Frequency-dependent dielectric coefficients of TlInS₂ amorphous films
The frequency dispersion of the loss tangent (tgδ) and the ac conductivity (σac) of amorphous films prepared by evaporation of TlInS₂ has been investigated at frequencies f = 5⋅10⁴…3.5⋅10⁷ Hz. It is shown that, at f > 10⁶ Hz, relaxation losses take place. It is established that the hopping...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2007
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| Цитувати: | Frequency-dependent dielectric coefficients of TlInS₂ amorphous films / S.N. Mustafaeva, M.M. Asadov, K.Sh. Qahramanov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 2. — С. 58-61. — Бібліогр.: 11 назв. — англ. |
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irk-123456789-1179162017-05-28T03:04:06Z Frequency-dependent dielectric coefficients of TlInS₂ amorphous films Mustafaeva, S.N. Asadov, M.M. Qahramanov, K.Sh. The frequency dispersion of the loss tangent (tgδ) and the ac conductivity (σac) of amorphous films prepared by evaporation of TlInS₂ has been investigated at frequencies f = 5⋅10⁴…3.5⋅10⁷ Hz. It is shown that, at f > 10⁶ Hz, relaxation losses take place. It is established that the hopping conduction near the Fermi level occurs in TlInS₂ amorphous films at frequencies up to 3⋅10⁶ Hz. The density of localized states at the Fermi level, the mean time for phonon-assisted tunneling, and the hopping distance have been evaluated for polymorphic TlInS₂ films. For frequencies above 10⁷ Hz, σac( f ) ~ f₂. Such a behavior is caused by optical transitions in TlInS₂ amorphous films. 2007 Article Frequency-dependent dielectric coefficients of TlInS₂ amorphous films / S.N. Mustafaeva, M.M. Asadov, K.Sh. Qahramanov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 2. — С. 58-61. — Бібліогр.: 11 назв. — англ. 1560-8034 PACS 71.20.Nr; 71.23.Cq; 71.55.Jv; 72.20.Ee; 72.30.+q; 73.20.At; 73.20.Hb http://dspace.nbuv.gov.ua/handle/123456789/117916 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The frequency dispersion of the loss tangent (tgδ) and the ac conductivity (σac)
of amorphous films prepared by evaporation of TlInS₂ has been investigated at
frequencies f = 5⋅10⁴…3.5⋅10⁷ Hz. It is shown that, at f > 10⁶ Hz, relaxation losses take
place. It is established that the hopping conduction near the Fermi level occurs in TlInS₂
amorphous films at frequencies up to 3⋅10⁶ Hz. The density of localized states at the
Fermi level, the mean time for phonon-assisted tunneling, and the hopping distance have been evaluated for polymorphic TlInS₂ films. For frequencies above 10⁷ Hz, σac( f ) ~ f₂.
Such a behavior is caused by optical transitions in TlInS₂ amorphous films. |
| format |
Article |
| author |
Mustafaeva, S.N. Asadov, M.M. Qahramanov, K.Sh. |
| spellingShingle |
Mustafaeva, S.N. Asadov, M.M. Qahramanov, K.Sh. Frequency-dependent dielectric coefficients of TlInS₂ amorphous films Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Mustafaeva, S.N. Asadov, M.M. Qahramanov, K.Sh. |
| author_sort |
Mustafaeva, S.N. |
| title |
Frequency-dependent dielectric coefficients of TlInS₂ amorphous films |
| title_short |
Frequency-dependent dielectric coefficients of TlInS₂ amorphous films |
| title_full |
Frequency-dependent dielectric coefficients of TlInS₂ amorphous films |
| title_fullStr |
Frequency-dependent dielectric coefficients of TlInS₂ amorphous films |
| title_full_unstemmed |
Frequency-dependent dielectric coefficients of TlInS₂ amorphous films |
| title_sort |
frequency-dependent dielectric coefficients of tlins₂ amorphous films |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/117916 |
| citation_txt |
Frequency-dependent dielectric coefficients of TlInS₂ amorphous films / S.N. Mustafaeva, M.M. Asadov, K.Sh. Qahramanov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 2. — С. 58-61. — Бібліогр.: 11 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT mustafaevasn frequencydependentdielectriccoefficientsoftlins2amorphousfilms AT asadovmm frequencydependentdielectriccoefficientsoftlins2amorphousfilms AT qahramanovksh frequencydependentdielectriccoefficientsoftlins2amorphousfilms |
| first_indexed |
2025-07-08T13:00:52Z |
| last_indexed |
2025-07-08T13:00:52Z |
| _version_ |
1837083817912827904 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 2. P. 58-61.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
58
PACS 71.20.Nr; 71.23.Cq; 71.55.Jv; 72.20.Ee; 72.30.+q; 73.20.At; 73.20.Hb
Frequency-dependent dielectric coefficients
of TlInS2 amorphous films
S.N. Mustafaeva1, M.M. Asadov2, K.Sh. Qahramanov3
1Institute of Physics, Azerbaijan National Academy of Sciences
2Institute of Chemical Problems, Azerbaijan National Academy of Sciences
3“Selen” Production Association, Azerbaijan National Academy of Sciences
AZ 1143 Baku, G. Javid Ave., 33
E-mail: solmust@gmail.com
Abstract. The frequency dispersion of the loss tangent (tgδ) and the ac conductivity (σac)
of amorphous films prepared by evaporation of TlInS2 has been investigated at
frequencies f = 5⋅104…3.5⋅107 Hz. It is shown that, at f > 106 Hz, relaxation losses take
place. It is established that the hopping conduction near the Fermi level occurs in TlInS2
amorphous films at frequencies up to 3⋅106 Hz. The density of localized states at the
Fermi level, the mean time for phonon-assisted tunneling, and the hopping distance have
been evaluated for polymorphic TlInS2 films. For frequencies above 107 Hz, σac( f ) ~ f 2.
