Influence of cation substitution on electrical conductivity and optical absorption edge in Cu₇(Ge1–xSix)S₅I mixed crystals
Electrical conductivity of Cu₇(Ge₁₋xSix)S₅I mixed crystals was measured in the frequency range 1.0x10⁶ –1.2x10⁹ Hz and in the temperature interval 100–300 K. The frequency and temperature behaviour of the electrical conductivity were analyzed. The optical absorption edge of Cu₇(Ge₁₋xSix)S₅I mixed cr...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2012
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| Cite this: | Influence of cation substitution on electrical conductivity and optical absorption edge in Cu₇(Ge1–xSix)S₅I mixed crystals / I.P. Studenyak, M. Kranjcec, V.V. Bilanchuk, A. Dziaugys, J. Banys, A.F. Orliukas // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 3. — С. 227-231. — Бібліогр.: 17 назв. — англ. |
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irk-123456789-1183172017-05-30T03:05:47Z Influence of cation substitution on electrical conductivity and optical absorption edge in Cu₇(Ge1–xSix)S₅I mixed crystals Studenyak, I.P. Kranjčec, M. Bilanchuk, V.V. Dziaugys, A. Banys, J. Orliukas, A.F. Electrical conductivity of Cu₇(Ge₁₋xSix)S₅I mixed crystals was measured in the frequency range 1.0x10⁶ –1.2x10⁹ Hz and in the temperature interval 100–300 K. The frequency and temperature behaviour of the electrical conductivity were analyzed. The optical absorption edge of Cu₇(Ge₁₋xSix)S₅I mixed crystals within the temperature range 77–300 K was studied. The compositional dependences of the electrical conductivity, activation energy, optical pseudogap and Urbach energy were obtained. The influence of Ge→Si cation substitution on the optical absorption processes in the Cu₇(Ge₁₋xSix)S₅I mixed crystals is investigated. 2012 Article Influence of cation substitution on electrical conductivity and optical absorption edge in Cu₇(Ge1–xSix)S₅I mixed crystals / I.P. Studenyak, M. Kranjcec, V.V. Bilanchuk, A. Dziaugys, J. Banys, A.F. Orliukas // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 3. — С. 227-231. — Бібліогр.: 17 назв. — англ. 1560-8034 PACS 77.80.Bh, 78.40.Ha http://dspace.nbuv.gov.ua/handle/123456789/118317 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Electrical conductivity of Cu₇(Ge₁₋xSix)S₅I mixed crystals was measured in the frequency range 1.0x10⁶ –1.2x10⁹ Hz and in the temperature interval 100–300 K. The frequency and temperature behaviour of the electrical conductivity were analyzed. The optical absorption edge of Cu₇(Ge₁₋xSix)S₅I mixed crystals within the temperature range 77–300 K was studied. The compositional dependences of the electrical conductivity, activation energy, optical pseudogap and Urbach energy were obtained. The influence of Ge→Si cation substitution on the optical absorption processes in the Cu₇(Ge₁₋xSix)S₅I mixed crystals is investigated. |
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Studenyak, I.P. Kranjčec, M. Bilanchuk, V.V. Dziaugys, A. Banys, J. Orliukas, A.F. |
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Studenyak, I.P. Kranjčec, M. Bilanchuk, V.V. Dziaugys, A. Banys, J. Orliukas, A.F. Influence of cation substitution on electrical conductivity and optical absorption edge in Cu₇(Ge1–xSix)S₅I mixed crystals Semiconductor Physics Quantum Electronics & Optoelectronics |
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Studenyak, I.P. Kranjčec, M. Bilanchuk, V.V. Dziaugys, A. Banys, J. Orliukas, A.F. |
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Studenyak, I.P. |
| title |
Influence of cation substitution on electrical conductivity and optical absorption edge in Cu₇(Ge1–xSix)S₅I mixed crystals |
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Influence of cation substitution on electrical conductivity and optical absorption edge in Cu₇(Ge1–xSix)S₅I mixed crystals |
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Influence of cation substitution on electrical conductivity and optical absorption edge in Cu₇(Ge1–xSix)S₅I mixed crystals |
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Influence of cation substitution on electrical conductivity and optical absorption edge in Cu₇(Ge1–xSix)S₅I mixed crystals |
