Supplemental materials
Coupling of Er light emissions to plasmon modes on In2O3: Sn nanoparticle sheets
Hiroaki Matsui 1, 2, Wasanthamala Badalawa 2, Takayuki Hasebe 3, Shinya Furuta 4, Wataru Nomura 2,
Takashi Yatsui 2, Motoichi Ohtsu 2, and Hitoshi Tabata 1, 2
1
Department of Bioengineering, The University of Tokyo, 1-3-7 Hongo, Bunkyo-ku,
Tokyo 113-8656, Japan
2
Department of Electronic Engineering and Information Systems, The University of Tokyo,
1-3-7 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
3
Central Customs Laboratory, Ministry of Finance, 5-3-6 Kashiwanoha, Chiba 270-0882, Japan
4
Tomoe Works Co., Ltd, 1-3-6 Namiyoke, Minato-ku, Osaka 552-0001, Japan
1. Fabrications of In2O3: Sn nanoparticles
The synthesis procedure used for the production of an In2O3: Sn nanoparticle (ITO NP) is as follows
1
. In and Sn carboxylates: (C9H22CO2)3In and (C9H22CO2)4Sn as starting materials were heated without
use of organic solvent at 350oC for 4 h after the air in a three-neck flask used synthesis of NPs was
replaced by nitrogen gas, which produced a pale blue suspension, to which excess ethanol was added
to induce precipitation. Centrifugation and repeated washing with ethanol yielded pale blue to blue
powders of ITO NPs, which were redispersed in a toluene medium. The Sn content in ITO NPs
([Sn]XFS) was about 5%, as confirmed by X-ray florescence spectroscopy (XFS).
2. Identification of crystallite size by X-ray diffraction
X-ray diffraction (XRD) patterns of nanocrystalline samples exhibit significant broadening. The
crystalline quality of In2O3: Sn nanoparticles (ITO NPs) was analyzed by XRD (Rigaku, smart Lab).
The mean crystallite size of NPs was evaluated from line broadening of the (222) diffraction peak
using Scherrer’s equation 2, 3:
D
K
B cos
(1)
where K (= 0.9) is Scherrer’s constant, is the X-ray (CuK) wavelength ( = 1.5405Å),  is the
diffraction angle, and B is the half width of the (222) peak. The crystallite sizes obtained from
Scherrer’s equation based on the (222) peak were 1.58 and 2.20 nm for NPs with Sn contents of 0 and
5%, respectively, which differed from the particle sizes obtained from TEM measurements [inset of
Fig. 1(a)] and dynamic scattering spectroscopy [Fig. 1(c)]. In general, broadening of the line-width of
the XRD pattern is attributed to various structural defects, such as impurities, lattice disorders and
strains. Equation 1 is commonly used to estimate particle size in the case of a strain-free sample with
no structural defects. Therefore, the large difference between crystallite and particle sizes obtained by
TEM and XRD is related to the presence of structural defects in the ITO NPs.
3. Theoretical parameter-fitting to the optical spectrum of ITO NPs
The extinction spectrum of ITO NPs dispersed in toluene was fitted using Mie theory with frequencydependent damping () because of ionized impurity scattering related to Sn dopants incorporated
into the NPs. The following theoretical fitting of optical extinction (E) to the experimental data in the
quasistatic limit was employed 4:
  p ( )   H 

 P ( )  2 H 
 E  4kR3 Im
(2)
where k = 2(H)1/2/c with c representing the speed of light, p() is the particle dielectric function, R
is the particle radius, and H indicates the host dielectric constants of toluene. In addition, the effective
dielectric function (eff) was used to obtain real nanoparticle dispersion by the Maxwell-Garnett
effective medium approximation 5:
 eff ( )   H
 p ( )   H
 fV
 eff ( )  2 H
 p ( )  2 H
(3)
where fv is the particle volume fraction, and since this was in the order of 10 -5 owing to sufficiently
dispersed NPs. p() used the free-electron Drude term with a damping constant () because ITO
consists of free electron carriers owing to the absence of interband transitions 3:
 p ( )  1 
 p2
 (  i )
(4)
The plasma frequency (p) is given by  p2  ne /   0 m* , where m* is the effective electron mass, ∞ is
the high-energy dielectric constant, and 0 is the vacuum permittivity. Fitted extinction was used with
parameter values of H = 2.23, ∞ = 3.8 and m* = 0.3m0 to determine p(). Frequency-dependent
damping () resulting from ionized impurity scattering is introduced into the Drude term 6:
 

