Results in Physics 16 (2020) 102856
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Dielectric properties of GeSbSe glasses prepared by the conventional meltquenching method
T
⁎
N. Nedelcua, , V. Chiroiua, C. Ruginăa, L. Munteanua, R. Ioana,b, I. Giripa, C. Dragnea
a
b
Institute of Solid Mechanics, Romanian Academy, 15 Ctin Mille, Bucharest 010141, Romania
University Spiru Haret, 13 Ion Ghica, Bucharest 030045, Romania
A R T I C LE I N FO
A B S T R A C T
Keywords:
GexSb40−xSe60 glasses
Dielectric constants
Hilliard theory
We report on the dielectric properties of the chalcogenide ternary GexSb40−xSe60 glasses with composition
x = 12, 25, 30 at%. By combining the Swanepoel method with a formalism based on the Hilliard theory of the
surface tension, the linear dielectric constants and the third-order optical susceptibility are predicted. The glasses
are synthesized from elements with 5N purity (Ge, Sb, Se) by the conventional melt-quenching method. The
mixture was sealed into quartz ampoules after evacuation down to a pressure of 10−3 Pa, in a rotary furnace for
24 h at 950 °C.
Introduction
Chalcogenide ternary GeSbSe glasses Chalcogenides are known as
stable amorphous, quasi-amorphous and crystalline materials with applications in several fields as thermoelectric, optics, medicine, etc., due
to their special properties of infrared transmission and high refractive
index that can be modified as desired [1]. Chalcogenide compounds are
the combinations of Group VI elements of the Periodic Table, especially
the sulfur, selenium, and tellurium compounds. This name comes from
the Greek language, showing that they occur in nature in the copper
ores (χαλκοζ – copper, γενναω – to born and ειδοζ – type) [1]. Chalcogenide is a chemical compound containing at least one chalcogen
anion (S2−) and an electropositive element (Cd2+, Zn2+). The chalcogenide glasses transmit longer wavelengths in the infrared region (IR)
than fluoride glasses and silica. Nowadays there is an increased demand
for materials with high a level (> 96%) of their transmission index in
the visible, in the near-infrared as well as in the mid-infrared spectral
ranges. The chalcogenide layers deposited on both sides of a surface
onto fused silica (quartz), silicon (Si), germanium (Ge), calcium
fluoride (CaF2) and zinc sulfide (ZnS) cover a large spectral range from
0.6 µm to 20 µm with a high transmission ratio, of over 90% [2,3].
The influence of Sb, Se and Ge on the physicochemical properties of
the composition have been intensively studied in the last years. The
presence of Sb strengthens the composition by stable SbSe bonds, the
cross-linkages in the structural chains and memory switching in the
bulk [4]. The Se introduces the versatility in the forming, while Ge
increases the glass transition temperature. The network undergoes
⁎
structural changes reflected in the phase transformations [5–7], doping
in the electronic structures [8], and the transport properties [9] by
varying the chemical composition. Many different applications of
GeSbSe glasses exist such as the infrared-transmitting lenses based on
the broken chemical order [10], the ultrafast optical signal processing
[11], the miniaturization and increased sensor fusion [12] and the
evidence for trap-limited transport in the subthreshold conduction regime.
The chalcogenide coatings are expected to increase the transmission
ratio, bringing the highest 96%. Fused silica (quartz) substrates, which
have relatively low cost compared to the previous substrates, will also
be tested to check for the transmission index improvement due to the
chalcogenide coating in its high transmission spectral range
(200–2600 nm and 2900–4000 nm).
Our previous investigations have revealed that new chalcogenide
materials exhibit interesting properties for sensing with wide infrared
transparency as well as the almost limitless capability for composition
alloying and property tailoring, that is likely to revolutionize the broad
infrared sensing for biological, temperature and radiation sensors.
We can classify the existent approaches to describing the behavior
of the GeSbSe glasses in three classes. The first class is based on the
existence of the structural transition from a layered structure to a 3D
network around a critical, topological or chemical point [13]. The
chemical threshold can exist only in the stoichiometric composition.
The topological threshold can be revealed by varying the composition
and moving away from stoichiometry. The second class investigates the
band-gaps behavior defined by the Bloch's theorem [14]. Lord Rayleigh
Corresponding author.
