Dielectric spectroscopy of CuInSe₂ single crystals
The results of high-frequency dielectric measurements with obtained α-CuInSe₂ single crystals provided an opportunity to determine the mechanisms of dielectric losses and charge transport, and also to evaluate the density of states at the Fermi level; the average time of charge carrier hopping betwe...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2016
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| Zitieren: | Dielectric spectroscopy of CuInSe₂ single crystals / S.N. Mustafaeva, S.M. Asadov, D.T. Guseinov, I. Kasimoglu // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2016. — Т. 19, № 2. — С. 201-204. — Бібліогр.: 7 назв. — англ. |
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irk-123456789-1215682017-06-15T03:03:51Z Dielectric spectroscopy of CuInSe₂ single crystals Mustafaeva, S.N. Asadov, S.M. Guseinov, D.T. Kasimoglu, I. The results of high-frequency dielectric measurements with obtained α-CuInSe₂ single crystals provided an opportunity to determine the mechanisms of dielectric losses and charge transport, and also to evaluate the density of states at the Fermi level; the average time of charge carrier hopping between localized states, average hopping distance, scattering of trap states near the Fermi level; concentration of deep traps responsible for hopping conductivity in alternate electric fields. 2016 Article Dielectric spectroscopy of CuInSe₂ single crystals / S.N. Mustafaeva, S.M. Asadov, D.T. Guseinov, I. Kasimoglu // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2016. — Т. 19, № 2. — С. 201-204. — Бібліогр.: 7 назв. — англ. 1560-8034 DOI: 10.15407/spqeo19.02.201 PACS 71.20.Nr, 72.15.Rn, 72.20.Ee, 72.20.Jv, 72.30.+q, 73.20.At http://dspace.nbuv.gov.ua/handle/123456789/121568 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The results of high-frequency dielectric measurements with obtained α-CuInSe₂ single crystals provided an opportunity to determine the mechanisms of dielectric losses and charge transport, and also to evaluate the density of states at the Fermi level; the average time of charge carrier hopping between localized states, average hopping distance, scattering of trap states near the Fermi level; concentration of deep traps responsible for hopping conductivity in alternate electric fields. |
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Article |
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Mustafaeva, S.N. Asadov, S.M. Guseinov, D.T. Kasimoglu, I. |
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Mustafaeva, S.N. Asadov, S.M. Guseinov, D.T. Kasimoglu, I. Dielectric spectroscopy of CuInSe₂ single crystals Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Mustafaeva, S.N. Asadov, S.M. Guseinov, D.T. Kasimoglu, I. |
| author_sort |
Mustafaeva, S.N. |
| title |
Dielectric spectroscopy of CuInSe₂ single crystals |
| title_short |
Dielectric spectroscopy of CuInSe₂ single crystals |
| title_full |
Dielectric spectroscopy of CuInSe₂ single crystals |
| title_fullStr |
Dielectric spectroscopy of CuInSe₂ single crystals |
| title_full_unstemmed |
Dielectric spectroscopy of CuInSe₂ single crystals |
| title_sort |
dielectric spectroscopy of cuinse₂ single crystals |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2016 |
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http://dspace.nbuv.gov.ua/handle/123456789/121568 |
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Dielectric spectroscopy of CuInSe₂ single crystals / S.N. Mustafaeva, S.M. Asadov, D.T. Guseinov, I. Kasimoglu // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2016. — Т. 19, № 2. — С. 201-204. — Бібліогр.: 7 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT mustafaevasn dielectricspectroscopyofcuinse2singlecrystals AT asadovsm dielectricspectroscopyofcuinse2singlecrystals AT guseinovdt dielectricspectroscopyofcuinse2singlecrystals AT kasimoglui dielectricspectroscopyofcuinse2singlecrystals |
| first_indexed |
2025-07-08T20:08:16Z |
| last_indexed |
2025-07-08T20:08:16Z |
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1837110708033028096 |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 2. P. 201-204.
