Role of Sb additive in the dielectric properties of f Se₉₀In₁₀ and Se₇₅In₂₅ glassy alloys
In this paper, we report the effect of Sb additive on dielectric properties of two binary − InSe glassy systems, comparing the properties of a- Se₉₀In₁₀ a- Se₇₅In₂₅ and a Se₇₅In₂₅Sb₁₅ glassy alloys. The temperature and frequency dependence of ε′ and ε′′ in glassy Se₉₀In₁₀ , Se₇₅In₂₅, and Se₇₅In₂...
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Sharma, J. Kumar, S. 2017-05-26T12:26:20Z 2017-05-26T12:26:20Z 2011 Role of Sb additive in the dielectric properties of Se₉₀In₁₀ and Se₇₅In₂₅ glassy alloys / J. Sharma, S. Kumar // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 2. — С. 152-156. — Бібліогр.: 17 назв. — англ. 1560-8034 PACS 61.43.Dq, 71.55.Jv, 78.40.Fy https://nasplib.isofts.kiev.ua/handle/123456789/117703 In this paper, we report the effect of Sb additive on dielectric properties of two binary − InSe glassy systems, comparing the properties of a- Se₉₀In₁₀ a- Se₇₅In₂₅ and a Se₇₅In₂₅Sb₁₅ glassy alloys. The temperature and frequency dependence of ε′ and ε′′ in glassy Se₉₀In₁₀ , Se₇₅In₂₅, and Se₇₅In₂₅Sb₁₅ alloys are studied by measuring the capacitanceand dissipation factor within the frequency 1 kHz–5 MHz and temperature 300–350 K ranges. Debye like relaxation of dielectric behavior has been observed, which is in agreement with the Guintini theory of dielectric dispersion based on two electron hopping over a potential barrier and is applicable in the present case. ε′ , ε′′ and loss tangent (Tan δ) are found highly frequency and temperature dependent. Dependence of these dielectric parameters on the Sb metallic impurity has also been found in the present glassy system. The peculiar role of the third element Sb, as an impurity in the pure binary Se₉₀In₁₀ and Se₇₅In₂₅ glassy alloys, is also discussed in terms of electronegativity difference and covalent character between the elements used in making the aforesaid glassy system. We are very much grateful to UGC, New Delhi for providing us financial support as a major research project during the span of this work. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Role of Sb additive in the dielectric properties of f Se₉₀In₁₀ and Se₇₅In₂₅ glassy alloys Article published earlier |
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Role of Sb additive in the dielectric properties of f Se₉₀In₁₀ and Se₇₅In₂₅ glassy alloys |
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Role of Sb additive in the dielectric properties of f Se₉₀In₁₀ and Se₇₅In₂₅ glassy alloys Sharma, J. Kumar, S. |
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Role of Sb additive in the dielectric properties of f Se₉₀In₁₀ and Se₇₅In₂₅ glassy alloys |
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Role of Sb additive in the dielectric properties of f Se₉₀In₁₀ and Se₇₅In₂₅ glassy alloys |
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Role of Sb additive in the dielectric properties of f Se₉₀In₁₀ and Se₇₅In₂₅ glassy alloys |
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Role of Sb additive in the dielectric properties of f Se₉₀In₁₀ and Se₇₅In₂₅ glassy alloys |
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role of sb additive in the dielectric properties of f se₉₀in₁₀ and se₇₅in₂₅ glassy alloys |
| author |
Sharma, J. Kumar, S. |
| author_facet |
Sharma, J. Kumar, S. |
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2011 |
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English |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Article |
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In this paper, we report the effect of Sb additive on dielectric properties of two
binary − InSe glassy systems, comparing the properties of a- Se₉₀In₁₀ a- Se₇₅In₂₅ and a Se₇₅In₂₅Sb₁₅ glassy alloys. The temperature and frequency dependence of ε′ and ε′′ in
glassy Se₉₀In₁₀ , Se₇₅In₂₅, and Se₇₅In₂₅Sb₁₅ alloys are studied by measuring the capacitanceand dissipation factor within the frequency 1 kHz–5 MHz and temperature 300–350 K ranges. Debye like relaxation of dielectric behavior has been observed, which is in
agreement with the Guintini theory of dielectric dispersion based on two electron
hopping over a potential barrier and is applicable in the present case. ε′ , ε′′ and loss
tangent (Tan δ) are found highly frequency and temperature dependent. Dependence of
these dielectric parameters on the Sb metallic impurity has also been found in the present
glassy system. The peculiar role of the third element Sb, as an impurity in the pure binary
Se₉₀In₁₀ and Se₇₅In₂₅ glassy alloys, is also discussed in terms of electronegativity
difference and covalent character between the elements used in making the aforesaid
glassy system.