E-mail address: nicoleta_dulgheru@yahoo.com (N. Nedelcu).
https://doi.org/10.1016/j.rinp.2019.102856
Received 5 November 2019; Received in revised form 29 November 2019; Accepted 30 November 2019
Available online 05 December 2019
2211-3797/ © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Results in Physics 16 (2020) 102856
N. Nedelcu, et al.
attacked this problem in 1887 and demonstrated that any 1D photonic
crystal has a band-gap. The third class consists of experimental investigations as the neutron and X-ray diffraction correlated with RMC
[15], the surface topography, the spectroscopic ellipsometry [16,17]
and other methods.
Despite employing relevant properties of GeSbSe glasses, they still
suffer from little-understood of structural and morphological characterization of the bulk, and also the description of the dielectric constants.
In this paper, we focused on the dielectric characterization of
Gex Sb40 − x Se60 composition where x varied between 12 and 30 at%. The
Lambda 950 Spectrophotometer and a formalism based on the Hilliard
theory of the surface tension are used to predict the dielectric properties.
Experimental
Fig. 2. Envelope function of the spectral transmission.
The melt-quenching technique is the most common technique for
the production of chalcogenide glasses. The procedure includes mixing
of elements Ge, Sb and Se of 99.999% purity and heating up in a rotary
furnace at 950 °C. Appropriate quantities of Ge, Sb, and Se were sealed
into quartz ampoules after evacuation down to a pressure of 10−3 Pa.
For a homogeneous melting, the mixture was kept at this temperature
for 24 h, and quenched in the ice water. The heating resistance was
coupled at the 4 × 10−3 Pa, to ensure 300 °C in the evaporation
chamber while the dome was rotating. The powder material was evaporated at least to 400 mA. After evaporation, the samples were measured by Lambda 950 Spectrophotometer. Using the transmission
spectra, the optical and dielectric properties by the Swanepoel method
and also the band-gaps were computed. The spectrophotometer’s
measurements were recorded on Lambda 950 Spectrophotometer with
double beam and double monochromator at the room temperature, in
the spectral range ultraviolet–visible-near-infrared (UV–VIS-NIR) with
266 nm/min a scanning speed for normal incidences. The radiant energy transmittance T [%] of the surface of the glass is plotted with respect to the wavelength λ in Fig. 1. The total transmission T is given for
a normal incidence [18]
T (λ ) =
Ax~
B − Cx~ cos φ + Dx~2
(2)
4πnd ~
,x
λ
= exp(−αd) (n − 1)3 (n − s 2)
4π nd
x
λ
Table 1
Thickness, wavelengths and refractive index of Gex Sb40 − x Se60 with composition
x = 12, 25 and 30 at%.
(1)
A = 16ns 2, B = (n + 1)3 (n + s 2), C = 2(n2 − 1)(n2 − s 2)
S 2 (n + 1)3 (n + s 2) D = (n − 1)3 (n − s 2), φ =
Fig. 3. Refractive index n (λ ) .
Chalcogenide layers
Thickness
d [nm]
λ1
[nm]
λ2
[nm]
n1
(λ1)
n2
(λ2)
Ge12Sb28Se60
Ge25Sb15Se60
Ge30Sb10Se60
1328
1253
1192
1014
922
876
917
836
790
3.105
2.988
2.836
3.153
3.041
2.889
(3)
e−α d
=
is the refractive index, s is the index of the
where nφ =
quartz substrate, d is thickness, φ is the phase difference between the
Fig. 4. Thickness according to Ge content [%].
direct and multiple reflected transmitted beams, x~ is the absorbance
and α is the absorption coefficient.
Construction of the transmission envelope function with respect to
Fig. 1. Spectral transmission.
2
Results in Physics 16 (2020) 102856
N. Nedelcu, et al.
Fig. 3 shows the variation of the refractive index n with respect to λ .
We see that n decreases with increasing of the Ge concentration, or with
decreasing of Sb concentration, in full agreement with the results
available in [15–19]. The transmission spectrum gives the thickness d
[20,21]
d=
λ1 λ2
2(λ1 n2 − λ2 n1)
(6)
The wavelengths and refractive index are obtained by replacing n1
and n2 in (6) (Table 1).