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Influence of cation substitution on electrical conductivity and optical absorption edge in Cu₇(Ge1–xSix)S₅I mixed crystals |
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influence of cation substitution on electrical conductivity and optical absorption edge in cu₇(ge1–xsix)s₅i mixed crystals |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2012 |
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http://dspace.nbuv.gov.ua/handle/123456789/118317 |
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Influence of cation substitution on electrical conductivity and optical absorption edge in Cu₇(Ge1–xSix)S₅I mixed crystals / I.P. Studenyak, M. Kranjcec, V.V. Bilanchuk, A. Dziaugys, J. Banys, A.F. Orliukas // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 3. — С. 227-231. — Бібліогр.: 17 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 227-231.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
227
PACS 77.80.Bh, 78.40.Ha
Influence of cation substitution on electrical conductivity
and optical absorption edge in Cu7(Ge1–xSix)S5I mixed crystals
I.P. Studenyak1, M. Kranjčec2, V.V. Bilanchuk1, A. Dziaugys3, J. Banys3, A.F. Orliukas3
1Uzhhorod National University, Physics Faculty,46, Pidhirna str. 88000 Uzhhorod, Ukraine
2University of Zagreb, Geotechnical Faculty, Hallerova Aleja 7, 42000 Varaždin, Croatia
3Vilnius University, Physics Faculty,
Saulėtekio al. 9, LT-10222 Vilnius, Lithuania, e-mail: studenyak@dr.com
Abstract. Electrical conductivity of Cu7(Ge1–xSix)S5I mixed crystals was measured in the
frequency range 1.0106–1.2109 Hz and in the temperature interval 100–300 K. The
frequency and temperature behaviour of the electrical conductivity were analyzed. The
optical absorption edge of ISSiGeCu 5xx17 mixed crystals within the temperature
range 77–300 K was studied. The compositional dependences of the electrical
conductivity, activation energy, optical pseudogap and Urbach energy were obtained.
The influence of GeSi cation substitution on the optical absorption processes in the
ISSiGeCu 5xx17 mixed crystals is investigated.
Keywords: mixed crystals, electrical conductivity, activation energy, absorption edge,
Urbach rule.
Manuscript received 25.06.12; revised version received 16.08.12; accepted for
publication 10.09.12; published online 25.09.12.
1. Introduction
Cu7GeS5I and Cu7SiS5I superionic crystals belong to
argyrodite family compounds [1]. Due to their high ionic
conductivity, these crystals are attractive materials for
applications in different functional elements of solid
state ionics [2].
Structural, electrical and optical properties of
Cu7GeS(Se)5I and mixed crystals based on them were
studied in papers [3–7]. It is shown that the electrical
conductivity of Cu7GeSe5I crystal at room temperature
was found to be rather high (64 S/m at 295 K and
106 Hz) and typical for advanced superionic conductors
[5, 6]. At SSe anionic substitution, the nonlinear
increase of the electric conductivity by more than an
order of magnitude was observed in
ISeSGeCu 5xx17 mixed crystals [7]. Optical studies
have shown that the absorption edge of Cu7GeS(Se)S5I
crystals and mixed crystals based on them exhibits
Urbach behaviour in a wide temperature range [3,5–7].
A nonlinear decrease of the optical pseudogap in the
ISeSGeCu 5xx17 mixed crystals at SSe anionic
substitution is observed [7].
Some of the chemical and physics properties of
ISeSGeCu 5xx17 mixed crystals were presented in the
paper [8]. Chemical interaction in the Cu7GeS5I–
Cu7SiS5I system was studied by X-ray phase analysis,
microstructural analysis and density determination. The
short-wave edge of the diffuse reflection spectra of
ISSiGeCu 5xx17 mixed crystals is shown to shift
towards shorter wavelengths after the substitution of Ge
atoms by Si [8].
This paper is aimed at investigation of temperature
and compositional behaviour of the electrical conductivity
and optical absorption edge in ISSiGeCu 5xx17 mixed
crystals. Moreover, the influence of different types of the
crystal lattice disordering on absorption edge formation
will be in focus of the paper.
