaks get larger and larger as filling factor is increased from f = 0.
001 − 0.006, in steps of 0.001. In other words, when the filling factor (f)
is increased, the intensity of the refractive index is highly enhanced
suggesting that the shell thickness and the density of the packed nano­
sphere arrays can play great role to improve the photoluminescence
[34]. It is worth noting that unlike that of observed with β and εh (see
Figs. 3 and 4), varying the filling fraction f does not result to a shift of the
resonance peaks of both the real and imaginary parts of n, i.e., it only
results in their enhancement with no shift in the location of the peaks.
5. Optical absorbance
An important parameter that is used to characterize the optical
6
K. Yeneayehu et al.
Physica E: Low-dimensional Systems and Nanostructures 134 (2021) 114822
Fig. 6. The absorbance versus wavelength for different values of β; with f =
0.001, r2 = 30 nm and εh = 1.77.
Fig. 5. The real (a) and imaginary (b) parts of the refractive index versus
wavelength for different values of filling fraction f ; with β = 0.65, r2 = 30 nm
and εh = 1.77.
Fig. 7. The absorbance versus wavelength for different values of εh ; with β =
0.65, r2 = 30 nm and f = 0.001.
properties of a sample is the absorbance. Assuming that the incident
electromagnetic wave is polarized along the positive z-axis, the in­
tensity, I(z), of light that passes through a thickness z of a sample is given
by [34].
I(z) = I(0)e−
αz
;
1.77) versus wavelength for different values of β (or thickness tAg ) of the
metallic shell are shown in Fig. 6. The filling fraction and the size of the
NPs are kept constant - f = 0.001 and r2 = 30 nm, respectively. The
Figure shows that there are two sets of absorption peaks - the first in the
UV spectral region in the vicinity of λ = 300 nm and the second set
located in the visible region above λ = 420 nm. It is seen that as tAg is
increased the absorption peaks of the first set of resonant peaks in the UV
region increases with the peaks shifting towards low energy values (red
shift) and the second set of peaks also increases with a shift towards high
energy values (blue shift).
It is worth noting that the absorption peaks of the first sets arise due
to near band edge absorption of the free exciton recombination while the
red shift of the absorption edge with an increase of tAg (or a decrease of
the core radius r1 ) is attributed to increase in the energy gap of the core
nanoparticles [40]. On the other hand, the absorption peaks of the
second set located above the wavelength of λ = 420 nm arises due to the
deep level emissions which are attributed to the surface plasmon reso­
nance of silver nanoshell - this explains as to why the absorption peaks
gets enhanced as well as blue shifted as the thickness of the silver shell
increased from 7.5 − 15.0 nm (or β = 0.578 − 0.875).
Furthermore, the effect of varying the dielectric host matrix εh on the
optical absorbance as a function of the wavelength of the incident ra­
diation is plotted as shown in Fig. 7. Here, the following parameter
values kept constant: f = 0.001, r2 = 30 nm and β = 0.65. It shows that
the absorbance have two sets of peaks - the first around λ = 300 nm in
the UV region and the second peaks located above λ = 465 nm in the
visible spectral region. In addition, unlike that obtained in Fig. 6 both
(48)
where I(0) is the intensity of light before passing through the sample (at
z = 0) and α is the absorption coefficient defined by
α=
4πn2
.
λ
(49)
Here λ is the wavelength of the incident radiation and n2 is the imagi­
nary part of the refractive index.
[ ]
I(z)
The absorbance of the system is defined as A = ln I(0)
. In our case,
setting z = tAg in Eq. (48), we find that the absorbance to be:
A(λ) =
4πn2
tAg ;
λ
(50)
where tAg = r2 − r1 is the thickness of the silver shell.
Optical properties and enhanced optical-tunability of core/shell
nanoparticles (NPs) are determined by shape, size, permittivity, and
geometrical arrangement of building blocks. However, the properties of
magnetite core particles such as reactivity, thermal stability, and optical
properties could be investigated in order to achieve overall stability of
particles and the dispersibility of core particles.
The graphs of the optical absorbance of an ensemble of spherical
Fe3 O4 @Ag nanoparticles embedded in a dielectric host matrix (εh =
7
K. Yeneayehu et al.
Physica E: Low-dimensional Systems and Nanostructures 134 (2021) 114822
host matrix) is because of the strong coupling/interactions of the surface
plasmon oscillations of silver with the semiconductor/dielectric at the
inner (Fe3 O4 /Ag) nano-core. It means that the silver nanoshell strongly
modify the optical properties of Fe3 O4 nanoparticles which corre­
spondingly alter/modify its potential applications. The results obtained
may be utilized in device fabrication and applications that integrates the
plasmonic effects of noble metals with magnetic semiconductors (e.g.,
Fe3 O4 ) in a core/shell nanostructure.
Declaration of competing interest
The authors declare that we have no significant competing financial,
professional or personal interests that might have influenced the per­
formance or presentation of the work declared in this manuscript.
Acknowledgements
Fig. 8. The absorbance versus wavelength for different values of metal fraction,
f ; with β = 0.65, r2 = 30 nm and εh = 1.77.
This work was financially supported by Addis Ababa University and
Adama Science and Technology University.
sets of resonance peaks are red shifted as the value of the dielectric
function of the host matrix is increased. Also, it is found that both sets of
absorbance peaks increase as εh is increased with more enhancement
being observed in the second set of peaks than the first. The absorption
efficiency spectra of Fe3 O4 NPs with different radius coated by Ag outer
shell thickness and the LSPR peak wavelength of Fe3 O4 @Ag NPs with the
volume fraction of the shell which is in good agreement with Refs [33,
40,41].
Fig. 8 shows the dependence of the optical absorbance on the filling
factor f as a function of the wavelength of the incident radiation, with
the following parameter values kept constant: β = 0.65, r2 = 30 nm and
εh = 1.7689. It can be observed that both sets of resonance peaks of the
absorbance increase with an increase of the filling factor from f =
0.001 − 0.006 in 10 steps of 0.001; with no shift in the respective peaks
position. The inset highlights the set of peaks located around λ =
300 nm.
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In this paper, we investigated the effects of changing the metal
fraction, host matrix, and filling fraction on the optical properties of
systems of spherical core/shell Fe3 O4 @Ag nanoparticles embedded in a
dielectric matrix. It is found that the real and imaginary parts of the
polarizability, and refractive index as well as the optical absorbance of
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possess two sets of resonance peaks in the UV (in the vicinity of λ ∼
300 nm) and visible (above λ ∼ 420 nm) spectral regions. These sets of
peaks arise due to the coupling/interactions of the surface plasmon os­
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in the UV region are red-shifted which is mainly attributed to the
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the thickness of the metallic shell.
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refractive index and absorbance as a function of wavelength for different
values of host matrix (for fixed β = 0.65 and f = 0.001) possess two set
of peaks - the first in the UV (around λ ∼ 300 nm) and the second in the
visible (above λ ∼ 460 nm) spectral regions. It is found that with an in­
crease in the permittivity εh of the host, n1 ,n2 , and the absorbance A are
enhanced. In this case, both sets of peaks are red shifted with an increase
in εh . We also found that the increase in f enhances the peak intensity
without a shift in position for all cases.
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(spherical core/shell Fe3 O4 @Ag nanoparticles embedded in a dielectric
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9
J Nanopart Res
(2020) 22:355
https://doi.org/10.1007/s11051-020-05086-0
RESEARCH PAPER
Rapid synthesis of triple-layered cylindrical
ZnO@SiO2@Ag core-shell nanostructures
for photocatalytic applications
Gashaw Beyene & Teshome Senbeta &
Belayneh Mesfin & Ni Han & Gamachis Sakata &
Qinfang Zhang
Received: 3 August 2020 / Accepted: 10 November 2020
# Springer Nature B.V. 2020
Abstract Core-shell nanocomposites are promising materials in the degradation of harmful chemicals released
from industries/factories. In this work, ZnO@SiO2@Ag
triple–layered core-shell nanocomposites synthesized by
a facile chemical precipitation route at 400 °C using asprepared ZnO@SiO2 samples as a precursor were investigated for photocatalytic application. The synthesized
ZnO@SiO2 and ZnO@SiO2@Ag samples were characterized using XRD, SEM, TEM, XPS, and UV-Vis spectrometer. The XRD studies showed that both nanocomposites possess the hexagonal wurtzite crystalline phase
of the core ZnO. Moreover, the average crystallite sizes
of ZnO@SiO2@Ag composites determined from the
XRD spectra were found to be 27.98 nm and 30.56 nm
for reaction times of 4 h and 12 h, respectively. The SEM
Highlights
• Cylindrical triple layered ZnO@SiO2@Ag CSNSs synthesized
using three techniques
• Optical properties of ZnO@SiO2 and ZnO@SiO2@Ag were
investigated
• Synthesized nanoparticles were applied for the degradation of
methylene blue dye
• The use of Ag as a coat enhanced photocatalytic activity of
ZnO@SiO2
• ZnO@SiO2@Ag CSNSs were very stable even after recycling of
five times
G. Beyene : N. Han : G. Sakata : Q. Zhang (*)
School of Materials Science and Engineering, Yancheng Institute
of Technology, Yancheng, China
e-mail: qfangzhang@gmail.com
G. Beyene : T. Senbeta : B. Mesfin : G. Sakata
Department of Physics, Addis Ababa University, Addis Ababa,
Ethiopia
and TEM analyses indicate that the morphologies of the
samples were rod-shaped. The UV-Vis spectroscopy
showed that the ZnO@SiO2@Ag nanoparticles exhibited
maximum absorbance peak at 363 nm with a calculated
band gap energy of 3.13 eV. In addition, the photocatalytic activity and stability were analyzed by a photoreduction method using the photodegradation property of
organic methylene blue under UV-Vis light irradiation.
Compared with the “bare” ZnO@SiO2 samples, the stability and photocatalytic performance of the Ag coated
ZnO@SiO2@Ag nanocomposites were highly enhanced,
and the reasons for the enhancement are discussed.
Keywords Core-shell nanostructure . Methylene blue .
Crystallite size . Band gap energy . Photodegradation .
Chemical stability
Introduction
Large number of industries/factories release untreated
waste water to the environment. The byproduct from
dye industries are aromatic compounds, potentially toxic, and difficult to degrade. The discharge of waste water
from these industries can directly affect aquatic organisms as well as human health. Moreover, these harmful
byproducts have the potential to mix with water
reservoirs/dams that can be used for drinking and indirectly affect human health through the food chain, reduce soil fertility, and cause serious problems in their
day-to-day activities (Taghvaei et al. 2018; Sethi
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Page 2 of 14
and Sakthivel 2017; Zhuang et al. 2019; Yousefi and
Hashemi 2019). Therefore, the treatment of these
byproducts is essential before they are released to the
environment/community. For the treatment of such waste
products, photocatalytic degradation method is a promising technique. In particular, core-shell nanostructures
(CSNSs) are found to be promising new materials for the
degradation of these byproducts (Salem et al. 2018; Rosi
and Kalyanasundaram 2018; Joo et al. 2009), since they
are friendly with environment and cost effective. Nowadays, nanotechnology and nanoscience have given great
attention for the fabrication of desirable nanomaterials with
large surface to volume ratios, unique surface functionalities, and low band-gap energy to treat industrial pollutants
through oxidation processes. Among the advanced oxidation process methods, photocatalytic degradation is the
effective means of degrading organic pollutants (Dong
et al. 2015). In this process, hydroxyl radical is applied
for degrading pollutants via conversion to harmless minerals (Taghvaei et al. 2018).
Recently, core-shell nanostructured materials have
attracted great attention in various fields due to their
unique electrical, catalytic, magnetic, plasmonic, and optical properties. Due to quantum confinement effect, large
surface-to-volume ratio of the constituents, and the interaction between the constituents; core-shell nanoparticles
(CSNPs) exhibit high thermal/chemical stability and high
light harvesting ability with new and/or modified material
properties (Gawande et al. 2015; Kim et al. 2014; Beyene
et al. 2020; Naik et al. 2019). The properties of CSNPs
can be modified by changing the constituent materials’
geometry, core size, spacer, shell thickness, and the hostmedium (Bartosewicz et al. 2017; Kassahun 2019;
Encina et al. 2013). These new and/or modified properties of the CSNS materials have various potential applications; such as in bionanotechnology, enhanced optical
devices, tailored magnetic devices, electronic and optical
devices (Mondal and Sharma 2016), bioimaging systems,
pharmaceutical analysis (Guidelli et al. 2015), energy
storage materials (Mondal and Sharma 2016; Guidelli
et al. 2015; Lee et al. 2016), genetic engineering, dye
sensitized solar cells (DSSC) (Wang et al. 2018), and
many important catalytic processes (Gawande et al. 2015;
Aranishi et al. 2011; Shao et al. 2016). The fabrication of
CSNSs requires careful selection of the core and shell
materials with the aim to optimize the passivation and to
reduce the structural defects induced by positive mismatch of their lattice parameters. Both double- and
triple-layered core-shell nanostructures can be assembled
J Nanopart Res
(2020) 22:355
from semiconductor, dielectrics, metal, or organic/
inorganic in different possible combination (Gawande
et al. 2015; Kassahun 2019; Senthilkumar et al. 2018).
Among the widely used types of core-shell structures
is the zinc-oxide (ZnO) based nanocomposite. The
wurtzite form of zinc-oxide (ZnO) has a wide band-gap
of 3.37 eV and high exciton binding energy (∼ 60 meV)
at room temperature (Beyene et al. 2019; Aminuzzaman
et al. 2018). In addition to these bulk material properties,
ZnO nanoparticle exhibits a unique and controllable
features which makes it suitable for a variety of new/
additional potential applications in laser diodes, solar
cell, field emission displays, field effect transistor, optoelectronics devices, gas sensor, photocatalysis, antibacterial activity, and ultraviolet laser (Shao et al. 2016;
Gomez-Solís et al. 2015; Jin et al. 2019). Recently, much
effort has been devoted to study ZnO as a promising
photocatalyst for the photodegradation of waste water,
owing to its high activity, ease of morphology control,
low cost, abundance, and environmental friendly feature.
However, the drawback of ZnO NPs for photocatalytic is the large band gap and charge carrier recombination of the photogenerated electron/hole pairs that
occurs within a few nanoseconds (Galedari et al. 2017;
Zhang et al. 2019a; Xu et al. 2019; Yang et al. 2014),
and hence, its photocatalytic activity is relatively weak.
On the other hand, silica (SiO2) is used in many fields
for applications like catalysis (Galedari et al. 2017; Zhai
et al. 2010), drug delivery, chemical sensor, biomedical
(Zhai et al. 2010; Verma and Bhattacharya 2018), which
motivated us to synthesize and characterize core-shell
nanocomposites consisting of ZnO and SiO2. We believe that, this core-shell nanocomposite will enable us
to achieve novel properties resulting from the synergic
interaction of these two chemical components. In addition to providing large surface area and inhibit recombination of electron-hole pairs (Xu et al. 2019; Giesriegl
et al. 2019), SiO2 can also help to improve the dispersion properties of other third layer like noble metals on
the surface and create new catalytic active sites due to
the interaction between semiconductor photocatalysts
and SiO2. The absorption threshold of SiO2 core-shell
nanocomposites from the UV to visible light spectral
regions can be enhanced and extended by employing
various techniques such as coating by plasmonic materials (Kim et al. 2014; Pant et al. 2012; Parthasarathi
and Thilagavathi 2011). The noble metals Ag, Cu, Au,
and Pt are preferred as a coating material because they
act as a trap and assist separation of electron and hole
J Nanopart Res
(2020) 22:355
pairs, and they have high chemical stability, bioaffinity,
and strong absorption of light (Guidelli et al. 2015;
Ismail et al. 2016; He et al. 2013). Particularly, for
photocatalytic application the plasmonic Ag is used as
a shell because it has high electrical and thermal conductivity, high work-function, nontoxicity, improved
overall photocatalytic performance of its composite,
and antibacterial characteristics (Zhang et al. 2019b;
Song and Shi 2019; Zhai et al. 2019).
In the present work, we report the photocatalytic application of plasmonic triple-layered ZnO@SiO2@Ag
cylindrical-shaped core-shell nanostructures for the first
time. These rod-shaped nanocomposite samples were
synthesized by combining three methods: rapid thermal
decomposition, stöber, and precipitation. The plasmonic
Ag shell has a great role for the enhancement of
photodegradation, chemical stability, reusability, and optical absorbance. The as-prepared samples were characterized by X-ray diffraction (XRD), scanning electron
microscopy (SEM), transmission electron microscopy
(TEM), X-ray photoelectron spectroscopy (XPS), and
ultraviolet-visible (UV-Vis) spectrometer. The photocatalytic activity of the synthesized nanoparticles was analyzed by the photodegradation of methylene blue (MB)
(as a model for pollutants in waste water) under UV
irradiation. To the best of our knowledge, plasmonic
coated, rod-shaped triple layered ZnO@SiO2@Ag coreshell composite nanostructure for photocatalytic application is investigated.
Page 3 of 14 355
Synthesis of core-shell nanoparticles
ZnO nanoparticles
Initially, samples of ZnO nanoparticles were prepared according to the procedures outlined in Ref.
(Mishra et al. 2012). The zinc acetate dihydrate,
Zn(CH3COO)2.2H2O were used as a precursor material. Twelve grams of Zn(CH3COO)2·2H2O was
placed into a silica crucible and calcined at 400 °C for
two reaction times—4 h and 12 h in a muffle furnace
without any special atmospheric condition. Finally, the
resulting samples were grinded using mortar and pestle
to obtain ZnO NPs in powder form.
ZnO@SiO2 core-shell nanoparticles
The core-shell ZnO@SiO2 nanoparticles were prepared
using Stber method. About 2 g of the prepared ZnO
nanoparticles were dispersed into a mixture of 20-mL
ethanol, 9-mL deionized water, and 0.5 mL ammonia
solution (NH 4OH) under ultrasonic condition for
30 min, and then 0.5 mL of TEOS was added into the
mixture. After a reaction time of 3 h, the precipitate was
isolated using centrifuge and washed with ethanol and
water several times. The as-obtained products were
dried at 80 °C under vacuum for 2 h. The samples
synthesized using the ZnO NPs with reaction times of
4 h and 12 h at 400 °C were labeled as ZS4 and ZS12,
respectively. Both samples were grinded and prepared
for synthesis of the next triple-layered CSNS.
Materials and methods
ZnO@SiO2@Ag core-shell nanoparticles
Materials
The triple-layered ZnO@SiO2@Ag NPs were synthesized from the as-prepared ZS4 and ZS12 samples using
the precipitation method. About 0.7 mmol of
ZnO@SiO2 NPs was dispersed in 50-mL deionized
water using ultrasonication for 30 min. After sonication,
0.09 mmol of CTAB was dissolved in the solution under
constant stirring by magnetic stirrer, heated at 50 °C,
and then cooled down gradually to room temperature.
Then, 25 mL aqueous solution of 0.7 mmol of AgNO3
was slowly added dropwise to the solution, while the
mixture was continuously stirred for about 1 h. Next,
25-mL aqueous solution of 0.7 mmol of NaBH4 was
added to the resulting mixture with constant stirring to
reduce the Ag NPs. Then, the solution was centrifuged
with ethanol and deionized water. After centrifugation,
The materials used for the synthesis of ZnO@SiO2@Ag
triple-layered core-shell nanoparticles were zincacetate-dihydrate (Zn(CH3COO)2.2H2O; 99%), silver
nitrate (AgNO3, 99.8%), and tetraethoxysilane (TEOS,
Si(OC2H5)4, 98%) as precursor materials, ammonia solution (NH4OH, 25%), and sodium hydroxide (NaOH,
96%). In addition, the following materials were used:
sodium borohydrate (NaBH 4 ) as reducing agent,
c et yl t r i m e t h y l a m m on i um b r o m i d e ( C T A B ,
C19H42BrN) as capping as well as stabilizing agent,
ammonia solution (NH4OH, 25%), absolute ethanol
(EtOH, C2H5OH), methylene blue (MB, C16H18ClN3S),
and deionized water.
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J Nanopart Res
(2020) 22:355
the obtained product was dried overnight in an oven at
80 °C. Finally, the synthesized materials were grind
using mortar and pestle to obtain ZnO@SiO2@Ag
NPs in powder form suitable for characterization. The
triple-layered samples prepared using the ZS4 and ZS12
were labeled as ZSA4 and ZSA12, respectively.
where PDE is the photocatalytic degradation efficiency,
the parameters Co and Ct are the concentration of MB
dye at the initial time and at a later time, respectively.
Characterization of the samples
XRD patterns of core-shell nanostructures
To determine the crystalline phase and estimate the
crystalline size of the prepared ZnO@SiO 2 and
ZnO@SiO2@Ag NP samples, X-ray diffractometer
(XRD) (PANalytical X-pert3 power) measurements
were taken. The morphologies were characterized by
using field emission scanning electron microscopy
(SEM) (Nano Nova SEM450) and transmission electron
microscopy (TEM) (JEOL TEM-2100F). The physical
state and elemental composition of the composite were
investigated by X-ray photoelectron spectroscopy
(XPS). The optical absorption spectra were measured
by ultraviolet-visible (UV-Vis) spectrophotometer
(Shimadzu UV-2450). All the measurements were carried out at room temperature.
The crystal structures of the “bare” and Ag-coated
ZnO@SiO2 core-shell nanoparticles were investigated
by XRD analysis and the diffraction patterns were recorded in the 2θ range from 20 to 73°, as shown in
Fig. 1. It is shown from the XRD spectra that for both
core-shell NP samples ZS4 and ZS12 (i.e., ZnO@SiO2
NPs prepared at reaction times of 4 h and 12 h), the
diffraction peaks are detected at 2θ angles of 31.75°,
34.43°, 36.25°, 47.55°, 56.60°, 62.90°, 66.45°, 67.98°,
and 69.08° corresponding to the lattice planes (100),
(002), (101), (102), (110), (103), (200), (112), and
(201), respectively. It is found that all the major diffraction peaks are well matched with the standard hexagonal
wurtzite phase of ZnO (JCPDS No. 36-1451, space
group P63mc[186]) confirming the formation of a crystalline structure. Moreover, the absorption peak of SiO2
was expected around 2θ = 25° (indicated by blue arrow
in Fig. 1), but no peaks were detected. This indicates that
SiO2 is amorphous and does not change the crystalline
structure of the core material (Alzahrani 2017).
In addition, Fig. 1 depicts the XRD pattern of the Agcoated samples ZSA12 and ZSA4. Due to the Ag coating of ZnO@SiO2, additional diffraction peaks (JCPDS
No. 04-0783, space group-Fm-3m[225]) were observed
at 2θ angles of 38.13°, 44.30°, and 64.44° corresponding to the Ag lattice planes (111), (200), and (220),
respectively. In this pattern, no extra diffraction peaks
of other phases were detected, indicating the phase
purity of the composite powder. The result indicates that
the core material is successfully modified with the shell
material. Also, as shown in Fig. 1, the intensities are
increased when the duration of reaction temperature is
increased while it decreased when ZnO@SiO2 is coated
by plasmonic Ag. From this result, we understand that
the crystallite or the atomic arrangement in the crystal is
affected by temperature for prolong time (Xu et al. 2013,
Tahir and Hee Jae 2017, Terohid et al. 2018). In addition
to the duration of reaction temperature, the intensity is
decreased when the concentration of Ag is increased
(see the result of EDS). The reason for this is that Ag
Photocatalytic activity and stability of the samples
The photodegradation effect of methylene blue (MB)
dye was used to investigate the photocatalytic activity
and stability of the prepared ZnO@SiO 2 and
ZnO@SiO2@Ag samples. Accordingly, 85 mg of these
samples were suspended, each into two separate
100-mL aqueous solution of MB (10 g/L) dye which
were, in advance, prepared using deionized water. Magnetic stirrer was also used to keep the solution chemically uniform (to attain adsorption-desorption equilibrium) at dark place (Liu et al. 2015; Vignesh et al. 2019).
The mixture was poured into a photoreactor. Samples
were collected at regular time intervals (20 min) and
immediately centrifuged to remove the nanoparticles for
analysis. Finally, the UV-Vis absorption spectra of the
purified solutions were measured in the wavelength
intervals ranging from 350 to 800 nm. Moreover, the
photodegradation efficiency of methylene blue was calculated by applying the following equation (Taghvaei
et al. 2918; Salem et al. 2018; Alzahrani 2017; He et al.
2019):
PDEð%Þ ¼
C o −C t
100;
Co
ð1Þ
Results and discussion
J Nanopart Res
(2020) 22:355
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Fig. 1 XRD pattern of
ZnO@SiO2 and ZnO@SiO2@Ag
nanoparticles may be dispersed in the structure of
ZnO@SiO2 or large amount of Ag is deposited at the
surface of ZnO@SiO2 (Yousefi and Hashemi 2019).
The average crystallite size of the samples was calculated using Debye-Scherer formula, Eq. (2) (Jin et al.
2019; Kumar et al. 2018):
D¼
0:9λ
;
βcosθ
ð2Þ
where D is the average crystallite size, λ is the wavelength of the incident X-ray beam (1.540598 Å for the
Cu Kα), β is the full-width at half-maximum (FWHM)
in radians, and θ is the scattering angle (Bragg’s diffraction angle) in degrees. Accordingly, the estimated average crystallite sizes as summarized in Table 1, were
about 25.04 nm and 26.18 nm for ZS4 and ZS12, respectively; and for the triple-layered ZnO@SiO2@Ag
were 27.98 nm and 30.56 nm for ZSA4 and ZSA12,
respectively.
TEM analysis
TEM analysis reveals whether the intended nanocomposite material is formed, and in particular, it helps to
check the formation of a shell over the core NP
(Bartosewicz et al. 2017). The TEM images and the
corresponding EDS analysis of the prepared samples
are shown in Fig. 2a–f. It is observed that SiO2 NPs
are successfully deposited on the surface of the rod-like
ZnO NPs with a thickness of around 6 nm. The Ag NPs
deposited on the surface of the inner core-shell
ZnO@SiO2 as shown in Fig. 2c and d are attributed to
the electrostatic attraction between the Ag NPs and the
CTAB functionalized SiO2 NPs. However, some areas
of ZnO@SiO2 are not to “fully” covered by Ag NPs
which may due to the presence of interfacial interaction
between the SiO2 and Ag NPs. Figures 2e and f show
the EDS spectra of the ZnO@SiO2@Ag CSNCs synthesized by coating the ZS12 and ZS4 samples with Ag
NPs. The EDS analysis indicates the elemental composition of the prepared samples. Accordingly, it is confirmed from the figures that for the ZSA12 and ZSA4
samples, the elements present in the samples are Si
(7.20 wt%, 5.24 wt%), Zn (55.65 wt%, 62.03 wt%), O
(30.82 wt%, 25.85 wt%), and Ag (6.33 wt%, 6.88 wt%),
and there were no other impurities detected.
SEM analysis
The morphology of the prepared nanocomposites was
studied by using scanning electron microscope (SEM) at
different magnification for an applied potential of 10 V.
Figure 3a–d illustrates the SEM images of the
ZnO@SiO2 and ZnO@SiO2@Ag CSNPs which were
Table 1 Crystallite size of the nanoparticles prepared at a reaction
temperature of 400 °C
Samples
Reaction time, (hours)
Average size, D (nm)
ZS4
4
25.04
ZS12
12
26.18
ZSA4
4
27.98
ZSA12
12
30.56
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Fig. 2 TEM image of ZnO@SiO2 (a, b) and ZnO@SiO2@Ag (c, d) cylindrical CSNPs, and EDS result of ZnO@SiO2@Ag (e, f)
prepared at different reaction times. Due to the morphology of the initially prepared core material, (see Fig. S1),
the SEM images clearly indicate that the surface morphology of both ZnO@SiO2 and ZnO@SiO2@Ag
CSNPs are rod-shaped.
Optical study
UV-Vis absorption spectroscopy is an important technique to study the optical properties of nanocomposites.
The absorption spectra of the as-prepared ZnO@SiO2
J Nanopart Res
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Fig. 3 SEM image of ZnO@SiO2 CSNPs (ZS12, ZS4) and ZnO@SiO2@Ag CSNPs (ZSA12, ZSA4)
Fig. 4 UV-Vis absorption
spectra of ZnO@SiO2 and
ZnO@SiO2@Ag nanoparticles
synthesized from two ZnO NPs,
which are calcinated at different
reaction time
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355
Page 8 of 14
J Nanopart Res
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Fig. 5 The optical absorption
energy band gap estimated using
Tauc’s plot relation for
ZnO@SiO2 and ZnO@SiO2@Ag
CSNPs
and ZnO@SiO2@Ag samples recorded using UV-Vis
spectrophotometer at room temperature are shown in
Fig. 4. The UV-Vis spectra showed that all the four
samples exhibited maximum absorbance peak at a
wavelength of about 363 nm, which conform to the
well-known intrinsic band-gap absorption of the ZnO.
Generally, the optical absorption is related to the excitation of electrons from the valence band (VB) to the
conduction band (CB), and it is used to analyze the
optical band gap energies of the samples. Moreover,
the energy band gaps of the prepared samples were
estimated using Tauc’s relation (Encina et al. 2013;
Kumar et al. 2018),
αhv ¼ A hv−E g
0:5
;
ð3Þ
where α is absorption coefficient, hν is the incident
photon energy, A is a constant, and Eg is the band gap
energy. The optical band gap energies of the samples
Fig. 6 The survey scan XPS
spectrum of ZnO@SiO2@Ag
CSNPs
were estimated by extrapolating the straight line portion
of the graph of (αhν)2 versus hν to the hν-axis. Figure 5
shows the UV-Vis spectra of the four samples. Accordingly, the band gaps of the ZS12, ZS4, ZSA12, and ZSA4
samples are found to be 3.21 eV, 3.21 eV, 3.13 eV, and
3.13 eV, respectively.
X-ray photoelectron spectroscopy
The surface elemental composition and chemical states
of the triple-layered core-shell ZnO@SiO2@Ag nanostructures were studied using XPS technique, as shown
in Fig. 6. After calibrating by the C 1s at 284.80 eV,
which is contained in the instrument (He et al. 2014), the
survey scan XPS spectrum indicates the binding energies with the existence of Zn, Si, Ag, and O elements in
the core-shell nanocomposite. The elemental compositions of the two composites are similar to the result
obtained by EDS.
J Nanopart Res
(2020) 22:355
Figure 7a–d displays the high resolution XPS spectra
for Zn 2p, Si 2p, Ag 3d, and O 1s. Figure 7a, shows that
the binding energy of Zn 2p at 1046 eV and 1022.85 eV,
which is attributed to Zn2+ in ZnO@SiO2@Ag (ZSA12)
composite. For low reaction time of the composite
(ZSA4), the binding energy slightly shifted to higher
values due to low density of oxygen. In Fig. 7b, the peak
with the binding energy of 102.55 eV and 103.20 eV,
respectively, for ZSA12 and ZSA4 are attributed to Si 2p,
which represent the typical Si4+. Similarly, in Fig. 7c, the
two peaks with the binding energies of 373.30 eV and
Page 9 of 14 355
367.30 eV are attributed to Ag 3d3/2 and Ag 3d5/2, respectively, of Ag nanoshell in ZSA12 nanocomposite. These
two peaks for ZSA4 shifted to higher energy values by
0.83 eV. The splitting of the Ag 3d doublet at approximately 6 eV confirms that Ag is present as Ag0 in the
CSNSs (Song and Shi 2019). The peak ascribed to Ag
3d5/2 exhibit negative shift relative to pure metallic Ag,
which might be due to the interaction between Ag shell
and ZnO@SiO2 core. As we have seen from the results,
the XPS and XRD data further confirmed the formation
of Ag shell in the nanocomposites. Figure 7d shows the
Fig. 7 High resolution XPS spectra of a ZnO 2p, b SiO2 2p, c Ag 3d, and (d) O 1s
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Page 10 of 14
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Fig. 8 Percentage of degradation (a), photocatalytic activity (b), the summery of percentage of degradation and photocatalytic activity (c) of
double- and triple-layered CSNPs, and schematic of mechanism for MB degradation over the triple-layered CSNPs under UV irradiation (d)
binding energy of O 1s at ∼ 32 eV for both ZSA12 and
ZSA4 CSNSs which may be attributed to the metal bound
oxide component (O2−) of Zn2+ or Si 4+.
Photocatalytic activity and stability of the samples
The evaluation of the photocatalytic activity of the synthesized double (ZS12, ZS4) as well as the triple-layered
(ZSA12, ZSA4) core shell nanostructures were carried
out using one of the important dye, methylene blue
(MB). The metallic shells (i.e., Ag nanoparticles) were
used to make the synthesized nanocomposite chemically stable. The photocatalytic activity of the nanocomposite was evaluated by monitoring the degradation of
MB in an aqueous solution, under irradiation with UV
light. It is found out that as the irradiation time is
increased; the maximum absorption decreased slowly
and faded after 120 min of irradiation time, which
indicates the discoloration of MB or remove of waste
materials from polluted water.
When the composites were irradiated with energy
equal to or greater than the band gap energy of the
composites, electrons move to the conduction band
(CB) to generate holes in the valence band (VB). The
generation of electron-hole pairs due to radiation leads
to the formation of radicals, which are responsible for
the photodegradation of organic pollutants (Lee et al.