Variation of thickness with respect to the Ge content is plotted in
Fig. 4. The absorption coefficient α (λ ) is obtained by the envelop
function of the spectral transmission [22]
α (λ ) =
⎤
( a + a2 − s 2 − 1)3 ( a + a2 − s 2 − s 2)
1 ⎡
ln ⎢
⎥
d ⎢ b − b2 − (a + a2 − s 2 − 1)3 (a + a2 − s 2 − s 4 ) ⎥
⎣
⎦
(7)
where
Fig. 5. Absorption and extinction coefficients.
a=
wavelength λ , in the room temperature is presented in Fig. 2. The envelope method gives the maxima TM and minima Tm for the whole
wavelength range to calculate the refractive index n (λ ) , the thickness d
and the absorption coefficient α (λ ) .
The refractive index n (λ ) is given by the Swanepoel method [18]
⎡ T − Tm
s2 + 1
n (λ ) = ⎢2s M
+
+
T
T
2
M
m
⎢
⎣
2
=
2
⎜
⎟
(9)
⎟
with s notes the refractive index from the quartz substrate, and d is the
thickness.
Fig. 5 shows the variation of α (λ ) with λ . The attenuation of light
passing through a medium can be taken into account by considering the
complex refractive index n + iκ , where the real part n is the refractive
index that indicates the phase velocity, while the imaginary part k (λ ) is
called the extinction coefficient. The extinction index k (λ ) is given by
where s = 1.458 is done by
1/2
1
1
+ ⎛ 2 − 1⎞
T
T
⎝
⎠
8s 2 (TM − Tm)
4s (TM − Tm)
[TM − Tm + (s 2 − 1) TM Tm] +
(TM Tm)2
(TM Tm)2
2
⎛ 4s (TM − Tm) + (s + 1) TM Tm ⎞ − s 2
2TM Tn
⎠
⎝
2 1/2
(4)
s=
(8)
b
2
⎛ 2s (TM − Tm) + s + 1 ⎞ − s 2 ⎤
⎥
T
T
2 ⎠
M
m
⎝
⎥
⎦
⎜
2s (TM − Tm )
s2 + 1
+
TM Tm
2
(5)
Fig. 6. The optical band-gap energy Eg for a) Ge12 Sb28 Se60 b) Ge25 Sb15 Se60 , c) Ge30 Sb10 Se60 , d) Eg according to Germanium content [%].
3
Results in Physics 16 (2020) 102856
N. Nedelcu, et al.
Fig. 7. Variation of a)ε1 and b) ε2 with respect to λ .
k (λ ) =
λα (λ )
4π
(10)
The optical band-gap energy Eg is computed from (10). The results
are presented in Fig. 6. Fig. 6d shows that Eg increase with the increasing of the Germanium content [%]. Dielectric constants ε1 and ε2
are evaluated from
ε1 = n2 − k 2, ε2 = 2nk
(11)
The variation of ε1 and ε2 with respect to λ are presented in Fig. 7
A theoretical formalism to calculate the dielectric constants
The linear dielectric constants of the GeSbSe glasses are the dielectric constant ε1d = ε1 = n2 − k 2 and the optical susceptibility
ε2d = χ2 = n 2 − 1, where n is the refractive index. These constants are
provided by the experiment as shown in the previous section. The
nonlinear dielectric constant, i.e. the third-order optical susceptibility
ε3d = χ3 defined by the third harmonic generation cannot be experimentally predicted [23].
In order to estimate theoretically both the linear and nonlinear dielectric constants, the theory of surface tension of Hilliard is applied
[24–26]. In this theory, the predominant term in the evaluation of the
atomic pseudopotentials of Ge, Sb and Se atoms, is the local energy
calculated from the interaction of two atoms. To calculate this energy
for an amorphous material as the GeSbSe glass, the distribution functions of the pairs of atoms must be computed. These distributions
functions are evidence of the presence of atomic bonds within a short
distance of the GeSbSe glasses, and allow the building of the representations of the nearest neighbours of each atom in a given
Fig. 8. Representation of 25 nearest neighbours of a green Se atom in the reference system ( x , y, z ) for Ge12 Sb28 Se60 .