2. Experimental
Cu7(Ge1–xSix)S5I mixed crystals were grown by chemical
vapour transport [8]. For synthesis, the calculated
stoichiometric amounts of Cu, Si, Ge, S and CuI were
loaded in silica glass ampoules, thoroughly mixed,
pumped out to 0.13 Pa and sealed. Additional amount of
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 227-231.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
228
CuI used as a transport agent (20 mg/cm3 of the ampoule
free volume) was also loaded in the ampoules. Thus, the
crystal growth was carried out in atmosphere of CuI
chemical active vapour. The as-grown crystals had the
shape of plane-parallel platelets or distorted tetrahedra
533(2.5) mm in size.
For X-ray studies, the DRON-3 diffractometer was
used (conventional 2 scanning technique, Bragg
angle 2 10–60, Cu Kα, Ni filtered radiation). It is
shown that in the Cu7GeS5I–Cu7SiSeI system a row of
continuous solid solutions is formed with mF 34 cubic
symmetry at room temperature (Fig. 1).
The measurements of complex electrical
conductivity were carried out within the frequency range
1.0106–1.2109 Hz and the temperature interval 100–
300 K by using a coaxial impedance spectrometer set-
up [9].
Spectrometric studies of the optical absorption edge
were carried out within the temperature range 77–300 K
by using the LOMO KSVU-23 grating monochromator
[10]. For these measurements, the samples were oriented
at room temperature while being in the cubic phase. For
low temperature studies cryostat of UTREX type was
used. The relative error in determination of the relative
change in the absorption coefficient / did not exceed
10% at 0.3 d 3 [11].
3. Results and discussion
It should be noted that measurements of the real bulk
conductivity are limited to low frequencies (up to MHz
range) due to contact effects. The frequency
dependences of the real part of complex electrical
conductivity are illustrated for Cu7(Ge0.4Si0.6)S5I
mixed crystal and at various temperatures are presented
in Fig. 2. Influence of the contact effect is observed at
low temperatures within the low-frequency range. With
temperature increase, only relaxation dispersion of the
electrical conductivity due to bulk conductivity takes
place (Fig. 2). Besides, it is shown (Fig. 2) that with the
temperature increase the value for Cu7(Ge0.4Si0.6)S5I
mixed crystal increases linearly in a semilogarithmic
scale and obeys the Arrhenius law:
kT
E
T
aexp0 , (1)
where aE is the activation energy, 0 is some
constant, k is the Boltzmann constant, T is the
temperature.
Substitution of Ge atoms with Si atoms leads to
decreasing the electrical conductivity (Fig. 3). It
should be noted that in comparison with Cu7GeS5I, in
Cu7SiSe5I crystals the value decreases by more than
an order of magnitude. With the increase of Si content,
the value of ISeSGeCu 5xx17 mixed crystals
decreases nonlinearly with downward bowing, besides
reaches a minimum at x = 0.4. The activation energy
aE in the mixed crystals under investigation increases
within the composition interval 0 < x 0.4 achieves its
maximum at x = 0.4 and decreases within the
composition interval 0.4 < x < 1 (Fig. 3).
Fig. 1. X-ray diffraction patterns for Cu7(Ge1–xSix)S5I mixed
crystals: 1 – Cu7GeS5I, 2 – Cu7(Ge0.8Si0.2)S5I, 3 –
Cu7(Ge0.6Si0.4)S5I, 4 – Cu7(Ge0.4Si0.6)S5I, 5 – Cu7(Ge0.8Si0.2)S5I,
6 – Cu7SiS5I.
Fig. 2. Frequency dependences of the real part of complex
electrical conductivity for Cu7(Ge0.4Si0.6)S5I mixed crystal
measured at various temperatures T (K): 1 – 180, 2 – 200, 3 –
220, 4 – 240, 5 – 260, 6 – 280. The insert shows the
temperature dependence of electrical conductivity for
Cu7(Ge0.4Si0.6)S5I mixed crystal.
Fig. 3. Compositional dependences of the real part of complex
electrical conductivity (1) and activation energy Ea(2) for
Cu7(Ge1–xSix)S5I mixed crystals.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 227-231.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
229
Table. Urbach edge parameters and EPI parameters of Cu7(Ge1–xSix)S5I mixed crystals.