2016; Majhi et al. 2020). The possible photocatalytic
mechanism, for instance, for the ZSA samples, may be
described as follows:
J Nanopart Res
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Page 11 of 14 355
Fig. 9 Cyclic photodegradation
curve for the triple-layered
ZnO@SiO2@Ag CSNSs
photocatalyst
ZSA þ hv→ZSA e−CB þ hþ
VB ;
MB þ hv→M B* þ e−CB ;
e−CB þ O2 → O−2 ;
þ
hVB þ H 2 O→H þ þ OH;
−
2 O2 þ 2H 2 O→H 2 O2 þ O2 þ 2OH − ;
H 2 O2 þ e−CB þ → OH þ OH − ;
−
MB þ hþ
VB = OH= O2 →CO2 þ H 2 O þ Other:
Charge carries are expected to be produced from the
catalyst and dye. In this photodegradation reaction,
electrons from MB dye are injected to the CB of the
catalyst. The photogenerated electrons and holes are
transferred to the surface and reacted with the absorbed
reactants as shown in Fig. 8d. The photoinduced holes
and electrons are trapped O2 and H2O and produced
radicals, which are extremely strong oxidants for the
degradation of organic chemicals.
All photocatalytic degradations of methylene blue
(MB) follow pseudo-first-order degradation kinetics described by (Giesriegl et al. 2019; Liu et al. 2017):
C t ¼ C o exp ð−ktÞ;
ð4Þ
where k is the photocatalytic degradation constant (photocatalytic activity) and t is the time for degradation. As
shown in Fig. 8a, about 88.13%, 70.69%, 67.77%,
95.37%, and 90.14% of the MB dye were degraded after
120 min for ZnO, ZS12, ZS4, ZSA12, and ZSA4 coreshell NPs, respectively. As shown in the result, the
photodegradation of the composite depend on the calcination time even for one constituent, i.e., for the core
ZnO. In this case, both double- and triple-layered coreshell nanostructures which have their core material
calcined for a long time, their photodegradation activity
was found to be enhanced.
The enhancement of photodegradation activity of a
certain catalyst was studied using the LangmuirHinshelwood kinetics model (Kadam et al. 2018). Here,
to determine the degradation rates from our data, the
linear form of Eq. (4) was rewritten as (Aminuzzaman
et al. 2018; Kunarti et al. 2017), where in this form is the
slope. From this logarithmic equation, the photocatalytic
activity can be obtained from the graph of versus, as
shown in Fig. 8b. The values of for the samples ZS12,
ZS4, ZSA12, and ZSA4 were found to be 9.94 m(min)−1,
8.81 m(min)−1, 24.08 m(min)−1, and 19.27 m(min)−1,
respectively.
Cyclic stability of the triple-layered core-shell
nanostructure
A stable and reusable photocatalyst has much more
importance in the field of catalysis from the perspective
economic and environmental objectives (Yousefi and
Hashemi 2019). In this study, the cyclic stability of the
as-prepared triple-layered CSNS (ZSA12) for the photocatalytic degradation was evaluated for five catalytic
runs. After separating the photocatalyst from the degraded solution by using centrifugation method, the separated photocatalyst was washed with DI water several
times and then dried in an oven. The triple-layered
ZnO@SiO2@Ag CSNSs synthesized from ZS12 was
reused and the cyclic stability evaluated. The cyclic
stability of ZnO@SiO2@Ag CSNSs was evaluated by
monitoring the photocatalytic degradation of the same
355
Page 12 of 14
MB dye under UV irradiation. For the consecutive five
cycles, we used the photocatalyst separated from the
preceding degraded solution. As shown in Fig. 9, it was
found that the recycled triple-layered CSNPs did not
show any change in the photodegradation, even after five
cycles indicating the high chemical stability and does not
photocorrode during the photocatalytic oxidation of
model pollutant molecules (Liu et al. 2015). This new
type of composite nanostructure has excellent photocatalytic stability and reusability than Ag-doped ZnO (Raji
et al. 2018). Hence, the triple-layered ZnO@SiO2@Ag
CSNSs can be recycled and reused, which can be potentially used in practical applications. For further confirmation, we can check the stability of photocatalyst by using
XRD and FTIR techniques before and after catalytic
reactions (Vignesh et al. 2019). For the first and the last
runs, the absorption spectra changes of the UV irradiated
MB solution after centrifugation is illustrated in Fig. S2
and Fig. S3, respectively (see Supplementary data). As
shown in these figures, the absorption intensity peaks in
both cases were observed at the wavelength of about ∼
664 nm.
J Nanopart Res
(2020) 22:355
the opportunity for broad-band absorption and light harvesting applications.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s11051020-05086-0.
Funding This work is supported by financially by the NSFC
(11474246, 11750110415, 11850410442), the Natural Science
Foundation of Jiangsu Province (20KJA430004), Addis Ababa
University (AAU), and Adama Science and Technology University (ASTU).
Compliance with ethical standards
Conflict of interest The authors declare that they have no conflict of interest.
Disclaimer The funders had no role in the design of the study; in
the collection, analysis, or interpretation of data; in the writing of
the manuscript, and in the decision to publish the results.
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affiliations.
AIMS Materials Science, 7(6): 705–719.
DOI: 10.3934/matersci.2020.6.705
Received: 25 August 2020
Accepted: 13 October 2020
Published: 30 October 2020
http://www.aimspress.com/journal/Materials
Research article
Effect of core size/shape on the plasmonic response of spherical ZnO@Au
core-shell nanostructures embedded in a passive host-matrices of MgF2
Gashaw Beyene1,2,*, Gamachis Sakata1,3, Teshome Senbeta1, and Belayneh Mesfin1
1
2
3
Department of Physics, Addis Ababa University, Addis Ababa, Ethiopia
Applied Physics Program, Adama Science and Technology University, Adama, Ethiopia
Department of Physics, Metu University, Metu, Ethiopia
* Correspondence: Email: gashaw.beyene@astu.edu.et; Tel: +(251)920218531.
Abstract: In this paper, we investigated the effect of shape and size of core on the plasmonic
response of spherical ZnO@Au core-shell nanostructures embedded in a passive host matrices of
MgF2 within the framework of the qausistatic approximation. The absorption cross-section and local
field enhancement factor of spherical ZnO@Au core-shell nanostructures are effectively studied by
optimizing the parameters for a fixed composite diameter of 20 nm. In this two-layered core-shell
nanostructures, four plasmonic resonances are found; the first two resonances associated with
ZnO/Au and Au/MgF2 interfaces, whereas the third and fourth resonances are associated with the
transverse and longitudinal modes, respectively. The peaks position and intensity of these resonances
are varied by optimizing the shape and size of the core material. The tunability of the plasmon
resonances of the composite systems enables it to exhibit very interesting material properties in a
variety of applications extending from the visible to infrared spectral regions.
Keywords: host-matrix; spherical core-shell; surface plasmon resonance; absorption cross-section;
dielectrics function; polarizability
1.
Introduction
Nowadays, due to the development of nanotechnology, new materials called nanocomposites
have attracted the attention of scientific communities. Nanocomposite materials are made of two or
more constituent materials having significantly different optical, plasmonic, catalytic, biological,
physical, and chemical properties [1–3], that, when combined, produce a material with a
706
characteristic different from the individual components. In a composite material, one of the
constituents is a continuous matrix which is called a host matrix while the others dispersed in the
host matrix are called inclusions or fillers.
Among the nanoinclusions, core-shell nanoparticles (CSNPs) that consists of two or more
nanomaterials by using encapsulation process are widely employed to obtain a new material with
combined and/or other unique properties neither shown by the components [4–6]. This new or
unique properties mainly arise from the interaction of plasmonic shell materials with the
electromagnetic field, which is greatly intensified by a phenomenon known as the surface plasmon
resonance (SPR) and the interaction of plasmon of the metallic shell with plasmon/exciton/plariton
of the inner material [7,8]. The plasmonic properties of the composite strongly depend on the
geometry, size, composition, and dielectric function (DF) of the host matrix [7,9,10]. The shell
material has a protective effect on the inner material; such as dissolution, corrosion, enhancement of
the structural stability, and can also impart its plasmonic, catalytic, magnetic, and optical properties
and functions to the inner material.
Recently, noble metal nanoparticles (NPs) (like Ag, Au, Cu, Pt) have attracted the attention of
the researchers due to their unique catalytic, electronic, plasmonic and optical properties [11] as well
as their high chemical stability, bio-affinity, strong absorption of light from visible to infrared (IR)
regions [1,12,13], which are dominated by the localized surface plasmon resonance (SPR) [14]. In
addition to these properties, the potential applications of noble metal NPs are preferable as coating
material.
As stated above, CSNPs have unique/new properties and such unique, useful and tailorable
properties have also advanced CSNPs as a very important class of emerging nanocomposites for a
wide range of applications in, for instance, catalysis, biomedical, energy/data storage, solar cell,
antibacterial, renewable energy, photonics, electronics [15–23]. With all these advantages, core-shell
nanostructures (CSNSs) have been broadly investigated experimentally and/or theoretically [4,24,25]
by many research groups in the past decade and applied to a wide variety of fields. CSNPs can be
assembled from metals, semiconductors, dielectrics or organic/inorganic materials; one used as a
core and another or the same material used as a shell [7,21,26,27].
In this paper, the authors studied the effect of core size/shape on the plasmonic properties of
spherical ZnO@Au core-shell nanostructures embedded in passive host matrix, with highly tunable
plasmonic response of the composites. The shell metal, i.e., Au NP, has been investigated most
extensively because of its high catalytic, universal biocompatibility, optical sensitivity, facile
preparation, resistance to oxidation, and surface plasmon resonance (SPR) band that can absorb and
scatter visible light relative to other noble metals [28]. ZnO NP is wurtzite zinc oxide wich has wide
band gap (3.37 eV), high exciton binding energy (~60 meV) at room temperature, and high dielectric
constant [29–31], and it is reliable material for visible and near-UV applications [29,30]. ZnO NP
has attracted extensive attention due to its potential applications in laser diodes, solar cells, fieldemission displays, light emitting diodes, optoelectronics devices, photovoltaic cells, gas sensors,
photo-catalysis, ultraviolet lasers [32–34]. ZnO nanoparticles have been experimentally synthesized
for various applications with different morphologies; like rod shape [34–37], flower like shape [38–40],
spherical shape [34,35,41,42], ellipsoidal shape [42–46], tube like structure [47], and plate/sheet like
shape [34,48]. Due to this noble properties, different morphologies, and noble applications of
ZnO and Au NPs, core-shell combination of them is a desirable way to generate new/unique
properties and enhanced applications. Indeed, ZnO@Au CSNSs have been investigated for various
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applications [28–34,49,50] and display improved properties. In the present work, the plasmonic
resonance of ZnO@Au CSNSs is shown to be tuned from visible region to infrared spectral regions.
To the best of our knowledge, the plasmonic response of spherical ZnO@Au CSNSs by varying the
core shape and size for a fixed composite size embedded in the passive host-matrix of MgF2 is not
reported yet. The authors choice MgF2 as a host matrix, which is good transparent over a wide range
of wavelengths and used to optical coating. MgF2 is low refractive index, high band gap energy,
antireflective, stable, and light polarizer material, which is a promising candidate for the desired
optical performance and future investigation [51–54].
In this work, mainly the absorption cross-section and local field enhancement factor (LFEF) of
noble metal Au-coated ZnO nano-composite with the diameter of composite of 20 nm is
systematically studied by optimizing the size and shape of the ZnO core. For the nanocomposites
which have the size <40 nm, the quasistatic limit is an appropriate method to study the plasmonic
response and the dipolar mode resonance is more enhanced than the other higher-order multipoles.
The paper is organized as follows: in Section 2, we will discuss the basic idea of nanoinclusion
with a representative model by using electrostatic approximation. Section 3, describes the plasmonic
response of spherical core-shell nanostructures: absorption cross-section and local field enhancement
factor by optimizing the parameters. Finally, the main result of the work is summarized in Section 4.
2.
Theoretical model and calculation
The plasmonic properties of two-layered core-shell nanoparticles consisting of a core and shell
can be successfully described within the framework of classical electrodynamics of continuous
media. Consider an array of spherical core-shell nanoparticle consisting of a semiconductor core
(ZnO) of dielectric function (DF) 𝜀𝒄 , and a metallic shell (Au) of DF  s embedded in a nonabsorptive (passive) host matrix having a real DF  m , as shown in Figure 1, i.e., cross-sectional view
of the composite. As shown in the figure, the composite is spherical shape with fixed radius 10 𝑛𝑚
𝑎
𝑡
𝑎
𝑡
10 𝑛𝑚), however, the core is oblate Figure 1a and prolate Figure
(i.e., 𝑏 𝑡
1b with semi-principal axes 𝑎 , 𝑎 , and 𝑏. The thickness of the Au-shell is not homogeneous due to
𝑡 ,𝑎
𝑎
𝑏 for oblate core and (ii) 𝑡
𝑡 ,
the alignment of ZnO core nanoparticles: (i) 𝑡
𝑎
𝑎
𝑏 for prolate core.
Figure 1. (Color online) The cross-sectional view of spherical CSNSs embedded in the
dielectrics host medium of MgF2: oblate core (a) and prolate core (b).
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When the system is irradiated (placed in) with an electromagnetic field, assumed to be polarized
along 𝑥𝑦 plane (along 𝑏, see Figure 1), the applied filed causes the polarization of the system. As
explain in Eq 1, the effective polarizability 𝛼 of the system depends on the dielectrics function of
the constituents, which can be expressed as [55]:
𝛼
𝑉
(1)
where 𝑉 is the volume of the core-shell nanocomposite, 𝑓 is the fraction of the total volume occupied
by the core (or core concentration); 𝐿 and 𝐿 , are the depolarization factors of the composite (core +
shell) and core, respectively, and the subscripts 𝑖 1, 2, 3 refer to the longitudinal (𝑖 1) and
transverse modes (𝑖 2, 3). The other parameters in Eq 1 are given from Eq 2 to 4 as
𝑓
𝐴
(2)
𝜀
𝜀
𝜀
𝐿
𝑓𝐿
𝐵
𝜀
𝜀
𝐴
(3)
(4)
The polarization factor of the spherical shape is 𝐿
𝐿
𝐿
1/3, while the polarization factors
of the spheroidal shapes (oblate and prolate) depend on the ellipticity (𝑒). For the spheroidal prolate
core, the polarization factors along the 𝑏, 𝑎 , and 𝑎 axes, respectively, are given by Eqs 5 and 6 [56]:
𝑙𝑛
𝐿
𝐿
𝐿
1
0.5 1
𝐿
(5)
(6)
where the ellipticity of the prolate core is given by Eq 7
𝑒
1
(7)
Similarly, the corresponding depolarization factors for the oblate spheroidal core are given by Eqs 8
and 9 [57]:
𝐿
𝑎𝑟𝑐𝑡𝑎𝑛 𝑔
𝐿
𝐿
0.5 1
where the ellipticity of the oblate core is given by Eq 10
𝑒
1
(8)
𝐿
,𝑔
(9)
(10)
The aspect ratios (ARs) of the prolate and oblate core ZnO nanoparticles are defined by 𝐴𝑅 𝑏⁄𝑎
and 𝐴𝑅 𝑎 ⁄𝑏, respectively.
In the quasistatic limit, the extinction cross-section 𝜎 of the ensembles (systems) have the
form of Eq 11:
𝜎
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𝜎
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709
where 𝜎 and 𝜎
rspectively
are the absorption and scattering cross-sections defined by Eqs 12 and 13,
𝜎
𝜆
𝜎
𝜆
∑
𝐼𝑚 𝛼 𝜆
|𝛼 𝜆 |
∑
(12)
(13)
where 𝑘 is a parameter which depends on the wavelength (𝜆) of the incident light (see Eq 14). That is,
𝑘
𝜀
(14)
The local electric field inside the composites can be enhanced due to the difference between the
dielectric properties of the two materials ZnO/Au and Au/MgF2 as well as the surface plasmon
resonance of the Au-shell. The local field enhancement factor (𝐹) is defined as the ratio of the
intensities of the electric field around the composite to the applied electric field. The square of the
local field enhancement factor (LFEF) (|𝐹| ) of the nanocomposite is expressed as Eq 15 [58]:
|𝐹|
| |
|
1
|
(15)
where 𝐸 is the electric field inside the composite, 𝐸 is the applied electric field, and 𝑟 is the radius
of the composite.
3.
Numerical result and discussion
For the dimension of composite less than the wavelength of the incident light, the quasistatic
approach is appropriate for the calculation of the polarizability and then the absorption cross-section
and local field enhancement factor. For small size composite, the incident electric field may be
regarded as being spatially uniform over the extent of the particle; so that the particle can be replaced
by an oscillating dipole and this is referred to as the quasistatic approximation. In this study, the
observed spectra of the two-layered spheroidal core of spherical core-shell nanostructures extends
from the visible to the infrared (IR) spectral region, i.e., between 400–1300 nm. In this type of
composite nanostructure, four plasmonic resonances are observed, two resonances corresponding to
the two interfaces (ZnO/Au and Au/MgF2) and the other two resonances corresponding to the two
oscillating modes [55,58,59].
Below, we theoretically investigated the effect of the core material’s size and shape on the
plasmonic response of ZnO@Au core-shell composite nanostructures. For numerical calculations,
we considered a system that consists of spherical nanocomposite ZnO@Au with spheroidal core ZnO
dispersed in MgF2 host of DF 𝜀
1.98. In the frequency domain of interest, we assumed that the
DF of the ZnO core to be a real constant that is independent of frequency (𝜀
8.5) [31]. In addition,
the DF of the Au-shell is chosen to be of the Drude form as written in Eq 16.
𝜀 𝜔
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where 𝜀∞ 9.84 is the phenomenological parameter describing the contribution of bound electrons
to the polarizability, 𝜔
9.01 𝑒𝑉 is the bulk plasmon frequency, and 𝛾 0.072 𝑒𝑉 is the damping
constant of the bulk material [9].
3.1. Absorption cross-section
Among the parameters which affect the plasmonic properties of nanocomposites are the size
and shape of the core material. Here, we investigated the plasmonic response of spherical core-shell
nanostructures by optimizing the core shape to oblate-prolate-spherical and also its size for a fixed
composite size.
Absorption cross-sections of the oblate core spherical core-shell nanostructure as a function of
wavelength are depicted in Figure 2, for non-uniform Au-shell material distribution. In addition to
core shape and size, the non-uniform distribution of the coating material on the surface of the inner
material also affects the palsmonic response of the composite. Figure 2a, shows the simulated 𝜎
spectra of the oblate core spherical CSNSs when the 𝐴𝑅 values are 1.57, 1.50, 1.44, 1.39
corresponding to the core concentrations (𝑓) of 61.94%, 57.04%, 52.94%, 48.94%, respectively. The
parameters are derived by removing some portion of core ZnO from 𝑥 and 𝑧 direction, while the
𝑦 direction is kept constant. The first two resonance peaks (located between 340–500 𝑛𝑚 )
correspond to the surface plasmon resonances of the Au-shell at the inner and outer interfaces. The
peaks of these two resonances are found to increase as well as blue- and red-shifted, respectively,
with a decrease of the core concentration. The third and fourth set of resonance peaks (around 600
nm and 1000 nm, respectively) are due to the polarization of charges along the principal axes of the
spheroid core ZnO. In particular, the third resonance peaks are associated with the transverse
plasmon mode (TM), while the fourth peaks correspond to the longitudinal mode (LM). The peaks of
the TM mode are increased and blue-shifted when the core’s aspect ratio is decreased. However, the
peaks of the LM mode decrease and are red-shifted with a decrease of the core’s aspect ratio.
Here, in order to compare the plasmonic response of different size of oblate core by keeping
0.1 𝑛𝑚 remain the same, the absorption cross-section of the composite is depicted in Figure 2b.
𝑡
Here, the size of core is changed by increasing the core thickness along the 𝑦 direction (or along 𝑏
dimension); i.e., by decreasing 𝑡 . Due to this, the aspect ratio of the core are changed to 1.57, 1.54,
1.52, 1.50, and correspondingly the concentrations of the ZnO core are 61.94%, 62.94%, 63.90%,
64.88%. Accordingly, two resonances are observed associated with the interfaces of the metallic
shell: the first resonances corresponding to the inner interface and the second resonances associated
with the outer interface. The peaks of these two resonances are increased without shifting. The
remaining third and fourth resonances, associated with the transverse and longitudinal plasmon
resonance, respectively, are the same as that obtained in Figure 2a; but, the third peaks resonance
slightly shifted and the fourth resonance peaks are more shifted to higher wavelength. When the
electromagnetic wave interacts with the composite, positive and negative charges are generated; the
induced charges move and are collected on the surface of the inner and outer materials. The
interaction that arises due to the separation of these positive and negative charges is more
pronounced when the size of the core becomes bigger or the shell thickness is decreased. Due to this,
the resonance peaks associated with the inner interface are more enhanced than the other resonance
peaks, as shown in the figure.
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Figure 2. (Color online) The absorption cross-sections for oblate core ZnO spherical
ZnO@Au CSNS; (a) 𝑡 = 3.68 nm, 𝐴𝑅 = 1.57, 1.50, 1.44, 1.39 and (b) 𝑡 = 0.1 nm, 𝐴𝑅 =
1.57, 1.54, 1.52, 1.50.
The plasmonic response of ZnO@Au CSNSs is also varied by changing the oblate core to a
prolate shaped core. The absorption cross-section of the CSNSs with prolate core materials is depicted
in Figure 3, for a fixed size of nano-composites. As shown in the Figure 3a, the absorption crosssection of the system with prolate core is investigated by removing some portion from 𝑦 axis, so
that the aspect ratios of the ZnO NPs are 1.31, 1.26, 1.19, 1.13 with the corresponding concentrations
being 56.28%, 54.01%, 51.17%, 48.32%, respectively. From the figure, it is seen that when the
concentrations of the ZnO NPs are increased, all peaks of the plasmon resonances are increased
except the first resonances which are associated with the inner interface of the shell. Moreover, both
the TM and LM peaks of resonances are increased and blue-shifted. Note that the dipolar modes are
accompanied by higher-order multipoles modes, such as the fifth peaks (indicated by arrow head)
associated with quadrapole appear between the peaks of the inner and outer interface’s resonances.
These fifth resonances are more enhanced for higher aspect ratios, as shown in both Figure 3a,b.
As shown in Figure 3b, when 𝑡 is decreased from 2.46 to 0.96 nm with the concentration of
ZnO being 56.28%, 64.00%, 72.20%, 80.90%; i.e., the core material becomes spherical and the shell
becomes thinner, the first two resonance peaks are increased and shift towards each other, whereas
the peaks of the TM and LM resonances are decreased and red-shifted. The resonance with high
tunability of nanocomposite from near UV to near IR spectral regions is used for biomedical
application [60].
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Figure 3. (Color online) The absorption cross-sections for prolate core ZnO spherical
ZnO@Au CSNS; (a) 𝑡 = 2.46 nm, 𝐴𝑅 = 1.31, 1.26, 1.19, 1.13 and (b) 𝑡 = 0.1 nm, 𝐴𝑅 =
1.31, 1.23, 1.16, 1.10.
Furthermore, to see the effect of shell thickness on the optical response of the ZnO@Au CSNSs,
we investigated both systems by fixing the core size while increasing the shell thicknesses.
Accordingly, in the numerical analysis the size of the composites is changed from 10 to 13 nm (with
a range of 0.5 nm) without changing the shape and size of the core material. Figure 4 shows the
absorption cross-section as a function of the incident wavelength for different shell thickness. For the
two morphologies (i.e., ZnO@Au CSNSs with oblate and prolate cores are depicted in Figure 4a,b,
respectively), the optical responses are almost the same. Except for the first resonances,
all plasmonic resonance peaks are enhanced, when the thickness (𝑡 and 𝑡 are increased with the
range 0.5 nm) is increased or when the concentration of ZnO is decreased. The corresponding
concentration of the ZnO NP is summarized in Table 1. The plasmonic resonance associated with the
interface of the host medium and shell materials is highly enhanced accompanied with red-shifts,
whereas the resonance peaks associated with the transverse and longitudinal modes are enhanced and
blue-shifted. As shown in Figure 4b, the third resonance peaks corresponding to the TM are
becoming diminished which is dominated by the resonance of the LM.
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Figure 4. (Color online) The absorption cross-sections for a fixed core size of ZnO@Au
core-shell nanostructures; for (a) oblate with b/𝑎 /𝑎 = 6.32/8.8/8.8 nm and (b) prolate
with 𝑎 /𝑎 /b = 8.54/8.54/9.5 nm.
Table 1. The concentration of ZnO for the increment of 𝑡 and 𝑡 , simultaneously.
Shape
Oblate
Prolate
Concentration (%)
48.94
42.28
69.29
59.85
36.77
52.06
32.18
45.56
28.32
40.10
25.06
35.47
22.28
31.54
In addition to the oblate and prolate core spherical ZnO@Au CSNSs, the plasmonic properties
of the spherical core is also studied for the same size of nanocomposite. As shown in Figure 5, the
plasmonic response of the spherical shape with different size: the first plasmonic peaks associated
with the inner interface are decreased without shifting; while the second peaks associated with the
outer interface are increased and red-shifted. For the spherical core nano-composite, the charge
distribution on each surface is the same; in the special case, due to the separation of positive and
negative charges on surface of the core and shell, respectively, or vice versa, the third resonances are
observed. The peaks of these resonances are increased with a decrease of the core concentration or
an increase of the shell thickness.
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Figure 5. (Color online) The absorption cross-sections of spherical core ZnO@Au core𝑡
1.1, 1.5, 2.0, 2.5 𝑛𝑚).
shell nanostructures for different shell thicknesses (with 𝑡
The corresponding concentrations of the core ZnO NPs are 70.41%, 61.41%, 51.20%,
42.19%, respectively.
3.2. Local field enhancement factor
When an electric field is applied to the core-shell structure, charges are induced which resides
on the core’s surface as well as the surface of the shell material. This separation of negative and
positive charges on the surfaces results in the generation of internal electric field. The electric field in
the composite is the superposition of the applied field in the composite and the generated electric
field. The electric field in the composite is much larger than the local electric field. The enhancement
of electric field in the composite depends on the shape as well as the size of the core materials or the
separation distance of holes and electrons.
The local field enhancement factor for oblate, prolate, and spherical shaped CSNSs having
different sizes is depicted in Figure 6. For the oblate core ZnO@Au CSNSs, as the thickness is
increased the local field enhancement factor is enhanced and shifted apart for the first and second set
of resonances (see Figure 6a). Similar to that in Figure 2a, with an increase of thickness the peaks of
the TM resonances increase and blue-shifted, while the peaks of the LM resonances decrease and
red-shifted. As shown in the Figure 6b, the first resonances decrease, whereas the second resonances
increase without shifting. However, the peaks of the TM and LM resonances are seen to increase and
blue-shifted when the concentration of the core is decreased.
Figure 6c illustrates the local field enhancement factor of spherical ZnO@Au core-shell
nanostructure with spherical core. The first peaks of resonance decrease, whereas the second peaks
of resonance increase and shifted to higher wavelengths when the core concentration is decreased.
The third peaks of resonance associated with induced charge separation are seen to decrease with a
decrease in core concentration. It is worth noting that as the shell thickness is increased (i.e., charge
separation distance is increased), the electric field developed in the composite is decreased.
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Figure 6. (Color online) Local filed enhancement factor for different core shape and size;
(a) oblate core, (b) prolate core, and (c) spherical core. The other parameters are similar
to that used in Figure 2a, Figure 3a, and Figure 5, respectively, for (a), (b), and (c).
Generally, these results are directly or indirectly related to the interaction of the plasmons of the
metallic shell with the polaritons of the core material. In particular, when the size of the core material
is becoming bigger for the same size of nanocomposite, the interaction between the plasmons and
polaritons gets stronger and vice versa.
4.
Conclusions
In this work, we studied the effect of shape and size of the core material on the plasmonic
response of two-layered spherical ZnO@Au core-shell nanostructures embedded in the passive hostmatrices of MgF2 using the method of quasistatic approximation. In particular, the absorption crosssection and local field enhancement factor (LFEF) of the nanocomposites of fixed radius (𝑟
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10 𝑛𝑚) are investigated as a function of the wavelength of the incident light. For both the prolate
and oblate core spherical ZnO@Au CSNSs, the absorption cross-sections as well as the enhancement
factor possess four plasmonic resonances with peaks extending from the visible to infrared spectral
regions. The first and second peaks of the resonances are associated with the inner and outer
interfaces of Au-shell; i.e., ZnO/Au and Au/MgF2 interfaces, whereas the third and fourth peaks of
the resonances are associated with the transverse and longitudinal modes of resonances, respectively.
The peaks position, enhancement of the resonances, and shifting of resonance peaks depend on the
shape and size of the ZnO core, the shell distribution on the inner material, and shell thickness. Note
that the results obtained show that the two-layered spherical ZnO@Au CSNSs, which are composed
of a semiconductor core of ZnO coated by thin Au NPs exhibit high tunable optical responses that
extends from the visible to infrared spectral regions, and hence can be ideal candidates for enhancing
biological, solar-cell, catalysis, renewable energy, and energy storage applications.
Acknowledgements
This work is supported financially by the Addis Ababa University and Adama Science and
Technology University
Conflicts of interests
The authors declare no conflict of interest. The funders had no role in the design of the study; in
the collection, analysis, or interpretation of data; in the writing of the manuscript, and in the decision
to publish the results.
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© 2020 the Author(s), licensee AIMS Press. This is an open access
article distributed under the terms of the Creative Commons
Attribution License (http://creativecommons.org/licenses/by/4.0)
AIMS Materials Science
Volume 7, Issue 6, 705–719.
Optical and Quantum Electronics
(2020) 52:157
https://doi.org/10.1007/s11082-020-2263-4
Plasmonic properties of spheroidal spindle and disc
shaped core–shell nanostructures embedded in passive
host‑matrices
Gashaw Beyene1,2 · Teshome Senbeta2 · Belayneh Mesfin2 · Qinfang Zhang1
Received: 12 August 2019 / Accepted: 12 February 2020
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
Metal coated semiconductor nanoparticles are excellent absorbers or scatterers of electromagnetic radiation, depending on their shape, size, material composition, and the refractive
index of the host medium. In this work, we investigated the optical and plasmonic properties of spheroidal spindle- and disc-shaped ZnO@Ag core–shell nanocomposites embedded in a dielectric passive host-matrix by varying the size, thickness of the metallic shell,
and the dielectrics function of the host matrix. The theoretical and numerical analysis is
carried out for the core–shell nanoparticles having volume less than 1.34 × 105 nm3 within
the framework of quasistatic approximation. We found that the core–shell nanoparticles
possess four resonances—two of which correspond to the silver/core and silver/host-matrix
interfaces, while the other two correspond to the bonding/antibonding pairs due to separation of charges in the composite along the principal axes. The tunability of the plasmon
resonances of the composite system enables it to exhibit very interesting material properties in a variety of applications extending from the UV to near-infrared spectral regions.
The wavelength of disc-shaped core–shell nanostructure exhibits a red-shift relative to the
spindle-shaped one for both longitudinal and transverse resonance modes.
Keywords Core–shell nanostructure · Absorbtion cross-section · Surface plasmon
resonance · Longitudinal and transverse mode
* Gashaw Beyene
gashaw4nuclear@gmail.com
Teshome Senbeta
teshomesenbeta@gmail.com
Qinfang Zhang
qfangzhang@gmail.com
1
School of Material Science and Engineering, Yancheng Institute of Technology, Yancheng,
P.R. China
2
Department of Physics, Addis Ababa University, Addis Ababa, Ethiopia
13
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G. Beyene et al.
1 Introduction
Core–shell nanosystems essentially involve two or more particles/compounds formed
by using the encapsulation process in different shape and size to obtain a new composite material with combined properties and other unique properties neither shown by
the constituents core nor shell nanostructures (NSs) (Kim et al. 2014). Incorporating
nanoparticles (NPs) in complex, multilayer, or core–shell nanostructures have attracted
significant interest. These particles, can offer additional opportunities for innovation
with tailored materials in the fields of physics, nanomaterials, biomedical nanosystems, optical, chemical and biological sensors (Loo et al. 2015), magnetic nanocomposite (Shahamirifard et al. 2017), engineering chemistry (Shah et al. 2016) photocatalysts (Grady et al. 2004), solar cells (Pillai et al. 2006), and electrical nanosystems. This
unique property that originates from the confined spatial distribution of the polarization
charges over the surface of the nanostructure is taken as one of the main secret of their
potential applications. Among these special structures, the core–shell structure is a particular class of NPs, consisting of a core and one or more shell layers.
Recently, noble metal nanoparticles (NPs) have attracted the attention of the scientific community due to their unique catalytic (Chen and Goodman 2006), electronic
(Yang et al. 2004), plasmonic and optical (Wilcoxon and Abrams 2006) properties as
well as they have high chemical stability, bio-affinity, strong absorption of light (Beyene
et al. 2019), which are dominated by the localized surface plasmon resonance (SPR).
Beside thse properties, the key concept in the field of plasmonic is the SPR - a collective resonant oscillation of the conduction electrons in the metal confined to the interface between the metal and a dielectric (or semiconductor), which are described by evanescent electromagnetic waves that are not necessarily located at the interface (Noguez
2007). SPR spectra of the composite nanoparticles have been shown to vary with the
particle size, shape, composition, and the surrounding medium (Jain and El-sayed 2007;
Chen and Johnston 2009; Kassahun 2019).
Different types of core–shell nanoparticles (CSNPs) based on various core and shell
materials have been investigated, including CSNPs with metal@metal, metal@dielectrics, and dielectrics@metal, as well as dielectrics@dielectrics structures (Senthilkumar 2018). In particular, ZnO@noble-metal CSNPs possess a wide variety of potential
applications in many developing technologies (Gorokhova et al. 2018; Pal et al. 2016).
It is found that surface coating with noble metals like Ag, Au, Cu, or Pt can dramatically change the properties of ZnO nanocrystallites as well as its applications. Silver
nanoparticles with thicknesses ranging between 5 and 10 nm are widely preferred as
a shell material on ZnO nanospindle and nanodisc due to its non-toxicity (Zeng et al.
2016), strong absorption in/near visible spectrum (Sambou et al. 2016), high electrical and thermal conductivity, high work function, antibacterial characteristics, and cost
effectiveness (Zeng et al. 2016).