|
| issn |
1560-8034 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/117703 |
| citation_txt |
Role of Sb additive in the dielectric properties of Se₉₀In₁₀ and Se₇₅In₂₅ glassy alloys / J. Sharma, S. Kumar // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 2. — С. 152-156. — Бібліогр.: 17 назв. — англ. |
| work_keys_str_mv |
AT sharmaj roleofsbadditiveinthedielectricpropertiesoffse90in10andse75in25glassyalloys AT kumars roleofsbadditiveinthedielectricpropertiesoffse90in10andse75in25glassyalloys |
| first_indexed |
2025-11-25T22:20:33Z |
| last_indexed |
2025-11-25T22:20:33Z |
| _version_ |
1850563088510615552 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 152-156.
PACS 61.43.Dq, 71.55.Jv, 78.40.Fy
Role of Sb additive in the dielectric properties of Se90In10
and Se75In25 glassy alloys
J. Sharma, S. Kumar1
Department of Physics, Christ Church College, Kanpur-208001, India
1Corresponding author phone: +91-512-2573069, e-mail: dr_santosh_kr@yahoo.com
Abstract. In this paper, we report the effect of Sb additive on dielectric properties of two
binary glassy systems, comparing the properties of a-SeInSe − 90In10, a-Se75In25 and a-
Se75In10Sb15 glassy alloys. The temperature and frequency dependence of ε and ′ ε ′′ in
glassy Se90In10, Se75In25, and Se75In10Sb15 alloys are studied by measuring the capacitance
and dissipation factor within the frequency 1 kHz–5 MHz and temperature 300–350 K
ranges. Debye like relaxation of dielectric behavior has been observed, which is in
agreement with the Guintini theory of dielectric dispersion based on two electron
hopping over a potential barrier and is applicable in the present case. , ε′ ε ′′ and loss
tangent (Tan δ) are found highly frequency and temperature dependent. Dependence of
these dielectric parameters on the Sb metallic impurity has also been found in the present
glassy system. The peculiar role of the third element Sb, as an impurity in the pure binary
Se90In10 and Se75In25 glassy alloys, is also discussed in terms of electronegativity
difference and covalent character between the elements used in making the aforesaid
glassy system..
Keywords: chalcogenide glasses, dielectric measurement, defect state.
Manuscript received 26.01.11; accepted for publication 16.03.11; published online 30.06.11.
1. Introduction
Work was supported by University Grants Commission (UGC), New Delhi.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
The study of dielectric behavior of chalcogenide glasses
is expected to reveal structural information which, in
effect, can be useful for understanding the conduction
mechanism as well. In addition, a study of temperature
dependence of dielectric permittivity, particularly in the
range of frequencies where dielectric dispersion occurs,
can be of great importance to understand the nature and
origin of losses occurring in these materials. Recently
[1, 2] it has been reported that in chalcogenide glasses
the dielectric dispersion does exist at low frequencies
even though these materials are covalently bonded
semiconductors. Glassy Se – In alloys have attracted
great attention because of their potential application in
solar cells [3-5]. The effect of incorporation of a third
element into binary chalcogenide glassy alloys has
always been an interesting problem in getting relatively
stable glassy alloys as well as to change the conduction
type from p to n as most of these glasses show p-type
conduction only. In Ge – Se and Se – In systems, some
metallic additives have been found to change conduction
from p- to n-type and hence these binary systems are of
great importance. However, in these glasses limited
reversibility and low crystallization temperatures are
serious problems. These problems can be overcome by
addition of a third element as a chemical modifier. The
addition of dopant can modify the lattice perfection.