Crystal x = 0 x = 0.2 x = 0.4 x = 0.6 x = 0.8 x = 1
0 (cm–1) 1.1106 2.6104 8.3104 6.2104 8.3104 7.8105
E0 (eV) 2.371 2.801 3.146 3.128 3.034 2.593
*
gE (300 K) (eV) 2.125 2.136 2.148 2.171 2.207 2.250
EU(300 K) (meV) 35 206 228.6 235 190 52
0 0.81 0.199 0.187 0.185 0.213 0.60
p (meV) 28.7 73.7 77.2 78.6 71.0 43.1
E (K) 333 855 896 912 824 511
(EU)0 (meV) 17.8 185.4 206.9 213.3 167.1 35.9
(EU)1 (meV) 35.1 365.8 403.5 425.6 327.2 75.1
)0(*
gE (eV) 2.247 2.200 2.228 2.251 2.271 2.365
*
gS 8.5 14.2 19.8 20.4 13.2 12.3
Temperature studies of the optical absorption
spectra have shown that in the temperature interval 77–
300 K, within the range of direct allowed interband
transitions, the absorption edge in ISSiGeCu 5xx17
mixed crystals has an exponential shape, which is
described by the Urbach rule [12]
)(
exp),(
U
0
0 TE
Eh
Th , (2)
where UE is the Urbach energy (a reciprocal of the
absorption edge slope )(/)ln(1
U hE ),
U/ EkT is the absorption edge steepness parameter,
0 and 0E are the convergence point coordinates of the
Urbach bundle, h is the photon energy. Temperature
behaviour of the Urbach absorption edge for
Cu7(Ge0.4Si0.6)S5I crystal, which is typical for the mixed
crystals under investigation, is shown in Fig. 4. The
constants 0 and E0 for ISSiGeCu 5xx17 mixed
crystals are given in Table.
Our analysis of the absorption edge has shown that
the temperature dependence of the absorption edge
steepness parameter T for ISSiGeCu 5xx17
mixed crystals is well described by the Mahr formula
kT
kT
T
p
p 2
tanh
2
)( 0
, (3)
where p is the effective phonon energy in the one-
oscillator model, describing the electron-phonon
interaction (EPI), and 0 is a parameter related to the
EPI constant g as 1
0 )3/2( g [13]. The obtained
using Eq. (3) values of the effective phonon energy p
and the EPI parameter 0 for ISSiGeCu 5xx17
mixed crystals are listed in Table. For pure Cu7Ge(Si)S5I
crystals as well as for Cu7(Ge1–xSix)S5I mixed crystals,
the value 0<1 that indicates a strong EPI. It should be
noted that EPI in mixed crystals is enhanced (Table).
Temperature dependences of the optical pseudogap
*
gE ( *
gE is the absorption edge energy position at a
fixed value of the absorption coefficient
13cm10 [10]) and Urbach energy UE for
Cu7(Ge0.4Si0.6)S5I crystal are depicted in Fig. 5. It is
shown that *
gE value decreases nonlinearly with
temperature, and UE value increases nonlinearly
without any singularities (Fig. 5). Besides, the
temperature dependences of *
gE and UE for
ISSiGeCu 5xx17 mixed crystals are well described
in the framework of the Einstein model by the
relationships [14, 15]
1)/exp(
1
)0()(
E
E
***
T
kSETE ggg , (4)
1)/exp(
1
)(
E
1U0UU T
EEE , (5)
where *
gS is a dimensionless constant of interaction, E
is the Einstein temperature, corresponding to the average
frequency of phonon excitations of a system of non-
interacting oscillators, 0UE and 1UE are constant
values. The adjustment parameters )0(*
gE , *
gS , E ,
0UE and 1UE are listed in Table.
The compositional studies show that the increase of
content for Si atoms in the ISSiGeCu 5xx17 mixed
crystals leads to a nonlinear increase with downward
bowing of the optical pseudogap *
gE (Fig. 6). At GeSi
cationic substitution, the Urbach energy UE in the
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 227-231.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
230
composition interval 0 x 0.2 drastically increases (by
a factor higher than 5) and at х = 0.6 it reaches the
maximum value, then in the composition interval
0.8 х 1 decreases with x by a factor higher than 3.
The significant increase of the Urbach energy UE in
ISSiGeCu 5xx17 mixed crystals is caused by the
substantial compositional disordering of their crystal
lattice.