doi: 10.15407/spqeo19.02.201
© 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
201
PACS 71.20.Nr, 72.15.Rn, 72.20.Ee, 72.20.Jv, 72.30.+q, 73.20.At
Dielectric spectroscopy of CuInSe2 single crystals
S.N. Mustafaeva1, S.M. Asadov2, D.T. Guseinov1, I. Kasimoglu1
1Institute of Physics, Azerbaijan National Academy of Sciences,
G. Javid Pr. 131, AZ-1143 Baku, Azerbaijan
E-mail: solmust@gmail.com
2Institute of Catalysis and Inorganic Chemistry, Azerbaijan National Academy of Sciences,
G. Javid Pr. 113, AZ-1143 Baku, Azerbaijan
E-mail: mirasadov@gmail.com
Telephone: (99412)539-59-13; Fax: (99412)539-59-61
Abstract. The results of high-frequency dielectric measurements with obtained
α-CuInSe2 single crystals provided an opportunity to determine the mechanisms of
dielectric losses and charge transport, and also to evaluate the density of states at the
Fermi level; the average time of charge carrier hopping between localized states, average
hopping distance, scattering of trap states near the Fermi level; concentration of deep
traps responsible for hopping conductivity in alternate electric fields.
Keywords: single crystal, X-ray diffraction, frequency dispersion, dielectric permittivity,
loss tangent, hopping conductivity.
Manuscript received 25.11.15; revised version received 12.04.16; accepted for
publication 08.06.16; published online 06.07.16.
1. Introduction
There are two polymorphic forms of the compound
CuInSe2: low temperature α-CuInSe2, crystallizes in the
tetragonal system with a chalcopyrite structure, and
high-temperature β-CuInSe2 with sphalerite structure.
Chalcopyrite phase α-CuInSe2 has a high efficiency for
conversion of solar energy into electricity. Below we
shall consider the low-temperature modification.
The chalcopyrite structure of ternary CuInSe2
compounds have a high absorption coefficient (104 cm–1
[1]) making them well-suited for light-emitting diodes,
photovoltaic detectors and solar cells. The melting
temperature of CuInSe2 is 1260 K [2]. X-Ray diffraction
analysis of CuInSe2 samples indicated them to have
lattice parameters of a = 5.782 Å, c = 11.620 Å [3].
According to [4] a = 5.781 Å; c = 11.552 Å. CuInSe2
single crystals have the p-type of conductivity and
bandgap 1.02 eV [2]. In [3], the dielectric permittivity ε0
was calculated (13.6±0.8) for CuInSe2. Capacitance
measurements of CuInSe2 in the low-frequency range
(1…5 kHz) showed a slight frequency dependence of ε0.
In [2], the following values for dielectric permittivity of
CuInSe2 were given: ε(0) = 15.2 (E||C), ε(0) = 16.0
(E⊥C), ε(∞) = 8.5 (E||C), ε (∞) = 9.5 (E⊥C) at 300 K.
Reported here are the results of our high-frequency
dielectric measurements performed with CuInSe2 single
crystals.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 2. P. 201-204.
doi: 10.15407/spqeo19.02.201
© 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
202
2. Experimental technique
Cu, In and Se elements of high purity were used to
synthesize CuInSe2 compound. The 1:1:2 molar ratio of
Cu, In and Se with 0.1% excess of selenium as the
precursor materials were taken in a silica ampoule. In
order to prevent the component deviation from
stoichiometry resulting from all possible volatile loss
of sulfur during initial steps, it was found necessary to
add some excess selenium. The starting materials were
taken in a silica ampoule (15 mm in diameter and
150 mm in length) evacuated to 10–3 Pa and then sealed
off. The ampoule was placed into the single zone
horizontal electrical furnace. The furnace was
controlled by a thermocouple with the accuracy close
to ±0.1 K. During the first stage, the furnace was
slowly heated up at the rate approximately 10 K/h. The
temperatures of the growth zones were allowed to
reach up to 1263 K. Heating duration was 20 h. After
this, the temperature of zone synthesizing compound
CuInSe2 was maintained at 1263 K for the next 2 days.
After these 2 days, the furnace was slowly cooled off at
the rate close to 20 K/h down to room temperature.
When the temperature of the ampoule reached the room
temperature, it was opened to obtain black colored
CuInSe2 crystals. The crystals were then cleaned and
subjected to physical and chemical analysis. The
experiments confirmed the identity of the synthesized
compound CuInSe2. The melting temperature of
CuInSe2 is 1263 K.