For spheroidal shaped CSNSs embedded in a host matrix, three plasmon resonance
frequencies are expected; corresponding to the oscillation of electrons along the three
axes. The resonance wavelength depends on the orientation of applied filed relative to
the particle. In addition to this, by changing the axes length, the plasmon resonance
wavelength of the nanospheroid can be turned systematically. Recently, a large variety of new synthesis methods have been developed to fabricate elongated (Oliver et al.
2006) as well as flattened CSNSs. In view of the interesting material properties of
CSNPs described above, we seek to further investigate theoretically and numerically the
13
Plasmonic properties of spheroidal spindle and disc shaped…
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157
optical and plasmonic properties of prolate (spindle) and oblate (disc) shaped ZnO@
Ag core–shell NPs embedded in a dielectric host matrix by varying the core size, shell
thickness, size of the composite and the host medium.
The paper is organized as follow: In Sect. 2, theoretical description of a spheroidal
(spindle and disc) ZnO@Ag core–shell NPs are carried out using the electrostatic approximation. Numerical analysis and results are presented in Sect. 3. Finally, in Sect. 4 concluding remarks are given.
2 Theoretical model of spheroidal core–shell nanostructure
The optical as well as plasmonic properties of two layer nanoparticles consisting of a core
and shell can be successfully described within the framework of classical electrodynamics of continuous media. Consider an array of spheroidal core–shell composite nanoparticles consisting of a semiconductor core and a metallic shell embedded in a non-absorbing
(passive) host matrix of the dielectrics function (DF) ɛc, ɛs, and ɛh (real), respectively, as
shown in Fig. 1a. Figure 1b depicts the cross-sectional views of prolate and oblate shaped
core–shell nanocomposite. The core ellipsoidal NPs are characterized by shell thickness t
and semi-principal axes a1, a2, and a3 with (i) a1 > a2 = a3 for prolate and (ii) a1 < a2 = a3 for
oblate. Note that the prolate (spindle-shaped) spheroid can be generated by the rotating an
ellipse about its major axis (a1 in Fig. 1b(i)), while the oblate (disc-shaped) spheroid may
be generated by rotating an ellipse about its minor axis (a1 in Fig. 1b(ii)).
Fig. 1 (Color online) The array (a) and the model (b) of core–shell nanostructure, with prolate (b(i)) oblate
(b(ii)) shaped CSNS embedded in passive host matrix
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G. Beyene et al.
Page 4 of 12
The polarizability of the composite depends on the dielectric function of constituents
i.e.,𝜀c , ɛs, and ɛh. When the system is irradiated with electromagnetic waves, assumed to
be polarized along the xy plane (along a1 in Fig. 1b), the applied field causes the polarization of the system. The effective polarizability αi of the system can be shown to have
the form (Beye et al. 2017; Liu and Guyot-Sionnest 2006):
]
[
(
)
B + f 𝜀s 𝜀c − 𝜀s
𝛼i = V s
) ,
(
(1)
Li B + A𝜀h + fLis 𝜀s 𝜀c − 𝜀s
where V is the volume of the core–shell nanocomposite; f is the fraction of the total volume
occupied by the core (or core concentration); Lsi and Lci , are the depolarization factors of the
composite (core + shell) and core respectively, i = 1, 2, 3 refer to the longitudinal (i = 1) and
transverse (i = 2, 3) modes. The other parameters in Eq. (1) are given by
)(
)(
)
4𝜋 (
a1 + t a2 + t a3 + t ,
3
a1 a2 a3
f = (
)(
)(
),
a1 + t a2 + t a3 + t
(
)(
)
(
)
A = 𝜀s + 𝜀c − 𝜀s Lic − fLis , B = 𝜀s − 𝜀h A.
V=
It is worth noting that in the frequency domain of interest, we assumed that the DF of
the ZnO core to be a real constant (ɛc = constant) independent of frequency, whereas the
DF, 𝜀s = 𝜀s1 + i𝜀s2 , of the silver shell is chosen to be of the Drude form. That is,
𝜀s (𝜔) = 𝜀∞ −
𝜔2p
𝜔(𝜔 + i𝛾)
,
(2)
where ɛ∞ is the permittivity at high frequency, ωp is the plasma frequency, γ is the electron collision frequency (damping constant describing dissipative losses), and ω is the frequency of the incident radiation.
For convenience, we introduce the following notations ac = a2 = a3, as = a2 + t = a3 + t,
cc = a1, and cs = a1 + t; for both prolate and oblate spheroids (refers to Fig. 1b).
For prolate spheroid, the depolarization factors along a1, a2, and a3 axes, respectively, are given by (Beye et al. 2017)
L1s,c =
)
]
(
1 − e2s,c [ 1
1 + es,c
−
1
ln
,
2es,c
1 − es,c
e2s,c
(3)
(
)
L2s,c = L3s,c = 0.5 1 − L1s,c ,
(4)
where the subscripts ‘c’ is for the core and ‘s’ is for the composite (core + shell), and es,c
are the ellipticity of the core and the composite, respectively, which are defined by
e2s,c = 1 −
a2s,c
c2s,c
.
(5)
Similarly, the corresponding depolarization factors for oblate spheroid are given by
(Kajikawa 2013),
13
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Plasmonic properties of spheroidal spindle and disc shaped…
2
Ls,c
=
] g2
g [𝜋
−
arctan(g)
− ,
2
2e2s,c 2
(
)
L2s,c = L3s,c = 0.5 1 − L1s,c ,
157
(6)
(7)
where
e2s,c = 1 −
c2s,c
a2s,c
, g2 =
1 − e2s,c
e2s,c
.
(8)
The aspect ratio (AR) of the prolate and oblate nanoparticles are defined by
ARc = cc/ac = a1/a2, ARc = ac/cc = a2/a1 for the cores and ARs = cs/as = (a1 + t)/(a2 + t) and
ARs = as/cs = (a2 + t)/(a1 + t) for the composite, respectively.
In the quasistatic limit, the extinction cross-section σecs of the ensemble (system) has the
form:
𝜎ecs = 𝜎acs + 𝜎scs ,
(9)
where σacs and σscs are the absorption and scattering cross-sections defined by;
𝜎acs (𝜆) =
3
]
k∑ [
Im 𝛼i (𝜆) ,
3 i=1
(10)
𝜎scs (𝜆) =
3
k2 ∑ |
2
𝛼 (𝜆)| ,
18𝜋 i=1 | i |
(11)
and
where k is a parameter which depends on the wavelength (λ) of the incident light. That is,
k=
2𝜋 √
𝜀h .
𝜆
(12)
Furthermore, among the important parameters that are used to characterize the plasmonic properties of NS is the radiation efficiency, ηrad. It is defined by (Tanabe 2016; Stuart and Hall 1998)
(
)
𝜎acs −1
𝜎scs
.
= 1+
𝜂rad =
(13)
𝜎ecs
𝜎scs
It is worth nothing that, the radiation efficiency represents how much of the incident
light interacting with the nanoparticles is scattered rather than being absorbed.
3 Numerical analysis
Unlike spherical shape nanostructures, NPs with different symmetry axis have more than
one plasmonic modes (Alsawafta et al. 2012). Since a spheroid have threefold symmetry
axes, it exhibits both longitudinal and transverse plasmon modes corresponding to the
redistribution of the polarization charges along each principal axes. For an electromagnetic
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G. Beyene et al.
field applied on a core–shell nanocomposite, changing size and shape of the composite
results in charge separation and hence tailoring the frequency and the intensity of the SPR
in different wavelength of the incident radiation. The oscillatory shift of the negative electrons cloud relative to the positive core along each principal axis results in two plasmonic
modes (PM): longitudinal mode (LM) and transverse mode (TM).
Below, we numerically investigate the effect of size, shape, thickness of the metallic shell, and the host matrix on the optical and plasmonic properties of spindle and
disc shaped ZnO@Ag core–shell. For numerical analysis, we used ɛc = 8.5, ɛ∞ = 4.5,
𝜔p = 1.46 × 1016 rad∕s, and 𝛾 = 1.67 × 1013 rad∕s (Beyene et al. 2019).
3.1 Absorption cross‑section
The absorption cross-sections of spindle- and disc-shaped spheroidal core–shell NSs as a
function of wavelength are depicted in Fig. 2; for shell thicknesses of 5 nm, 10 nm, 15 nm,
and a constant core–shell aspect ratio of ARs = 2.00. Figure 2a shows the simulated σacs
spectra of the spindle-shaped CSNSs for the parameters ARs are 2.33, 3.00, and 5.00, corresponding to the core concentrations (f) of 49.22%, 18.75%, and 3.91%, respectively. It
is observed that there are four resonance peaks. The first two resonance peaks (located
between 300 and 500 nm) correspond to surface plasmon resonances of the silver shell at
the inner and outer interfaces (Beyene et al. 2019). The peaks of these two resonances
are found to decrease and red-shifted with an the increase of core concentration; in agreement with that reported in Ref. (Oldenburg et al. 1998). On the other hand, the third and
fourth set of resonance peaks (located above 500 nm) are due to the polarization of charges
along the principal axes of the spheriod. In particular, the third resonance peaks (counted
from left) are associated with the transverse plasmon mode (TM), while the fourth peaks
correspond to the longitudinal mode (LM). The peaks of the TM modes decrease and are
blue-shifted when the core’s aspect ratio and shell thickness increases. Moreover, the longitudinal surface plasmon resonances (fourth resonance peaks) are found to be very sensitive to the aspect ratio, ARc (Beye et al. 2017)—it is seen that as ARc is increased, the
longitudinal band maximum is shifted to shorter wavelengths with a relative increase in the
peak intensity.
The plasmonic properties of NSs vary based on the shape of the core–shell NPs. In
Fig. 2b, σacs versus wavelength for the disc-shaped CSNSs are shown for the same parameters as that used in Fig. 2a with the corresponding core concentration being f = 57.42%,
Fig. 2 (Color online) The absorption cross-sections for a spindle and b disc shaped CSNSs; for
ARc = 2.33, 3.00, 5.00 and constant ARs = 2.00, 𝜀h = 2.25 (Pan et al. 2001)
13
Plasmonic properties of spheroidal spindle and disc shaped…
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157
28.13%, 9.77%. Similar to the previous case, there are four resonance peaks—the first two
(counted from left) corresponding to the plasmon resonances of the silver shell while the
third and fourth peaks corresponding to the TM and LM, respectively. It is seen that all
the peaks decrease and are blue-shifted with an increase in the core’s aspect ratio and shell
thickness. Moreover, comparison of Fig. 2a, b shows that (i) the corresponding resonance
peaks are more pronounced for the disc-shaped CSNSs than that for the spindle-shaped
and (ii) the TM and LM resonance peaks of the disc-shaped spheroid are more broader
and blue-shifted withrespect to that of the spindle-shaped. For small NPs, the SPRs are
influenced by the NP size for the same constituentes of the composite, such that, for particles of a few nanometers the resonances do not change their position or wavelength, but
they become broader because of dispersion effect. When its size increases (here the volume
of nanodisc is almost twice of nanospindle) the SPR are now affected by the secondary
radiation which moves the resonance peaks to larger wavelength (blue-shifted) and makes
the peaks more broader (Noguez 2007). The results may indicate that with appropriate
design of core–shell nanoparticles, it is possible to achieve broadband response for light
harvesting in photovoltaic applications (Piralaee and Asgari 2016; Piralaee et al. 2016)
or extremely narrow band width response for applications such as bio-sensing, lasing and
photo-switching (Zhang and Zayats 2013).
Also, note from Fig. 2a, b that for ARc = 5.00 the third and fourth resonance peaks associated with the LM and TM modes effectively merge. This may be attributed to the fact that
as synergetic effect between the components and their structural details can be designed in
such a way that they positively interact with each other.
For the particles of sizes larger than 100 nm, the spectrum of the scattering cross-section is larger than the absorption cross-section even at low wavelengths of the incident light
(Penninkhof et al. 2008). However, NPs of sizes less than 100 nm have smaller scattering
cross-section at high wavelengths and larger at low wavelengths than the corresponding
absorption cross-section (Penninkhof et al. 2008). Figure 3 shows the absorption, scattering and extinction spectra, which is plotted for the shell thickness of 5 nm and core concentration f = 46.88%. It is seen that the spectrum of the scattering cross-section lies above the
absorption cross-section at higher wavelengths. In all cases, there are four peaks, including
the longitudinal and transverse resonance peaks attributed to the two interfaces of silver
nanoparticles and the bonding/antibonding pairs of the composite at the surfaces for large
concentrations of the core ZnO NPs around 50%.
We also analyzed the plasmonic response of both spindle and disc shape spheroidal ZnO@Ag core–shell nanostructures for the TM and LM plasmonic modes. Figure 4
Fig. 3 (Color online) The
spectra σacs,𝜎scs and σesc of the
same size of spindle shaped; for
ARc = 1.67, ARs = 1.20, t = 5 nm
and ɛh = 2.25
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G. Beyene et al.
Fig. 4 (Color online) The
spectrum of the LM and TM
resonance modes of spindleand disc-shaped spheroids as
a function of wavelength. The
parameters used are ARs = 2.0,
ARc = 2.33, and t = 5 nm
depicts these plasmonic modes plotted as a function of wavelength both for the spindleand disc-shaped spheroidal core–shell NPs; for equal lengths of the major and minor
axes, i.e., the aspect ratio of core ZnO of both NPs is arranged at ARc = 2.33. Consistent
with that obtained in Fig. 2, the spectra shown in Fig. 4 confirms that the resonance
peaks of the disc-shaped (oblate) core–shell nanoparticles have the largest absorbance
and are red-shifted compared with the spindle-shaped (prolate) CSNSs.
The effect of shape on the plasmonic properties of spheroidal ZnO@Ag core–shell
nanostructures is depicted in Fig. 5. As shown in Fig. 5a, b, both the TM and LM resonance peaks for the disc-shaped NPs are enhanced compared with those for the spindleshaped NPs. In addition, the spectrum of the TM and LM peaks for the disc-shaped
NPs extends well beyond the visible spectrum, i.e., one of the peak for ARc = 1.88 &
ARs = 1.67 lies in the near infrared region. However, when the aspect ratios of both
core and composite are increased, the longitudinal resonance modes are red-shifted
for the disc-shaped spheroids and blue-shifted for the spindle shaped structures. The
transverse resonance modes of the spindle-shaped core–shell NSs coincide, while that
for the disc-shaped structure the resonance peaks are enhanced and red-shifted. These
properties arise for the same freedom of charge oscillation and AR, due to the shape
of the composites as well as the core’s concentration, which are strongly related to the
size and quantum confinement effects. Here, the core concentration varies from 49.22%
to 49.70% with ARs = 2.0 for the spindle-shaped and from 57.21% to 55.94% with
ARs = 1.67 for the disc shaped nanostructures.
Fig. 5 (Color online) The effect of shape on the LM and TM resonance modes of the absorption crosssection spectra for a spindle-shaped and b disc-shaped spheroids, for ARs = 2.0, 1.67. The parameters used
are ARc = 2.33, 1.88 and t = 5 nm
13
Plasmonic properties of spheroidal spindle and disc shaped…
Page 9 of 12
157
Fig. 6 (Color online) The absorption cross-section of spindle shaped spheroid as a function of wavelength,
for a passive host matrix of five dielectrics function ɛh. The other parameters are ARs = 2.0, ARc = 2.33 and
t = 5 nm
The other factor that affects the plasmonic properties of core–shell NSs is the dielectric
function (or refractive index (RI)) of the host matrix. Figure 6 depicts the effect of varying
the DF of the host medium on the spindle-shaped ZnO@Ag spheroidal core–shell NSs. It
is observed that the RI considerably affects the plasmonic properties, i.e., the spectra of the
absorption cross-section of the spindle shaped CSNSs is red-shifted in both near-UV/visible
and infrared spectral regions, when the refractive index of the host medium is increased. For
a refractive index larger than 2, the location of the LM resonance modes shift toward the
infrared region with the spectra becoming broader and broader. The absorption cross-section spectrum of the CSNSs attains maximum peak value for small refractive index, except
for the medium of vacuum in the UV region, and decrease with an increase in the refractive
index of the medium. On the other hand, the peaks of the TM resonance modes increase
while that of the LM slightly decrease with an increase in the refractive index. Similar
effects are observed for the disc-shaped spheroidal CSNSs (not shown here).
3.2 Radiation efficiency
Finally, we plotted the radiation efficiency (ηrad) of both geometry as shown in Fig. 7a for
disc-shaped and Fig. 7b for the spindle-shaped NPs by using the same parameters as that
used in Fig. 2. As shown in the Figures, ηrad is more intense and red-shifted for disc-shaped
CSNS than for a spindle-shaped. The radiation efficiency tells us how much the incident
energy radiated depends on the strength of the resonance at given wavelength. As depicted
in Fig. 7, due to the interband transition of the metal silver coat, the radiation efficiency is
low at low wavelengths for small concentration of the silver shell. When the thickness of
the silver on the ZnO nanoparticles increase, the radiation efficiency becomes intense and
broader. For a thick thickness of silver, the CSNSs has higher polarizability (Stuart and
Hall 1998), resulting to large values of radiative rate for high wavelengths.
In the long wavelength regions, the spectra with the minimum peak value of the radiative efficiency exhibits more red-shift, while there is a little red shift for the “Fano-like”
resonances (Wang et al. 2011; Jule et al. 2015) observed around 430 nm, which tell us
that at the particular wavelength, ηrad is dominated by absorption rather than scattering.
13
157
Page 10 of 12
G. Beyene et al.
Fig. 7 (Color online) Radiation efficiency of a the disc-shaped, b the spindle-shaped CSNSs as a function
of wavelength; for three different values of ARc. The other parameters are similar to that used in Fig. 2
In the quasi-static limit approximation method, the ratio of scattering to absorption rate
increases for large particles, which is valid for subwavelength scale particles, while particles with sizes comparable to or larger than the incident wavelengths are likely to suffer
from electrodynamic damping, causing energy loss through particle heating. In particular,
for applications in thin photovoltaic layers, plasmonic particles with high optical radiation
efficiencies can positively harness their supportive ability as well as enhance the effective
absorption length at longer wavelengths (Tanabe 2016).
4 Conclusion
In this work, we studied the effect of size, shape, shell thickness, and the nature of the surrounding environment on the plasmonic and optical properties of spindle- and disc-shaped spheroidal
ZnO@Ag core–shell nanostructures. It is found that the absorption and scattering efficiencies
of semiconductor ZnO nanoparticles strongly depend on the thickness of the silver shell with
the optical properties being strongly modified as a result of the metal coating. In particular, the
numerical analysis for different values of shell thickness, size, shape, and refractive index of
the host medium, the spectra of the absorption cross-section of ZnO@Ag nanoinclusion as a
function of wavelength possess four plasmon resonance peaks with the peaks extending from
the UV to near-IR spectral regions. These resonance peaks correspond to the silver/core, silver/
host-matrix interfaces, and the bonding/antibonding pairs due to separation of charges in the
composites along the principal axes. Moreover, the position of the resonance peaks strongly
depends on the aspect ratio and refractive index of the medium exhibiting a shift towards higher
wavelengths with an increase in the refractive index of the host medium and thickness of the
silver shell. The results obtained in this work may be utilized in various applications which
employs shape-dependent plasmonic effects of core–shell spheroidal nanostructures.
Acknowledgements This work is supported financially by the NSFC (11474246, 11750110415,
11850410442), Addis Ababa University (AAU) and Adama Science and Technology University (ASTU).
Compliance with ethical standards
Conflict of interest The authors declare no conflict of interest. The funders had no role in the design of the
study; in the collection, analysis, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.
13
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Page 11 of 12
157
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13
Bulg. J. Phys. 46 (2019) 37–48
Investigation of Size Dependent
Thermoluminescence Emission from
Amorphous Silicon Quantum Dots
B. Mesfin, T. Senbeta
Department of Physics, Addis Ababa University, Addis Ababa, Ethiopia
Received: 22 November 2018
Abstract. We studied the size dependent thermoluminescence emission from
small amorphous silicon quantum dots using the model of interactive multiple
traps system (IMTS). The model consists of two active electron traps having
activation energies E1 = 0.65 eV and E2 = 0.80 eV, a thermally disconnected
deep trap (TDDT), and a luminescent center. For quantum dots of diameters
between 3–6 nm, numerical evaluations are carried out to generate the glow
curve and determine relevant parameters such as the symmetry factor (µg ) and
the order of kinetics (b). It is observed that as the size of the quantum dots decrease, the intensity of the thermoluminescence signal increase, the glow peaks
positions are almost independent of the size of dots, and the curves follow firstorder kinetics (µg → 0.42 and b → 1). In addition, the glow curves possess
two peaks corresponding to the two active electron trap levels with the intensity
due to E2 being larger than that due to E1 . Furthermore, numerical analysis of
the same quantum dots using the two-traps-one-recombination center model (no
TDDT traps) shows that, unlike that obtained using the IMTS model, the glow
curves seems to obey second-order kinetics (µg → 0.52 and b → 2) and the
peaks positions shift towards high temperature values with an increase in size of
the dots. In addition, the numerical simulations enable us to determine how the
concentration of carriers in the traps/center evolves as a function of temperature
and quantum dots size.
PACS codes: 78.60.Kn, 78.56.Cd, 78.67.Hc
1
Introduction
Nanostructured materials provides unprecedented control over the optical, electrical, magnetic, and thermal properties of semiconductors and insulators due to
quantum confinement effect [1,2]. For indirect band gap materials, the extremely
reduced dimensions lead to a major spread of the wave vector in k-space, thus
producing a relaxation of the moment selection rule and the possibility of zerophonon direct radiative optical transitions [3–5]. Furthermore, the confinement
1310–0157 c 2019 Heron Press Ltd.
37
B. Mesfin, T. Senbeta
results to an increase of the overlap between electron and hole wave functions
in k-space, thereby increasing the probability of radiative recombination and a
decrease in the probability of nonradiative recombination. Accordingly, quantum confinement effect enables indirect band gap nanostructured materials to be
viable candidates for potential applications as optoelectronics devices.
In the last decade, the emission of light from silicon nanostructures (NSs) has
become a research topic of current interest due to its potential for applications in
silicon-based optoelectronic devices [6, 7]. In particular, it has been found that
amorphous silicon (a-Si) quantum dots are more efficient luminescence materials than crystalline silicon. This is mainly attributed to the structural disorder
and relatively wide band gap energy of a-Si compared with crystalline Si, enabling nanostructured a-Si to be a viable candidate for short wavelength light
emitters [7–9].
Thermoluminescence (TL) is a temperature-stimulated light emission from a
system of insulating or semiconducting materials, after the removal of ionizing radiation. A plot of the light intensity as a function of temperature is known
as the glow curve, which depending on the materials properties may have one
or more maxima, called glow-peaks, each corresponding to an energy level of
different traps [10, 11]. Various theoretical models have been proposed to describe TL processes. The simplest TL model is the one-trap-one-recombination
center (OTOR) model, which is capable of describing the main features of TL
processes. However, in most ‘real’ materials, there are several electron traps
with different thermal activation energies, deep traps which retain their trapped
charges during a heating cycle that empties the shallower traps, and recombination centers [12, 13]. Accordingly, a more detailed and accurate description of a
TL phenomena, entails the use of more complex TL kinetic models that take into
account of competitions among multiple electron traps and luminescent centers.
Among such models are the interactive multiple traps system (IMTS) and noninteractive multiple traps system (NMTS). These models consist of thermally
disconnected deep electron traps (TDDT), which are assumed to be thermally
stable during the heating process.
An alternative version of the OTOR model is the kinetic model which consists of
two/three active electron traps and a recombination center (TTOR). Size dependent TL emission and the effect of retrapping on TL peak intensities in small a-Si
quantum dots (QDs) has been investigated using the TTOR model [14,15]. Their
analysis show that the TL glow curve possesses two/three peaks corresponding
to the two/three trapping levels, the TL intensity increases with a decrease in the
size of QDs, and the simulated glow curves corresponding to each trap levels
follow the second-order kinetics. Motivated with these reports, we find it interesting to study further the effect of size variation on the shape of the glow curve
and TL intensity of Si nanostructures by introducing TDDT traps to the TTOR
model. In this work, we investigate the effect of varying the size of spherical a-Si
QDs of diameters between 3–6 nm on the TL intensity using the IMTS model. In
38
Investigation of Size Dependent Thermoluminescence Emission from ...
addition, we numerically simulated the instantaneous concentrations of carriers
in the traps/center and determine the order of kinetics of the glow curves.
The paper is organized as follows: In Section 2, we present the proposed IMTS
model and the corresponding rate equations. Numerical simulations, results, and
discussions are displayed in Section 3. Finally, concluding remarks are given in
Section 4.
2
The Thermoluminescence Kinetic Model
Consider the IMTS TL kinetic model that consists of two active electron traps
(AT1 and AT2 ), one thermally disconnected deep trap (TDDT), and a luminescent center (RC), as shown in Figure 1. It is assumed that the process of
traps/center filling is already attained with priori irradiations. During trap emptying (via application of heat), electrons trapped in AT1 and AT2 traps will be
released back to the conduction band (transitions 2 and 4) when the trapped electrons absorb enough energy that is comparable to the activation energies (E1 for
AT1 ) and (E2 for AT2 ). Subsequently, these thermally elevated free electrons
may be released back so that they may either recombine with the holes in the
RC (transition 6) yielding luminescence, or becomes retrapped at the electron
traps (transitions 1, 3, 5).
For the given IMTS model, the transport of carriers during heating may be de-
Figure 1. The IMTS model with two active electron traps AT1 and AT2 having activation
energies E1 and E2 , respectively; a thermally disconnected deep electron trap (TDDT);
and a recombination center (RC).
39
B. Mesfin, T. Senbeta
scribed by the following rate equations [12, 16]:
dn1
E1
= −s1 n1 exp −
+ (N1 − n1 )nc An1 ,
dt
kT
dn2
= −s2 n2 exp
dt
E2
−
kT
+ (N2 − n2 )nc An2 ,
(1)
(2)
dm
= (M − m)nc Am ,
dt
(3)
dnh
dn1
dn2
dm dnc
=
+
+
+
,
dt
dt
dt
dt
dt
(4)
dn1
dn2
dm
dnc
=−
−
−
− n c n h Ah ,
dt
dt
dt
dt
(5)
dnh
= n c n h Ah ,
(6)
dt
where I [cm−3 s−1 ] is the TL intensity; N1 , N2 , and M [cm−3 ] are the total
concentrations of the AT1 , AT2 , and TDDT electron traps, respectively; n1 , n2 ,
and m [cm−3 ] are the corresponding instantaneous concentrations of filled traps,
nc [cm−3 ] is the concentration of electrons in the conduction band, nh [cm−3 ] is
the concentration of holes in the recombination center. Also, An1 , An2 , and Am
[cm3 /s] are the capture coefficients for the two active and one TDDT electron
traps, Ah [cm3 /s] is the capture coefficient of the recombination center, E1 and
E2 [eV] are the activation energies of the active traps, s1 and s2 [s−1 ] are the
frequency factors for these traps, and k [eV/K] is the Boltzmann’s constant. Note
that the charge neutrality condition nh = n1 + n2 + m + nc is implied in Eqs.
(1)-(6).
I(t) = −
Furthermore, in our analysis we assumed a linear heating given by
T (t) = T0 + βt,
(7)
where T [K] is the temperature of the QDs at time t [s], T0 is the temperature at
t = 0, and β [Ks−1 ] is the heating rate.
It is worthwhile noting that Eqs. (1)-(6) are coupled nonlinear first-order differential equations, which in general do not have exact analytical solutions. Often,
analytical expressions for TL glow curves are obtained by imposing simplifying
assumptions, such as the quasi-equilibrium conditions. In this paper, the kinetic
equations will be solved numerically using MATHEMATICA 9 software.
A particular TL glow curve may be characterized by its symmetry factor (µg ),
which is defined by
δ
µg = ,
(8)
ω
40
Investigation of Size Dependent Thermoluminescence Emission from ...
where ω = T2 − T1 is the full width at half maxima, δ = T2 − Tm is the halfwidth toward the fall-off side of the glow peak, T1 and T2 (T2 > T1 ) are the
temperatures corresponding to half the TL intensity on either side of the peak
temperature, Tm . For first- and second-order kinetics, µg = 0.42 and 0.52,
respectively. Moreover, for a particular value of µg , the order of kinetics, b, may
be approximated by the following empirical equation [17, 18]:
µg = C0 + C1 b − C2 b2 ,
(9)
where C0 = 0.25 and C1 = 0.186. In the analysis, we used C2 = 0.024 and
0.016 for symmetrical- and asymmetrical-looking glow curves, respectively. It
is worth noting that the concept of symmetry factor is applicable for TL glow
curves where the numerically simulated TL curves possess isolated broad peaks
[17].
Table 1. Approximate values of the size dependent radiative recombination rate of
electron in the conduction band to recombine with hole in the RC of a-Si QDs. [4]
Diameter, d [nm]
Radiative recombination rate, γr [s−1 ]
3
4
5
6
7.0 × 106
3.0 × 106
9.0 × 105
4.0 × 105
3
Results and Discussions
For numerical computation of TL curves by using the set of Eqs. (1)-(6), the
initial concentrations of carriers n10 , n20 , and m0 in the traps AT1 , AT2 , and
TDDT, respectively, are computed according to a saturating exponential function in which the filling rate constant is assumed to be proportional to the corresponding trapping coefficients [13, 17]. Typical values of the retrapping and
recombination coefficients vary between 10−10 –10−5 cm3 s−1 [12]. Accordingly, neglecting possible corrections associated with confinement, we choose
An1 = An2 = Am = 10−9 cm3 /s. The radiative recombination rate (γr ) and
the recombination coefficient are related by Ah = γr n−1
h [10]. Hence, using the
values of γr tabulated in Table 1, the size dependent recombination coefficients
are calculated to be Ah = (3.50, 1.50, 0.45, 0.20)×10−8 cm3 s−1 , for the QDs
of size d = (3, 4 , 5, 6) nm, respectively. Below, we simulated the various TL
parameters of interest using theses values.
Figures 2 and 3 show the concentration of electrons in the active electron traps
AT1 and AT2 , respectively, as a function of temperature. The concentration
of electrons in the traps AT1 (E1 = 0.65 eV) decreases as the temperature
increases, almost independent of the QDs size. Furthermore, it is seen that
41
Mesfin,T.
T.SENBETA
Senbeta
B. B.
MESFIN,
n
on the
the size
size of
of the
the QDs,
QDs, contrary
contrary to
to that
thatreported
reported
n111(T
(T )) are
are almost
almost independent
independent on
contrary
to
that
reported
in
was obtained
obtained using
using the
the TTOR
TTOR model.
model. On
On the
the other
other
in Refs.
Refs. [14,
[14, 15],
15], which
which was
model.
On
the
other
hand,
the concentration
concentration of
of electrons
electrons in
in the
the traps
traps
electrons
in
the
traps
hand, as
as the
the temperature
temperature increases, the
◦
AT
0.80 eV
eV)) initially
initially increases
increases just
justafter
afteraatemperature
temperatureof
about50
C,
temperature
ofofabout
about
505000C,
C,
AT222 (E
(E22 = 0.80
◦
0
until
peak value
value at
at about
about110
110 C,
C, and then decreases
thereafterbebedecreases thereafter
thereafter
beuntil it reaches a peak
1.0
-3L
nn11Hcm-3
0.8
66 nm
nm
0.6
55 nm
nm
0.4
44 nm
nm
33 nm
nm
0.2
0.0
0
20
40
60
80
Temperature, 00C
100
100
120
120
Figure 2.
2. The
The normalized concentration of trapped
Figure
trapped electrons
electronsin
inthe
thetraps
trapsAT
AT111as
asaaafunction
function
the
traps
AT
as
function
of
temperature
for
four
different
quantum
dot
sizes.
The
values
used
for
the
of temperature
dot sizes. The values
values used
used for
for the
the plots
plotsare:
are:
plots
are:
16
−3
14
16
14 cm−3
−3, A
N11 =
= N22 = M = 1016
N
cm−3 , n10
n20
=m
m000 =
= 22 ×
×10
1014
cm−3
An1
=
cm
×
10
cm
,, A
=
10 = n
20 =
n1 =
20
n1
−9
3 −1
−9
−1 β = 1 Ks−1
−1, E = 0.65 eV , E = 0.80 eV , and
An2
n2 = A
m
A
Am
= 10
10−9
cm33ss−1
E222 =
= 0.80
0.80eV
eV,, and
and
cm
,, β = 1 Ks−1
,, E111 = 0.65 eV,, E
m =
−1
−1
= ss22 =
= 10
1088 sss−1
ss111 =
...
1.0
1.0
0.8
0.8
-3L
nn22Hcm
Hcm-3
L
66 nm
nm
0.6
0.6
55 nm
nm
44 nm
nm
0.4
0.4
33 nm
nm
0.2
0.2
0.0
0.0
00
50
50
100
150
100
150
0
0C
Temperature,
Temperature, C
200
200
Figure 3.
3. The
The normalized
normalized concentration of
trapped electrons
in the
trap AT
(E22 =
Figure
Figure
3. The
normalized concentration
concentration of
of trapped
trapped electrons
electrons in
in the
the trap
trap AT
AT222 (E
(E2 =
=
0.80 eV
eV )) as
as aa function
function of
of temperature;
temperature; with
the
same
parameters
as
in
Fig.
2.
0.80
with
the
same
parameters
as
in
Fig.
2.
0.80 eV) as a function of temperature; with the same parameters as in Figure 2.
66
42
Investigation of Size Dependent Thermoluminescence Emission from ...