It should be noted that the Urbach energy UE
characterizes the degree of the edge smearing due to the
different types of disordering of the crystal lattice. In
ISSiGeCu 5xx17 mixed crystals, besides the
temperature-related (due to the lattice thermal
vibrations) and structural (static and dynamical)
disordering characteristic for pure Cu7Ge(Si)S5I crystals,
compositional disordering should also be revealed. In
[16], it was shown that the temperature-related,
structural, and compositional disordering affect the
Urbach absorption edge shape, i.e. the Urbach energy
UE is described by the following equation
Fig. 4. Spectral dependences of the Urbach absorption edge for
Cu7(Ge0.4Si0.6)S5I mixed crystal at various temperatures Т (K):
1 – 77, 2 – 200, 3 – 250, 4 – 300. The insert shows the
temperature dependence of steepness parameter.
Fig. 5. Temperature dependences of the optical pseudogap
*
gE (1) and Urbach energy EU (2) for the Cu7(Ge0.4Si0.6)S5I
mixed crystal: circles – experiment, curves – calculations.
CXT EEEE UUUU , (6)
where TUE , XUE , and CUE are contributions of
temperature-related and structural disordering to UE ,
respectively. The first term in the right-hand side of
Eq. (5) represents the static structural disordering for
pure crystals or sum of static structural disordering and
compositional disordering for mixed crystals, and the
second one – the temperature-related types of
disordering: temperature disordering due to thermal
lattice vibrations and dynamic structural disordering due
to presence of mobile ions in superionic conductors. The
calculations have shown that the contribution of static
structural disordering into the Urbach energy UE at T =
300 K for Cu7GeS5I crystals is 51%, while for Cu7SiSe5I
it is 69%. Within the framework of the procedure,
described in [17], the relative contributions of different
type disordering into the Urbach energy were estimated
and adduced in Fig. 7. It is shown for
ISeSGeCu 5xx17 mixed crystals that GeSi cation
Fig. 6. Compositional dependences of the optical pseudogap
*
gE (1) and Urbach energy EU (2) for the Cu7(Ge1–xSix)S5I
mixed crystals.
Fig. 7. Relative contributions of static structural disordering
UstatXU EE , (1), temperature-related disordering
UTU EE (2) and compositional disordering UCU EE (3)
into EU at Т = 300 K for Cu7(Ge1–xSix)S5I mixed crystals.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 227-231.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
231
substitution results in a linear decrease of the relative
contribution of the static structural disordering
UstatXU EE , , a nonlinear decrease with a downward
bowing of the temperature-related disordering UTU EE ,
and a nonlinear increase with an upward bowing of the
compositional disordering UCU EE into UE at 300 K.
4. Conclusions
The linear increase of electrical conductivity with
temperature, which obeys the Arrhenius law, is observed
in ISSiGeCu 5xx17 mixed crystals. The GeSi
cationic substitution results in a nonlinear decrease of
the electrical conductivity by more than an order of
magnitude. It is noted that ISSiGeCu 5xx17 mixed
crystals are characterized by rather high electric
conductivity and low activation energy what puts them
in line with the most efficient solid electrolytes.
It is shown that the Urbach absorption edge is
observed in ISSiGeCu 5xx17 mixed crystals within
the temperature interval 77–300 K. Urbach behaviour of
the absorption edge is related to the electron-phonon
interaction that is strong for ISSiGeCu 5xx17 mixed
crystals. It should be noted that the temperature
dependences of optical pseudogap and Urbach energy
for ISSiGeCu 5xx17 mixed crystals are well
described in the framework of the Einstein model.
A nonlinear increase of the optical pseudogap in
ISSiGeCu 5xx17 mixed crystals at GeSi cationic
substitution is revealed while the compositional
dependence of the Urbach energy exhibits typical
behaviour for mixed crystals. The Urbach energy in
ISSiGeCu 5xx17 mixed crystals is shown to be
determined by the effect of the temperature-related,
structural and compositional disordering.
References
1. W.F. Kuhs, R. Nitsche, K. Scheunemann, The
argyrodites – a new family of the tetrahedrally
close-packed srtuctures // Mater. Res. Bull. 14,
p. 24-248 (1979).