Such a behavior is caused by optical transitions in TlInS2 amorphous films.
Keywords: amorphous film, vapour deposition, Fermi level, dielectric properties,
electrical conductivity.
Manuscript received 11.04.07; accepted for publication 24.04.07; published online 19.10.07.
1. Introduction
TlInS2 single crystals are typical representatives of
layered wide-band semiconductors [1, 2] which are
characterized by a low mobility of current carriers. Such
materials are very perspective for the fabrication of
solid-state electron devices on their base. Layered
crystals usually contain structural defects, such as
dislocations and vacancies. The presence of these defects
results in a high density of localized states near the
Fermi level. In [3, 4], it is established by experiments
that, in TlInS2 single crystals along the C-axis in
constant (dc) and alternative (ac) electric fields at
T ≤ 200 K and f = 105…106 Hz, the hopping conducti-
vity in localized states near the Fermi level takes place.
Of some interest is the study of the dielectric
properties of thin evaporated TlInS2 films in alternate
electric fields. The investigation of the electric properties
of semiconductor materials in ac-electric fields gives
information about the nature of charge transport and
localized states in the forbidden gap. Such measurements
allow one to determine the permittivity (ε), dissipation
factor (tgδ), and optical absorption coefficient. In order
to establish the mechanism of charge transport, it is
necessary to know the frequency dependence of these
parameters. The aim of the given paper is the investi-
gation of the frequency-dependent dielectric parameters
of TlInS2 amorphous films and the clarification of the
mechanism of charge transport.
2. Experimental techniques
Conditions for TlInS2 thin films to be formed have been
studied by the method of electron diffractometry. It has
been established that amorphous films of TlInS2 are
polymorphous, i.e. there appear three different
amorphous films with various S = 4πsinθ / λ that are
crystallized in tetragonal, monocline, and rhombic
syngonies on the condensation surface [5]. Amorphous
films TlInS2 – I with S = 20.32; 26.06; 38.43 nm–1 are
crystallized in monocline syngony [6]. Amorphous films
TlInS2 – II with S = 23.61; 39.25; 62.74 nm–1 are
crystallized in tetragonal syngony [7]. And amorphous
films TlInS2 – III with S = 15.02; 24.73; 38.86 nm–1 are
crystallized in rhombic [7] syngony. TlInS2 – I, TlInS2 –
II, TlInS2 – III films were prepared by the vacuum
evaporation. Glass plates with conducting SnO2 layer
were used as substrates. The method of “three-
temperatures” [9] or the evaporation from different
sources was used for preparation of TlInS2 films. At
condensation of TlInS2 films, the temperature of the
glass substrate was equal to 300 K. This method of
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 2. P. 58-61.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
59
evaporation produces films of the stoichiometric
composition; which was verified by X-ray spectroscopic
analysis. An electron microscopic study demonstrated
the amorphous structure of TlInS2 – (I, II, III) films
obtained under these conditions. The thickness of the
TlInS2 films was of the order of 1 µm. Thin film samples
for dielectric measurements were prepared in a sandwich
structure (Fig. 1). The contact materials used were silver
and SnO2.
Measurements of the dielectric coefficients of
TlInS2 – (I, II, III) films were performed at fixed
frequencies in the range 5⋅104…3.5⋅107 Hz by the
resonant method using a TESLA BM 560 Qhmmeter.
For electrical measurements, the samples were placed in
a specially constructed screened cell. All measurements
were performed at T = 298 K. The accuracy in
determining the resonance capacitance and the quality
factor Q = 1 / tgδ of the measuring circuit was limited by
errors related to the resolution of the device readings.
The accuracy of the capacitor graduation was ±0.1 pF.
The reproducibility of the resonance position was
±0.2 pF in capacitance and ±(1.0 – 1.5) scale divisions in
quality factor.
3. Experimental results and discussion
Figure 2 shows the experimental frequency dependences
of the dissipation factor tgδ for TlInS2 – I (curve 1);
TlInS2 – II (curve 2), and TlInS2 – III (curve 3)
amorphous films.