After completion of the synthesis, homogeneity and
phase purity of the samples were checked using X-ray
diffraction. α-CuInSe2 crystals were characterized using
X-ray diffraction by using the D8-Advance powder X-
ray automatic diffractometer within the angular range 2θ
= 0.5...80° (CuKα radiation, λ = 1.5418 Å, 40 kV,
40 mA). The X-ray diffraction results were analyzed
using the EVA and TOPAZ programs and ICDD Powder
Difraction File data. The angular resolution of the record
was 0.1°. The errors of determining the reflection angles
were no higher than ∆θ = ±0.02°.
The single crystals of α-CuInSe2 were grown using
the Bridgman method in a two-zone furnace with top
zone temperature close to 1263 K. The temperature
differences within the limits 50 to 80 K were maintained
between melt and growth zones so that the temperature
of the growth zone was maintained at 973 K. The growth
was carried out at a rate 3-5 mm/h. The obtained α-
CuInSe2 single crystals were black in color. Single
crystals were thermally annealed for 150 hours to
provide homogenization. The structure of the compound
α-CuInSe2 identified by X-ray diffraction and consistent
stable under normal conditions is the tetragonal structure
of chalcopyrite (Fig. 1).
A typical diffraction pattern of a powder CuInSe2
sample at room temperature is shown in Fig. 2. X-ray
diffraction characterization showed that the samples
had a tetragonal crystal structure, a = 5.781 Å, c =
11.642 Ǻ.
Fig. 1. Tetragonal structure of chalcopyrite α-CuInSe2.
Investigated polished CuInSe2 samples for
dielectric measurements were formed as flat capacitors.
Ohmic contacts of the samples were made using Ag
paste. Measurements of the dielectric coefficients of the
studied single crystals were performed at fixed
frequencies within the range 5×104…3.5×107 Hz by the
resonant method using TESLA BM 560 Qmeter. For
electrical measurements, the samples were placed into a
specially designed screened cell. An ac-electric field was
applied along the C-axis of CuInSe2 single crystals. The
amplitude of the applied field corresponded to the
Ohmic region of the current-voltage characteristics of
the samples. All measurements were performed at T =
300 K. The accuracy in determining the resonance
capacitance and the quality factor Q = 1/tanδ of the
measuring circuit were limited by errors related with
resolution of the device readings. The accuracy of the
capacitor graduation was ±0.1 pF. Reproducibility of the
resonance position was ±0.2 pF in capacitance and
±(1.0…1.5) scale divisions in quality factor. The largest
deviations from the average were 3…4% in ε and 7% in
tanδ.
3. Results and discussion
The electrical properties (loss tangent, real ε׳ and
imaginary ε״ parts of complex dielectric permittivity,
and ac-conductivity of CuInSe2 single crystals have been
studied within the frequency range from 50 kHz to
35 MHz. The adduced results demonstrate that the
dielectric dispersion in the studied crystals has a
relaxation nature (Fig. 3). However, if the ε׳ value
descended from 17.3 down to 13.5 within the mentioned
frequency range with an increase in frequency, then the
value of ε״ was subjected to stronger frequency
dispersion decreasing by a factor of 10.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 2. P. 201-204.
doi: 10.15407/spqeo19.02.201
© 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
203
Fig. 2. X-ray diffraction pattern of the powder α-CuInSe2
sample at room temperature.
Fig. 3. Frequency dependences of real (1) and imaginary (2)
parts of complex dielectric permittivity of α-CuInSe2.
Fig. 4 shows the experimental frequency
dependence of the dielectric loss tangent in the CuInSe2.
It is seen from Fig. 4 that tanδ descends with an increase
in frequency, which indicates conductivity losses [5].
Fig. 5 presents the frequency dependence of the
ac-conductivity of CuInSe2 single crystal at T = 300 K.
The value of σac is increased from 2×10–8 up to
1.5×106 Ohm–1cm–1 within the mentioned frequency
range with increasing the frequency. It must be noted
that dc-conductivity of CuInSe2 single crystal was equal
to 6.7×10–9 Ohm–1cm–1 at T = 300 K. The frequency
dependence of conductivity is described by the power
law σac ~ f n, where n = 0.8 at f = 4×105…3.5×107 Hz. It
is known that the band-type ac-conductivity is mainly
frequency independent up to 1010…1011 Hz. The
experimental dependence σac ~ f 0.8 that we observed
indicates that it is conditioned by hops of charge carriers
between the states localized in the forbidden band of
CuInSe2. These can be states localized near the edges of
allowed bands or localized near the Fermi level [6].