2. A. Dziaugys, J. Banys, A. Kezionis, V. Samulionis,
I. Studenyak, Conductivity investigations of
Cu7GeS5I family fast-ion conductors // Solid State
Ionics, 179, p. 168-171 (2008).
3. I.P. Studenyak, M. Kranjčec, Gy.Sh. Kovacs,
I.D. Desnica-Frankovic, A.A. Molnar, V.V. Panko,
V.Yu. Slivka, Electrical and optical absoprtion
studies of Cu7GeS5I fast-ion conductor // J. Phys.
Chem. Solids, 63, p. 267-271 (2002).
4. I.P. Studenyak, O.P. Kokhan, M. Kranjčec,
V.V. Bilanchuk, V.V. Panko, Influence of SSe
substitution on chemical and physical properties of
ISSiGeCu 5xx17 superionic solid solutions // J.
Phys. Chem. Solids, 68, p. 1881-1884 (2007).
5. I.P. Studenyak, V.V. Bilanchuk, O.P. Kokhan,
Yu.M. Stasyuk, A.F. Orliukas, A. Kezionis,
E. Kazakevicius, T. Salkus, Electrical conductivity,
electrochemical and optical properties of
Cu7GeS5I-Cu7GeSe5I superionic solid solutions //
Lit. J. Phys. 49, p. 203-208 (2009).
6. I.P. Studenyak, M. Kranjčec, V.V. Bilanchuk,
O.P. Kokhan, A.F. Orliukas, E. Kazakevicius,
A. Kezionis, T. Salkus, Temperature variation of
electrical conductivity and absorption edge in
Cu7GeSe5I advanced superionic conductor // J.
Phys. Chem. Solids, 70, p. 1478-1481 (2009).
7. I.P. Studenyak, M. Kranjčec, V.V. Bilanchuk,
O.P. Kokhan, A.F. Orliukas, A. Kezionis,
E. Kazakevicius, T. Salkus, Temperature and
compositional behaviour of electrical conductivity
and optical absorption edge in ISSiGeCu 5xx17
mixed superionic crystals // Solid State Ionics, 181,
p. 1596-1600 (2010).
8 I.P. Studenyak, O.P. Kokhan, M. Kranjčec, M.I.
Hrechyn, V.V. Panko, Crystal growth and phase
interaction studies in Cu7GeS5I–Cu7SiS5I superionic
system // J. Cryst. Growth, 306, p. 326-329 (2007).
9. A.F. Orliukas, A. Kežionis, and E. Kazakevičius,
Impedance spectroscopy of solid electrolytes in the
radio frequency range // Solid State Ionics, 176,
p. 2037-2043 (2005).
10. I.P. Studenyak, M. Kranjčec, Gy.Sh. Kovacs,
V.V. Panko, D.I. Desnica, A.G. Slivka, P.P. Guranich,
The effect of temperature and pressure on the optical
absorption edge in Cu6PS5X (X = Cl, Br, I) crystals //
J. Phys. Chem. Solids, 60, p. 1897-1904 (1999).
11. F. Oswald, Zur megenauigkeit bei der
bestimmung der absorptionskonstanten von
halbleitern im infraroten spektralbereich // Optik,
16, p. 527-537 (1959).
12. F. Urbach, The long-wavelength edge of
photographic sensitivity and electronic absorption
of solids // Phys. Rev. 92, p. 1324-1326 (1953).
13. M.V. Kurik, Urbach rule (Review) // Phys. Status
Solidi (a), 8, p. 9-30 (1971).
14. M. Beaudoin, A.J.G. DeVries, S.R. Johnson,
H. Laman, T. Tiedje, Optical absorption edge of
semi-insulating GaAs and InP at high temperatures
// Appl. Phys. Lett. 70, p. 3540-3542 (1997).
15. Z. Yang, K.P. Homewood, M.S. Finney, M.A. Harry,
K.J. Reeson, Optical absorption study of ion beam
synthesized polycrystalline semiconducting FeSi2 // J.
Appl. Phys. 78, p. 1958-1963 (1995).
16. G.D. Cody, T. Tiedje, B. Abeles, B. Brooks,
Y. Goldstein, Disorder and the optical-absorption
edge of hydrogenated amorphous silicon // Phys.