H 
 ( )  f ( ) L  [1  f ( )] H 
f ( ) 
1
  X 
1  exp 

  
3 / 2
(5)
(6)
where L and H represent the low-energy ( = 0) and high-energy ( = ∞) damping factors,
respectively. The changeover energy and width of the function are defined by X and , respectively.
The exponent of (-3/2) of Eq. (5) is characteristic of ionized impurity scattering.
The fitted extinction spectrum and physical parameters are
Differences in H and L values were found. In particular,
Experiment
0.8
Extinction
shown by the red line of Fig. S1 and Table SI, respectively.
Theory
0.4
electron-impurity scattering is reflected by L, which results in
an asymmetric spectral feature followed by spectral
0 0.5
0.7
0.9
1.1
Photon energy (eV)
thought that ionized impurity scattering related to Sn dopants
Figure S1. Experimental (black)
and theoretical (red) extinction
spectra of ITO NPs dispersed in
toluene.
in the NPs produced the asymmetric LPR spectrum.
Table SI. Fitted physical parameters
broadening in the low photon energy region. Therefore, it is
Parameter
n (cm-3)
1.12×1021
H (eV)
0.105
L (eV)
0.177
X (eV)
0.751
 (eV)
0.049
4. Theoretical calculations of ITO NP sheets based on FDTD
The extinction spectra and electric fields of NP sheets were simulated using the finite-difference
time-domain (FDTD) method. It was assumed that the NP sheet has a hexagonal packed structure with
an interparticle distance of 2 nm, which was located on the ZnO: Er layer with a spacer layer of 10 nm.
The ellipsometric data of the ITO layer was used to obtain the complex dielectric constants of NPs 7.
The Medium between the NPs was determined using the refractive index (n = 1.437) of capric acid
because capric acid was used for the organic ligands on the NP surfaces 8. The modeled hybrid
structures were illuminated with light directed in the Z-direction from the ZnO: Er layer sides. The
direction of the electric field was perpendicular to the light and parallel to the X direction. The electric
field distributions were analyzed at the XZ plane. Periodic boundary conditions were applicable to the
X and Y axes. The number of NP sheets was varied from 1 to 22 NP layers. Figure S3 represents a
typical outcome and shows the electric field distribution of a NP sheet with 5 and 10 NP layers for
FDTD simulations.
NP sheet Spacer
ZnO: Er layer
1.5
0.5
0
0.6
0.8
1
Photon energy (eV)
1.2
● 1 layer
● 5 layers
● 7 layers
● 10 layers
● 22 layers
Ez intensity (a.u.)
1 layer
5 layers
7 layers
10 layers
22 layers
1
(c)
(b)
E intensity (a.u.)
Extinction
(a)
0
5
10
15
20
Number of NP layer
25
0
10
20
30
Depth (nm)
Fig. 2. (a) Simulated extinction spectra of ITO NP sheets with different NP layers. (b) The E intensity at
0.80 eV at an interface between the NP sheet and spacer as a function of NP layer. (c) The decay length of
Ez intensity along the Z-direction at 0.80 eV as a function of NP layer.
Figure S2(a) shows extinction spectra of NP sheets with different numbers of NP layers, indicating
that extinction gradually enhanced with increasing number of sheet layers. In a NP sheet with 22
layers, the extinction spectrum showed a maximum peak at 0.58 eV in addition to a shoulder
component at around 0.80 eV. The simulated extinction spectra of NP sheets were similar to those of
experimental extinction spectra. Furthermore, the electric field (E) intensity at 0.80 eV, corresponding
to Er PL energy, was evaluated at an interface between the NP sheet and spacer [Fig. S2(b)]. The E
intensity gradually enhanced with increasing NP layer, which showed a tendency to saturate. Figure
S2(c) shows decay lengths of Ez intensity along the Z-direction at 0.80 eV. The behavior of the NP
sheet with a single NP layer was localized near the surface of NP sheet, and exponentially decayed
into the ZnO: Er layer by passing through the spacer layer. The decay length of the electric field for
the NP sheet was enhanced with increasing number of NP layers. It was found that a thick NP sheet
forms a high electric field on the sheet surface, which is highly effective in establishing coupling
between the plasmons and Er emitters in ZnO layers. Therefore, a thick ITO sheet with a layer
thickness of 300 nm was chosen in order to obtain enhancement of Er PL in this study.
ITO NP sheet
Gap
E-field (I)
Interface
E-field (II)
Z
Y
1
X
ZnO: Er layer
Spacer
0
ZnO: Er layer
Fig. S3. The electric field distribution at a photon energy of 0.80 eV for a
NP sheet with 5 and 10 NP layers. The electric distribution of a NP sheet
with 5 NP layers mainly represents the interface region between the NP
sheet and ZnO: Er layer.
5. References
1
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2
A.L. Patterson, Phys. Rev. 56, 972 (1939).
3
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A. Pflug, V. Sittinger, F. Ruske, E. Szyszka, and G. Dittmar, Thin Solid Films 455/456, 201 (2004).
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