As seen from Fig. 2, the tgδ(f) curves have two
branches: a monotonically descending one (at f < f0) and
a rising one (at f > f0). The hyperbolic decrease of tan δ
with increase in the frequency is the evidence of the fact
that conductivity loss becomes the main dielectric loss
mechanism at f < f0. A significant dispersion in tgδ at
f > f0 is observed for TlInS2 – I film (curve 1). The
increasing branches of tgδ(f) curves in TlInS2 films
allow us to confirm that relaxation losses take place at
f > 106 Hz.
Figure 3 shows the experimentally measured
frequency dependence of the ac-conductivity of TlInS2 –
(I, II, III) amorphous films at 298 K (curves 1-3).
Curve 4 is the frequency-dependent ac conductivity of a
TlInS2 single crystal with tetragonal structure (a = 0.80;
c = 0.67 nm).
The values of dark resistivity (ρ) of the studied
materials at 298 K and the dark dc- and ac-conductivities
at f = 2⋅105 Hz are listed in Table 1. It is seen from
Table 1 that the dark resistivities of TlInS2 – (I, II, III)
evaporated amorphous films are much greater than those
of a TlInS2 single crystal (by 30…800 times). For all
investigated samples, the magnitude of ac-conductivity
at f = 2⋅105 Hz is much greater than that of the dc
hopping conductivity: σac /σdc = (3.0…5.4) 102.
The ac-conductivity of TlInS2 amorphous films can
be expressed by the following equation
Fig. 1. Configuration of the sample on the base of a TlInS2
amorphous film.
Fig. 2. Dispersion curves of tgδ in amorphous films TlInS2 (I);
TlInS2 (II) and TlInS2 (III) at T = 298 K.
Fig. 3. Frequency-dependent ac-conductivities of TlInS2 –
(I, II, III) amorphous films (curves 1-3) and a single crystal
(curve 4) at room temperature.
σac(f) = σ0 + σf, (1)
where σ0 is dc-conductivity, and
σf = σ1 + σ2 + σ3. (2)
σ a
c,O
hm
–1
⋅c
m
–1
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 2. P. 58-61.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
60
Table 1. The dc- and ac-conductivities of TlInS2 amorphous
films.
In (2), σ1 ~ f n (n ≤ 0.5), σ2 ~ f, and σ3 ~ f 2. The
σac ~ f dependence indicates that the mechanism of
charge transport is the hopping over localized states near
the Fermi level [10]. This charge transport mechanism is
characterized by the following expression obtained
in [11]:
4
ph52
F
2
3
ac ln
96
)(
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ νπ
=σ
f
faNTkef , (3)
where e is the elementary charge, k is the Boltzmann
constant, NF is the density of localized states near the
Fermi level, a = 1/α is the localization length, α is the
decay parameter of the wave function of a localized
charge carrier, Ψ ~ e–αr, and νph is the phonon frequency.
Using expression (3), we can calculate the density of
states at the Fermi level from the measured values of the
conductivity σac(f ). Calculated values of NF for
investigated TlInS2 – (I, II, III) amorphous films are
given in Table 2. The localization radius is chosen as
0.8 nm for TlInS2 amorphous films (usually, a =
0.8 nm [10] in amorphous materials).
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 using
the formula [10]
τ –1 = νph exp(–2Rα), (4)
where R is the average hopping distance:
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ ν
α
=
f
R ph ln
2
1 . (5)
The calculated values of τ and R for TlInS2
amorphous films are given in Table 2.
As seen from Fig. 3, at f > 107 Hz, σac ~ f 2 in TlInS2
amorphous films. The conductivity proportional to f 2 is
related to optical transitions in semiconductors
Table 2. Parameters of TlInS2 amorphous films obtained
from high-frequency dielectric measurements.
and is dominant at high frequencies. Such a conduction
is characterized by the expression [10]
( ) ( )
4
0252
2
ln
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ π
=σ
hf
I
hfaNef F
h
, (6)
where I0 is determined from the equation
I = I0exp (–Rα), (7)
where I is the resonance energy of two localized centers,
and distance between these centers is
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟
⎠
⎞
⎜
⎝
⎛
α
=
fh
I
R f
02
ln1 . (8)
6. Conclusions
Thus, the experimental results of high frequency
dielectric measurements on TlInS2 amorphous films
allow us to establish the nature of dielectric losses and
the mechanisms of charge transport at various
frequencies and to evaluate the density of localized
states near the Fermi level, average hopping time, and
distance.
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crystal
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amorphous
film
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amorphous
film
TlInS2 – III
amorphous
film
1011
3⋅1012
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8⋅1013
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3⋅10–9
1.4⋅10–10
7⋅10–11
7⋅10–12
3⋅102
4.2⋅102
5.4⋅102
5⋅102
Material NF, eV–1⋅cm–3 τ, µs R, nm
TlInS2 – I
amorphous film
TlInS2 – II
amorphous film
TlInS2 – III
amorphous film
2.2⋅1018
1.7⋅1018
3.6⋅1017
0.65
0.65
0.63
5.4
5.4
5.3
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 2. P. 58-61.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
61
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