INVESTIGATION OF SIZE DEPENDENT ...
coming zero just above 220◦0C. Note that the activation energy of the traps AT1
coming zero just above 220 C. Note that the activation energy of the traps AT1
is less than that of the traps AT2 (E1 < E2 ), which means that electrons iniis less than that of the traps AT2 (E1 < E2 ), which means that electrons initially
tially trapped during irradiation in AT1 are released into the conduction band
trapped during irradiation in AT1 are released into the conduction band before
before those trapped in AT2 are activated. This accounts for the initial increase
those trapped in AT2 are
◦ activated. This accounts for the initial increase in n2
in
n2 (between
50–110
some
of the
electrons
released
0
(between
50 − 110
C) C)
thatthat
some
of the
electrons
released
fromfrom
trapstraps
AT1 AT
are1
are
retrapped
in
AT
thereby
increasing
the
value
of
n
.
2
2
retrapped in AT thereby increasing the value of n .
2
2
As
theinstantaneous
instantaneousconcentration
concentrationofofelectrons
electronsm(T
m(T))inin the
the
As shown
shown in
in Figure
Fig. 4,4,the
◦
TDDT
traps
increases
with
an
increase
in
temperature
until
about
210
0 C and
TDDT traps increases with an increase in temperature
until about 210 C and
then
saturation values
values above
above ≈≈ 210
2100◦C.
C. Moreover,
the saturation
saturation values
values
then reach
reach saturation
Moreover, the
are
seen
to
increase
with
an
increase
in
the
size
of
the
QDs.
This
may
be
exare seen to increase with an increase in the size of the QDs. This may be explained
in
terms
of
the
difference
in
the
recombination
coefficients,
A
.
That
is,
h
plained in terms of the difference in the recombination coefficients, Ah . That is,
as
the
size
of
the
QDs
increases,
A
decreases
which
in
turn
means
lesser
numh
as the size of the QDs increases, Ah decreases which in turn means lesser number
electron traps
traps reaching
reaching the
the RC
RC and
and producing
producing
ber of
of electrons
electrons from
from the
the active
active electron
TL
electrons are
are more
more likely
likely to
to be
be retrapped
retrappedin
inthe
the
TL emission;
emission; instead
instead many
many more
more electrons
TDDTs
before
reaching
the
RC.
Also note
note that
that when
when the
the temperature
temperature isis between
between
TDDTs
before
reaching
the
RC.
Also
◦
◦0
100
may be
be acac100 0CCand
and130
130 C,
C,the
theincrease
increaseininm(T
m(T))isis small
small (plateau),
(plateau), which
which may
counted
AT11 is
is on
on the
the verge
verge of
of being
being fully
fully emptied,
emptied, while
while
counted with
with the
the fact
fact that
that trap
trap AT
electrons
sufficiently activated,
activated, and
and hence
hence the
the number
number of
of
electrons in
in trap
trap AT
AT22 are
are not
not yet
yet sufficiently
electrons
TDDT traps
traps is
is reduced
reduced significantly.
significantly.
electrons to
to be
be retrapped
retrapped by
by the
the TDDT
Figure
of concentrations
concentrations of
of electrons
electrons in
in the
the conduction
conduction
Figure 55 shows
shows the
the variation
variation of
band
as
a
function
of
temperature
for
the
QDs
of
diameters
between
band as a function of temperature for the QDs of diameters between 33–6
− 6nm.
nm.It
is
observed
that
the
concentration
of
electrons
in
the
conduction
band
possess
It is observed that the concentration of electrons in the conduction band possess
two
peaks in
in the
thevicinity
vicinityofofTT==85
850◦CCand
andTT ==165
1650◦C
C corresponding
correspondingto
to
two sets
sets of
of peaks
the
trap
levels
E
and
E
,
respectively.
Moreover,
it
is
seen
that
when
the
quanthe trap levels E11 and E22 , respectively. Moreover, it is seen that when the quantum
also increase.
increase. It
It is
is because
because that
that the
the recombination
recombination
tum dots
dots sizes
sizes increase,
increase, n
ncc (T
(T )) also
1.0
0.9
6 nm
m Hcm-3L
0.8
5 nm
0.7
0.6
0.5
4 nm
0.4
3 nm
0
50
100
150
200
250
Temperature, 0C
Figure 4.
4. The
The normalized
normalized concentration
concentration of
Figure
of trapped
trapped electrons
electrons in
in the
the TDDT
TDDT traps
traps as
as aa
function of
of temperature;
temperature; with
with the
the same
2. 2.
function
same parameters
parameters as
as in
in Fig.
Figure
43
7
Mesfin, T.
T. SENBETA
Senbeta
B. B.
MESFIN,
B. MESFIN, T. SENBETA
lifetime,
by an
an electron
electron in
in the
the conduction
conductionband,
band,isis
lifetime,which
which isis the
the mean
mean time
time spent
spent by
lifetime,QDs
which islarger
the mean time
spent by an
electron
in the
conduction
band,
is
large
free
electrons
in the
the
conduction
band
largefor
for QDs of
of larger size.
size. It
It means
means that
that free
electrons
in
conduction
band
large for QDs of larger size. It means that free electrons in the conduction band
spend
the holes
holes in
in the
the RC
RC centers
centersfor
forQDs
QDs
spend more
more time
time before
before recombining
recombining with
with the
spend more time before recombining with the holes in the RC centers for QDs
with
Since A
Ahh represents
represents the
the recombirecombiwith larger
larger size
size than
than those
those with small size. Since
with larger size than those with small size. Since Ah represents the recombination
transition coefficient
for electrons the conduction
conduction band to
to recombine
nation
nation transition
transition coefficient
coefficient for electrons in
in the conduction band
band to recombine
recombine
with
holes
in
the
luminescent
centers, small Ahh (larger
(larger QD
QD size)
size) means
means slow
slow
with
holes
in
the
luminescent
with holes in the luminescent centers, small Ah (larger QD size) means slow
rate
of
recombination
with
the holes, with the electrons
electrons spending
spending more
moretime
timeinin
rate
of
recombination
with
rate of recombination with the holes, with the electrons spending more time in
the
conduction band,
and vice
versa.
the
the conduction
conduction band,
band, and
and vice
vice versa.
1.0
1.0
6 nm
6 nm
-3-3 L
Hcm
ncncHcm
L
0.8
0.8
5 nm
5 nm
0.6
0.6
4 nm
4 nm
0.4
0.4
3 nm
3 nm
0.2
0.2
0.0
0.0
0
0
50
50
100
150
100
150
0
Temperature,
0C
Temperature, C
200
200
Figure
The
normalized
concentration
of
temFigure
electrons
in the
the conduction
conduction band
bandversus
versustemtemFigure5.5.
5. The
Thenormalized
normalized concentration
concentration of
of electrons
electrons in
in
the
conduction
band
versus
perature;
with
the
same
parameters
as
in
Fig.
2.
perature;
perature;with
withthe
thesame
same parameters
parameters as
as in
in Figure
Fig. 2. 2.
1.0
1.0
6 nm
6 nm
Hcm-3-3L L
nnh hHcm
0.9
0.9
5 nm
5 nm
0.8
0.8
4 nm
4 nm
0.7
0.7
3 nm
3 nm
0.6
0.6
00
50
50
100
150
100
150
0
Temperature,
0C
Temperature, C
200
200
Figure
The
normalized
concentration
of
the recombination
center as
a function
Figure6.6.
6.The
Thenormalized
normalizedconcentration
concentration of
of holes
holes in
in
recombination
Figure
holes
in the
the
recombinationcenter
centeras
asaafunction
function
of
temperature;
with
the
same
parameters
as
in
Fig.
2.
of
temperature;
with
the
same
parameters
as
in
Fig.
2.
of temperature; with the same parameters as in Figure 2.
88
44
InvestigationINVESTIGATION
of Size Dependent OF
Thermoluminescence
Emission
from ...
SIZE DEPENDENT
...
Figure
concentration of
of holes
holes in
in the
the RC
RC as
as aa funcfuncFigure 66 depicts
depicts the
the instantaneous
instantaneous concentration
tion
of
temperature.
Recall
that
the
charge
neutrality
condition
dictates
that
tion of temperature. Recall that the charge neutrality condition dictates that
n
(T
)
=
n
(T
)
+
n
(T
)
+
m(T
)
+
n
(T
)
and
since
initially
(just
before
h
1
2
c
nh (T ) = n1 (T ) + n2 (T ) + m(T ) + nc (T ) and since initially (just before
starting
nc(0)
(0) = 0 so
so that
that its
its peak
peak value
value is
is nnh(0)
(0) =
=
starting the
the heating
heating process),
process), n
c 14 = 0
h
−3
14 cm−3 (or, the normalized peak value of
n
(0)
+
n
(0)
+
m(0)
=
6
×
10
1
2
n1 (0) + n2 (0) + m(0) = 4 × 10 cm (or, the normalized peak value ◦of
n
= 1).
1). As
As the
the temperature
temperature increase,
increase,nnh(T
(T))decrease
decreaseuntil
untilabout
about210
2100 CC
nhh(0)
(0) =
h
and
thereafter
reach
saturation
values.
It
is
seen
that
the
decrease
in
n
(T
beh
and thereafter reach saturation values. It is seen that the decrease in nh (T )) becomes
very
rapid
with
a
decrease
of
the
QDs
size.
In
addition,
the
saturation
comes very rapid with a decrease of the QDs size. In addition, the saturation
values
the QDs
QDs sizes
sizes increases,
increases, which
which means
means that
that the
the number
number
values also
also increases
increases as
as the
of
the conduction
conduction band
band and
and end
end up
up being
being retrapped
retrapped in
in
of electrons
electrons released
released from
from the
the
reaching the
the RC
RC increases
increases with
with an
an increase
increase in
in size
size resultresultthe TDDT
TDDT traps
traps before
before reaching
ing
7).
ing to
to aa corresponding
corresponding reduction
reduction in
inthe
theintensity
intensityofofthe
theTL
TLsignal
signal(see
(seeFigure
Fig. 7).
This
with the
the fact
fact that
that as
as the
the size
size of
of the
the QDs
QDs increases,
increases, the
the
This result
result is
is consistent
consistent with
recombination
(Ahh )) decreases
decreases which
which in
in turn
turn means
means lesser
lesser number
number of
of
recombination coefficient
coefficient (A
electrons
electron traps
traps AT
AT11 and
and AT
AT22 reach
reach the
the RC
RC resulting
resulting to
to
electrons from
from the
the active
active electron
aa relatively
instead many
many more
more electrons
electrons are
are retrapped
retrapped in
in the
the
relatively weak
weak TL
TL emission;
emission; instead
TDDTs
the RC
RC as
as it
it is
is evident
evident from
from Fig.
Figure
TDDTs before
before reaching
reaching the
4. 4.
At
2–6cannot
cannot be
be
At this
this point,
point, ititisisworth
worthnoting
notingthat
thatthe
theresults
resultsobtained
obtainedininFigures
Figs. 2-6
realized
techniques. However,
However, the
the numerical
numerical method
method enables
enables
realized using
using experimental
experimental techniques.
us
of electrons
electrons and
and holes
holes in
in the
the system
system behaves
behaves
us to
to observe
observe how
how the
the concentration
concentration of
as
a
function
of
temperature
and
the
size
of
the
quantum
dots.
as a function of temperature and the size of the quantum dots.
Figure
of the
the TL
TL emission
emission as
as aa function
function of
of temperature.
temperature.
Figure 77 shows
shows the
the intensity
intensity of
◦ 0
◦
0
The
two
sets
of
glow
peaks
around
T
=
85
C
and
T
=
165
C
The two sets of glow peaks around Tmm = 85 C andmTm = 165 correspond
C correto
the
trap
levels
E
=
0.65
eV
and
E
=
0.80
eV,
respectively.
It
is
observed
1
2 and E2 = 0.80 eV , respectively.
spond to the trap levels
E1 = 0.65 eV
It
that
when
the
quantum
dots
size
decreases,
the
intensity
of
the
TL
is observed that when the quantum dots size decreases, the intensity ofemission
the TL
1.0
3 nm
Intensity Ha.u.L
0.8
4 nm
0.6
0.4
5 nm
0.2
6 nm
0.0
0
50
100
150
200
0
Temperature, C
Figure7.7.The
TheTL
TLintensity
intensityversus
versustemperature
temperaturefor
forthe
thesame
samevalues
valuesasasininFigure
Fig. 2.2.
Figure
45
9
B. MESFIN, T. SENBETA
B. Mesfin,
T. Senbeta
emission increases, while the peak
temperature
almost remains constant independent of the size of the QDs (with maximum ∆Tm ≈ 7 0 C for both set of
increases,
while the peakoftemperature
almost
constant
independent
of
peaks).
The enhancement
the TL signal
withremains
a decrease
of QDs
size is due
the quantum
size of theconfinement
QDs (with maximum
∆Tismbecause
≈ 7◦ C that
for both
set of peaks).effect
The
to the
effect. This
the confinement
enhancement
of in
thethe
TLnumber
signal of
with
a decrease
QDs size
is duetotomore
the quancauses
an increase
surface
states of
thereby
resulting
holes
confinement
effect. This
because
that the confinement
an
andtum
electrons
to be accessible
foristhe
TL recombination,
and theeffect
wave causes
functions
increase
in theand
number
states
resulting
to more resulting
holes and to
elecof the
electrons
holesofinsurface
the QDs
arethereby
overlapped
effectively,
an
trons to
accessible
the TL recombination,
the wave
functions
of the
increase
of be
their
radiativeforrecombination
rate [3, 4]and
as well
as the
enhancement
electrons
and holes in the QDs are overlapped effectively, resulting to an inof the
TL emission.
crease of their radiative recombination rate [3, 4] as well as the enhancement of
Notice
that
the simulated TL glow curve has a very similar shape to that of
the TL
emission.
the instantaneous concentration of electrons in the conduction band. The peak
Notice that the simulated TL glow curve has a very similar shape to that of
values of the TL intensity occur at the same temperature as that of nc (T ), shown
the instantaneous concentration of electrons in the conduction band. The peak
in Fig. 5. Also, it is worthwhile to note that the temperature (∼ 210 0 C) at
values of the TL intensity occur at the same temperature as that of n (T ), shown
which m(T ) saturates coincides with the value, where the TL glow ccurves◦ ends
in Figure 5. Also, it is worthwhile to note that the temperature (∼ 210 C) at
(seewhich
Fig. 7).
m(T ) saturates coincides with the value, where the TL glow curves ends
Setting
M = 7).
m0 = 0 (Am = 0) in Eq. (3), the IMTS model becomes the
(see Figure
TTOR
model
The
graphmodel
of the becomes
TL intensity
Setting
M reported
= m0 =in0Ref.
(Am[14].
= 0)
incorresponding
Eq. (3), the IMTS
the
as aTTOR
function
of
temperature
are
depicted
in
Fig.
8,
with
the
same
parameters
model reported in Ref. [14]. The corresponding graph of the TL
intensity
as that
for of
thetemperature
IMTS model.
Similar to
IMTS
model,
the glow
curves
as a used
function
are depicted
in the
Figure
8, with
the same
parameters
possess
sets
peaks:
first around
= IMTS
90 0 Cmodel,
and thethesecond
above
as thattwo
used
forofthe
IMTSthe
model.
Similar Ttomthe
glow curves
0
◦
Tmpossess
= 190two
C,sets
corresponding
thearound
trap levels
E2 ,the
respectively.
It
1 and
of peaks: thetofirst
Tm =E90
C and
second above
◦ when the quantum dots size decrease, the intensity of the TL
is observed
that
Tm = 190
C, corresponding to the trap levels E1 and E2 , respectively. It is
intensity
increase;
while
peak temperatures
shift towards
higherofvalues
observed
that when
thethe
quantum
dots size decrease,
the intensity
the TLwith
inan tensity
increaseincrease;
in the QDs
Further,
close observation
of Fig.
8 and
Table
whilesize.
the peak
temperatures
shift towards
higher
values
with2
shows
that the widths
of thesize.
glowFurther,
curves become
broader and
an increase
in the QDs
close observation
of broader
Figure 8(maximum
and Table
1.0
0.8
0.6
3
4 nm
0.4
5
0.2
6 nm
0.0
0
100
200
300
400
0
Temperature, C
Figure
8. 8.
TheThe
TLTL
intensity
versus
temperature
Figure
intensity
versus
temperaturefor
forMM==m
m00 == 00(TTOR
(TTOR model).
model). The
other
parameter
values
areare
thethe
same
asasthat
2. 2.
other
parameter
values
same
thatininFig.
Figure
10 46
Investigation of Size Dependent Thermoluminescence Emission from ...
2 shows that the widths of the glow curves become broader and broader (maximum ∆ω = 21.3◦ C) with an increase in the QDs size. It is well known that
the size of the width is associated with the dissipation (scattering) in a material
medium [20]. Consequently, as the size of the quantum dots increases, collision
between the atoms increases thereby increasing the dissipation which is reflected
via an increased broadening of the width of the glow curve.
Table 2. The calculated values of the symmetry factor µg and order of kinetics b for the
simulated glow peaks corresponding to E2 = 0.80 eV.
Model
Trap
IMTS
AT2
TTOR
AT2
d [nm]
Tm [◦ C]
ω [◦ C]
δ [◦ C]
µg
b
3
4
5
6
165.5
167.7
170.6
172.3
49.5
49.7
49.6
49.7
21.2
21.2
21.4
21.3
0.428
0.427
0.432
0.429
1.052
1.046
1.079
1.059
3
4
5
6
177.1
188.0
208.5
227.2
66.2
71.1
79.7
87.5
33.8
37.4
43.1
46.7
0.511
0.526
0.541
0.534
1.840
2.000
2.175
2.091
Furthermore, the numerically computed symmetry factor, order of kinetics, and
other relevant parameters corresponding to the glow peaks (corresponding to
E2 = 0.80 eV) of Figures 7 and 8 are presented in Table 2. The results show
that for the IMTS model, the peaks in the vicinity of 165◦ C follow almost firstorder kinetics with µg = 0.427–0.432 and b = 1.052–1.079; while the peaks
for the TTOR model located between 177–227◦ C follow approximately secondorder kinetics with µg = 0.511–0.541 and b between 1.840–2.175. The result
is consistent with the fact that irrespective of the presence of retrapping, the
IMTS model lead to first-order looking glow curves due to the large number
of electrons in the TDDT traps [19]. Also, it is worth noting that the concept
of symmetry factor is applicable for TL glow curves, where the numerically
simulated TL glow curves possess isolated broad peak [17].
4
Conclusions
We studied the effect of size variation on TL emission of a-Si QDs using the
IMTS model. The size effect is taken into account by introducing the size dependent recombination probability coefficient. We find that as the size of the
quantum dots decrease, the intensity of the TL signal increase. Further, comparison of the results for the IMTS and TTOR models, i.e., Figures 7 and 8 as
well as Table 2, show that: (i) the IMTS model lead to first-order looking glow
curves with µg ∼ 0.42, while the glow curve for the TTOR model resembles
second-order with µg ∼ 0.52, and (ii) in the TTOR model, the peak temperature
shifts towards higher values and the widths of the glow curves gets broader and
47
B. Mesfin, T. Senbeta
broader with an increase in the QDs size, whereas it is almost independent of
size for the IMTS model. We believe that the results may be used in the design
and fabrication of devices for TL applications employing compounds enriched
with silicon.
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48
Chinese Journal of Physics 58 (2019) 235–243
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Chinese Journal of Physics
journal homepage: www.elsevier.com/locate/cjph
Size dependent optical properties of ZnO@Ag core/shell
nanostructures
T
⁎
Gashaw Beyene , Teshome Senbeta, Belayneh Mesfin
Department of Physics, Addis Ababa University, Addis Ababa, Ethiopia
A R T IC LE I N F O
ABS TRA CT
Keywords:
Core/shell nanostructure
Dielectric function
Polarizability
Refractive index
Optical absorbance
In this paper, we studied the effect of size and thickness variation on the optical properties of a
system that consists of spherical ZnO@Ag core/shell composite nanostructures embedded in a
dielectric host matrix. The effective dielectric function, polarizability, refractive index, and absorbance of the composite nanostructures are determined using the Maxwell-Garnett effective
medium theory within the framework of the electrostatic approximation. The numerical simulations using nanoinclusions of radii 20 nm show interesting behavior in the optical responses of
the ensemble. In particular, it is shown that for different values of metal fraction and filling
factor, the polarizability, refractive index, and optical absorbance of the ensemble exhibit two
sets of resonance peaks in the UV (around 300 nm) and visible (between 400 and 640 nm)
spectral regions. These peaks are attributed to the surface plasmon resonance of silver at the
ZnO/Ag and Ag/host-matrix interface. Moreover, when the Ag shell thickness is increased, the
observed resonance peaks are enhanced; accompanied with slight red shifts in the UV and blue
shifts in the visible regions. The results obtained may be used in various applications such as
sensors and nano-optoelectronics devices in optimizing material parameters to the ‘desired’ values.
1. Introduction
Zinc-oxide (ZnO) is a direct band gap semiconducting material. The Wurtzite ZnO has wide band gap (3.37 eV), high exciton
binding energy ( ∼ 60 meV) at room temperature, and high dielectric constant. These bulk material properties enable ZnO important
in various applications including in the fabrication of electronic and optical devices such as UV/blue lasers [1]. However, compared
to their bulk counterparts, ZnO nanoparticles (NPs) exhibit significantly different optical, electrical, and physical properties, which
can be controlled simply by varying their size and/or shape [2]. Due to these size and shape tunability, ZnO NPs have attracted great
interest for a diverse potential applications in optoelectronics devices such as sensors, light emitting diodes, diode lasers, and
photovoltaic cells [3,4].
Furthermore, NPs coated with a noble metal exhibit strong coupling between the plasmon resonance of the metal and the
quantum size effect of the NPs that give rise to new properties [2]. In particular, core/shell nanostructure (CSNS) composites with
metal-oxide core and metallic shell have several unique optical, photocatalytic, and electronic properties neither shown by the bare
metal nor by metal-oxide nanostructures [5–7]. Their physical and chemical properties can be tuned by varying the size of the core
and/or the thickness of the shell. Besides their unique electrical and optical properties, noble metals like Ag, Au, and Pt are preferred
as a shell material because of their high chemical stability, bio-affinity, strong absorption of light. ZnO/Ag and ZnO/Au CSNC
⁎
Corresponding authors.
E-mail address: gashaw.beyene@astu.edu.et (G. Beyene).
https://doi.org/10.1016/j.cjph.2019.01.011
Received 18 July 2018; Received in revised form 16 January 2019; Accepted 17 January 2019
Available online 11 February 2019
0577-9073/ © 2019 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved.
Chinese Journal of Physics 58 (2019) 235–243
G. Beyene, et al.
Fig. 1. The schematic diagram of a core/shell spherical nanoinclusion.
nanocomposites have been utilized in a wide range of applications such as photovoltaics, light emitting diodes, photocatalysis,
photodetectors, sensors, and also have fascinating properties such as transparent conduction, resistance switching, and biophysical
functionalities [5,8].
The fabrication of core/shell nanostructure needs a careful selection of both the core and shell materials with the aim to optimize
the passivation and to reduce the structural defects induced by positive mismatch of their lattice parameters [5]. The properties of
core/shell NS materials depend on the compositions and arrangements of both components present in the materials [9] as well as
local environment [10]. Recently, new variety of CSNSs which integrate inorganic NPs with metal-organic frameworks (MOFs) into
NP@MOF core/shell NSs has been demonstrated [11–13]. This newly introduced technique of coating inorganic NPs with MOF shells
is expected to provide the core NPs with high stability and additional functionalities [11,12]. In inorganic core/shell nanocomposites,
silver with thicknesses ranging between 5 and 10 nm is selected as a shell material for many applications [14] of ZnO nanosphere/
nanodot due to its non-toxicity, strong absorption in/near visible spectrum [15] and surface plasmon resonance [16,17].
In this paper, we studied the size dependent optical properties of an ensemble consisting of spherical core/shell ZnO@Ag nanoparticles embedded in a dielectrics host matrix. The core size and the thickness of the metallic shell are varied, simultaneously. The
paper is organized as follows: In Section 2, the effective permittivity (εeff), polarizability (η), refractive index (n), and optical absorbance of spherical core/shell NPs are derived using the Maxwell-Garnett mixing formula and the electrostatic approximation.
Numerical analysis and discussions are presented in Section 3. Finally, the main results are summarized in Section 4.
2. Model of core/shell nanostructure
Consider a spherical core/shell composite nanoparticle consisting of a semiconductor core of dielectric function (DF) ε1 and a
metallic shell of DF ε2 embedded in a dielectric host matrix, as shown in Fig. 1. The host medium is assumed to be isotropic and nonabsorbing with dielectric constant ε3. The parameters a1 and a2 are the radii of the core and core/shell NP, respectively. When an
electromagnetic wave is incident on the composite core/shell NP, electric field is induced in the system due to polarization. For NPs of
sizes (diameter = 2a2 ) much smaller than the wavelength of the incident light, the distribution of the electrostatic potential Φ associated with the induced field can be obtained by solving the Laplace equation, ∇2 Φ = 0 .
Suppose a uniform, static electromagnetic field polarized along the z-axis is applied on the spherical core/shell NP embedded in a
host matrix. If the center of the NP is assumed to coincide with the origin of a spherical coordinate system, then the distribution of the
potentials in the system may be found to be:
Φ1 (r , θ) = A1 r cos θ ,
r < a1,
B
Φ2 (r , θ) = ⎜⎛A2 r + 21 ⎟⎞ cos θ ,
r ⎠
⎝
a1 < r < a2 ,
B
Φ3 (r , θ) = ⎜⎛A3 r + 22 ⎟⎞ cos θ .
r ⎠
⎝
r > a2 ,
(1)
(2)
(3)
where Φ1, Φ2, and Φ3 are the potentials in the dielectric core, metal shell, and host matrix, respectively, A3 is a quantity associated
with the external applied field, r is the distance from the center of the NP, θ is the zenith angle, and the coefficients A1, A2, B1, B2 are
constants to be determined by using the appropriate boundary conditions at the interfaces.
It is worthwhile to note that the second term on the right-side of Eq. (3) represents the induced potential outside the core/shell
NP. The optical properties of the system may readily described by the induced field outside the concentric spheres. Consequently, it is
suffice to determine the value of the coefficient B2. Imposing the relevant boundary conditions in Eqs. (1)–(3), we obtain the following relation:
(ε1 + 2ε2)(ε2 − ε3) + vf (ε1 − ε2)(2ε2 + ε3) ⎤
B2 = ⎡
A a 3,
⎢ (ε1 + 2ε2)(ε2 + 2ε3) + 2vf (ε1 − ε2)(ε2 − ε3) ⎥ 3 2
⎣
⎦
where vf = (a1/ a2
(4)
)3 .
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In view of Eq. (3), the induced potential outside the concentric spheres is then given by
Φind =
B2
cos θ .
r2
(5)
Moreover, employing the dipole approximation, the induced potential may also be expressed as [18]
Φind =
p cos θ
,
4πε3 r 2
(6)
where p is the magnitude of the electric dipole moment of the system. In view of Eqs. (5) and (6), the dipole moment becomes
p = 4πε3 B2 = ε3 αA3 ,
(7)
where α is the polarizability of the composite given by
(ε1 + 2ε2)(ε2 − ε3) + vf (ε1 − ε2)(2ε2 + ε3) ⎤ 3
α = 4π ⎡
a .
⎢ (ε1 + 2ε2)(ε2 + 2ε3) + 2vf (ε1 − ε2)(ε2 − ε3) ⎥ 2
⎣
⎦
(8)
Further, the polarizability of an equivalent sphere of effective DF εI embedded in a host matrix of DF ε3 can be expressed in form of
the Clausius–Mossotti relation [19,20]. That is,
α = 4πa23
εI − ε3
.
εI + 2ε3
(9)
Equating Eqs. (8) and (9), we get the effective DF of the core/shell spherical inclusion to be
εI = ε2
(ε1 + 2ε2) + 2(ε1 − ε2) vf
(ε1 + 2ε2) − (ε1 − ε2) vf
.
(10)
Introducing the volume fraction (β) of a spherical core/shell NS by
a
β = 1 − ⎛⎜ 1 ⎞⎟ 3,
⎝ a2 ⎠
(11)
the effective DF, Eq. (10), may be rewritten as
εI = ε2
ε1 (3/ β − 2) + 2ε2
.
ε1 + ε2 (3/ β − 1)
(12)
Next, we consider an ensemble where identical spherical core/shell NPs (nanoinclusions) are homogeneously dispersed in a
continuous host matrix of DF, ε3. The polarizability and effective permittivity of the system may be described by using the ClausiusMossotti relation together with the Maxwell-Garnett mixing theory. If N denotes the density number of the inclusions in the system,
then the polarizability expressed in terms of the permittivity becomes [21]
εeff − ε3
Nα
=
,
3
εeff + 2ε3
(13)
where εeff is the effective permittivity and α is the polarizability defined by Eq. (9). In addition, Eq. (9) may conveniently be rewritten
as α = 4πa23 η , where η is the dimensionless polarizability defined by
η=
εI − ε3
.
εI + ε3
(14)
Substituting Eq. (12) into (14) and rearranging, we find that
η=1−
ε2 ε3 (3/ β − 1) + ε1 ε3
3⎡
⎤.
2
2⎢
ε
ε
ε
β ) − 1] + ε2 ε3 (3/ β − 1) + ε1 ε3 ⎥
+
[3/(2
1 2
⎣ 2
⎦
(15)
Furthermore, the effective permittivity of the ensemble may be obtained by substituting Eqs. (9) and (14) into Eq. (13). That is,
1 + 2ξη ⎞
εeff = ε3 ⎜⎛
⎟,
⎝ 1 − ξη ⎠
(16)
which is similar with that obtained in Ref. [22]. Here, ξ is the filling factor of the inclusions given by
ξ=N
4πa23
.
3
(17)
It is worthwhile to note that Eqs. (15) and (16) are general expressions for any two-layered spherical core/shell composite NPs
that are embedded in a dielectrics host matrix, regardless of whether the core/shell composites are metals, semiconductors/dielectrics or a combination.
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3. Numerical analysis
For numerical evaluation, we considered an ensemble that consists of spherical ZnO@Ag core/shell quantum dots distressed in
vacuum (ε3 = 1). In the frequency domain of interest, we assumed that the DF of the ZnO core to be a real constant that is independent
of frequency (ε = 8.5). In addition, the DF of the silver shell is chosen to be the modified Drude form that takes into account its nanosize. That is,
ε2 (ω) = ε∞ −
ωp2
ω [ω + iΓ(le )]
,
(18)
where ε∞ is the permittivity at high frequencies, ωp is the plasma frequency, Γ(le) is the size dependent electron collision frequency,
and ω is the frequency of the incident radiation. The size dependent damping parameter for silver can be expressed as [23,24]
Γ(le ) = Γ0 + A
Vf
le
,
(19)
where Γ0 = 1.67 × 1013 rad/s is the bulk damping constant which is associated with dissipative losses, Vf = 1.39 × 106 m/s is the
velocity of electrons at the Fermi level, and A is a constant that accounts for the details of the electron scattering processes at the
interfaces [25,26]. The quantity le is the electrons effective mean free path, which for a spherical NP of core radius a1 and core/shell
radius a2 is given by [27,28]
le =
a2
2/3 1/3
[(1 − v1/3
.
f )(1 − v f )]
2
(20)
Further, separating Eq. (18) into real and imaginary, we have
ε2 (ω) = ε2′ (ω) + iε2″ (ω),
(21)
where
ε2′ = ε∞ −
1
z 2 + ρ2
and ε2″ =
ρ
,
z (z 2 + ρ2 )
(22)
with z = ω/ ωp and ρ = Γ(le )/ ωp .
3.1. Polarizability
Since the permittivity (ε2) is complex, the electric polarizability is also a complex function of the frequency ω. That is,
η = η ′ + iη ″,
′
(23)
″
where η is the real part and η is the imaginary part. Substituting Eq. (21) into (15), we obtain
η′ = 1 −
′
″
3 ⎡ (ε2 Δ1 + ε1 ε3) γ + (ε2 Δ1) δ ⎤
2
2
⎥,
⎢
2⎣
γ +δ
⎦
(24)
and
η″ =
′
″
3 ⎡ (ε2 Δ1 + ε1 ε3) δ − (ε2 Δ1) γ ⎤
2
2
⎥,
⎢
2⎣
γ +δ
⎦
(25)
where
3
Δ1 = ε3 ⎜⎛ − 1⎟⎞,
⎝β
⎠
γ = (ε2′)2 − (ε2″)2 + ε2′ Δ2 + ε1 ε3,
δ = 2ε2′ ε2″ + ε2″ Δ2 ,
3
Δ2 = Δ1 + ε1 ⎜⎛
− 1⎟⎞.
2
β
⎝
⎠
Below, the real and imaginary parts of the polarizability of the ZnO@Ag core/shell NPs embedded in vacuum are analyzed using
Eqs. (24) and (25). The parameter values used for the numerical simulations are: ε1 = 8.5, ε∞ = 4.5, ωp = 1.46 × 1016 rad/s [29,30],
Γ0 = 1.67 × 1013 rad/s, Vf = 1.39 × 106 m/s, and A = 1 [23,24].
Fig. 2 depicts the real part of the polarizability of the nanoinclusions as a function of the wavelength of the incident radiation for
different values of volume fraction, β. It is observed that the real part of the polarizability has two sets of resonances in the UV
spectral region around λ = 310 nm and in the visible region above λ = 440 nm. The two sets of resonance peaks occur as a result of
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Fig. 2. The real part of the polarizability of the spherical nanoinclusions as a function of wavelength for different values of β.
the surface plasmon resonances of silver at the inner and outer (ZnO/Ag and Ag/host-matrix) interfaces [29]. Due to the abundance
of free carriers within the silver shell, the first set of the resonance peaks are more pronounced than the second peaks. Moreover,
when the value of β is increased, which may be realized either by decreasing the size of the core or increasing the thickness of the
shell, the two resonances become closer and closer to each other indicating that the real part of the polarizability is dominated by that
of the metal shell.