Fig. 9. Dielectric constant ε1d versus λ .
4
Results in Physics 16 (2020) 102856
N. Nedelcu, et al.
Fig. 10. Dielectric constant ε2d versus λ .
The pseudopotential energy per unit volume W is
Table 2
Thickness, wavelengths and refractive index of Gex Sb40 − x Se60 with composition
x = 12, 25 and 30 at%.
Chalcogenide layers
Ge-Se
bond
[Å]
Se-Sb
bond
[Å]
Ge-Sb
bond
[Å]
β
[u.a]
α × 106
[Ryd]
θ
[rad]
Ge12Sb28Se60
Ge25Sb15Se60
Ge30Sb10Se60
2.13
2.14
2.15
2.11
2.16
2.21
2.21
2.23
2.24
12.25
12.32
12.42
0.26
0.27
0.28
0.76
0.78
0.82
W=
V = Di En δin =
1
1
εikl Ek El + εiklm Ek El Em + ...
2!
3!
1
1
1
εij Ej Ei + εikl El Ek Ei + εiklm Em El Ek Ei + ...
2!
3!
4!
(15)
The constants are determined from (15) as
εij =
1 ∂ 2V
1
∂3V
1
∂ 4V
|E = 0 , εikl =
|E = 0 , εiklm =
|E = 0
2! ∂Ej ∂Ei
3! ∂El ∂Ek ∂Ei
4! ∂Ei ∂Ek ∂El ∂Em
(16)
For 1D case, (13) becomes
D / ε0 = ε1d E + ε2d E 2 + ε3d E 3
ε1d
n2
k2
(17)
= ε1 =
−
is the linear dielectric constant,
where
ε2d = χ2 = n 2 − 1, is the linear optical susceptibility, n is the refractive
index, and ε3d = χ3 is the third-order optical susceptibility measured by
the third harmonic generation [29].
In order to estimate εij, i, j = 1, 2, 3, εikl, i, k , l = 1, 2, 3,
εiklm, i, k , l, m = 1, 2, 3, the theory of surface tension of Hilliard is
applied [27,28]. In this theory, the predominant term in the local energy of the interaction of two atoms. V is computed by using the atomic
pseudopotentials of Ge, Sb and Se atoms, respectively. The atomic
pseudopotentials represent the interactions between individual atoms i
and i + 1, linked by atomic bonds bij , i, j = 1, ...,n . Here, n is the number
of Ge, Sb and Se atoms in a representative cell of the GeSbSe glass.
(12)
with ε0 ≈ 8.854 × 10−12farad/m , is [14,27–29].
This nonlinearity can be described by non-dispersive quadratic and
cubic laws [29]. The dielectric displacements Di , i = 1, 2, 3 are
Di / ε0 = εij Ej +
(14)
where V is the pseudopotential energy, and Ω the cell volume. From
(13) and (14), V we have
reference system.
Good identification of the distribution functions of the pairs of GeSe and Sb-Se atoms can be done by 3D simulations of a small configuration of 200 atoms in the glass [27].
The components Di , i = 1, 2, 3 of the dielectric displacement vector
are expressed in terms of the components εij , i, j = 1, 2, 3 of the dielectric constant tensor, and the components Ej, j = 1, 2, 3, of the
electric field vector E in an arbitrary coordinate system, in a linear
theory
Di (λ )/ ε0 = εij (λ ) Ej
V
, V = Di Ek δik
Ω
(13)
Fig. 11. Dielectric constant ε3d versus λ .
5
Results in Physics 16 (2020) 102856
N. Nedelcu, et al.
investigations are needed to obtain a real map of the properties of the
chalcogenide glasses synthesized from elements with 5 N purity (Ge, Sb,
Se) by the conventional melt-quenching method.
The computing of V needs a unit cell with a known number of atoms
and bonds. The cell can be built from the distribution functions of the
pairs of atoms Ge-Sb, Ge-Se and Sb-S. An example of this cel is represented by 25 nearest neighbours of a green atom in the reference
coordinate system ( x , y, z ) for Ge12Sb28Se60, where θ is the angle between Ge and Se bonds, and Z is the direction ⟨1 0 0⟩ (Fig. 8).