Thus, there is need to predict the suitability of various
glass compositions, with the dielectric relaxation being a
key parameter.
From the above viewpoint, the effect of
incorporation of some metallic impurities into glassy
Se – In alloys has been reported by many workers in a
series of papers. Electrical conductivity and relaxation of
Se – S – In glasses has been studied by [6]. Electrical
conduction mechanism in Se – In – Pb has been studied
by [7]. Thermoelectric power measurements in the
glassy Se – In system have been made by [7]. Optical
band gap of amorphous thin films Se – In has been
determined by [8]. Enthalpy recovery during relaxation
and crystallization kinetics before and after slow neutron
radiation has also been reported in glassy Se96In4 alloy
by [9, 10].
152
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 152-156.
10 30 50 70 90 110
In
te
ns
ity
(a
. u
.)
2θ (degrees)
Se90In10
Se75In10Sb15
Fig. 1. X-ray diffraction pattern of Se90In10 and Se75In10Sb15
glassy alloys.
In view of the above, we have decided to study the
effect of Sb impurity on dielectric properties of two
well-known binary Se90In10 and Se75In25 glassy systems.
The next section describes the experimental details of
the measurements. The results are presented and
discussed in the third section. The final section deals
with the conclusions drawn from this work.
2. Experimental details
2.1. Preparation of glassy alloys
Glassy alloys of Se90In10, Se75In25 and Se75In10Sb15
systems were prepared by quenching technique. High
purity (99.999 %) materials were weighed according to
their atomic percentages and were sealed in silica
ampoules (length ~5 cm and internal diameter ~8 mm)
with vacuum ~ . The ampoules containing the
materials were heated up to 900 °C and held at that
temperature for 10-12 hours. The temperature of the
furnace was raised slowly at a rate ~3-4 °C/min. During
heating, all the ampoules were constantly rocked, by
rotating a ceramic rod to which the ampoules were
tucked in the furnace. This was done to obtain
homogenous glassy alloys.
Torr10 5−
After rocking for about 10 hours, the obtained
melts were cooled rapidly by removing the ampoules
from the furnace and dropping to ice-cooled water. The
quenched samples were taken out by breaking the silica
ampoules. The amorphous nature has been checked by
XRD. Fig. 1 shows XRD plots of Se90In10 and
Se75In10Sb15 glassy alloys. Compositional analysis was
performed using electron probe microanalysis (EPMA)
technique.
Pellets of diameter ~10 mm and thickness
~(1-2) mm were prepared by compressing the finely
grounded powder in a die in a hydraulic press under a
load of ~3-4 tons. Measurements were performed after
coating the pellets with indium film deposited by
vacuum evaporation technique.
2.2. Dielectric relaxation measurements
A specially designed metallic sample holder was used
for the measurements of dielectric parameters in vacuum
~ . The pellets were mounted in between two
steel electrodes of the sample holder. The temperature
was measured using a calibrated copper-constantan
thermocouple mounted very near to the sample, which
could provide measurements of temperature with an
accuracy of 1 °C. The temperature dependence of the
dielectric constant (
Torr10 3−
ε′ ) and dielectric losses ( ε ′′ ) were
studied in a heating run at a heating rate of 1 K/min. The
frequency dependences of and were also
measured by maintaining constant temperature inside the
sample holder.
ε′ ε ′′
Dielectric measurements were made using a “Hioki
3532-50 LCR Hi TESTER”. The parallel capacitance
and dissipation factor were measured, and then ε′ and
ε ′′ were calculated using it. Three-terminal
measurements were performed to avoid the stray
capacitances.