The imaginary part of the polarizability of the nanoinclusions as a function of wavelength are shown in Fig. 3, for different values
of β. Similar to the previous case, two sets of resonance peaks are observed in the UV and visible regions. In particular, for β = 0.875,
the first peak is located in the UV region at the wavelength λ = 306.8 nm, whereas the second resonance peak is at λ = 446.3 nm in the
visible region.
From Figs. 2 and 3, it is observed that the scattering of electrons at the interface is maximum from metal surface to the dielectrics
ZnO and also transmission of electrons in the metal is maximum when the metal thickness is increased. Moreover, the proposed
theoretical model derived via polarization in an external electric field may be valuable in controlling and designing highly absorbing
electrostatic resonance and emission from nanosphere arrays particularly for hybrid photovoltaic applications. In light of the present
model, we suggest that spherical core/shell NS could be the optimal geometrical configuration in order to enhance optical absorbance.
3.2. Refractive index
The response of a medium to an incident electromagnetic wave may be described by a complex refractive index (ñ ), which for a
nonmagnetic medium is defined by
n˜ =
where εeff =
εeff ,
′
εeff
+
(26)
″
iεeff
is the complex effective DF of the medium. Introducing the real (n) and imaginary parts (k), ñ may be written as
(27)
n˜ = n + ik .
Further, manipulating Eq. (26) together with εeff, we find that
′
″
n˜ 2 = n2 − k 2 + 2ikn = εeff
+ iεeff
.
(28)
Fig. 3. The imaginary part of the polarizability of the nanoinclusions obtained for different values of β.
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Fig. 4. The real part of the refractive index as a function of wavelength for fixed filling factor ξ = 0.001 and different values of β. An increase in the
metal fraction is indicated by the ‘heads’ of the dashed arrows.
Hence, the real and imaginary parts of the refractive index, respectively, takes the form:
n=
1 ⎡ ′2
″2
εeff + εeff
2⎢
⎣
)1/2 + εeff′ ⎤⎥ 1/2,
(29)
1 ⎡ ′2
″2
εeff + εeff
2⎢
⎣
)1/2 − εeff′ ⎤⎥ 1/2.
(30)
(
⎦
and
k=
(
⎦
Below, the real and imaginary parts of the refractive index of an ensemble consisting spherical ZnO@Ag core/shell nanoinclusions
embedded in vacuum are analyzed using Eqs. (29) and (30) with εeff given by Eq. (16). The parameter values used for the numerical
evaluations are the same as that used in Section 3.1.
Fig. 4 shows the real part of refractive index as a function of wavelength of the incident light for a fixed value of the filling factor
ξ = 0.001 and five different values of β. The graph shows that the refractive index varies between 0.9935 and 1.008 and possess two
sets of resonances corresponding to two anomalous dispersion regions; the first set in the UV region around 300 nm and the second
peaks in the visible region between 400 and 640 nm. The peaks show slight red shifts in the UV region and blue shifts in the visible
region when the volume fraction, β, is increased. In addition, when β increases the two resonance peaks gets closer and closer to each
other, and eventually merge for β = 1.
Furthermore, we analyzed the effect of varying the filling factor, ξ, on the real part of the refractive index, as shown in Fig. 5. It is
observed that the refractive index in the vicinity of the two resonances progressively increases as ξ increases from 0.001 to 0.011 in
steps of 0.002. However, the peaks position remain almost constant independent of the values of ξ. The result suggests that light
propagates in the ensemble more readily when the concentration (ξ) of the nanoinclusions is small. Hence, as Fig. 5 depicts, the
refractive index near the resonances can be tuned by changing the filling factor (ξ), the shell thickness, and the density of the packed
nanosphere arrays, which can play a great role in applying the core/shell structure in sensors.
The imaginary part of the refractive index, shown in Fig. 6, has two resonances for the two anomaly dispersions of the system.
When the volume fractions of the concentric spheres are nearly unity, the imaginary part of the refractive index in the UV region is
maximum. The positions and values of the maxima strongly depend on β (with the other parameters kept constant). In particular, for
β ≳ 0.75; the second maxima are about one-half smaller than the first one and the peaks are almost constant independent of β. In
addition to the volume fraction, this phenomena can occur if the electric fields are comparable with the inner atomic fields [31].
When β is increased, the peaks in the UV region and visible regions show red shift and blue shift, respectively.
Fig. 5. The real part of the refractive index obtained for β = 0.875 and different values of ξ.
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Fig. 6. The imaginary part of the refractive index of the spherical inclusions obtained for different values of β and a fixed filling factor, ξ = 0.001.
The most prominent UV emission from a bare ZnO is considered as the characteristic band edge emission of ZnO or the excitonic
recombination, whereas those observed in the different regions of the UV/visible (the so-called deep level emissions) spectrum are
attributed to intrinsic or extrinsic defects [26,32]. Defects are boundaries and interior regions of crystals which disrupt their
translational symmetry. In ZnO NPs, the intrinsic defects are those due to both oxygen and zinc vacancies, interstitials, and anti-sites
[33]; and the extrinsic defects arises when a foreign atom (impurity) is inserted into the lattice. In the ZnO@Ag nanostructure, the
Fermi level of Ag is near the defect levels of ZnO [34,35]; therefore, electrons can be transferred from the Ag defect levels to the Fermi
level of ZnO, where these electrons are excited by incident ray. The energy level of the excited electrons is near the conduction band
of Ag, which may subsequently be transferred to the conduction band of Ag where they become a part of the electron-hole recombination process thereby increasing the near band edge emission. In this model, as a consequence of the electrons’ transfer, the
visible emission will be reduced and the UV emission will be enhanced [36]. Due to such enhancement mechanisms, the refractive
index in UV region may be used for medical application in nanofields like cancer treatment and cancer detection.
3.3. Optical absorbance
The spherical inclusions in the ensemble are polarizable, with field-induced dipoles, due to the interaction of the dipole moments
with the applied uniform electric field. In our case, the incident field is assumed to be polarizable along the z-axis, and hence may be
˜ − ct )/ c], where E0 is the amplitude of the field, ñ is the complex refractive index, and c is the speed of
expressed as E = E0 exp[iω (nz
light in vacuum. Because of the presence of the term exp(−kωz / c ), the wave decays as it propagates in the composite nanostructure.
An incident light, in general, propagating in a medium is attenuated both by absorption and scattering [26]. However, for NPs
that are much smaller than the wavelength of light, scattering effects may be neglected so that only the absorption contributes
significantly to the attenuation. The intensity (I) of the propagating wave is related to the electric field by I ∼ |E|2. Generally, as the
wave traverses in the medium, the intensity is attenuated as [26,37]:
I = I0 e−αz ,
(31)
where I0 is the intensity at z = 0 and α is the absorption coefficient defined by
α=
2kω
4πk
,
=
c
λ
(32)
where λ = 2πc / ω is the wavelength of the incident radiation and k is the imaginary part of the refractive index.
The typical length of light propagation in a material medium is represented by the absorption length l, which is defined by
l = 1/ α . The quantity in the exponent of Eq. (31) is the absorbance (A) which may generally be expressed as A = ln(I0/ It ) = tα, where
It is the intensity at z = t . Thus, for the ZnO@Ag NPs, the absorbance at metal/shell interface is given by [38]:
A (λ ) =
2kω
4πk
tAg =
tAg ,
c
λ
(33)
where tAg = a2 − a1 is the thickness of the silver shell.
Fig. 7 depicts the absorbance of the spherical ZnO@Ag nanoinclusions as a function of wavelength for ξ = 0.001 and different
values of β, (or tAg); while the core/shell radius (20 nm) is kept constant. It shows two sets of absorption peaks: the first in the UV and
the second in the visible spectral regions.
It is observed that when the shell thickness is increased from tAg= 5 to 10 nm, the resonance peaks located in the vicinity of
300 nm (UV region) are enhanced and slightly red shifted. These resonances may be attributed to near band edge absorption (NBA)
due to free exciton recombination. Decreasing the size of the ZnO core (or increasing tAg) moved the absorption edge in the UV
spectral region towards high wavelengths (red shift). The shift of the absorption edge is attributed to the change in the energy gap of
the nanoparticles [39]. It means that since the band gap of NS semiconductors is increased with a decrease of their size, the so-called
quantum size effect, it leads to the shift of the absorption edge towards high energy (blue shift) [1]. For a single ZnO NP, absorption
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Fig. 7. The absorbance of the nanoinclusions obtained for different values of tAg and ξ = 0.001. The radii of the QDs is a2 = 20 nm.
peaks originate due to the interaction between electrons in the valance band and incoming photons, which lead to the excitation of
these electrons to the conduction band.
The second resonance peaks located above 420 nm are in the visible spectral region. The absorption is still enhanced when the
thickness of the shell is increased, but blue shifted contrary to that in the UV region. These resonance peaks are due to deep level
emissions (DLE) which are attributed to the surface plasmon resonance of silver nanoshell. Such absorptions in the visible spectral
region in ZnO has been frequently ascribed to several intrinsic and extrinsic effects [39]. The DLE or blue radiation is due to electron
recombination in oxygen vacancy (VO) with a hole in the valance band. The absorption becomes stronger as the thickness of the silver
shell increases from 5 to 10 nm. On the other hand, the resonance peaks show a red shift with an increase in shell thickness, while the
broadening of the absorption spectra are observed when the thickness of the shell is decreased [26]. This broadening of the spectra
are caused because of the incorporation of the NPs size effect in our analysis via Eq. (19).
It may be concluded that the direct contact between quantum dots of ZnO and Ag NPs can lead to interfacial charge transfer
process that are of paramount importance in highly relevant topics such as photocatalytic reactions and light energy conversion
[40–43], via the application of the core/shell nanostructure.
4. Conclusions
In summary, we studied the effect of varying the core radius and thickness of the metallic shell on the optical response of
nanocomposites consisting of spherical ZnO@Ag core/shell nanoinclusions embedded in vacuum. The polarizability, refractive index,
and optical absorbance of the system are determined by employing the electrostatic approximation and the Maxwell–Garnett effective medium theory. Moreover, the DF of the silver shell is chosen to be of the modified Drude form that takes into account its
nano-size. It is shown that for different values of the metal fraction β and filling factors ξ, the graphs of the real and imaginary parts of
the polarizability and refractive index of the nanocomposites as a function of wavelength possess two resonance peaks in the UV
(around 300 nm) and visible (between 400 and 640 nm) spectral regions. These resonance peaks correspond to the surface plasmon
resonances of Ag at the ZnO/Ag and Ag/host-matrix interfaces, respectively. The resonance peaks show slight red shift in the UV
region and blue shift in the visible region when β or ξ is increased. Similarly, for a fixed core/shell radius of 20 nm, the graphs of the
optical absorbance versus wavelength for fixed ξ = 0.001 and different values of shell thicknesses (tAg= 5–10 nm) show also two sets of
absorption peaks - in the same spectral regions. It is observed that when the Ag shell thickness increases, the two sets of resonance
peaks are enhanced; accompanied with slight red shift in the UV and blue shift in the visible spectral regions.
The enhancement in the optical properties is mainly attributed to strong coupling of the surface plasmon resonance of the Ag shell
and the energy gap of the ZnO NPs in both spectral regions. Indeed, compared with the bare ZnO, the silver coated ZnO NPs possess
improved potential device applications in the optical frequency region. The results may be used to optimize ‘desired’ device parameters of nanocomposites consisting of ZnO@Ag core/shell nanostructures that are designed for various applications such as sensors
and nano-optoelectronics devices.
Acknowledgments
This work was supported financially by the Addis Ababa University and Adama Science and Technology University.
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243
Photonics and Nanostructures - Fundamentals and Applications 33 (2019) 48–54
Contents lists available at ScienceDirect
Photonics and Nanostructures - Fundamentals and
Applications
journal homepage: www.elsevier.com/locate/photonics
Invited Paper
Surface plasmon resonances in ellipsoidal bimetallic nanoparticles
a,⁎
b
Sioma Debela , Belayneh Mesfin , Teshome Senbeta
a
b
T
b
Department of Physics, Dilla University, Dilla, Ethiopia
Department of Physics, Addis Ababa University, Addis Ababa, Ethiopia
A R T I C LE I N FO
A B S T R A C T
Keywords:
Confocal ellipsoids
Effective polarization
Plasmon modes
Aspect ratio
Thickness of shell
The surface plasmon response of three-layered bimetallic nanoparticles embedded in a SiO2 host matrix is
studied for different geometries. The analytical solution for the electromagnetic response in relation to the
extinction cross section of the bimetallic nanoparticles is obtained by means of quasistatic theory. To show the
extinction spectra of the three-layered bimetallic nanoparticles, we chose two different metals, namely, Ag and
Au-Ag 50:50 alloy. The optical properties of the metals studied are described within the modified DrudeSommerfeld model of the dielectric function with parameters accounting for the contribution of conduction
electrons and interband transitions. We found that the position of the surface plasmon resonance depends on the
dielectric function of the intermediate medium between the Au-Ag 50:50 alloy core and the Ag shell, the
thickness of the Ag shell, the thickness of the intermediate medium, and the aspect ratio of the three-layered
nanoparticles.
1. Introduction
plasmon modes of the inner-core metal and the outer nanoshell. The
hybridized plasmon modes are the result of antisymmetric coupling
between the outer antibonding shell plasmon mode and the innersphere plasmon mode (∣ω++⟩), the symmetric coupling between the outer
antibonding shell plasmon mode and the inner-sphere plasmon mode
(∣ω+−⟩), the symmetric coupling between the outer bonding shell
plasmon mode and the inner-sphere plasmon mode (∣ω−+⟩), and the
antisymmetric coupling between the outer bonding shell plasmon mode
and the inner-sphere plasmon mode (∣ω−−⟩). Nonetheless, the ∣ω++⟩ mode
very weakly couples to EM radiation, which makes it too difficult to
observe in the optical spectrum [7,10].
To describe the optical response of nanoparticles, it is crucial to
understand the number, position, and width of the SPRs as a function of
the nanoparticle shape, size, and environment [11]. In this article, we
investigate the influence of geometry, aspect ratio (AR), and composition on the SPR properties of three-layered bimetallic nanoparticles. We
use the quasistatic approximation to obtain the analytical solution for
the EM response in relation to the local field distribution. The quasistatic approximation is often used to describe the optical properties of
sub-wavelength-sized spherical and ellipsoidal metallic nanoparticles.
However, as the particle's size becomes larger, retardation effects and
higher-order responses such as a quadruple response become significant
and have to be incorporated into the calculations by retention of higher
orders of the Mie theory scattering coefficients [12,13].
Bimetallic nanoparticles have attracted tremendous attention [1–4]
in recent years because of their unique optical properties beyond those
of pure metallic nanoparticles. These properties result from the coherent oscillations of electron density on the surface of metal particles
because of interaction between the metal and the electromagnetic (EM)
field of light known as surface plasmon resonances (SPRs). These materials have possible applications ranging from sensing and biomedicine
to imaging and information technology [5].
The composition-dependent plasmonic response of bimetallic
core–shell nanoparticles has been studied experimentally [4,6] and
theoretically [7]. Arnold et al. [8] showed that operating near the
plasma frequency of bimetallic core–shell nanoparticles offers widely
tunable plasmon modes as compared with their monometallic counterparts. In two-layered bimetallic nanoparticles, the interaction between the core-sphere plasmon and bonding and antibonding plasmons
of the outer nanoshell results in three hybridized plasmons, although
only two resonance modes can be observed in the extinction spectrum
of such core–shell nanoparticles. In particular, for Au-Ag bimetallic
nanoparticles, at most two SPR bands are observed in the UV-visible
region [9,6].
In the reports of Prodan and Nordlander [7] and Qian et al. [10],
there are four dipolar plasmon resonances for three-layered bimetallic
nanoparticles, which correspond to the interaction between the
⁎
Corresponding author.
E-mail address: sioma@du.edu.et (S. Debela).
https://doi.org/10.1016/j.photonics.2018.11.007
Received 29 September 2017; Received in revised form 27 November 2018; Accepted 27 November 2018
Available online 07 December 2018
1569-4410/ © 2018 Published by Elsevier B.V.
Photonics and Nanostructures - Fundamentals and Applications 33 (2019) 48–54
S. Debela et al.
nanoparticle, respectively).
The dipolar potential distribution inside and outside the threelayered ellipsoidal bimetallic nanoparticle subjected to z-polarized light
is as follows:
Φ1 (ξ , η , ζ ) = −β1 F1 (ξ ) G (η , ζ ),
(1)
Φ2 (ξ , η , ζ ) = [β2 F1 (ξ ) + β3 F2 (ξ )] G (η , ζ ),
(2)
Φ3 (ξ , η , ζ ) = [β4 F1 (ξ ) + β5 F2 (ξ )] G (η , ζ ),
(3)
Φ4 (ξ , η , ζ ) = Φ0 + β6 F2 (ξ ) G (η , ζ ),
(4)
with
F1 (ξ ) = (c12 + ξ )1/2 ,
Fig. 1. A confocal three-layered bimetallic ellipsoidal nanoparticle in a matrix.
The dielectric functions of the Ag-Au 50:50 alloy (i.e., for equal molar fraction
of Au and Ag in the alloy) core, intermediate dielectric layer, outer Ag shell, and
embedding medium are ε1, ε2, ε3, and ε4, respectively; a1, b1, and c1 denote the
semi-principal axes of the core ellipsoid, a2, b2, and c2 denote the semi-principal
axes of the intermediate layer, and a3, b3, and c3 denote the semi-principal axes
of the outer nanoshell.
F2 (ξ ) = F1 (ξ )
∫ξ
∞
(5)
dq
,
F12 (q) f1 (q)
(6)
f1 (q) = [(q + a12)(q + b12)(q + c12)]1/2 ,
(7)
and
1/2
(η + c12)(ζ + c12) ⎤
G (η , ζ ) = ⎡ 2
⎢ (a1 − c12)(b12 − c12) ⎥
⎦
⎣
2. The model
.
(8)
Here Φ1(ξ, η, ζ), Φ2(ξ, η, ζ), Φ3(ξ, η, ζ), and Φ4(ξ, η, ζ) are potentials in
the core metallic nanoparticle, intermediate dielectric layer, metal coat,
and host matrix, respectively. Φ0 denotes the potential due to the external field E0. ξ, η, and ζ are ellipsoidal coordinates, β1, β2, β3, β4, β5,
and β6 are coefficients to be determined (see the Appendix) from the
continuity of the potential and the normal component of the displacement vector at interfaces.
The second term in Eq. (4) denotes the induced electric potential
surrounding the three-layered ellipsoidal nanoparticle as a result of
polarization. Accordingly, the electric field due to polarization Epol of
the
nanoparticle
can
be
obtained
from
the
relation
Epol =− ∇ (Φ4 − Φ0). At distance r much larger than the largest semiaxis a3 of the ellipsoid, Epol takes the form
In this theoretical investigation, we consider a three-layered confocal ellipsoidal nanoparticle composed of a metallic core (made of AuAg 50:50 alloy) with dielectric constant ε1, an intermediate dielectric
layer with dielectric constant ε2, and an outer Ag shell with dielectric
constant ε3 embedded in a uniform unbounded medium with permittivity ε4 as shown in Fig. 1. The three-layered ellipsoidal nanoparticle is
characterized by semi-principal axes ai, bi, and ci (where ai > bi > ci,
i = 1, 2, 3). The ellipsoidal geometry considered allows us to study the
effect of shape, AR, and transverse and longitudinal components of the
plasmonic response in addition to the effect of composition in bimetallic three-layered nanoparticles. The study is restricted to the plasmon
modes generated in the three-layered confocal ellipsoids. The analysis is
performed in the electrostatic approximation in which the size of the
nanoparticles is much less than the wavelength of incident light.
Therefore the analytical solution for the electrostatic potential Φ inside
and outside the three-layered bimetallic nanoparticles is obtained by
our solving the Laplace equation for ellipsoidal symmetry (i.e.,
∇2Φ = 0).
Four plasmon modes are generated in a three-layered metal/dielectric/metal ellipsoidal nanoparticle when the direction of the applied field is along any one of the semi-principal axes. Fig. 2 illustrates
the four plasmon modes that are produced in a confocal three-layered
bimetallic ellipsoidal nanoparticle for transverse mode (TM) excitation
and longitudinal mode (LM) excitation (i.e., when the applied electric
field is perpendicular and parallel to the semi-major axis of the
E pol ≃
1
[3(pnp ·eˆ r ) eˆ r − pnp],
r3
(9)
where pnp = 4πa3b3c3ε4(δell/3Δell)E0, with δell and Δell are defined in
Eqs. (31) and (30) (see the Appendix), respectively, and êr is a unit
vector in the radial direction. Eq. (9) is identical to the field produced
by a dipole located at the origin with dipole moment equal to pnp. In the
linear optical regime, the induced polarization in the nanoparticle depends on the electric field according to the relation [14,15]
pnp = ε4 α np E0 ,
(10)
where αnp is the polarizability, which is a measure of the ease with
which the ellipsoidal nanoparticle is polarized [15]. This means the
applied field induces an effective polarization αnp on the nanoparticle of
ν
α np
=
4
δ
πa3 b3 c3 ⎛ ell ⎞,
3
⎝ Δell ⎠
⎜
⎟
(11)
where δell = δell (Lνk , εi, pc , pm ) and Δell = Δell (Lνk , εi, pc , pm ) (see the Appendix), where pc = 1 − a1b1c1/a2b2c2 is the volume fraction of the
dielectric layer relative to the inner core–shell (i.e., metal core and the
dielectric intermediate layer) part of the nanoparticle and
pm = 1 − a2b2c2/a3b3c3 is the volume fraction of the metal coat. Here
pm is defined relative to the total volume of the nanoparticle, while pc is
defined relative to the inner core–shell part of the nanoparticle. Lνk are
geometric factors, with the subscript ν = 1, 2, 3 denoting the direction
of the field along the x, y, and z axes, respectively, and the superscript
k = 1, 2, 3 representing the inner, middle, and outer ellipsoids, respectively. εi, with i = 1, 2, 3, 4, denotes the dielectric constant of the
three layers and the host matrix, as shown in Fig. 1.
The attenuation of the EM wave as it goes through a material results
Fig. 2. Distribution patterns of charge densities in a three-layered bimetallic
confocal ellipsoidal nanoparticle irradiated by light with polarization parallel to
the three semi-principal axes. The longitudinal plasmon modes (e–h) and the
transverse plasmon modes (a–d, i–l) are generated when the polarization of the
incident light is parallel and perpendicular to the major axis of the particle,
respectively.
49
Photonics and Nanostructures - Fundamentals and Applications 33 (2019) 48–54
S. Debela et al.
in EM extinction [11]. The dipolar contribution of the EM extinction
cross section (the sum of scattering and absorption cross sections) Cext
of sub-wavelength-sized metallic nanoparticles in response to incident
light can be represented as [15]
Cext = k Im{α } +
k4 2
|α| ,
6π
(12)
where α is the polarizability of the nanoparticle and the wavevector
k = 2π ε4 / λ , with λ and ε4 being the wavelength of light and the
permittivity of the surrounding medium, respectively.
The first and second terms in Eq. (12) are attributed to the absorption cross section and scattering cross section of the nanoparticle,
respectively. For nanoparticles that are much smaller than the wavelength of light, only the absorption cross section contributes significantly to the extinction cross section [15,16]. The extinction cross
section of metallic nanoparticles is often normalized to the particle's
geometric cross-sectional area projected onto a plane perpendicular to
the incident beam and expressed as [16]
Qext =
Cext
,
σ⊥
Fig. 3. The shape-dependent extinction spectra of three-layered bimetallic nanoparticles composed of a Au-Ag 50:50 alloy core (ε1(ω)), a SiO2 (ε2 = 3.90)
intermediate layer, and a Ag shell (ε3(ω)) embedded in a SiO2 (ε4 = 3.90) host
matrix according to Eq. (14): the longitudinal mode (LM) extinction spectrum
of prolate spheroidal bimetallic nanoparticles with a3 = 22.06 nm,
b3 = 21.45 nm, and c3 = 21.45 nm (I); the LM extinction spectrum of oblate
spheroidal bimetallic nanoparticles with a3 = 21.45 nm, b3 = 21.45 nm, and
c3 = 22.06 nm (II); the extinction spectrum parallel to the intermediate axis
(axis b3) of ellipsoidal bimetallic nanoparticles with a3 = 21.50 nm,
b3 = 20.50 nm, and c3 = 20.00 nm (III); the extinction spectrum of spherical
bimetallic nanoparticles with a3 = b3 = c3 = 20.66 nm (IV); the transverse
mode (TM) extinction spectrum of oblate spheroidal bimetallic nanoparticles
(V); and the TM extinction spectrum of prolate spheroidal bimetallic nanoparticles (VI).
(13)
where Qext is the extinction efficiency of the particle and σ⊥ is the
geometric cross section perpendicular to the direction of light propagation. For instance, when the particle is illuminated by light propagating parallel to semi-major axis a3, σ⊥ = πb3c3.
Substitution of Eq. (11) into Eq. (13) leads to the expression for the
extinction efficiency of the three-layered bimetallic ellipsoidal nanoparticle:
2
Qext
⎜
⎟
⎜
∣ω+−⟩, ∣ω−+⟩, and ∣ω−−⟩ modes. Notably, the influence of shape on the position and height of the SPRs is clearly visible. For spheroidal nanoparticles, the resonance frequency of transverse plasmons lies at slightly
shorter wavelengths (higher energy) with respect to spherical nanoparticles, while the resonance frequency of longitudinal plasmons shifts
toward longer wavelengths (lower energy) except for the ∣ω+−⟩ mode.
For the ∣ω+−⟩ mode, the direction of shifting reverses for the TMs and
LMs. The extinction spectrum of bimetallic ellipsoidal nanoparticles
with an intermediate axis (axis b3) parallel to the incident light lies
between the TM and LM extinction spectra of spheroidal nanoparticles.
On the other hand, the extinction spectra parallel to the semi-major axis
(axis a3) and the semi-minor axis (axis c3) exhibit the largest redshift
and blueshift, respectively (not shown in Fig. 3).
The TMs are more intense than the LMs in the higher (∣ω+−⟩) energy
region, while the LMs dominate the TMs in the intermediate (∣ω−+⟩)
region. The position and plasmon peaks of spherical nanoparticles are
located between the LMs and TMs of spheroidal nanoparticles.
The dielectric constant of the intermediate layer influences the
plasmonic response of the three-layered nanoparticles. The effects are
demonstrated by our considering ellipsoidal nanoparticles that are illuminated by incident light with polarization parallel to the intermediate axis (b3) of the nanoparticle. Similar effects can be observed if
other geometries are considered. As can be clearly seen from Fig. 4, the
choice of the intermediate medium strongly affects the plasmon resonance features of the three-layered bimetallic nanoparticles. Particularly, when the dielectric function (ε2) of the intermediate layer increases from 2 to 7, the ∣ω−−⟩ plasmon peak decreases and eventually
disappears, while the ∣ω−+⟩ and ∣ω+−⟩ peaks increase. The effects follow
from the dielectric screening of the electric fields illustrated in [7]. The
increase of the dielectric constant of the intermediate layer compensates some of the induced charge density distributions on the core and
the inner surface of the outer shell, resulting in a reduction of the local
electric field between the core and the metal shell. This effect severely
limits the ∣ω−−⟩ plasmon peak, as can be seen from Fig. 4.
Moreover, the increase in dielectric constant is synchronous with
the movement of the plasmon peaks toward longer wavelengths (lower
energy). Therefore, the position, height, and numbers of the plasmon
modes excited in three-layered bimetallic nanoparticles are strongly
2
V
δ
σ V
δ
= ⎛ ⎞ k Im ⎧ ell ⎫ + ⊥ ⎛ ⎞ k 4 ell ,
⎨
⎬
σ
Δ
6
π
σ
Δ
⊥
⊥
ell
ell
⎝ ⎠
⎝ ⎠
⎩
⎭
⎟
(14)
where V = (4/3)πa3b3c3 is the volume of the three-layered ellipsoidal
nanoparticle.
For Au-Ag alloys, the composition- and frequency-dependent multiparametric equation of the dielectric function εm of the metal is described by the modified Drude form given by [17]
εm= ε∞ −
ωp2
ω (ω + iγ )
+ εcp1 (ω, ω01, ωg1, γ1, A1 )
+ εcp2 (ω, ω02 , γ2, A2 ),
(15)
where ε∞ is a real constant, ωp is the bulk plasma frequency of the
metal, γ is the size-dependent decay constant of plasma vibrations, ω is
the frequency of radiation, and εcp1 and εcp2 are the interband contributions to the dielectric function of the plasmonic metals. The sizedependent decay constant of plasma vibrations γ given by [18]
γ = γbulk + A
vF
,
R
(16)
where γbulk is the bulk decay constant of plasma vibrations, vF is the
velocity of the electrons at the Fermi surface, R is the radius of the
nanoparticle, and A is a parameter that depends on the details of the
scattering process [18]. The expression for γ can easily be extended to
consider a shell of thickness a [19]; in this case, a is used instead of R.
We will use the effective polarizability of the three-layered nanoparticle, Eq. (11), with consideration of the complex dielectric function
of the core and shell metals, Eq. (15), and the tabulated parameters in
[17] to calculate the extinction efficiency.
3. Results and discussion
The resonance of surface plasmons is strongly influenced by the
shape of the three-layered bimetallic nanoparticles. Fig. 3 shows examples of extinction spectra for three-layered bimetallic nanoparticles
with spherical, prolate spheroidal, oblate spheroidal, and ellipsoidal
geometric shapes (with identical effective volume). In the extinction
spectra, one can observe three resonance peaks corresponding to the
50
Photonics and Nanostructures - Fundamentals and Applications 33 (2019) 48–54
S. Debela et al.
electric field around the metal shell. Thus more pronounced peaks are
expected to emerge at the three plasmon bands.
Notably, as the thickness of the Ag shell is increased, the three resonance peaks increase and the resonance peaks for the ∣ω−−⟩ mode
shows a considerable blueshift, while the resonance peak for the ∣ω+−⟩
mode exhibits a slight redshift, as can be clearly seen from Fig. 5a. On
the other hand, the position of the ∣ω−+⟩ mode seems insensitive to the
thickness of the Ag shell.
As can be clearly seen from Fig. 5b, when the thickness (i.e., pc) of
the intermediate dielectric medium is increased, the ∣ω−−⟩ and the ∣ω+−⟩
plasmon peaks increase and move to shorter wavelength (higher energy), while the ∣ω−+⟩ plasmon peak decreases without a noticeable peak
shift. The decrease of the intermediate dielectric layer thickness results
in enhancement of plasmon interaction between the core metallic nanoparticle and the outer nanoshell accompanied by a redshift of the
antisymmetric and symmetric coupling modes as illustrated in [10].
When the dielectric volume fraction pc ≤ 75%, we can clearly observe
two resonance modes, similar to what was observed for the two-layered
bimetallic nanoparticles in [6], as the ∣ω−−⟩ peak disappears completely.
On the other hand, a progressively pronounced peak of the ∣ω−−⟩ mode
begins to emerge when pc > 75%.
The AR, that is, the ratio between the major and minor axes of the
three-layered confocal prolate and oblate spheroids, can be defined as
AR = ak/bk and AR = ak/ck (with k = 1, 2, 3; see the Appendix), respectively. The variation of the extinction spectra with increasing AR
can be clearly observed when the composition (i.e., pm and pc) and total
volume of the three-layered nanoparticle are kept fixed. Fig. 6 nicely
illustrates the AR-dependent plasmon modes of the three-layered prolate spheroidal bimetallic nanoparticles. For example, for fixed values
of pm = 60% and pc = 90%, increasing the AR of the three-layered
nanoparticle from 1.17 to 1.83 (Fig. 6a) results in a progressive shift of
the LM spectra. The ∣ω−−⟩ and the ∣ω−+⟩ modes shift toward longer
Fig. 4. The effect of the dielectric constant of the intermediate layer on the
extinction spectra of three-layered bimetallic ellipsoidal nanoparticles: ε2 = 2,
ε2 = 3, ε2 = 4, ε2 = 5, ε2 = 7. The nanoparticles are illuminated by incident
light with polarization parallel to the b3 axis of the nanoparticle. The core radii
are a1 = 6 nm, a2 = 4 nm, and a3 = 2 nm, the volume fraction of the dielectric
layer pc = 93%, and the volume fraction of the Ag coat pm = 50%.
affected by the dielectric constant of the intermediate layer.
The extinction spectra calculated for three-layered ellipsoidal nanoparticles with different values of Ag-coat volume fraction pm and SiO2
volume fraction pc are shown in Fig. 5. We consider the plasmon excitation along the b3 axis to demonstrate the effects. The thickness of
the Ag shell and the thickness of the intermediate dielectric layer can
cause drastic changes to the dipolar plasmon resonances of the bimetallic nanoparticles. The increase of the Ag shell thickness (i.e., increasing pm) enhances the charge density distributions both at the outer
surface and at inner surface of the Ag shell, resulting in an intense local
Fig. 5. Extinction spectra of bimetallic ellipsoidal nanoparticles with core radii
a1 = 2 nm, a2 = 4 nm, and a3 = 6 nm illuminated by incident light with polarization parallel to the b3 axis of the nanoparticle. (a) When the intermediate
SiO2 volume fraction is fixed at pc = 93% and the volume fraction of the Ag
coat pm = 45%, pm = 50%, pm = 55%, pm = 60%, and pm = 65%. (b) When the
volume fraction of the Ag coat is fixed at pm = 50% and the intermediate SiO2
volume fraction pc = 75%, pc = 86%, pc = 90%, pc = 93%, and pc = 95%.