The model of Jankowski and Tsakalakos for the energy Vi of an atom
i (the green atom) is adopted [30,31]
Vi =
1
2
∑ Vij (rij) =
i≠j
1
α ∑ exp(−βRi(n))
2 n
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence the work reported in this paper.
(18)
Acknowledgments
where Vij is a pair potential between the atom i ant its neighbour j , and
rij is the distance from atom i to the neighbour atom j , α is the repulsive
energy parameter, and δ is the repulsive range parameter which depends on bij , i, j = 1, ...,n (see Figs. 9 and 10).
1
The sum 2 α ∑ exp(−βRi(n)) is extended to all nearest neighbours
This work was supported by a grant of the Romanian Ministry of
Research and Innovation, CCCDI-UEFISCDI, project number PN-III-P11.2-PCCDI-2017-0221/59PCCDI/2018 (IMPROVE), within PNCDI III.
Ethics statement
n
points of coordinates (X , Y , Z ) located at distances R(n) ,
R = X 2 + Y 2 + Z 2 with respect to the green Se atom. In view of (9), V
can be interpreted as a measure of the Born-Mayer repulsive energy.
The value of α affects the absolute values of the dielectric constants and
the module as a multiplicative constant. The parameter α is measured in
Ryd (Rydberg) 1 Ryd = 13.6 eV = 2.092×10−21 J, and the parameter β
is measured in atomic units [ua ]. Given the energy of the i – atom, total
atomic energy V is computed from
V (r1, r2, ...,rN ) =
∑ Vi
The Hilliard theory of the surface tension is applied for predicting
the dielectric properties of the ternary GeSbSe glasses. The results revealed that the Ge-Se and Se-Se atom pairs have a significant contribution to the linear dielectric constants, while the Sb-Sb and Sb-Se
atom pairs have a dominant weight in the third-order optical susceptibility. On the other hand, the differences appeared for the Ge-Ge and
Ge-Sb atom pairs are not more significant in the dielectric properties
prediction. The final remarks are that the total energy and the forces
allow the application of the conjugate-gradient method to efficiently
minimize the total energy in order to obtain the static equilibrium
atomic configuration of the thin glass as a function of applied forces and
imposed displacements on specific atoms. We conclude that both, theoretical and experimental investigations are needed to obtain a real
map of the properties of the chalcogenide glasses synthesized from
elements with 5N purity (Ge, Sb, Se) by the conventional meltquenching method.
(19)
i
(r1, r2, ...,rN )
fi = −
∂V (r1, r2, ...,rN )
∂ri
(20)
The parameters α and β , the angle θ , and the atomic bonds bij ,
i, j = 1, ...,n for Ge-Se, Se-Sb and Ge-Sb have computed from this
equilibrium atomic configuration from the condition of zero applied
forces and zero imposed displacements on specific atoms [32,33]. The
results are displayed in Table 2.
The dielectric constants are determined from (16) with the following formulae with no summation over repeating indices
∂
∂ ∂rk
∂
∂2
∂2
=
= Xkj
,
= =Xmj Xni
∂Ej
∂rk ∂Ej
∂rk ∂Ej ∂Ei
∂rn ∂rm
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://
doi.org/10.1016/j.rinp.2019.102856.
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∂3
∂3
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∂El ∂Ek ∂Ei
∂rq ∂rm ∂rn ∂Ei ∂Ek ∂El ∂Em
= Xni Xmk Xql Xsm
∂
∂rs ∂rq ∂rm ∂rn
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In summary, the Hilliard theory of the surface tension is applied for
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optical susceptibility. On the other hand, the differences appeared for
the Ge-Ge and Ge-Sb atom pairs are not more significant in the dielectric properties’ prediction. The final remarks are that the total energy V (r1, r2, ...,rN ) and the forces fi allow the application of the conjugate-gradient method to efficiently minimize the total energy in order
to obtain the static equilibrium atomic configuration of the thin glass as
a function of applied forces and imposed displacements on specific
atoms. We conclude that both, theoretical and experimental
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