We preferred to measure dielectric behavior of the
pellet rather than of the bulk samples, as macroscopic
effects (gas bubbles, etc.) may appear in the bulk during
preparation. It has been shown by (Goyal et al., 1981),
both theoretically and experimentally, that bulk ingots
and compressed pellets exhibit similar dielectric
behavior in chalcogenide glasses for the suspected in-
homogeneities in case of compressed pellets in these
materials. The number of localized sites induced by
grain boundary effects can be neglected as compared to
charged defect states which are quite large (~ to
) in these glasses. Microsoft Excel
programming has been used for more accurate
calculations in this study.
1810
3119 cmeV10 −−
3. Results and discussion
3.1. Dielectric behavior of various glassy alloys
Temperature dependences of and were measured
at various frequencies (1 kHz to 5 MHz) for various
glassy alloys studied in our case. The measurements
have been performed within the temperature range 300
to 350 K.
ε′ ε ′′
ε′ and ε ′′ were found to be temperature
dependent in the above frequency range in all the glassy
samples studied here. (See Figs 2 and 3 for aforesaid
glassy alloys.) ε′ and ε ′′ increase with the increase of
temperature, the increase being different for various
frequencies. This type of behavior has been reported by
various workers [11, 12] in chalcogenide glasses. Since
in chalcogenide glasses, the dielectric properties can be
interpreted by considering a set of dipoles as long as the
temperature is increased high. Each dipole has a
relaxation time depending on its activation energy,
which is attributed to the existence of a potential barrier
over which the carrier can hop. Because of containing
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
153
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 152-156.
dipoles, the contribution due to dipolar or orientational
polarization dominates at low frequencies.
As the frequency increases high, dipolar or
orientational polarization normally removes due to
inertia of molecules and the electronic polarization
contributes. Thus, the dispersion is low at high
frequencies. Since the orientational or dipolar
polarization is associated with the thermal motion of pair
of charges. The orientation of the dipoles increases as
the temperature increases, leading to the increase of
dielectric constant.
It has been also found that ε decreases with
increasing the frequency.
′
In dielectric spectroscopy,
large frequency dependent contributions to the dielectric
response, especially at low frequencies, may come from
build-ups of charge. This, the so-called Maxwell-
Wagner polarization occurs either at inner dielectric
boundary layers on a microscopic scale, or at the
external electrode-sample interface on a macroscopic
scale. In both cases, this leads to a separation of charges.
The charges are often separated over a considerable
distance, and the contribution to dielectric response can
therefore be orders of magnitude larger than the
dielectric response due to molecular vibration that
occurs at high frequencies, because at high frequencies
the energy is too high to cause rotation, yet too low to
effect electrons directly, and is absorbed in the form of
molecular vibrations. Thus, ε′ decreases with increasing
the frequency. This type of behavior at low and high
frequencies comes under interfacial polarization.
0
5
10
15
20
25
30
290 300 310 320 330 340 350 360
T(K)
ε’
Se90In10
Se75In10Sb15
Se75In25
(At 5 MHz)
Fig. 2. Temperature dependences of the dielectric constant (ε′)
in all the glassy alloys at 5 MHz.
0
2
4
6
8
10
12
14
290 300 310 320 330 340 350 360
T(K)
ε"
Se90In10
Se75In10Sb15
Se75In25
(At 5 MHz)
Fig. 3. Temperature dependences of the dielectric losses (ε″) in
all the glassy alloys at 5 MHz.
In the above glassy alloys, is found to follow a
power law with frequency, i.e. . Fig. 4 (for a-
Se
ε ′′
mAω=ε ′′
75In10Sb15) confirms this behavior, where ε ′′ln versus
ωln dependences are found to be straight lines at
various temperatures. The power m is calculated from
the slopes of these curves and found that the values of m
are negative at all temperatures of measurements. The
magnitude of m increases with the increase of
temperature in all the samples studied here. Guintini [13]
had proposed a dipolar model for dielectric dispersion in
chalcogenide glasses. This model is based on Elliott [14]
hopping of charge carriers over a potential barrier
between charged defect states ( +D and −D ). These
defects are responsible not only for the position of the
Fermi level, but also for the transport properties of this
material. In addition, they act as traps and recombination
centers for carriers and ( ) is assumed to form a
dipole that has a relaxation time depending on its
activation energy; the latter can be attributed to the
existence of a potential barrier over which the carriers
hop. This potential barrier, as proposed by Elliot, is due
to the Coulombic interaction between neighboring sites
forming a dipole.