Fig. 6. The aspect ratio (AR)-dependent extinction spectra of three-layered
prolate spheroidal bimetallic nanoparticles, depicted by our considering equal
AR of the core, intermediate layer, and outer metal shell. (a) The effect of the
AR on the longitudinal mode plasmon excitation. (b) The effect of the AR on the
transverse mode plasmon excitation.
51
Photonics and Nanostructures - Fundamentals and Applications 33 (2019) 48–54
S. Debela et al.
wavelength (lower energy), while the ∣ω+−⟩ mode moves slightly to
shorter wavelength (higher energy). Moreover, the increase in the AR
results in increase of the intensity of the ∣ω−+⟩ mode while the intensity
of the ∣ω+−⟩ mode decreases. In Fig. 6, the ∣ω−−⟩ peak seems to be slightly
affected by the AR of the nanoparticle. However, a further increase in
the AR results in fading of the ∣ω−−⟩ mode (not shown in Fig. 6).
As can be seen from Fig. 6b, the increase in the AR shifts the spectral
positions of TMs. The intensities of the three plasmon modes increase
with increase of the AR of the nanoparticle. Moreover, the ∣ω−−⟩ and the
∣ω−+⟩ plasmon modes exhibit a blueshift with increase of the AR, while
the ∣ω+−⟩ mode seems to be unaffected.
by means of quasistatic theory. The interaction between the core metallic nanoparticle and outer metallic nanoshell results in three plasmon
bands. The increase in the dielectric constant of the intermediate layer
as well as the decrease in thickness of the intermediate layer leads to
fading and disappearance of the antisymmetric coupling between the
outer bonding shell plasmon mode and the inner-sphere plasmon mode.
The longitudinal plasmon modes of spheroidal bimetallic nanoparticles
are very sensitive to the AR of the nanoparticles, unlike the case of
transverse plasmon modes. We showed that the shape, AR, thickness of
the intermediate and outer layers, and dielectric constant of the intermediate layer provide a means to spectrally tune the optical absorption
of three-layered bimetallic nanoparticles, providing a way to engineer
the plasma frequency of the system to the desired spectral ranges.
4. Conclusions
The local SPR of three-layered bimetallic nanoparticles was studied
Appendix A. Calculation of the electric potential of a three-layered ellipsoidal nanoparticle
When a three-layered bimetallic ellipsoidal nanoparticle is irradiated by light, the electric field of the incident light induces a polarization of free
electrons with respect to the much heavier ionic core of the two metals. The polarization causes a large resonant enhancement of the local field inside
and near the nanoparticle. To determine the electric potential Φ surrounding the particle, we solve the Laplace equation, ∇2Φ = 0, for ellipsoidal
symmetry, thereby obtaining the electric field distribution from the relation E =− ∇ Φ.
The surface of an ellipsoid in ellipsoidal coordinates (ξ, η, ζ) is defined as [15]
a2
y2
x2
z2
+ 2
+ 2
= 1,
+ξ
b +ξ
c +ξ
x2
a2 + η
+
y2
b2 + η
z2
+
c2 + η
−c 2 < ξ < ∞ ,
= 1,
y2
x2
z2
+ 2
+ 2
= 1,
a2 + ζ
b +ζ
c +ζ
(17)
− b 2 < η < − c 2,
(18)
−a2 < ζ < − b2 ,
(19)
where a, b, and c are the semi-principal axes of the ellipsoid, with a > b > c.
The surface ξ = constant generates confocal ellipsoids, where the particular ellipsoid, ξ = 0, coincides with the boundary of the particle [15]. In
three-layered confocal ellipsoidal nanoparticles, the equation ξ = 0 coincides with the outer boundary of the core, whereas the equations ξ = t1 and
ξ = t2 correspond to the surface of the intermediate layer and the surface of the outer shell, respectively. Consequently, it is easy to establish the
relations
a12 + t1 = a22 ,
b12 + t1 = b22 ,
c12 + t1 = c22,
(20)
a22 + t2 = a32 ,
b22 + t2 = b32 ,
c22 + t2 = c32,
(21)
where t1 and t2 are constants to be determined from known values of a1, b1, c1, pc, and pm.
The Laplace equation of the electric potential Φ in ellipsoidal coordinates is [15]
∂
{
∂Φ
∇2 Φ= (η − ζ ) f (ξ ) ∂ξ f (ξ ) ∂ξ
+ (ζ − ξ ) f
∂
(η) ∂η
∂
+ (ξ − η) f (ζ ) ∂ζ
}
{f }
{f (ζ ) } = 0.
∂Φ
(η) ∂η
∂Φ
∂ζ
(22)
Here f is defined for a variable q as
fk (q) = [(q + ak2)(q + bk2)(q + ck2)]1/2
(k = 1, 2, 3),
(23)
where k = 1, 2, 3 corresponds to the three interfaces of the three-layered system.
The electric potential distribution inside and outside the three-layered ellipsoidal bimetallic nanoparticle is obtained according to Eqs. (1)– (4).
The continuity of the potential and the normal component of the displacement vector at interfaces leads to (with notation εi ± j = εi ± εj, where i,
j ≡ 1, 2 or 3) the following required coefficients of the potential inside and outside the three concentric ellipsoids:
β1 =
β2 =
β3 =
ε2 ε3 ε4
E0 ,
Δell
ε3 ε4 (L3(1) ε1 − 2
(24)
+ ε2)
Δell
E0 ,
(25)
a1 b1 c1 ε3 ε4 ε1 − 2
E0 ,
2Δell
(26)
52
Photonics and Nanostructures - Fundamentals and Applications 33 (2019) 48–54
S. Debela et al.
β4= −
+
β5= −
+
β6 =
ε4 (L3(1) ε1 − 2 + ε2)(L3(2) ε2 − 3 + ε3)
E0
Δell
ε4 L3(2) (1 − pc )(L3(2) − 1) ε1 − 2 ε2 − 3
Δell
E0 ,
a2 b2 c 2 ε4 ε1 − 2 (1 − pc )(L3(2) ε2 − 3 − ε2)
2Δell
a2 b2 c 2 ε4 (L3(1) ε1 − 2 + ε2) ε2 − 3
2Δell
(27)
E0
E0 ,
(28)
a3 b3 c3 δell
E0 ,
2Δell
(29)
where
Δell = C1 ε32 + C2 ε1 + C3
(30)
and
δell= (1 − pm )(1 − pc )[(1 − L3(3) ) ε3 + L3(3) ε4 ] q1 ε1 − 2
+ (1 − pm )[(1 − L3(3) ) ε3 + L3(3) ε4 ] q2 ε2 − 3
+ ε3 − 4 [L3(2) (1 − L3(2) )(1 − pc ) ε1 − 2 ε2 − 3 + q2 q3],
(31)
with
q1 = (1 − L3(2) ) ε2 + L3(2) ε3,
(32)
q2 = (1 − L3(1) ) ε2 + L3(1) ε1,
(33)
and
q3 = (1 − L3(2) ) ε3 + L3(2) ε2.
(34)
Here
C1= L3(3) pm (1 − L3(3) ){ε1 − 2 [L3(1) − L3(2) (1 − pc )] + ε2}
+ L3(3) (L3(3) − L3(2) ){ε1 − 2 [L3(1) − L3(2) (1 − pc )] + ε2},
(35)
C2= − M4 (L3(2) )2 (1 − pm ) ε(2 + 4) ε4 (1 − L3(3) )
+ M4 {L3(3) M1 ε(2 + 4) − L3(2) ε4}
+ (1 − pc ) ε1 − 2 {L3(2) ε4 (M2 L3(3) + L3(2) − M2)}
+ (1 − pc ) ε1 − 2 {M3 (M2 ε2 − ε2 M1 − L3(2) ε4},
(36)
and
C3= (1 − pc ) ε2 ε4 ε1 − 2 {M3 (M2 + M1) + (L3(2) )2 + L3(2) ε4}
+ ε2 ε4 M4 (L3(3) M2 + L3(2) − L3(3) M1),
(37)
with
M1 = 1 − pm + L3(2) ,
(38)
M2 = (1 − pm ) L3(3) ,
(39)
M3 =
L3(3)
(L3(2)
− 1),
(40)
and
M4 = (L3(1) ε1 − 2 + ε2),
(41)
where
and
are the geometric factors for the inner, middle, and outer ellipsoids, respectively, and pm = 1 − a2b2c2/a3b3c3 and
pc = 1 − a1b1c1/a2b2c2 are the metal fraction of the three-layered system and the spacer fraction with respect to the two inner layers.
L3(1) ,
L3(k ) =
L3(2) ,
ak bk ck
2
∫0
∞
L3(3)
dq
.
(ck2 + q) fk (q)
(42)
When the field is applied along the x and y axes, the corresponding geometric factors are defined as L1(k ) and L2(k ) , respectively. That is,
L1(k ) =
ak bk ck
2
∫0
∞
ak bk ck
2
∫0
∞
dq
(ak2 + q) fk (q)
(k = 1, 2, 3)
dq
(bk2 + q) fk (q)
(k = 1, 2, 3).
(43)
and
L2(k ) =
(44)
53
Photonics and Nanostructures - Fundamentals and Applications 33 (2019) 48–54
S. Debela et al.
Prolate (cigar-shaped) spheroids can be generated by rotation of an ellipse about its major axis, whereas oblate (pancake-shaped) spheroids are
generated by rotation of an ellipse about its minor axis.
Integration of Eq. (43) followed by some rearrangement leads to the expression for the depolarization factor for prolate spheroids (bk = ck and
L2k = L3k ) as a function of eccentricity e. That is,
L1(k )=
1 − ek2
ek2
⎡ 21e ln
⎣ k
ek2 = 1 −
bk2
ak2
( ) − 1⎤⎦,
1 + ek
1 − ek
(k = 1, 2, 3).
(45)
For three-layered oblate spheroids (ak = bk and
L1(k )=
{
g (ek ) π
2ek2 2
}
− arctan[g (ek )] −
g (ek ) =
L1k
=
L2k ),
the depolarization factor takes the form
g 2 (ek )
,
2
1 − e 2 1/2
⎛ 2k⎞ ,
⎝ ek ⎠
(46)
with
ek2 = 1 −
ck2
ak2
(k = 1, 2, 3).
(47)
For a three-layered sphere (a1 = b1 = c1, a2 = b2 = c2, a3 = b3 = c3), the depolarization factors are all degenerate and are
L1(k ) = L2(k ) = L3(k ) = 1/3.
References
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[11]
[12]
[13]
[14]
[15]
[1] K.D. Gilroy, A. Ruditskiy, H.-C. Peng, D. Qin, Y. Xia, Chem. Rev. 116 (2016)
10414–10472.
[2] A. Malasi, H. Taz, M. Ehrsam, J. Goodwin, H. Garcia, R. Kalyanaraman, Appl.
Photonics 1 (2016) 076101.
[3] E. Atmatzakisa, N. Papasimakisa, N.I. Zheludeva, Microelectron. Eng. 172 (2017)
30–34.
[4] R.J. Peláez, C.E. Rodríguez, C.N. Afonso, Nanotechnology 27 (2016) 105301.
[5] M.A. Noginov, G. Zhu, A.M. Belgrave, R. Bakker, V.M. Shalaev, E.E. Narimanov,
S. Stout, E. Herz, T. Suteewong, U. Wiesner, Nature 460 (2009) 1110–1112.
[6] M.P. Navas, R.K. Soni, Plasmonics 10 (2015) 681–690, https://doi.org/10.1007/
s11468-014-9854-5.
[7] E. Prodan, P. Nordlander, J. Chem. Phys. 120 (2004) 5444.
[8] M. Arnold, M. Blaber, M. Ford, Opt. Express 22 (2014) 3186–3198.
[9] J. Zhu, J.-J. Li, J.-W. Zhao, Plasmonics 10 (2015) 1–8, https://doi.org/10.1007/
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C. Dahmen, B. Schmidt, G. von Plessen, Nano Lett. 7 (2007) 318–322.
R.W. Boyd, Nonlinear Optics, Academic Press, Burlington, 2007.
C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles,
John Wiley and Sons, 1998.
C.S.S.R. Kumar (Ed.), UV–vis and Photoluminescence Spectroscopy for
Nanomaterials Characterization, Springer, 2013.
D. Rioux, S. Vallières, S. Besner, P. Muñoz, E. Mazur, M. Meunier, Adv. Opt. Mater.
2 (2014) 176–182.
U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters, Springer, Berlin, 1995.
O. Peña, U. Pal, L. Rodríguez-Fernández, A. Crespo-Sosa, J. Opt. Soc. Am. B 25
(2008) 1371–1379.
The African Review of Physics (2018) 13: 0003
Determination of Thermo-luminescence kinetic parameters of
phosphor
nano-
Nebiyu Gemechu, Teshome Senbeta, Belayneh Mesfin
Addis Ababa University, Department of Physics, P. O. Box, 1176, Addis Ababa, Ethiopia
E-mail address: ngjourn@gmail.com
Powder of calcium yttrium silicate, Ca Y Si 0 , were prepared by a solution combustion technique using CaNO , YNO , TEOS
and Urea as a starting materials. X-ray diffraction (XRD) result shows monoclinic phase of the powder and the diffraction peaks
match well with the standard JCPDS card (PDF#87-0459). The estimated band gap of this material using Kubelka-Munk (K-M)
method is 4.6eV for indirect allowed transition and 4.9eV for direct allowed transition. The photoluminescence (PL) emission
spectrum shows an intense emission band peaking at 432nm (photon energy of ~2.9eV). The Thermo-luminescence (TL) fading
was studied and important TL kinetic parameters such as activation energy E, the frequency factor s and the order of kinetics b
were determined by employing peak shape method. Increment in the intensity of the TL glow peaks was observed with increasing
UV dose within the range of the dose used. This shows that Ca Y Si 0
could be a suitable candidate for dosimetric applications.
1.
Introduction
Calcium yttrium silicate (Ca Y Si 0 ) is one of the
most important phosphors in the silicate family. It
belongs to a space group C2/c with Ca and Y atoms
randomly sharing 6-, 7- and 8-fold coordination
symmetry sites in the composition [1-3]. Though the
structural properties of this phosphor material are first
studied in 1997 by Yamane et al [2], it has attracted
much attention in the years following this first report.
The structure of this material can be seen as an
arrangement of two types of layers; namely, the metal
ions (Ca # /Y # ) and SiO% tetrahedrons. Two oxygen
atoms of every SiO% tetrahedron are shared with
another SiO% tetrahedron resulting in the formation of
ternary Si 0 rings with Ca/Y atoms coupled with
them [1-2]. This arrangement of the metal ions is
reported to reduce their interaction capability and
opens an opportunity to introduce a relatively high
content of luminescent impurities without thermal
quenching [1, 4]. The thermo-luminescence (TL)
properties of this material have not been investigated
to the best of our knowledge. Therefore, study of its
TL properties is important for possible applications in
the field of dosimetry.
the crystal is released with the emission of light while
heating the irradiated material and the intensity of the
emitted light as a function of temperature forms TL
glow curve. The nature of the glow peaks, which are
generated from the intensity of the emitted light as a
function of temperature, depends on the properties of
the trapping states responsible for TL [5]. In other
words, the position, shape, and intensities of the glow
peaks are related to the properties of the trapping states
responsible for the TL [5]. The main applications of
TL materials are in radiation dosimetry. TL kinetic
parameters such as activation energy E, the frequency
factor s and the order of kinetics b determine the
dosimetric properties of a material as they give us
valuable information about the mechanism responsible
for the TL emission in the material. Therefore, reliable
dosimetric studies of any TL material include a good
knowledge of its kinetic parameters. Therefore, in this
work, the TL kinetic parameters such as E, s, and b of
Ca Y Si 0
host material are reported. Moreover,
its isothermal decay curve and optical properties are
also investigated.
2.
Experimental details
Ca Y Si 0
white powder was synthesized with the
solution combustion route using CaNO , YNO , TEOS
and Urea as a starting materials. First, the starting
materials were dissolved in 10 ml de-ionized water
and kept under magnetic stirring for one hour. The
mixture was then contained in China crucible and
TL is one of the radiation induced defect related
process in which the energy stored in the material is
released in the form of emitted light by heating the
irradiated material [5-8]. The intensity of the emitted
light as a function of temperature forms TL glow
curve. TL finds favor in diverse scientific disciplines
because of its several applications. Energy stored in
17
The African Review of Physics (2018) 13: 0003
quickly put in to a muffle furnace pre-heated to 600oC.
After few minutes, the solution precursors boiled,
swelled, evolved a large amount of gases and were
ignited yielding product. After keeping the product for
10 minutes in the furnace, dry foam-like powder of
was then pulled out quickly. It was
Ca Y Si 0
then grinded into powder using mortar and pestle
which were pre-cleaned with water and ethanol. The
crystal structure of this material was studied by X-ray
diffraction (XRD) using a Bruker D8 advance X-ray
diffractometer operating at 40kV and 40mA using
Cu kα = 0.15406nm. For TL measurements, the
sample was prepared into disc of 5mm in diameter and
1mm thick. A UV source was used for TL excitation
prior to heating. The TL is detected using TL reader
type TL1009I offered by Nucleonix systems Pvt. Ltd.,
India interfaced to a PC where the TL signals were
analyzed. The sample was heated from 0 to 400oC after
a UV dose of 5 minutes.
3.
3.1. XRD analysis
Fig. 1 shows the XRD pattern of the synthesized
Ca Y Si 0
sample. It shows monoclinic phase of
the powder and the diffraction peaks match well with
the standard JCPDS card (PDF#87-0459). The average
crystallite size of the prepared powder was determined
from Scherrer equation [9], which is given by
D=
0.9λ
,
βcosθ
1
Where, D is the crystallite size, λ is the X-ray
wavelength (0.15406 nm), 6 is the FWHM
and θ is the
diffraction angle. The values of 2θ with the
corresponding values of FWHM and crystallite size
for some prominent peaks are given in Table 1. The
average crystallite size of the prepared phosphor is
28nm.
Results and discussion
Fig. 1. (a) XRD pattern of the synthesized Ca Y Si 0
size
sample, and (b) FWHM with the corresponding crystallite
ε=
The strain (7) developed in the synthesized powder
was evaluated by the following relation [10] and the
evaluated FWHM, crystallite size and strain of the
prepared sample are summarized in Table 1.
β cotθ
,
4
where θ and β are as defined above.
18
2
The African Review of Physics (2018) 13: 0003
2: (radians)
FWHM (radians)
Crystallite size (nm)
Strain
27.667
0.18260
44.80
0.18538
29.300
0.37715
21.77
0.26068
33.905
0.36133
24.21
0.29634
37.443
0.28635
29.29
0.21123
48.640
0.33667
25.89
0.18623
57.729
0.37470
22.98
0.16994
Table 1. FWHM, crystallite size and strain of the synthesized Ca Y Si 0
host material
based on the values of the peak temperature T> , and
the temperatures T? and T located on the left and right
sides of T> , respectively, corresponding to half of the
peak intensity. The order of kinetics depends on the
shape factor of the glow peak @, which is also related
to the temperatures AB , A? , and A as follows
3.2. Thermo-luminescence properties
The TL glow curve of Ca Y Si 0
host material
obtained at heating rate of 1℃/< after UV dose of 5
minutes is shown in Fig. 2(a). From the analysis of
glow curve deconvolution, it can be observed that the
glow peak is well fitted by three constituent peaks as
shown in Fig. 2(b). The determination of the TL
kinetic parameters of Ca Y Si 0
host material is
made using peak shape method. This method, which
considers the shape of the glow peaks [6, 7], is
reported to be a popular method of analyzing glow
curves in order to evaluate the kinetic parameters E, s
and the order of kinetics b. In other words, this
technique for evaluating the TL kinetic parameters is
@=
C A − AB
=
,
D A − A?
3
where D = A − A? is the total half width and C =
A − AB is the half width towards the fall off side of
the glow peak.
Fig. 2. (a) TL glow peak for heating rate of 1℃/< and UV dose of 5 minutes, and (b) deconvoluted glow curve
of Ca Y Si 0
host material.
The values of @ for first and second order kinetics are
0.42 and 0.52 respectively. In addition, there is
another parameter, F = AB − A? which is the half
width at the low temperature side of the peak. The
activation energy is evaluated from Chen’s equations
for general order kinetics which is given by [6, 7],
GH = IH J
KAB
M − NH 2KAB ,
L
Where, L represents D, F or C.
19
4
The African Review of Physics (2018) 13: 0003
IQ = 0.976 + 7.3 @ − 0.42 ,
IO = 1.510 + 3.0 @ − 0.42 ,
βE
kT>
IS = 2.52 + 10.2 @ − 0.42 ,
NO = 1.58 + 4.2 @ − 0.42 ,
NQ = 0,
NS = 1,
= s exp W−
E
X Y1
kT>
+ b
2kT>
−1 W
X[,
E
5
Where, β is the heating rate and k is the Boltzmann
constant. The values of the shape factor @, G, and < of
the glow peaks are summarized in Table 2. The glow
peaks obey general order kinetics. The relationship
between the order of kinetics b and the geometrical
factor @ is reported [6, 7].
Moreover, the frequency factor s can be calculated
using the following equation for general order kinetics
[6, 7]. That is,
Peaks
Peak 1
T? ℃
89
T> ℃
125
T ℃
162
τ
36
δ
37
ω
73
@
0.51
b
1.96
E eV
0.56
Peak 2
140
176
212
36
36
72
0.50
1.9
0.7
Peak 3
162
242
314
80
72
152
0.47
1.81
0.85
Table 2. @, G, and < of the glow peak of Ca Y Si 0
s s _?
4.6
× 10a
2.7
× 10b
6.8
× 10b
host material
Fig. 3. Graphs of (a) the sample quickly heated at 2oC/s to 58oC, and (b) its phosphorescence decay curve
20
The African Review of Physics (2018) 13: 0003
No
Temperature
Temperature
TL Intensity
TL Intensity
(oC)
(K)
(Experimental)
(Theoretical)
1
45.66017
318.66017
20.27676
13.4837
2
52.91186
325.91186
25.69919
20.9934
3
60.16356
333.16356
34.67155
31.8534
4
67.41525
340.41525
48.49479
47.0334
5
74.66695
347.66695
68.26884
67.4192
6
81.91864
354.91864
94.42865
93.4927
7
89.17034
362.17034
126.24341
124.866
8
103.67373
376.67373
196.3975
194.811
9
110.92542
383.92542
226.35149
225.249
10
118.17712
391.17712
246.70638
246.172
11
125.42881
398.42881
254.03313
254.076
12
132.68051
405.68051
247.04618
248.133
13
139.9322
412.9322
226.97204
230.351
14
147.1839
420.1839
197.19749
204.607
15
154.43559
427.43559
162.33579
175.208
Table 3. The first 15 data points for comparison of the experimental data
and theoretical result.
3(a)). Keeping the sample at this temperature, the
phosphorescence decay measured as a function of time
(Fig. 3(b)) and it is considerably fast.
Moreover, the isothermal decay curve of the prepared
sample was investigated. After 5 minutes of UV
exposure, the sample was quickly heated to a
temperature of 58oC at heating rate of 2℃/< (Fig.
21
The African Review of Physics (2018) 13: 0003
Fig. 4. The experimental data and the theoretically fitted graph using the equation by Kitis et al
Glow curve fitting using the equation by Kitis et al was
also performed. The following analytical equation of
temperature dependent TL intensity was developed by
Kitis et al for peaks following general order kinetics
[7].
compared with the experimental data in Table 3 for the
first 15 data points.
3.3. Optical properties
Among the optical methods, UV-VIS diffuse
reflectance spectroscopy is one of the most employed
techniques to describe the optical properties present in
is
the solids. The band gap energy of Ca Y Si 0
estimated from the reflectance spectrum shown in
Figure 5(a) by applying the Kubelka-Munk (K-M)
method. The K-M method is based on the following
equation [11-12]:
E
I T = I> bd_? exp W
kT
T − T>
2kT>
×
X e1 + b − 1
T>
E
+ b − 1 W1
−
×
2kT
T
E
Xf
exp W
E
kT
T>
i
_
ijk
T − T>
Xgh
T>
F R =
6
1−R
,
2R
7
where R is the reflectance and F R is a parameter that
is proportional to the absorption coefficient L. A
modified K-M function is obtained by multiplying the
function F R by hν, where h is Planck’s constant and
ν is the frequency of vibration. As it is proposed by
Tauc, et al [11-12] the modified function is related to
the band gap sEt u of the material by,
The expression depends on the maximum TL intensity
I> and the temperature corresponding to the maximum
TL intensity T> . Here, glow curve fitting of peak 1 is
presented. Using I> = 254, T> = 398 K, G =
0.56 mn, and N = 1.96, it is theoretically fitted
applying the above equation and a good fit was
obtained as shown in Fig. 4. The calculated values are
w
F R × hν = vshν − Et u ,
where C is a proportionality constant.
22
8
The African Review of Physics (2018) 13: 0003
Fig. 5. Graphs of (a) Reflectance as a function of wavelength, (b) F R × hν
transition (y = 2), and (c) F R × hν
sample
k
x
k
x
versus energy hν for indirect allowed
versus energy hν for direct allowed transition (y = 1/2) of the prepared
?
by solid state reaction can be roughly estimated using
a wavelength of 288nm which is of the order of 4.3eV.
The value of n is for direct allowed transition, for
direct forbidden transition, 2 for indirect allowed
transition and 3 for indirect forbidden transition. Figs.
5(a) and (b-c) show the reflectance as a function of
3.4. Photoluminescence properties
k
wavelength and F R × hν z versus hν, respectively.
The band gap energy of the sample is estimated by
Fig. 6a shows the room temperature photoluminescence excitation and emission spectra of the
prepared sample. The excitation spectrum consists of
two absorption peaks at 286nm and 365nm. The
emission spectrum shows an intense emission band
peaking at 432nm (photon energy of ~2.9eV). This PL
emission could be attributed to deep level emission,
which can be explained in terms of two models as
suggested by I. Shalish et al [14]. According to I.
Shalish et al., the first model involves electron
transitions from conduction band to a deep state in the
lower half of the band gap while the second involves
transitions from a deep state in the upper half of the
gap to valence band. Though the intense PL emission
at 432nm could be ascribed to this phenomenon in our
case, the nature of the transition and the deep level
itself requires further study.
k
extrapolating the slope of F R × hν z versus hν
curves to the energy axis, as shown in Figs. 5(b) and
(c). To the best of our knowledge, the type of the band
gap of Ca Y Si 0
(direct or indirect) has not been
reported in literature. Therefore, in this work, the
estimation of the band gap is made for both direct and
indirect allowed transitions and the two values are
compared. The bad gap of the synthesized phosphor
calculated using the modified K-M method is of the
order of 4.6 eV for indirect allowed transition and
4.9eV for direct allowed transition. The band gap
estimated for indirect allowed transition is in a good
agreement with estimated value reported by Yi-Chen
Chu et al [13]. Yi-Chen Chu et al reported that the
band gap of Ca Y Si 0
host material synthesized
23
The African Review of Physics (2018) 13: 0003
Fig. 6. (a) Room temperature PL excitation and emission spectra of Ca Y Si 0
The values of the chromaticity coordinates of
Ca Y Si 0 host material have been estimated from
the 1931 Commission Internationale de l’Eclairage
(CIE) system using the excitation wavelength of
365nm (Figure 6b). This system helps us visualize the
variation in color emitted from samples and the
coordinates are measured as (x, y) and they are found
to be in the white CIE domain for this material.
, (b) CIE coordinates
References
[1] Anna Dobrowolska, J. Solid State Chem. 184,
1707 (2011).
[2] Matthias Müller,Thomas Jüstel, J. Lumin. 155, 398
(2014).
[3] Zhiping Yang, Hongyan Dong, Xiaoshuang Liang,
Chuncai Hou, Lipeng Liu, and Fachun
Lu, Dalton Trans. 43, 11474 (2014).
[4] V.B. Mikhailik, Materials Letters 63, 803 (2009).
[5] M.T. Jose , S.R. Anishia , O. Annalakshmi , V.
Ramasamy, Radiat. Meas. 46, 1026 (2011).
[6] S.W.S. Mckeever, Thermoluminescence of solids,
Cambridge Solid State Science Series,
London 1988.
[7] Vasilis Pagonis, George Kitis and Claudio Furetta,
Numerical and Practical Exercises in
Thermoluminecsnce, Springer, USA 2006.
[8] K. Madhukumar et al., Bull. Mater. Sci. 30, 527
(2007).
[9] B. Cullity, Elements of X-ray Diffraction,
Addison-Wesley publishing, USA 1956.
[10] Shao-Ying Ting et al, J. Nanomat., 2012, 1
(2012).
[11] R. A. Zargar et al, Optic 127, 6997 (2016).
4. Conclusion
In conclusion, the structural, optical and luminescence
properties of solution combustion synthesized
Ca Y Si 0
was studied. An intense emission band
peaking at 432nm (photon energy of ~2.9eV) was
observed from PL spectrum. This PL emission could
be ascribed to electron transitions from conduction
band to a deep state in the lower half of the band gap
or transitions from a deep state in the upper half of the
gap to valence band. The CIE coordinates lie in the
white CIE domain. Important TL kinetic parameters
such as activation energy (E), the frequency factor s
and the order of kinetics b were determined by
employing peak shape method. Increment in the
intensity of the TL glow peaks was observed with
increasing UV dose within the range of the dose used
(5 − 50 min). This shows that Ca Y Si 0
could
be a suitable candidate for UV dosimetry up to
50 min.
[12] A. B. Murphy, Sol. Energ. Mat. Sol. C. 91, 1326
(2007).
[13] YI-Chin Chu et al, J. Electrochem. Soc. 156, 221
(2009).
Received: 02 February, 2017
Accepted: 29 April, 2018
[14] I. Shalish, et al., Phys. Rev. B 59, 9748 (1999).
24
Enhanced Emission and Improved
Crystallinity of $$ {\hbox{KY}}_{3}
{\hbox{F}}_{10} :{\hbox{Ho}}^{3 + } $$
KY3F10:Ho3+ Thin Films Grown at High
Deposition Temperature Using Pulsed
Laser Deposition Technique
Nebiyu G. Debelo, F. B. Dejene, Kitessa
Roro, Teshome Senbeta, Belayneh
Mesfin, et al.
Journal of Electronic Materials
ISSN 0361-5235
Journal of Elec Materi
DOI 10.1007/s11664-018-6089-9
1 23
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1 23
Author's personal copy
Journal of ELECTRONIC MATERIALS
https://doi.org/10.1007/s11664-018-6089-9
Ó 2018 The Minerals, Metals & Materials Society
Enhanced Emission and Improved Crystallinity of KY3F10 : Ho3þ
Thin Films Grown at High Deposition Temperature Using Pulsed
Laser Deposition Technique
NEBIYU G. DEBELO,1,2,6 F.B. DEJENE,2 KITESSA RORO,3
TESHOME SENBETA,4 BELAYNEH MESFIN,4 TAMIRAT ABEBE,1
and L. MOSTERT5
1.—Department of Physics, Jimma University, P. O. Box 378, Jimma, Ethiopia. 2.—Department of
Physics, University of the Free State, Qwa Qwa Campus, Private Bag X13, Phuthaditjhaba,
South Africa. 3.—Energy Center, Council for Scientific and Industrial Research, P.O.Box 395,
Pretoria 0001, South Africa. 4.—Department of Physics, Addis Ababa University, P. O. Box 1176,
Addis Ababa, Ethiopia. 5.—National Metrology Institute of South Africa, Private Bag X34,
Lynnwood Ridge 0040, South Africa. 6.—e-mail: nebgem.eyu@gmail.com
The effect of substrate temperature on the structural, morphological, and
luminescence properties of thin films prepared from a commercially available
KY3 F10 : Ho3þ phosphor powder is investigated. The thin films were grown on
silicon substrate at different substrate temperatures, ranging between 50°C
and 600°C, by the pulsed laser deposition method using Nd-YAG laser radiation
of wavelength 266 nm. The x-ray diffraction spectra show that the crystallinity
of the films is significantly improved with an increment of substrate temperature with the calculated average crystallite size between 39 nm and 74 nm. The
photoluminescence (PL) spectra also show enhanced emission at high deposition temperature. Green PL emission at 540 nm and faint red emission at
750 nm are observed from the PL spectra at excitation wavelengths of 362 nm,
416 nm, and 454 nm. The green emission is ascribed to the 5F4–5I8 and 5S2–5I8
transitions of Ho3þ and the faint red emission is due to 5F4–5I7 and 5S2–5I7
transitions of Ho3þ . The peaks of the PL emission are found to increase with an
increase in substrate temperature for all excitation wavelengths. For all the
prepared films, the highest PL intensity occurs at an excitation of 454 nm.
Key words: Pulsed laser deposition, thin film, photoluminescence, substrate
temperature
INTRODUCTION
Fluoride-based materials are very attractive since
they possess a reasonably high thermal conductivity,
good enough mechanical hardness, and high chemical
stability compared with other low phonon energy
materials such as chlorides, bromides, or sulfides.1–8
In particular, potassium triyttrium decafluorde
(KY3 F10 Þ host material has a much higher energy
transfer efficiency in it than other fluorides such as
BaY2 F8 and LiYF4 ,7 and this makes it even more
interesting for luminescence applications.
Because of its excellent material properties such as
high chemical and thermal stability, transparency,
(Received October 26, 2017; accepted January 12, 2018)
isotropy, ease of growing, suitability to build solidstate lasers, white-light emitters, and quantum
cutting systems to enhance solar cell efficiency,
potassium triyttrium decafluorde ðKY3 F10 Þ doped
with holmium and different rare earth elements has
attracted much attention and been extensively
studied.1–7 It is used for various applications
in a wide range of fields such as for optical
studies,2,3 laser applications,3 scintillation,4 and
displays.5,6
Doping of KY3 F10 host with holmium has significant advantage over other rare earth ions because
Ho3þ ion has a high-gain cross-section and long lifetime of 5I7 upper level emission that results in high
efficiency and energy storage capacity.8 Though this
material has been extensively studied in powder
Author's personal copy
Debelo, Dejene, Roro, Senbeta, Mesfin, Abebe, and Mostert
form,1–8 its thin films have not so far been much
investigated to the best of our knowledge.