However, since the conductivity over the states near the
Fermi level always surpasses the conductivity over the
states near the edges of allowed bands under
experimental conditions, law σac ~ f 0.8 that we found
indicates the hopping mechanism of the charge transfer
localized in the vicinity of the Fermi level:
( )
4
52
F
2
3
ln
96 ⎥
⎦
⎤
⎢
⎣
⎡ ν
⋅
π
=σ
f
fakTNef ph
Lac (1)
where e is the elementary charge, k – Boltzmann
constant, NF – density of localized states near the Fermi
level, aL = α/1 – localization length, α – decay
parameter of the wave function of a localized charge
carrier, ψ ∼ re α− , and phν – phonon frequency.
Using the expression (1), we can calculate the
density of states at the Fermi level from the measured
values of the conductivity σac(f). The calculated value
of NF for CuInSe2 single crystals was equal to
7.8×1017 eV–1cm–3 (localization radius is chosen to be
30 Å, by analogy with that of the CuInS2 single crystal
[7]). In our case, phν is generally of the order of
1012 Hz.
The theory of ac hopping conductivity provides an
opportunity to determine the average time τ of charge
carrier hopping from one localized state to another by
using the formula [6]:
( )α−ν=τ− Rph 2exp1 , (2)
where R is the average hopping distance.
Fig. 4. Frequency dispersion of loss tangent in α-CuInSe2.
Fig. 5. Frequency-dependent ac-conductivity of α-CuInSe2
single crystals at T = 300 K.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 2. P. 201-204.
doi: 10.15407/spqeo19.02.201
© 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
204
Experimentally, 1−τ has been determined as the
average frequency in the f 0.8-region, i.e., f/11 =τ− .
It follows that
.ln
2
1
f
R phν
α
= (3)
The calculated values of τ and R for CuInSe2
single crystals were equal to 5.6×10–2 μs and 166 Å,
correspondingly.
Knowing NF and R from [6]:
,1
23
4
F
3 =
Δ
⋅
π ENR (4)
we estimate scattering of trap states near the Fermi level:
ΔE = 0.13 eV for CuInSe2 crystals.
By formula:
ENNt Δ⋅= F (5)
we can determine the concentration of deep traps in
CuInSe2: Nt = 1017 cm–3.
4. Conclusions
The electrical properties (loss tangent, real and
imaginary parts of complex dielectric permittivity, and
ac-conductivity) of α-CuInSe2 single crystals have been
studied within the frequency range from 50 kHz to
35 MHz. The results demonstrate that the dielectric
dispersion in the studied crystals has a relaxation nature.
The experimental frequency dependence of the
dissipation factor for α-CuInSe2 single crystals is
characterized with a monotonic descending with
frequency, which is evidence of the fact that
conductivity loss becomes the main dielectric loss
mechanism within the studied frequency range. At
frequencies from the range of f = 4×105…3.5×107 Hz,
the ac-conductivity of the crystals varies according to
the law σac ~ f 0.8, characteristic of hopping conduction
through localized states near the Fermi level. The Fermi-
level density of states, dispersion of their energies as
well as the mean hop distance and time have been
estimated.
References
1. S. Prabahar, V. Balasubramanian, N. Surya-
narayanan, N. Muthukumarasamy, Optical
properties of copper indium diselenide thin films //
Chalcogenide Lett. 7(1), p. 49-58 (2010).
2. O. Madelung, Semiconductors: Data Handbook
(3-rd ed.). Springer, 2004.
3. P. W. Li, R.A. Anderson, R.H. Plovnick, Dielectric
constant of CuInSe2 by capacitance measurements
// J. Phys. Chem. Solids. 40, p. 333-334 (1979).
4. C. Rincon, F. J. Ramires, Lattice vibrations of
CuInSe2 and CuGaSe2 by Raman microspectrometry
// J. Appl. Phys. 72(9), p. 4321-4324 (1992).
5. V. V. Pasynkov and V. S. Sorokin, Materials of
Electron Techniques. St-Peterburg – Moscow, 2004
(in Russian).
6. N. Mott and E. Davis, Electron Processes in
Noncrystalline Materials. Clarendon Press, Oxford,
1971.
7. S. N. Mustafaeva, M. M. Asadov, D. T. Guseinov,
I. Kasimoglu, Dielectric properties of CuInS2 single
crystal at alternate electric fields of radio-frequency
range // Physics of Solid State, 57(6), p. 1079-1083
(2015).
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