−+ DD /
The relaxation time connected with a hop is given
by:
Τ = τ0 exp (W / kT). (1)
Combining the imaginary part of the permittivity
with the circular frequency ω of the applied electric
field, we can write:
( ) ( )
( )[ ] .d1
/4–
0
2242
00
ττω+ω×
×επεε=ωε ′′
∫
∞
∞
Re
nkTN
(2)
Where R (a function of τ) is the distance between
the localized sites. This integral has already been
evaluated [14, 15]. According to Guintini et al.,
assuming ωτ<<1, ε ′′ , at a particular frequency in the
temperature range where dielectric dispersion occurs, is
given by:
( ) ( ) ( ) m
m
m WTkneN ωτεπε−ε=ωε ′′ −
∞
4
0
3
0
22
0 /2 . (3)
Here, m is a power of the angular frequency, which
is negative in this case and given by:
mWTkm /4−= , (4)
where n is the number of electrons that hop, N –
concentration of localized sites, ε0 and ε∞ are the static
and optical dielectric constants, respectively, Wm –
energy required to move the electron from a site to
infinity.
According to (3), ε ′′ should follow a power law
with frequency, i.e., where m should be
negative and linear with T as given by (4). This equation
is consistent with the expression of obtained from
mAω=ε ′′
( )ωε ′′
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
154
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 152-156.
the Kramers-Kronig relations. In our samples, we found
also that follows a power law with frequency at
higher temperatures where dielectric dispersion occurs.
The values of m at various temperatures are negative and
follow a linear relation with temperature (see Fig. 5 for
Se
ε ′′
75In10Sb15 glassy alloy). Similar results have been also
found for other glasses. Using the values of m, Wm is
calculated and plotted in Fig. 6 (for a-Se75In10Sb15). The
values of loss tangent ( )ε′ε ′′=δ /Tan are also
calculated, and the results obtained are given in Table 1.
It is clear from this table that the value of Wm increases,
while decreases with impurity incorporation. The
values of and ε in aforesaid glassy alloys are given
in Table 2.
δTan
ε′ ′′
From the above discussion, it seems that the paired
defect states ( +D and −D ) behave as dipoles in the
aforesaid glasses studied here. These results are in
agreement with the theory of hopping of charge carriers
over a potential barrier as suggested by Elliott in case of
chalcogenide glasses.
Table 1. Values of Wm and Tan δ for various glassy alloys.
Glassy alloys Wm (eV)
Tan δ
(1 kHz, 300 K)
Se90In10 0.35 0.67
Se75In10Sb15 0.38 0.62
Se75In25 0.49 0.40
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Table 2. Dielectric parameters of various glassy alloys.
Glassy alloys
ε′
(1 kHz, 300 K)
ε ′′
(1 kHz, 300 K)
Se90In10 21.42 14.44
Se75In10Sb15 14.92 9.28
Se75In25 8.71 3.53
Se75In10Sb15
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
8 10 12 14 16 1
lnω
ln
ε"
8
300K
310K
320K
330K
340K
350K
Fig. 4. versus dependences in glassy Seεln ′′ ωln 75In10Sb15
alloy at certain fixed temperatures.
Se75In10Sb15
0
0.02
0.04
0.06
0.08
290 300 310 320 330 340 350 360
T(K)
Im
I
Fig. 5. ⎜m⎜ vs T dependence in glassy Se75In10Sb15 alloy.
Se75In10Sb15
1
1.5
2
2.5
3
3.5
4
290 300 310 320 330 340 350 360
T(K)
W
m
Fig. 6. Wm vs T dependence in glassy Se75In10Sb15 alloy.