In device applications such as field emission displays
(FED), thin film phosphor materials are more advantageous than powders in reducing outgassing problems as well as having high resolution and contrast.9
Therefore, the study of thin film phosphors is equally
important as that of their powder counterparts.
In the preparation of thin films, different deposition techniques such as pulsed laser deposition
(PLD), chemical vapor deposition, and magnetron
sputtering can be used. Among these methods, PLD
has been a popular, versatile, and highly flexible thin
film deposition technique for a wide range of materials. The method is based on the interaction of a high
power density laser beam with a solid target so that
the laser energy can easily be controlled externally.10
The quality of the films deposited on a substrate is
dependent on the deposition parameters, such as
background gas pressure, temperature, and the
type of background environment. In the previous
published articles,10–12 it has been reported that,
during the films growth process, the background gas
pressure and the substrate temperature are the two
major critical parameters that determine: (1) the
final step of the film formation; and (2) the amorphous or crystalline nature of the deposited films.
In this paper, the influence of temperature on the
structural, morphological, and photoluminescence
properties of thin films of KY3 F10 : Ho3þ deposited
over a wide temperature, ranging from 50°C to 600°C,
on a silicon substrate are investigated. Though a
similar growth mechanism can be obtained at low(including room temperature) and high-temperature
depositions for most materials,13–15 a completely
different growth mechanism and film quality were
obtained for KY3 F10 : Ho3þ at low- and high-temperature regions. This shows that the growth mechanism
and the film quality during the PLD process do not
only depend on the deposition parameters mentioned
above but also on the type of material ablated.
diffractometer (operating at 40 kV, 40 mA, and Cu
ka = 0.15406 nm) was employed to determine the
crystal structure of the films. Field emission scanning
electron microscopy (FE-SEM) and atomic force
microscopy (AFM) with ScanAsyst in tapping mode
were used to analyze the morphology of the films. The
elemental composition of the films was studied using
energy dispersive x-ray spectrometry (EDS). X-ray
photoelectron spectroscopy (XPS) was employed to
investigate the surface states. The measurement of the
room-temperature PL excitation and emission spectra
were performed by using a Cary Eclipse Fluorescence
Spectrometer (model: LS-55 with a built-in 150-W
Xenon flash lamp). For the excitation wavelength of
454 nm, the chromaticity coordinates of the prepared
thin films were estimated from the 1931 Commission
Internationale de l’Eclairage (CIE) system.
The average crystallite size (D) of the samples was
determined from the full width at half maximum
(FWHM) of the most intense (202) diffraction peaks
using the Scherrer’s formula,16 which is given by
0:9k
;
ð1Þ
D¼
bcosh
where k is the wavelength of the x-ray (0.15406 nm), b
is the FWHM, and h is the diffraction angle. In
addition, the strain (e) developed in the prepared films
was calculated using the following relationship17:
b
ð2Þ
e¼
4tanh
RESULTS AND DISCUSSION
Structural and Morphological Properties
Figure 1
depicts
the
XRD
pattern
of
3þ
KY3 F10 : Ho
thin films grown at different substrate temperatures for a constant background gas
MATERIALS AND METHODS
The KY3 F10 : Ho3þ thin film samples were prepared
from commercially available KY3 F10 : Ho3þ phosphor
using the PLD technique. Nd-YAG laser (wavelength
of 266 nm, pulse duration of 9.3 ns, repetition rate of
10 Hz), with the laser fluence kept at 1.2 J/cm2 was
used to grow KY3 F10 : Ho3þ thin films on a (100) Si
substrate in an argon environment. Before introducing the argon, the vacuum chamber was pumped to a
background pressure of 5:6 106 kPa. A commercially available KY3 F10 : Ho3þ powder was used to
prepare the target by compressing it at 6 MPa.
Keeping the gas pressure at the constant value of
0.23 kPa and the target-to-substrate distance at
5.2 cm, the thin films were grown at substrate temperatures of 50°C, 100°C, 350°C, 400°C, 500°C, and
600°C. XRD analysis by a Bruker D8 advance x-ray
Fig. 1. XRD spectra of KY3 F10 : Ho3þ thin films deposited at constant argon gas pressure of 0.23 kPa for various deposition temperatures. For comparison, the spectrum of the standard is included.
Author's personal copy
Enhanced Emission and Improved Crystallinity of KY3 F10 : Ho3þ Thin Films Grown at High
Deposition Temperature Using Pulsed Laser Deposition Technique
pressure of 0.23 kPa in an argon atmosphere. It can
be seen that, for the films deposited above the
substrate temperature of 350°C, the degree of
crystallinity is improved with an increase in substrate temperature.
The labels shown in Fig. 1 are according to
the Miller indices of the diffraction peaks of the
planes. The crystal structure of the films is found be
the tetragonal form of KY3 F10 which is in agreement with JCPDS card No. 27-0465.
For low substrate temperatures between 50°C
and 350°C, no diffraction peaks are visible (not
indicated in the figure) which indicates that the
deposited thin films are amorphous. When the
substrate temperature increases to 400°C and
above, the diffraction peaks become visible, That
is, at 400°C, the (202) diffraction peak is visible,
while at 500°C, in addition to the (202) peak, the
(113) diffraction peak becomes visible. Further,
Table I. The FWHM of the dominant (202) peaks,
the calculated average crystallite size, and the
strain developed in the samples for different
temperatures
Substrate
2h (°) FWHM Average Strain
temperature (°C)
crystallite
size (nm)
Fig. 2. The substrate temperature versus average crystallite size
and strain for KY3 F10 : Ho3þ thin films.
400
500
600
26.893 0.20940
26.834 0.16131
26.873 0.10966
Fig. 3. FE-SEM images of the thin films deposited at (a) 350°C, (b) 400°C, (c) 500°C, and (d) 600°C.
39
51
74
0.2189
0.1691
0.1148
Author's personal copy
Debelo, Dejene, Roro, Senbeta, Mesfin, Abebe, and Mostert
Fig. 4. AFM images of the thin films deposited at (a) 400°C, (b)
500°C, and (c) 600°C.
increasing the substrate temperature to 600°C,
three relatively intense diffraction peaks, namely
the (202), (400), and (422), as well as three less
intense peaks corresponding to the (200), (113), and
(321) diffraction planes, are observed. Consequently, it may be concluded that the degree of
crystallinity of the prepared thin films is improved
with an increase of the substrate temperature. The
(113) peak, which is normally not observed for the
film deposited at 400°C, and much less intense for
the film deposited 600°C, becomes dominant for the
one deposited at 500°C. This could be because of the
change in the preferred orientation of the films with
the change in substrate temperature.
The improvement of the crystallinity of the samples with an increase in substrate temperature can
be explained in terms of the dependence of the
mobility of the atoms as a function of temperature.
That is, for relatively low temperatures, the vapor
species have a low surface mobility and will be
located at different positions on the surface. However, as the substrate temperature is high enough,
the particles arriving at the substrate surface will
have a higher thermal energy that results in an
increase in the mobility of the ad-atoms. This, in
turn, makes the particles coalesce with each other to
form the nucleation centers, thereby increasing the
quality of the thin films.
The average crystallite size and the strain developed in the samples are evaluated from Eqs. 1 and
2, respectively. The calculated crystallite sizes and
the strain parameter at different temperatures are
displayed in Table I. The crystallite sizes are in the
range of 39 nm and 74 nm, whereas the corresponding strain varies between 0.2189 and 0.1148. Similar results showing an increase in crystallite size
with substrate temperature have been reported in
the literature.18–22 The substrate temperature versus average crystallite size and strain is depicted in
Fig. 2, from which it can be clearly observed that
the strain developed in the films decreases with
increasing substrate temperature in an approximately linear relationship, while the average crystallite size increases.
The morphology of the prepared thin films has
been analyzed using FE-SEM. Figure 3 shows the
FE-SEM images of the deposited films, from which
it can be seen that, for the film that is deposited at
50°C, the morphology is dominated by the presence
of loosely packed small and large droplet-like structures. Similar structures are observed for the films
grown at the substrate temperatures of 100°C and
350°C. For the film deposited at 400°C, smaller
irregular and denser structures appear to be superimposed over the droplet-like structures. A further
increase in substrate temperature to 500°C results
in the formation of a different morphology consisting of mainly irregular large structures which seem
to be composed of relatively tiny irregular particles.
Furthermore, at the substrate temperature of
600°C, the morphology becomes more ordered,
consisting of aggregates of regular structures with
straight edges and corners. This confirms that the
crystallinity of the films is significantly improved
with an increase in substrate temperature. The
AFM images shown in Fig. 4 are also in agreement
with the FE-SEM images. It can be deduced from
the images that there is a continuous improvement
of the structure from droplet-like ones to grains
with a well-defined shape as the substrate temperature increases to 600°C, showing improvement in
crystallinity.
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Enhanced Emission and Improved Crystallinity of KY3 F10 : Ho3þ Thin Films Grown at High
Deposition Temperature Using Pulsed Laser Deposition Technique
Fig. 5. EDS spectra of the thin films deposited at (a) 350°C, (b) 400°C, (c) 500°C, and (d) 600°C.
The chemical compositions of the deposited films
was analyzed using EDS and are depicted in Fig. 5,
which shows that all the constituent elements of the
powder are present in the films with the exception of
holmium. The absence of the Ho3þ ion indicates that
its concentration in the sample is below the sensitivity of the instrument.
The observed K:Y:F elemental ratios are
1:3.4:9.7, 1.1:3.8:9.3, 1.1:3.5:9.6, and 0.9:3.8:9.3 for
the films deposited at 350°C, 400°C, 500°C, and
600°C, respectively. As compared with the target
composition of 1:3:10, the elemental ratios show
decreases in the K and F elements and an increase
in Y for all the films. This may be due to the high
background gas pressure (0.23 kPa) which causes
some of the plasma species to lose their kinetic
energy before reaching the surface of the substrate
because of frequent collisions with the gas molecules. This phenomenon has the effect of decreasing
the deposition rate.10,23 In particular, for
KY3 F10 : Ho3þ phosphor thin films, the deposition
condition mainly depends on the masses of the
individual species. This is because the relative
amount of the heavier species (Y in this case) that
travels normal to the substrate will be higher than
that of the lighter species at relatively higher
pressures. This could be the reason why yttrium
is found to have a relatively higher elemental ratio
than the other two in the composition of the
deposited films. In other words, the mass of Y
which is approximately twice that of the mass of Ar
seems to enable Y to be little affected by the
scattering due to the Ar molecules.
XPS was employed to further investigate the
surface state of the film deposited at 600°C. Figure 6a and b shows the high resolution XPS spectra
of KY3 F10 : Ho3þ with peaks of Y 3d and F 1s. Highresolution Gaussian peak fits were performed to
obtain the identities of these peaks. Figure 6a
shows the fitted high-resolution Y 3d XPS peak.
There are two fitted peaks assigned to Y 3d5/2
situated at 157.24 eV and 159.18 eV, and the other
two peaks assigned to Y 3d3/2 are situated at
159.24 eV and 161.18 eV. Figure 6b shows the
high-resolution F 1s XPS peak with two fitted peaks
at 684.71 eV and 686.45 eV. The summary of the
XPS peak position, binding energy and area distribution of the film is given in Table II.
Photoluminescence Properties
The PL excitation and emission spectra of
KY3 F10 : Ho3þ thin films deposited at temperatures
of 400°C, 500°C, and 600°C are depicted in Fig. 7a,
b, and c, respectively. It can be seen that, for all the
substrate temperatures, the maximum PL intensity
occurred at an excitation of 454 nm. In particular,
the green emission at the wavelength of 540 nm was
studied for the excitation wavelengths of 362 nm,
416 nm, and 454 nm. Moreover, for all excitations, a
faint red (near infrared) emission was observed at
Author's personal copy
Debelo, Dejene, Roro, Senbeta, Mesfin, Abebe, and Mostert
Fig. 6. (a) Y 3d and (b) F 1s XPS spectra of the film deposited at 600°C.
Table II. XPS peak position, binding energy, and area distribution of KY3 F10 : Ho3þ thin film deposited at
600°C
KY3 F10 : Ho3þ
Y 3d
F 1s
Binding energy (eV)
Area contribution (%)
157.24
159.18
159.24
161.18
684.71
686.45
52.55
3.00
42.04
2.40
89.61
10.39
750 nm. This faint red emission is attributed to the
5
F4–5I7 and 5S2–5I7 transitions, whereas the green
emission spectrum observed at 540-nm wavelength
is due to the 5F4–5I8 and 5S2–5I8 transitions. It is
worth noting that such multiple emissions from
Chemical compound
Y in KY3 F10
YF3
Y in KY3 F10
Y2 O3
F in KY3 F10
F in KY3 F10
: Ho3þ
: Ho3þ
: Ho3þ
: Ho3þ
other holmium-doped phosphors have also been
reported.24,25
Moreover, the values of the chromaticity coordinates of KY3 F10 : Ho3þ thin films that have been
estimated from the 1931 Commission Internationale
Author's personal copy
Enhanced Emission and Improved Crystallinity of KY3 F10 : Ho3þ Thin Films Grown at High
Deposition Temperature Using Pulsed Laser Deposition Technique
Fig. 7. PL excitation and emission spectra of KY3 F10 : Ho3þ phosphor powder thin films prepared at (a) 400°C, (b) 500°C, (c) 600°C, and (d) the
corresponding variation in chromaticity coordinates.
de l’Eclairage (CIE) system for the excitation wavelength of 454 nm are depicted in Fig. 7d. The CIE
system enables us to visualize the variation in color
that is emitted from the prepared samples.
The values of the chromaticity coordinates, often
expressed as (x,y), are (0.235, 0.594), (0.245, 0.615),
and (0.245, 0.678) for the thin films deposited at
400°C, 500°C, and 600°C, respectively. These values
indicate that a relatively intense green emission is
expected to be seen for the thin films deposited
under relatively higher substrate temperatures, in
agreement with that observed in Fig. 7. Figure 8
shows the variation of emission peaks that correspond to the three excitation wavelengths of
362 nm, 416 nm, and 454 nm. It can be observed
that the intensity of the PL emissions significantly
improves with an increase of the substrate temperature. This could be attributed to the improved
crystallinity of the films at higher temperatures. In
general, higher substrate temperatures during
deposition results in an increase in the surface
mobility of the atomic species in the films, thereby
improving the crystallinity, which in turn enhances
the luminescence intensity.
CONCLUSION
The structural, morphological, and PL properties
of KY3 F10 : Ho3þ thin films have been studied in a
wide temperature range. The crystallite size of the
deposited films varied between 39 nm and 74 nm
depending on the substrate temperature. Yttrium is
the dominant composition in the deposited films and
this is attributed to its higher mass as compared to
potassium and fluorine. The green PL emission at
540 nm was investigated at three main excitation
wavelengths, 362 nm, 416 nm, and 454 nm. In
addition, a faint red (near infrared) emission was
Author's personal copy
Debelo, Dejene, Roro, Senbeta, Mesfin, Abebe, and Mostert
Fig. 8. Variation of emission peaks corresponding to excitation
wavelengths of 362 nm, 416 nm, and 454 nm with temperature.
observed at 750 nm for all the excitations. The
emission peaks of the films increases with an
increase of the substrate temperature which is
attributed to the improved crystallinity of the films
at such higher substrate temperatures. The green
emission at 540 nm is ascribed to the 5F4–5I8 and
5
S2–5I8 transitions and the faint red emission at
750 nm is due to the 5F4–5I7 and 5S2–5I7 transitions
of Ho3þ .
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Journal of Luminescence 196 (2018) 264–269
Contents lists available at ScienceDirect
Journal of Luminescence
journal homepage: www.elsevier.com/locate/jlumin
Plasmon coupled photoluminescence from silver coated silicon quantum
dots
T
⁎
Sioma Debela , Belayneh Mesfin, Teshome Senbeta
Department of Physics, Addis Ababa University, Addis Ababa, Ethiopia
A R T I C L E I N F O
A B S T R A C T
Keywords:
Local field
Surface plasmon
Spectral absorption
Radiative recombination
Photoluminescence
The surface plasmon enhanced photoluminescence (PL) emission of silver coated Si/SiO2 quantum dots (QDs) is
investigated theoretically and numerically for different parameters of the QDs. Due to the interaction of radiation with the silver coat, a local surface plasmon oscillation is established which in turn results in a considerable resonant enhancement of the local field in the QDs. The local field enhancement factor inside of the
silver coated spherical Si/SiO2 QDs is solved using the Laplace equation. Utilizing this enhancement factor, the
plasmon enhanced radiative recombination rate, the spectral absorption, and the PL intensity of ensembles of
silver coated Si/SiO2 QDs embedded in a SiO2 host matrix are studied. The induced electric field increases the
overlapping of the electron and hole wave functions in the QDs leading to an increase in radiative recombination
rate, spectral absorption, and the PL intensity. Moreover, by varying the thickness of silver coat and SiO2 spacer,
the surface plasmon resonance frequency can be tuned to the longer wavelength regions in the visible spectrum.
This enhances the coupling between surface plasmon resonance frequency of the silver coat and the energy gap
of silicon QDs. It is found that the radiative recombination rate, spectral absorption and photoluminescence
intensity increase up to 3 folds compared to the QDs without a metal coat.
1. Introduction
Silicon is the most dominant material in the microelectronics world.
Nevertheless, the electron-hole radiative recombination in the bulk
material is forbidden because of the fundamental property of the silicon
band structure [1,2]. On the other hand, silicon quantum dots (Si-QDs)
show quantum confined luminescence at wavelengths in the visible and
near infrared region [1,3]. Despite their high emission efficiency, SiQDs suffer from low radiative decay rates as compared to those of direct
band gap semiconductors [4]. To improve this state of affairs, the resonant effects of surface plasmons (SP) on PL emission attract a great
deal of attention [4–10].
In particular, A. Inoue et al. [11] reported that a significant amount
of PL emission enhancement of Si-QDs occurs when the emission energy
lies in the vicinity of the localized surface plasmon resonance of gold
NP. On the other hand, recent experimental work of S. K. Srivastava
et al. [12] revealed the surface plasmon coupled emission of quantum
confined excitons in the Ag2O layer in a composite nanorod composed
of silver core and Ag2O shell.
The stretching in the energy gap of silicon quantum dots, which are
sufficiently smaller than the Bohr exciton radius of the material
(∼ 5 nm ) as a consequence of quantum confinement [13] favors the
⁎
coupling of the energy gap of the QD with the SP energy of the metal
coat. The plasmon coupled emission becomes more important for sufficiently smaller Si-QDs when the energy gap of the QD is close to the
local surface plasmon resonance energy.
When the Si/SiO2/Ag QD (shown in Fig. 1) is illuminated by a radiation field, a local field is induced inside and outside of the metal coat
as a result of polarization. This field significantly changes the interaction of the optically generated electrons and holes in the QD emitter.
The induced field enhances the coupling between the electron and hole
wave functions in the QD. The coupling between the electron and hole
wave functions gets its maximum value at the local surface plasmon
resonance frequency of the metal coat.
In an ensemble of such QDs, the spectral absorption and emission
intensity strongly depends on the thickness of the metal coat, the size of
Si-QD, thickness of spacer, and the dielectric functions of the different
layers in the Si/SiO2 /Ag QDs structure as well as the surrounding
environment. By tuning the energy gap of a typical mean sized QDs in
the ensemble to the local surface plasmon energy of the silver coat,
enhancement of the spectral absorption and PL emission could be
achieved.
The paper is organized as follows. In Section 2, we present the expression of the local field enhancement factor. The effect of local field
Corresponding author.
E-mail address: sioma2007@gmail.com (S. Debela).
https://doi.org/10.1016/j.jlumin.2017.12.010
Received 31 July 2017; Received in revised form 2 December 2017; Accepted 4 December 2017
Available online 06 December 2017
0022-2313/ © 2017 Elsevier B.V. All rights reserved.
Journal of Luminescence 196 (2018) 264–269
S. Debela et al.
penetrate easily into the QD emitter.
For silver/gold alloys, the frequency dependent dielectric function
εm of the metal coat is described by the modified Drude form given by
[14]
ωp2
εm = ε∞ −
+ εcp1 (ω, ω01, ωg1, γ1, A1 )
ω (ω + iγ )
+ εcp2 (ω, ω02 , γ2, A2 ),
(4)
where, ε∞ is a real constant, ωp is the bulk plasma frequency of the
metal, γ is the decay constant of plasma vibrations, ω is the frequency of
radiation, εcp1 and εcp2 are the interband contributions to the dielectric
function of the plasmonic metals. The parameter γ is the size dependent
decay constant of plasma vibrations given by
γ = γbulk + A
Fig. 1. Schematic diagram of a three layered spherical Si/SiO2 /Ag QD in a SiO2 host
matrix. The central region shows the Si emitter with diameter dd and dielectric constant
εd , the middle layer represents the SiO2 spacer with diameter dc and dielectric constant εc ,
and the silver coat has a diameter dm and dielectric constant εm .
vF
,
a
(5)
enhancement in modifying the radiative recombination rate in silver
coated Si-QDs is discussed in Section 3. Section 4 is devoted to the
investigation of the effect of local field enhancement on the spectral
absorption and PL emission of an ensemble of noninteracting silver
coated Si-QDs. Section 5, summarizes the result obtained in the paper.
where γbulk is the bulk decay constant of plasma vibrations, vF is the
velocity of the electrons at the Fermi surface, a is the thickness of silver
coat and Ais a parameter which depends on the details of the scattering
process [15].
Later, we will use the local field enhancement factor, Eq. (2), with
account of the complex dielectric function of the metal coat, Eq. (4), to
calculate the plasmon enhanced radiative recombination rate, the
spectral absorption, and PL intensity of silver coated Si-QDs.
2. Local field enhancement factor
3. Plasmon coupled radiative recombination rate
Consider a metal coated Si-QDs embedded in a dielectric host matrix, as shown in Fig. 1. In the electrostatic approximation, the electric
field distribution inside and outside of the silver coated Si-QDs may be
obtained by employing the Laplace equation ∇2 Φ = 0 in spherical coordinates, where Φ is the electric potential (see Appendix). The magnitude of the spatially constant electric field, E, inside the QD is found
to be
The rate of a spontaneous transition Γr from an excited electron-hole
state ψi to the ground state ψf may be described by using Fermi's
golden
rule
in
the
first-order
perturbation
theory
as
int is the opint ψ 2 δ (Ef − Ei − ℏω) [16], where H
Γr = (2π /ℏ) ψ H
E=
εh εc εm
27
E0 .
2pm ηεm2 + βεm + φ
f
(1)
Γr =
The coefficient of E0 in Eq. (1) is the local field enhancement factor,
F = E / E0 . Writing the complex dielectric function of the metal coat as
εm = ε′m + iε″m , where ε′m and ε″m are its real and imaginary parts, and
manipulating the modulus square of the local field enhancement factor
becomes
(
2
F =
27 εc εh
2pm
2
) (ε ′
2
m
2
.
(2)
The coefficients η, β , and φ depend on the dielectric functions of the
host matrix, quantum dot, and the SiO2 layer (see Appendix).
To understand the penetration of light into the Si-QD emitter in the
three-layered composite NP, we may calculate the absorption coefficient (α ) with the help of the Maxwell-Garnett effective-medium theory,
thereby the penetration depth (d) can be computed. Accordingly, α is
found to be
ρχcs
⎤⎫
⎡
2ω
Im εh ⎢1 +
α=
⎥ ,
1
⎨
c
1 − 3 (ρχcs ) ⎬
⎦⎭
⎣
⎩
4e 2 n ω
 ψi
ψf p
3 m2ℏ c 3
2,
(6)
where e is the charge of an electron, n is the refractive index, ω is the
transition frequency, m is the electron rest mass, c is the speed of light,
 is the momentum operator.
ℏ is Planck's constant divided by 2π , and p
 ψi can be expressed in terms
The matrix element of transition ψf p
of the oscillator strength fosc , which can be regarded as a measure of
strength of a transition from an initial state with energy Ei to a final
state with energy Ef , i.e.,
+ εm″ 2)
[η (εm′ 2 − εm″ 2) + βεm′ + φ] + εm″ 2 (2ηεm′ + β )2
i
erator of the interaction Hamiltonian, ℏω is the emitted photon energy,
Ef and Ei are the energies of the highest occupied molecular orbital
(HOMO) and the lowest unoccupied molecular orbital (LUMO), respectively. Summing Γr over all light polarization gives [17,18]
fosc (ω) =
2
 ψi
ψf p
mℏω
2.
(7)
The oscillator strength is a function of the photoluminescence emission
energy which for silicon QDs can be described by using the following
empirical formula [19]:
ℏω (eV ) ⎞
fosc [ℏω (eV )] = 1.4 × 10−5 + 5.8 × 10−8 exp ⎛
,
⎝ 0.332 ⎠
⎧
(8)
where the size dependent fosc is described via the emission energy-size
relation (ℏω = 1.12 + 3.73/ dd1.39) suggested by Delerue et al. [20].
When a QD is coated with noble metals, the oscillator strength
changes. The change may be described by modifying the interaction
Hamiltonian of electron-hole pairs. In the dipole approximation, the
interaction
Hamiltonian
may
be
written
as
int = −F (ω, dd , dc , dm) μ ·̂ E
 , where μ ̂ is the dipole moment operator
H
 is the electric field operator. The matrix element of momentum
and E
operator is obtained from the dipole matrix element using the relation
 ψi = imω ψf r ̂ ψi [21]. Thus, the expression for the plasmon
ψf p
coupled oscillator strength fsp of electron-hole pairs takes the form:
(3)
where ω is the frequency of light, c is the speed of light, ρ is the density
of the dipole moments in the mixture, χcs = 4πrm3 (δsph/2pm Δsph ) . δsph and
Δsph are given by (see Appendix) Eqs. (28) and (31), respectively.
The penetration depth of light through the composite NP can be
estimated from the relation d ∼ 1/ α . Typical value of d lies between
500 nm and 1μm depending on the thickness of silver shell, SiO2 spacer,
size of Si-QD, and wavelength of light. Since the typical size of the
three-layered NP under consideration is below 40 nm , light can
265
Journal of Luminescence 196 (2018) 264–269
S. Debela et al.
Fig. 4. (color online) The plasmon coupled radiative recombination rate as a function of
energy of light for 2.8, 3.2, and 4.5 nm sized QDs with a fixed values of pm = 60% and
Fig. 2. (color online) The radiative recombination rate as a function of the emission
wavelength of the silver coated Si-QDs with (I) metal fraction pm = 65% and spacer vo-
pc = 97% . The other parameters are the same as in Fig. 2.
lume fraction pc = 90% , (II) pm = 60% , pc = 90% , and (III) without a metal coat. The
excitation energy is ℏω = 2.3 eV . The dielectric function of silver is used according to Eq.
(4) and the tabulated values in [14].
fsp = F (ω, dd , dc , dm) 2 fosc (dd ).
that, the control over the spacer thickness can also enhance the spontaneous recombination rate by adjusting the separation distance between the emitter and silver shell so that the energy transfer between
the emitter and silver shell may be reduced. Consequently, in order to
maximize fluorescence of silver coated Si/SiO2 QDs, it is advantageous
to use thick spacer. However, interfacial strain induced by lattice mismatch between the emitter and shell materials becomes a serious issue
for thick shells, and may severely limit the maximum thickness.
Fig. 4 depicts the graphs of Γsp as a function of the energy of light for
different sizes of the silver coated Si/SiO2 QDs and constant value of the
metal fraction. As it can be seen, the plasmon coupled spontaneous
transition rate strongly depends on the size of QD. As the size of QD
decreases, the plasmon coupled recombination rate increases. This
shows that plasmon coupling becomes stronger when the energy gap of
the QD increases there by approaching the surface plasmon resonance
frequency of the silver coat. The decrease in size of Si-QD results to blue
shift in the resonance peak as the band gap of QD stretches toward the
local surface plasmon resonance region. The radiative transition rate of
metal coated QDs have three resonant peaks. These peaks appear in the
vicinity of 1.8 eV , 3.6 eV , and 5 eV (not shown in the Figure) regions.
The first and second peaks are attributed to the plasmon modes at the
outer and inner boundary of the silver coat, respectively, whereas the
third peak is due to interband transition.
(9)
In view of Eqs. (7) and (9), the plasmon coupled rate of spontaneous
transition Γsp can be obtained from the plasmon coupled oscillator
strength, i.e.,
Γsp = F (ω, dd , dc , dm) 2
2n e 2 ω2
f (dd ).
3 m c 3 osc
(10)
Eq. (10) clearly shows that Γsp is enhanced compared with Γ for
F 2 > 1. Fig. 2 shows the spontaneous transition rate of the uncoated
and silver coated Si-QDs embedded in SiO2 matrix plotted using Eqs. (6)
and (10). It can be observed that the spontaneous transition rate is
enhanced for the silver coated QDs, the enhancement increasing with
an increase in the metal fraction pm . That is, up to 3-fold enhancement
in radiative recombination is achieved in Ag coated QDs compared with
the uncoated ones when the metal fraction is increased to a value of
65% of the total volume of silver coated Si-QD for a fixed SiO2 spacer
volume fraction of 90% to the inner Si/SiO2 core/shell QD. This is
because of the large resonant enhancement of the local field established
inside of the QDs, which in turn strengthen the overlapping of the wave
functions of optically generated electron-hole pairs in the quantum
dots.
The spontaneous recombination rate is strongly influenced by the
thickness of SiO2 spacer. This effect is shown in Fig. 3. One can see that
an increase in spacer thickness increase the spontaneous recombination
rate. The increase in the spontaneous recombination rate is attributed
to the enhanced local field inside of the emitter. It is worth mentioning
4. Plasmon coupled spectral absorption and PL intensity
Spectral absorption and photoluminescence intensity are among the
important parameters that are often employed to characterize the
performance of light emitting devices. Below, we discuss these parameters.
4.1. Spectral absorption
The spectral absorption A (ℏω) of Si-QDs ensemble with mean size
of d 0 and a geometrical standard deviation σ may be obtained by assuming that an individual nanoparticle behaves as an indirect semiconductor [22,23]. That is,
A (ℏω) = ω−1
∫0
∞
fosc (dd )
dn (dd )
(ℏω − Eg )2d dd ,
d dd
(11)
where ℏω is the energy of electromagnetic radiation, Eg is the size dependent energy gap of Si-QDs, and dn (dd , d 0, σ )/ d dd is the nanocrystal size distribution which we assumed to be governed by the lognormal function given by [23,24]
Fig. 3. (color online) The radiative recombination rate as a function of energy of light for
a 3 nm sized silver coated Si-QDs with (I) thickness of spacer ℓc = 5.46 nm , (II)
ℓc = 3.33 nm , and (III) ℓc = 1.73 nm when the metal fraction is kept fixed at 70%. The
other parameters are the same as in Fig. 2.
dn (dd )
=
d dd
1
1
1 (ln dd − ln d 0)2 ⎤
exp ⎡−
.
⎢
⎥
(ln σ )2
2π dd ln σ
⎣ 2
⎦
(12)
In view of Eqs. (9) and (11), we obtain the plasmon coupled spectral
266
Journal of Luminescence 196 (2018) 264–269
S. Debela et al.
mean size of the Si-QD decreases.
4.2. PL Intensity
The PL intensity INp for a single particle with a peak emission energy
of Eg is obtained by making the assumption that a single nanoparticle at
room temperature acts as an inhomogeneously broadened emitter with
a spectral width of ΔE [19]. That is,
INp (ℏ ω, Eg ) ∝
(ℏ ω − Eg )2 ⎤
1
exp ⎡−
.
⎢
(2ΔE )2 ⎥
ΔE 2π
⎦
⎣
(14)
The emission probability I (ℏ ω) of ensembles of Si nanoparticles with
mean size d 0 can be obtained from [19]
I (ℏ ω) =
Fig. 5. (color online) Calculated spectral absorption [Eq. (13)] for ensemble of silver
coated Si-QDs with a mean size of 4.5 nm as a function of emission energy for (I)
pm = 60% , pc = 45% , (II) pm = 50% , pc = 45% , and (III) the absorption curve due to the
absorption of ensembles of silver coated noninteracting Si-QDs in SiO2
matrix by
1
ω
∫0
∞
F 2 fosc (dd )
dn (dd )
(ℏ ω − Eg )2d dd .
d dd
∞
fosc (dd ) Q (dd )
dn (dd )
INp (ℏ ω, Eg ) d dd .
d dd
(15)
Here Q is the internal quantum efficiency of the emitter, which can
be expressed as Γr /(Γr + Γnr ) , where Γr and Γnr are the radiative and
nonradiative decay rates.
The plasmon coupled emission probability of silver coated ensemble
of noninteracting Si-QDs with mean particle diameter of d 0 can be
computed from the expression of plasmon coupled oscillator strength.
Thus, the emission intensity takes the form
uncoated QDs. The other parameters are the same as in Fig. 2.
A (ℏω) =
∫0
(13)
I ( ℏ ω) =
Using the above equation we can compute the absorption spectra of the
silver coated silicon nanoparticle ensemble.
In Fig. 5 the spectral absorption of a 4.5 nm mean sized silver coated
Si-QDs in an ensemble as a function of the emission energy are depicted
for uncoated and metal coated QDs having two different values of metal
fraction, pm . It is observed that an enhancement of the spectral absorption is attained for Si-QDs that are coated by silver with the absorption increasing with an increase in the metal fraction, i.e., from
pm = 50 % to pm = 60%. It may be explained by the fact that as the Ag
thickness increase, the induced local electric field inside the QD increases which in turn significantly modify the spectral absorption.
The dependence of the spectral absorption on the mean size of SiQDs in an ensemble is shown in Fig. 6. Changing the mean size of silver
coated Si-QDs in the ensemble from 3.5 nm to 4.5 nm by keeping
pm = 66% results in a red shift of the absorption edge. The spectral
absorption due to d 0 = 4.5 nm seems to dominate in the lower energy
limit (for energy less than ∼ 2 eV ). However, in the higher energy regime (for energy greater than ∼ 2 eV which is not shown in the Figure),
the absorption due to d 0 = 3.5 nm dominates. The result shows that the
spectral absorption edge of silver coated Si-QDs depends on the mean
size of a QD, which shift towards the shorter wavelength region as the
∫0
∞
F 2 fosc (dd ) Q (dd )
dn (dd )
INp (ℏ ω, Eg ) d dd .
d dd
(16)
As indicated by A. Inoue et al. Γr in Au/Si core/shell structured QDs
is independent of the separation distance between Au core and Si-QD
agglomerates, while Γnr of a dipole located in the vicinity of a Au-NP is
very large and approaches zero when the distance increases [11].
However, in Si/SiO2/Ag core/shell/shell QDs the wide gapped SiO2
layer act as surface passivation and effective separation between the
core (Si) nano-emitter and the metal coat. Consequently, the quantum
efficiency, can be practically assumed to approach 1.
The PL intensity of silver coated Si-QDs versus the emission energy
is shown in Fig. 7, for pm = 60% and three different values of mean
particle size d 0 . It is observed that as the mean particle size decreases
from 5 nm to 4 nm , the PL intensity curve is blue shifted and increases
significantly. However, as we keep on decreasing the mean particle size
from 4 nm to 3.5 nm , the emission intensity start to decline as the energy gap associated to the mean size of QDs becomes slightly larger
than the resonance formed around 1.7 eV . Further reduction in the
mean particle size might takes the advantages of the second surface
plasmon resonance peak formed around 3.6 eV to enhance the PL
emission intensity.
Fig. 7. (color online) The plasmon enhanced emission intensity [Eq. (16)] of silver coated
Si-QDs as a function of energy by fixing pm = 60 % and for different mean particle sizes;
Fig. 6. (color online) Absorption spectra [Eq. (13)] for the ensemble of silver coated SiQDs having a fixed value of pm = 66 % and different mean size of the QD;
d 0 = 3.5 nm , d 0 = 4.0 nm , and d 0 = 5.0 nm . The other parameters are the same as in
Fig. 2.
d 0 = 3.5 nm, 4.0 nm, 4.5 nm . The other parameters are the same as in Fig. 2.
267
Journal of Luminescence 196 (2018) 264–269
S. Debela et al.
5. Conclusions
Coating a QD emitter with silver allows a QD to interact with the
surface plasmon oscillation induced by radiation. When the frequency
of radiation is close to the surface plasmon frequency of the coated
metal, the local surface plasmon resonance occurs. As the energy gap of
the QD is tuned to this resonance energy, the coupling of electron and
hole wave functions in the QD increases resulting to a significant enhancement of the radiative recombination rate, spectral absorption, and
PL emission intensity.
Compared with uncoated Si-QDs, the radiative recombination rate,
Γsp , of Ag coated dots is enhanced considerably. In addition, Γsp of the
coated Si-QDs increase with an increase in the metal fraction whereas it
decreases with an increase in the size of the dots. The spectral absorption increases with an increase in metal fraction. It is found that the
PL intensity curve is blue shifted and increases significantly when the
mean particle size decreases from 5 nm to 4 nm . However, a further
decrease of the mean particle size from 4 nm to 3.5 nm results to a decrease in the emission intensity indicating that there is an optimum
mean particle size to attain a maximum PL enhancement. In addition, it
is observed that in the ensembles of metal coated Si-QDs with mean
particle size of 4 nm , an increase in metal fraction from 55% to 60% of
the total volume of the silver coated Si-QD result in a strong enhancement in PL emission intensity which increases up to 3 fold with respect
to the uncoated Si-QDs. This increase in PL emission intensity is due to
the strong plasmon coupling between a thick metal shell and a relatively small quantum dots.
Coating a Si-QD with silver not only affects the surface plasmon
resonance frequency, but also shifts the absorption edge of the QD. The
absorption edge of a relatively small sized Si-QD with thick metal coat
shifts toward longer wavelength region. The results obtained may be
applied to Si-based power-efficient light emitting materials.
Fig. 8. (color online) The plasmon enhanced emission intensity [Eq. (16)] of silver coated
Si-QDs as a function of energy by fixing d 0 to 4 nm and for two different values of metal
fraction pm = 55 % , and pm = 60 % . The reference emission intensity of the uncoated SiQDs is obtained according to Eq. (15). The other parameters are the same as in Fig. 2.
As it may be seen from Fig. 8, in the ensembles of metal coated SiQDs with mean particle size of 4 nm , the increase in metal fraction from
55% to 60% of the total volume of the silver coated Si-QD result in a
strong enhancement in PL emission intensity which increases up to 3
folds with respect to the uncoated Si-QDs. The increase in PL emission
intensity is attributed to the strong plasmon coupling established between a thick metal shell and smaller quantum dots. For smaller Si-QDs
coated with thick metal shell, the energy gap of the QD approach the
surface plasmon energy; however, since the surface plasmon energy is
still higher than the energy gap of the QDs as the silver shell increases,
it results to an enhancement in the PL intensity.
Appendix. Calculation of the electric field distribution inside of the three layered nanoparticle
Consider a metal coated Si-QDs embedded in a dielectric host matrix, as shown in Fig. 1. The size of the composite NPs considered in our analysis
is well below 50 nm so that the quasi-static approximation can be employed. Accordingly, the electric field distribution of the system may be
obtained by employing the Laplace equation ∇2 Φ = 0 (Φ is the electric potential). In the electrostatic approximation, the resulting solution for the
electric potential inside and outside the particle with azimuthal symmetry in spherical coordinates is then given by [25]
∞
Φ (r , θ) =
1
n+1
∑ ⎡⎢An r n + Bn ⎛ r ⎞
n=0
⎝ ⎠
⎣
⎤ p (cos θ)
n
⎥
⎦
(17)
where the coefficients An and Bn are constants. Using Eq. (17), the potentials in the four regions of metal coated core/shell structure are found to be
Φd = A1 r cos θ ,
(r ≤ rd )
Φc = A2 r cos θ + B1
cos θ
,
r2
Φm = A3 r cos θ + B2
cos θ
,
r2
Φh = −E0 r cos θ + B3
cos θ
,
r2
(18)
(rd ≤ r ≤ rc )
(19)
(rc ≤ r ≤ rm)
(20)
(r ≥ rm)
(21)
where Φd , Φc , Φm , and Φh are potentials in the Si-QD, SiO2 layer, silver coat, and the host matrix, respectively, E0 is the applied field, r and θ are the
spherical coordinates. A1, A2, A3, B1, B2, and B3 are constants. From the continuity conditions of the potential and the displacement vector on the
boundaries, we obtain a system of linear algebraic equations for A1, A2, A3, B1, B2, and B3. The solution of this system can be shown to be (with a new
notation, εs i ± t j = sεi ± tεj , where i, j ≡ c, d, h , or m and s, t ≡ 1, 2 , or 3)
A1 = −
27εc εh εm
E0 .
2pm Δ
(22)
A2 = −
9 ε2c + d εh εm
E0 .
2pm Δ
(23)
A3 = −
3εh [2 (1 − pc ) εc − d εc − m − ε2c + d εc + 2 m]
2pm Δ
E0 .
(24)
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Journal of Luminescence 196 (2018) 264–269
S. Debela et al.
B1 = −
B2 = −
B3 = −
9 rd3 εd − c εh εm
E0 .
2pm Δ
3εh rc3 [(1
(25)
− pc ) εc − d ε2c + m − ε2c + d εc − m]
2pm Δ
E0 .
(26)
δ
E0 .
2pm Δ
(27)
where
δ = rm3 εh − m [ε2c + d εc + 2 m λ1 − 2(1 − pc ) εc − d εc − m λ2],
(28)
with
λ1 = 1 − (1 − pm )
εc − m εh + 2 m
,
εc + 2 m εh − m
(29)
ε2c + m εh + 2 m
.
2 εc − m εm − h
(30)
and
λ2 = 1 + (1 − pm )
Δ = η εm2 + β εm + φ.
(31)
Here,
η = pc εd − c + 3εc ,
(32)
ε
β = ⎜⎛ 2c + d ⎟⎞ [3εc + 2 h − 2pm εc + h]
⎝ 2pm ⎠
1 − pc ⎞
+ ⎜⎛
⎟ εc − d [3εh − c + pm ε2c − h],
⎝ pm ⎠
(33)
φ = εc εh [2pc εc − d + 3εd].
(34)
pm = 1 − (dc / dm)3 is the metal fraction of the core/shell/shell structure, pc = 1 − (dd / dc )3 is the SiO2 coat fraction, εh , εd , εc , and εm are the dielectric
functions of the matrix, Si-QD, the SiO2, and silver coat, respectively.
Substituting Eq. (22) into (18), the electric potential inside the quantum dot becomes
Φd = −
27εc εh εm
E0 r cos θ .
2pm Δ
(r ≤ rd )
(35)
Then, using Eq. (35) and the relation E = −∇Φd , we find the magnitude of the electric field inside the QD to be
E=
27 εh εc εm
E0 .
2 pm Δ
(36)
[12] Sachin K. Srivastava, Christoph Grùner, Dietmar Hirsch, Bernd Rauschenbach,
Ibrahim Abdulhalim, Opt. Express 25 (2017) 5.
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Michel Meunier, Adv. Opt. Mater. 2 (2014) 176–182.
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[16] Jasprit Singh, Electronic and Optoelectronic Properties of Semiconductor
Structures, Cambridge University Press, 2003.
[17] Klaus Schulten, Notes on Quantum Mechanics, University of Illinois, 2000.
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(2007) 103112.
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367–370.
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Commun. Theor. Phys. 55 (2011) 688–692.
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[25] J. David Griffiths, Introduction to Electrodynamics, Prentice-Hall, New Jersey,
1999.
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269
Synthesis and luminescence
properties of $${\text{Ca}}_{3}
{\text{Y}}_{2} ({\text{Si}}_{3}
{\text{O}}_{9} )_{2} :x{\text{Ce}}^{{3
+ }}$$ Ca 3 Y 2 ( Si 3 O 9 ) 2 : x Ce 3 +
nanophosphor
N. G. Debelo, T. Senbeta, B. Mesfin &
F. B. Dejene
Journal of Materials Science:
Materials in Electronics
ISSN 0957-4522
Volume 28
Number 17
J Mater Sci: Mater Electron (2017)
28:12776-12783
DOI 10.1007/s10854-017-7105-1
1 23
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1 23
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J Mater Sci: Mater Electron (2017) 28:12776–12783
DOI 10.1007/s10854-017-7105-1
Synthesis and luminescence properties of Ca3 Y2 (Si3 O9 )2 :xCe3+
nanophosphor
N. G. Debelo1 · T. Senbeta1 · B. Mesfin1 · F. B. Dejene2
Received: 1 February 2017 / Accepted: 8 May 2017 / Published online: 19 May 2017
© Springer Science+Business Media New York 2017
Abstract Powder samples of calcium yttrium silicate,
Ca3 Y2 (Si3 O9 )2 :xCe3+ (x = 0, 0.01, 0.02, 0.04, 0.08, and
0.16 mol%), were prepared by a solution combustion technique using CaNO3 , YNO3 , TEOS and Urea as a starting
materials. X-ray diffraction (XRD) results show monoclinic
phase of the samples and the diffraction peaks match well
with the standard JCPDS card (PDF#87–0459). The photoluminescence (PL) emission spectra of the doped samples
monitored at excitation wavelength of 365 nm show a broad
band extending from about 350 to 600 nm and this band
can be ascribed to the allowed [Xe]5d1 to [Xe]4f1 transition of Ce3+. Moreover, the PL intensity increased for up to
critical concentration of x = 0.08 mol% and then decreased.
The reflectance spectra of the doped samples show a red
shift in their optical band gap as compared to the host. The
Thermoluminescence (TL) properties of the host material
(x = 0 mol%) shows increment in the intensity of the glow
curves for all the UV-doses applied. For the host, important
TL kinetic parameters such as the activation energy (E),
the frequency factor (s), and the order of kinetics (b) were
determined by employing peak shape method. The introduction of Ce3+ in to the host material completely changed
the TL properties of the samples.
* N. G. Debelo
nebgem.eyu@gmail.com
1
Department of Physics, Addis Ababa University, P. O.
Box 1176, Addis Ababa, Ethiopia
2
Department of Physics, University of the Free State, Qwa
Qwa Campus, Private Bag X13, Phuthaditjhaba, South Africa
13
Vol:.(1234567890)
1 Introduction
Inorganic compounds doped with rare earth elements form
an important class of phosphors and have recently attracted
much attention because of their versatile applications
[1–10]. Silicate family is an attractive class of materials
for wide range of applications due to their special properties such as visible light transparency, chemical resistance,
high temperature strength, low thermal expansion, high
conductivity, good chemical and
stability [11].
( thermal
)
Calcium yttrium silicate Ca3 Y2 Si3 O9 2 belongs to a space
group C2/c with Ca and Y atoms randomly sharing 6, 7 and
eightfold coordination symmetry sites in the composition
[12–14]. The structure of this material can be seen as an
arrangement of two types of layers; namely, the metal ions
(Ca2+ or Y 3+) and SiO4 tetrahedrons. Two oxygen atoms
of every SiO4 tetrahedron are shared with another SiO4 tetrahedron resulting in the formation of ternary Si3 O9 rings
with Ca/Y( atoms)coupled with them [12, 13].
Ca3 Y2 Si3 O9 2 is reported to be a suitable host material
for white emission when activated by different rare earth
elements [12, 13]. This is particularly important for white
light emitting diodes (w-LEDs) requiring a single host for
solid state lightening. It exhibits three different crystallographic Y sites namely, Y1 (coordination number (CN) 8),
Y2 (CN 7) and Y3 (CN 6) and they can be randomly occuY2 sites by Ce3+ has
pied by Ce3+. The occupation
of
(
) Y1 and
3+
been reported for Ca3 Y2 Si3 O9 2 : Ce , Mn2+ prepared by
the conventional solid state method [15]. In general, different dopant concentration and synthesis routes results in different luminescence properties of a material. In this aspect,
further investigation
(
)of the PL and study of the TL properties of Ca3 Y2 Si3 O9 2 :x Ce3+ prepared by solution combustion technique is quite interesting. TL is one of the radiation
induced defect related process in which the energy stored in
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the material is released in the form of emitted light by heating the irradiated material [16–19]. Therefore, in this paper,
in addition to(the structural
study, the PL and TL proper)
ties of Ca3 Y2 Si3 O9 2 :x Ce3+ are investigated for possible
applications in w-LEDs and radiation dosimetry.
2 Experimental details
Ca3 Y2 (Si3 O9 )2 :xCe3+
white
powder
was
synthesized with the solution combustion route for
x = 0.01, 0.02, 0.04, 0.08 and 0.16 mol% using
CaNO3 , YNO3 , TEOS and Urea as a starting materials.
First, the starting materials were dissolved in 10 ml deionized water and kept under magnetic stirring for 1 h.
The mixture was then contained in China crucible and
quickly put in to a muffle furnace pre-heated to 600 °C.
After few minutes, the solution precursors boiled, swelled,
evolved a large amount of gases and were ignited yielding
product. After keeping the product for (10 min) in the furnace, dry foam-like powder of Ca3 Y2 Si3 O9 2 was then
pulled out quickly. It was then grinded into powder using
mortar and pestle which were pre-cleaned with water and
ethanol. The crystal structure of this material was studied
by X-ray diffraction (XRD) using a Bruker D8 advance
X-ray diffractometer operating at 40 kV and 40 mA using
Cu kα = 0.15406 nm. Its optical properties were studied using UV–VIS spectrometer in the wavelength range
of 250–800 nm. The excitation and emission spectra were
measured at room temperature using Cary Eclipse fluorescence spectrometer model: LS-55 with a built-in 150W
xenon flash lamp. The values of the chromaticity coordinates of the phosphor have been estimated from the 1931
Commission Internationale de l’Eclairage (CIE) system
using the excitation wavelength of 365 nm. For TL measurements, the samples were prepared into disc of 5 mm in
diameter and 1 mm thick. A UV source was used for TL
excitation prior to heating. The TL is detected using TL
reader type TL1009I offered by Nucleonix systems Pvt.
Ltd., India interfaced to a PC where the TL signals were
analyzed. Samples were heated from 0 to 400 °C for different UV doses. Measurements of the TL fading were done
after keeping the sample for different storage times before
heating.
3 Results and discussion
3.1 XRD analysis
Figure 1 shows the XRD pattern of the synthesized
Ca3 Y2 (Si3 O9 )2 :xCe3+. It shows monoclinic phase of the
powder and the diffraction peaks match well with the
Fig. 1 a XRD pattern of the synthesized Ca3 Y2 (Si3 O9 )2 :xCe3+ samples
Fig. 2 The variation of the dominant diffraction peak around
2𝛉 = 29◦ with the concentration x. The values are normalized with
respect to the highest diffraction peak at x = 0.08 mol%
standard JCPDS card (PDF#87–0459) except for the relative intensity. This shows that Ce3+ ions entered into the
sample without changing the crystalline structure of the
samples. It is worth noting that the relative intensity of
the diffraction peaks increased when doped with relatively large concentration of Ce3+ up to x = 0.08 mol%
and then decreased at x = 0.16 mol% as shown in Fig. 2
using the dominant peak around 2θ = 29◦. The increment
in the intensity of the diffraction peaks up to x = 0.08 mol
% could be attributed to the improved crystallinity of the
samples with increase in Ce3+ concentration. However,
at higher doping concentration (x = 0.16 mol%) of Ce3+,
the decrease in the intensity of diffraction peaks could be
ascribed to the degradation in the crystalline quality due to
crystal distortion. Similar results have been reported in literature [9].
The strain (𝜀) induced in the samples due to crystal
imperfection and distortion is calculated from the following
13
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Table 1 Strain developed
in the synthesized
Ca3 Y2 (Si3 O9 )2 :xCe3+ samples
J Mater Sci: Mater Electron (2017) 28:12776–12783
x (mol%)
Strain (macrostrain)
0.01
0.02
0.04
0.08
0.16
0.65561
0.65534
0.34305
0.33153
0.33092
equation [9, 20] using the dominant diffraction peak around
2θ = 29◦ and is shown in Table 1.
ε=
β cot θ
.
4
(1)
If a sample is given a uniform tensile strain, the corresponding diffraction line shifts to lower angles. This macrostrain causes a shift of the diffraction lines to new 2θ
positions [21].
It can be seen that there is a decrease in the lattice strain with
increasing
doping concentration of
(
)
Ce3+ in Ca3 Y2 Si3 O9 2 and this could be because of
the reduction (minimization) of bonding defects. It has
been reported that lattice strain can either increase [6] or
decrease [9] with rise in doping concentration.
3.2 Photoluminescence properties
Figure 3a shows the room temperature PL emission spectra
of Ca3 Y2 (Si3 O9 )2 :xCe3+ at excitation of 365 nm. The spectra show a broad band extending from about 350–600 nm.
This band can be ascribed to the allowed [Xe]5d1 to [Xe]4f 1
transition of Ce3+ [13]. It is interesting to note that the
emission spectra correspond to three different emission
wavelengths and hence energies. It can be seen that the
curves obtained for x = 0.04 and 0.08 mol% correspond
to emission wavelength of 390 nm, the curve obtained for
x = 0.02 mol% corresponds to 396 nm and those obtained
for x = 0.01 and x = 0.16 mol% correspond to emission
wavelength of about 425 nm. The three different emission energies of the( PL spectra
are explained in terms of
)
the fact that Ca3 Y2 Si3 O9 2 exhibits three different crystallographic Y sites [15, 22]. These sites are Y1 (CN 8), Y2
(CN 7) and Y3 (CN 6) and they can be randomly occupied
by Ce3+. Matthias Müller and ThomasJüstel reported that
due to increasing crystal field splitting of the d-orbitals, the
emission energy of d–f transitions decreases with decreasing coordination number [15]. Therefore, the observed PL
emission spectra confirmed the occupation of three different sites. Curves obtained for x = 0.04 and x = 0.08 mol%
are assigned to Ce3+ occupying Y1 site, the curve obtained
for x = 0.02 mol% is assigned to Ce3+ occupying Y2 site
and curves obtained for x = 0.01 and x = 0.16 mol% are
assigned to Ce3+ occupying Y3 site.
13
Fig. 3 a Room temperature PL emission spectra of
Ca3 Y2 (Si3 O9 )2 :xCe3+. The inset shows the PL excitation of the host
material at emission of 432 nm and its PL emission at excitation of
365 nm, and b CIE chromaticity coordinates. (Color figure online)
The PL emission intensity of Ca3 Y2 (Si3 O9 )2 :xCe3+ is
enhanced gradually with increasing x value from 0.01 to
0.08 mol% and then decreases for x = 0.16 mol%. Thus,
x = 0.08 mol% is taken as the critical concentration. For
x = 0.16 mol%, the concentration of Ce3+ is excessive
leading to concentration quenching. It is reported that
the decrease in PL intensity for activator concentration
beyond a critical concentration shows the occurrence of
energy transfer among the activator ions (Ce3+ in this
case) at different sites in the lattice, resulting in concentration quenching [23, 24]. The probability of energy
transfer increase with increase in Ce3+ concentration as
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the distance between the Ce3+( becomes
small. The criti)
cal energy transfer distance RC can be approximated
using Blasse formula [23–25] which is given by,
)1
(
3
3V
RC ≈ 2
,
4𝛑XC Z
(2)
where V is the unit cell volume, XC is the critical concentration of Ce3+, and Z is the number of formula units
coupled in the unit cell. Here V = 1.5221 nm3 (calculated
from the XRD data using MDI Jade (v.6.0) software),
XC = 0.08, and Z = 4, as a result the calculated value of
RC is 2.087 nm. Thus, as Ce3+–Ce3+ distance is greater than
0.5 nm, multi-polar interaction is more effective as compared to exchange interaction. This situation was explained
by Dexter’s theory [26]. The type of the multi-polar interaction can be determined from the following equation [23,
24],
]
[
𝜃 −1
I
,
= k 1 + 𝛽 x3
(3)
x
where k and 𝛽 are constants for the same excitation condition for a given matrix crystal, 𝜃 = 6, 8and10 is corresponding to electric dipole–diploe (d–d), electric
dipole–electric quadrapole (d–q) and electric quadrapole–electric quadrapole (q–q) interactions, respectively,
and I is the PL intensity corresponding to the dopant concentration x.
Equation (3) can be written as,
( )
I
θ
log
= C − log(x),
(4)
x
3
where C is constant. The parameter θ has the electric
multipolar character and it can be obtained from the slope
(−θ∕3) of the plot of log(I∕x) versus log(x) as shown in the
Fig. 4. The slope of the linear fit of the graph log(I∕x) versus log(x) is found to be −1.827. Therefore, the calculated
value of θ is 5.481 which is close to 6 indicating that the
energy transfer mechanism for Ca3 Y2 (Si3 O9 )2 :xCe3+ phosphor is electric dipole- dipole interaction.
The inset of Fig. 3a shows the room temperature photoluminescence
(
) excitation and emission spectra of
Ca3 Y2 Si3 O9 2 host material. The excitation spectrum
consists of two absorption peaks at 286 and 365 nm. The
emission spectrum shows an intense blue emission band
with peak at 432 nm (photon energy of 2.9 eV ). This PL
emission could be attributed to deep level emission which
can be explained in terms of two models as suggested by
I. Shalish et al. [27]. According to I. Shalish et al., the first
model involves electron transitions from conduction band
to a deep state in the lower half of the band gap while the
second involves transitions from a deep state in the upper
Fig. 4 The graph of
Ca3 Y2 (Si3 O9 )2 :xCe3+
log(I∕x)
versus
log(x)
of
Ce3+
for
half of the gap to the valence band. Though, the intense PL
emission at 432 nm could be ascribed to the latter phenomenon in our case, the nature of the transition and the deep
level itself requires further study.
The values of the chromaticity coordinates of
Ca3 Y2 (Si3 O9 )2 :xCe3+ samples have been estimated from
the 1931 Commission Internationale de l’Eclairage
(CIE) system using the excitation wavelength of 365 nm
(Fig. 3b). This system helps us visualize the variation in color emitted from the samples and the coordinates are (0.154, 0.055), (0.161, 0.100), (0.172, 0.168),
(0.162, 0.113), (0.163, 0.124), (0.156, 0.068) for x = 0
(host), x = 0.01, x = 0.02, x = 0.04, x = 0.08
and
x = 0.16 mol%, respectively.
Among the various optical methods, UV–vis diffuse
reflectance spectroscopy is one of the most employed techniques to describe the optical properties present in solids.
The reflectance spectra of the undoped and Ce3+- doped
samples are shown in Fig. 5. A red shift in the optical band
gap of all the doped samples was observed as compared
to the host material. Impurity band formation is an obvious consequence of increased doping concentration and
the trapping of the Ce atoms at the grain boundary leads to
the introduction of the Ce defect states within the forbidden
band. With increasing Ce doping, density of this Ce induced
defect states increases, leading to the observed decrease of
band gap or red shift [28].
3.3 Thermoluminescence properties
(
)
The TL glow curves of Ca3 Y2 Si3 O9 2 host material for
different UV doses (measured in unit of exposure time) are
shown in Fig. 6a. It can be observed that the TL intensity
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Fig. 5 Graph of Reflectance as a function of wavelength. (Color figure online)
increases with increase in UV dose for all the doses used up
to 50 min as shown in Fig. 6b. The glow peaks in general
attained their peak maxima at different temperatures upon
variation of UV dose.
From analysis of glow curve deconvolution,
it is
(
)
observed that each glow peak of Ca3 Y2 Si3 O9 2 can be
well fitted by three constituent peaks as shown in Fig. 7.
The TL kinetic parameters such as activation energy
(E), the frequency factor (s), and order of kinetics (b) are
analyzed using peak shape method. It is a popular method
for analyzing glow curve in order to evaluate the kinetic
parameters: E, s, and b is by using the shape of the peak
[17, 18]. This method is based on the values of the peak
temperature TM, and the temperatures T1 and T2 located on
the left and right sides of TM, respectively corresponding to
half of the peak intensity. The order of kinetics depends on
the shape factor of the glow peak, 𝜇 which is in also related
to the temperatures TM, T1, and T2 as follows:
T − TM
𝛿
= 2
,
𝜔
T 2 − T1
Fig. 6 a TL glow curves for different UV exposure time, and b the
variation of TL maxima with UV dose. (Color figure online)
where 𝛼 represents 𝜔, 𝜏 or 𝛿. The expressions for c𝛼 and b𝛼
as a function of µ are given below:
(5)
c𝜏 = 1.510 + 3.0 (𝜇 − 0.42),
where 𝜔 = T2 − T1 is the total half width and 𝛿 = T2 − TM
is the half width towards the fall-off side of the glow peak.
The values of 𝜇 for first and second order kinetics are 0.42
and 0.52 respectively [17, 18]. The relationship between
the order of kinetics b and the geometrical factor𝜇 is given
in [17, 18]. The half width at the low temperature side of
the peak is denoted by 𝜏 = TM − T1. The activation energy
(E) is evaluated from Chen’s equations for general order
kinetics which is given by [17].
c𝛿 = 0.976 + 7.3 (𝜇 − 0.42),
𝜇=
E𝛼 = c𝛼
(
kTM 2
𝛼
13
)
(
)
− b𝛼 2kTM ,
(6)
c𝜔 = 2.52 + 10.2 (𝜇 − 0.42),
b𝜏 = 1.58 + 4.2 (𝜇 − 0.42),
b𝛿 = 0, b𝜔 = 1.
Moreover, the frequency factor (s) can be calculated using
the following equation for general order kinetics [17, 29].
That is,
𝛃E
kTM 2
)[
(
(
)]
2kTM
E
1 + (b − 1)
= s exp −
,
kTM
E
(7)
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(
)
Fig. 7 Deconvoluted glow curve of the prepared Ca3 Y2 Si3 O9 2
sample
Fig. 8 The TL glow curves of Ca3 Y2 (Si3 O9 )2 :xCe3+. (Color figure
online)
where 𝛃 is the heating rate and k is the Boltzmann’s
constant.
The values of the shape factor (𝜇), the activation energy
(E), and the frequency factor (s) of the glow peaks are summarized in Table 2.
The introduction of Ce3+ in to the host material completely changed the TL properties of the samples. Figure 8
shows the observed TL intensity of the prepared samples
for different concentration of Ce3+.
Despite that the doped samples give more physically
meaningful results than the host material, doping resulted
in a broad glow curves with low intensity which is not
desirable result. In other words, Ce3+ doping have a strong
effect on charge trapping processes taking place in the
phosphor material during and after irradiation and on the
TL kinetics as well. This could be the reason for the change
in the TL properties following the addition of Ce3+ into the
host material.
(
)
Finally, the TL fading profile of the Ca3 Y2 Si3 O9 2
was studied. During storage of a TL material after irradiation, there is a probability that charge carriers escape
from the trapping centers within the material even at low
temperature, resulting in the so-called fading of the TL
signal. Moreover, during the time between irradiation
and heating, the defect structures acting as trapping and
recombination centers, may undergo some transformations leading to change of sensitivity. The main external factors affecting fading are temperature and( storage
)
time. Figure 9a shows the TL fading of Ca3 Y2 Si3 O9 2
host material. It is worth noting that the glow curve with
quick measurement shows initial room temperature intensity that is likely to be TL emissions from traps with
peak temperatures at or below 25 °C. But after storage
time of 20 min, this initial room temperature intensity
was greatly reduced and there is smooth initial rise. This
is because of room temperature activation of electrons
Table 2 Shape factor,
activation energy, and frequency
factor of some glow peaks
UV-exposure Peaks
time (min)
T1 (◦ C)
TM (◦ C)
T2 (◦ C)
𝛕
5
89
125
162
36 37
73 0.51 1.96 0.56
4.6 × 106
Peak 2 140
176
212
36 36
72 0.50 1.9
2.7 × 107
20
30
Peak 1
𝛅
𝛚
𝜇
b
E (eV)
0.7
s(s−1 )
Peak 3 162
242
314
80 72 152 0.47 1.81 0.85
6.8 × 107
Peak 1
82
118
157
36 39
75 0.52 2
3.4 × 106
Peak 2 128
173
212
45 39
84 0.46 1.77 0.69
2 × 107
Peak 3 219
256
292
37 36
73 0.49 1.88 0.99
1.2 × 109
Peak 1
0.54
80
118
155
38 37
75 0.49 1.88 0.53
2.2 × 106
Peak 2 126
165
207
39 42
81 0.52 2
0.67
2.1 × 107
Peak 3 173
250
328
77 78 155 0.50 1.9
0.87
8.7 × 107
13
Author's personal copy
12782
J Mater Sci: Mater Electron (2017) 28:12776–12783
(
)
)
t
t
+ 317.5 exp −
.
0.012
1.216
(9)
In (general
the
observed
good
TL
behavior
of
)
Ca3 Y2 Si3 O9 2 host material is the increase in its TL intensity for all the UV-doses applied up to 50 min. Though this
is particularly important for dosimetric application of the
material, the fact that it undergoes fast TL fading puts its
utilization in practical application in question. In addition
to the linear dose response, a material to be used for TL
dosimetry purposes is required to have low or no fading.
For example, dosimeters with TL fading of the order of
only 10% at the end of the third month are reported in literature [30–32]. Thus, fading can be regarded as a quality
indicator for a dosimeter.
(
I(t) = 216.4 + 61.4 exp −
4 Conclusion
(
)
Fig. 9 a TL fading of Ca3 Y2 Si3 O9 2 host material, and b the variation of TL peak maxima with storage time. (Color figure online)
initially trapped in these shallow traps and recombination with holes during the storage time. Relatively deeper
traps populated by electrons were activated at higher temperatures during the heating stage.
The variation of the maximum of the TL peaks with
storage time and the corresponding exponential fit are
depicted in Fig. 9b. The obtained TL fading can be well
fitted with a second order exponential decay function
using the following equation:
(
)
(
)
t
t
I(t) = C + A1 exp −
+ A2 exp −
,
(8)
𝛕1
𝛕2
where I is the TL intensity, A1 and A2 are constants, t is the
time, and 𝛕1 and 𝛕2 are the partial lifetimes for the exponential components. Using Origin software, Eq. (8) is found to
be,
13
The structural and luminescence properties of
Ca3 Y2 (Si3 O9 )2 :xCe3+ synthesized by using the solution combustion
method were investigated. For the
(
)
Ca3 Y2 Si3 O9 2 host material, an intense emission band
with peak at 432 nm (photon energy of 2.9 eV ) was
observed from PL spectrum. This PL emission could be
ascribed to electron transitions from conduction band to a
deep state in the lower half of the band gap or transitions
from a deep state in the upper half of the gap to valence
band. The photoluminescence (PL) emission spectra of
the doped samples monitored at excitation wavelength of
365 nm show a broad band extending from about 350 to
600 nm which could be ascribed to the allowed [Xe]5d1 to
[Xe]4f 1 transition of Ce3+. The PL intensity increased for
up to critical concentration of x = 0.08 mol% and then
decreased because of energy transfer among Ce3+ ions
through electric dipole–dipole interaction resulting in concentration quenching. Important TL kinetic parameters
such as activation energy (E), the frequency factor (s), and
the order of kinetics (b) were determined by employing
peak shape method. Increment in the intensity of the TL
glow peaks was observed with increasing UV dose within
the range of the dose used (5–50 min). However, this material suffers from fast TL fading, which needs further investigations to minimize the fading to acceptable ranges for
dosimetric applications.
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