3.2. Impurity dependence of ε and ′ ε ′′
The degree of covalency of the studied compositions can
be estimated according to the following relation [17]:
The proportion of covalent character
= 100% exp [–0.25(χA – χB) ]. (5) B
2
Where χA and χB are the electronegativities of
atoms A and B, respectively. The values of covalent
characters are listed in Table 3.
B
Incorporation of Sb in both Se90In10 glassy system
leads to decreasing the value of the dielectric constant as
given in Table 2. This decrease can be understood in
terms of the nature of bonding in the system. It may be
assumed that incorporation of Sb in the binary alloy
leads to increasing density of stronger bonds SbSb − ,
InIn − and SeSe − than other bonds in the network
Table 3. Calculated covalent character of bonds for
considered compositions.
Bonds for bond type % covalent character
Se–Se 100
In–In 100
Sb–Sb 100
Se–In 88.47
Se–Sb 91.39
Sb–In 99.75
155
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 152-156.
structure, i.e, decreases the weaker bond density in the
investigated compositions, which are more responsive to
electric field than the stronger bonds. Thus, the value ε′
decreases with Sb incorporation in Se90In10 system. The
decrease in the dielectric losses may be caused by the
decrease in the density of defect states, when the third
element Sb as an impurity is incorporated in pure binary
Se90In10 glassy alloy. Similarly, when Sb is incorporated
in both Se75In25 glassy system at the cost of In leads to
increasing the value of the dielectric constant as given in
Table 2. This increase can be understood in terms of the
nature of bonding in the system. It may be assumed that
the incorporation of Sb in the binary alloy leads to
decreasing the density of stronger bonds InSb − ,
and than other bonds in the network
structure, i.e, increases the weaker bond density in the
investigated compositions, which are more responsive to
electric field than the stronger bonds. Thus, the value
InIn − SbSb −
ε′
increases with Sb incorporation in Se75In25 system.
When iso-electronic atom Te is added to amorphous
selenium, the density of defect states is increased, and
hence the residual potential increases in xerographic
experiment. Onozuka et al. [16] have therefore observed
that, when introducing Cl to system, the residual
potential is decreased again. This result was interpreted on
the basis of a structural defect model where Te was
assumed to form positively charged impurities due to
small electronegativity of Te as compared to Se, while Cl
atoms having higher electronegavity than selenium [17]
form negatively charged impurities, thereby compensating
the effect of Te.
TeSe −
Along the same lines, one can expect that when Sb,
having lower electronegativity than Se, is introduced in
Se90In10 at the cost of Se, positive charged defects will
be created, but the extent of their creation will be smaller
since the amount of In is the same in both. On the other
hand, when the same Sb is incorporated in Se75In25 at the
cost of In, the density of defect states increases.
As the dielectric losses in these glasses depend on
the total number of localized sites, the change in
dielectric losses with Sb incorporation can be understood
in terms of the change in the density of defects on
addition of Sb to glassy system. Due to the
change in number of dipoles (
InSe −
+D and −D ), the
dielectric constant is also expected to change as found
by us in the present study.
4. Conclusions
The temperature and frequency dependence of the
dielectric constants and the dielectric losses in a-Se90In10,
a-Se75In25, and a-Se75In10Sb15 glassy systems within the
frequency range 1 kHz–5 MHz and temperature range
300–350 K have been measured. It has been found that
both the dielectric constant and dielectric losses are
highly dependent on frequency and temperature as well
as found to be dependent on the impurity incorporated in
glassy system. The frequency dependence of the
dielectric losses in the above temperature range could be
interpreted in terms of the hopping of charge carriers
over a potential barrier between charged defect states
(
InSe −
+D and −D ). It is clear from the results obtained that
the addition of Sb affects the charged defect states in the
pure InSe − glassy network, which also affects the
dielectric properties. The difference in the order of
changing the defect states in two Se90In10 and Se75In25
binary glassy systems could be explained on the basis of
the electro-negativity difference and covalent character
between the constituent elements used in making the
above glassy alloys.
Acknowledgements
We are very much grateful to UGC, New Delhi for
providing us financial support as a major research
project during the span of this work.
References
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2. Experimental details
3. Results and discussion
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