Rev. Lett. 47, p. 1480-1483 (1981).
17. I.P. Studenyak, M. Kranjčec, M.V. Kurik, Urbach
rule and disordering processes in
yy-15xx16 IBrSeSPCu superionic conductors //
J. Phys. Chem. Solids, 67, p. 807-817 (2006).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 227-231.
PACS 77.80.Bh, 78.40.Ha
Influence of cation substitution on electrical conductivity
and optical absorption edge in Cu7(Ge1–xSix)S5I mixed crystals
I.P. Studenyak1, M. Kranjčec2, V.V. Bilanchuk1, A. Dziaugys3, J. Banys3, A.F. Orliukas3
1Uzhhorod National University, Physics Faculty,46, Pidhirna str. 88000 Uzhhorod, Ukraine
2University of Zagreb, Geotechnical Faculty, Hallerova Aleja 7, 42000 Varaždin, Croatia
3Vilnius University, Physics Faculty,
Saulėtekio al. 9, LT-10222 Vilnius, Lithuania, e-mail: studenyak@dr.com
Abstract. Electrical conductivity of Cu7(Ge1–xSix)S5I mixed crystals was measured in the frequency range 1.0(106–1.2(109 Hz and in the temperature interval 100–300 K. The frequency and temperature behaviour of the electrical conductivity were analyzed. The optical absorption edge of (
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals within the temperature range 77–300 K was studied. The compositional dependences of the electrical conductivity, activation energy, optical pseudogap and Urbach energy were obtained. The influence of Ge(Si cation substitution on the optical absorption processes in the (
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals is investigated.
Keywords: mixed crystals, electrical conductivity, activation energy, absorption edge, Urbach rule.
Manuscript received 25.06.12; revised version received 16.08.12; accepted for publication 10.09.12; published online 25.09.12.
1. Introduction
Cu7GeS5I and Cu7SiS5I superionic crystals belong to argyrodite family compounds [1]. Due to their high ionic conductivity, these crystals are attractive materials for applications in different functional elements of solid state ionics [2].
Structural, electrical and optical properties of Cu7GeS(Se)5I and mixed crystals based on them were studied in papers [3–7]. It is shown that the electrical conductivity of Cu7GeSe5I crystal at room temperature was found to be rather high (64 S/m at 295 K and 106 Hz) and typical for advanced superionic conductors [5, 6]. At S(Se anionic substitution, the nonlinear increase of the electric conductivity by more than an order of magnitude was observed in
(
)
I
Se
S
Ge
Cu
5
x
x
1
7
-
mixed crystals [7]. Optical studies have shown that the absorption edge of Cu7GeS(Se)S5I crystals and mixed crystals based on them exhibits Urbach behaviour in a wide temperature range [3,5–7]. A nonlinear decrease of the optical pseudogap in the
(
)
I
Se
S
Ge
Cu
5
x
x
1
7
-
mixed crystals at S(Se anionic substitution is observed [7].
Some of the chemical and physics properties of
(
)
I
Se
S
Ge
Cu
5
x
x
1
7
-
mixed crystals were presented in the paper [8]. Chemical interaction in the Cu7GeS5I–Cu7SiS5I system was studied by X-ray phase analysis, microstructural analysis and density determination. The short-wave edge of the diffuse reflection spectra of
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals is shown to shift towards shorter wavelengths after the substitution of Ge atoms by Si [8].
This paper is aimed at investigation of temperature and compositional behaviour of the electrical conductivity and optical absorption edge in
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals. Moreover, the influence of different types of the crystal lattice disordering on absorption edge formation will be in focus of the paper.
2. Experimental
Cu7(Ge1–xSix)S5I mixed crystals were grown by chemical vapour transport [8]. For synthesis, the calculated stoichiometric amounts of Cu, Si, Ge, S and CuI were loaded in silica glass ampoules, thoroughly mixed, pumped out to 0.13 Pa and sealed. Additional amount of CuI used as a transport agent (20 mg/cm3 of the ampoule free volume) was also loaded in the ampoules. Thus, the crystal growth was carried out in atmosphere of CuI chemical active vapour. The as-grown crystals had the shape of plane-parallel platelets or distorted tetrahedra 5(3(3(2.5) mm in size.
For X-ray studies, the DRON-3 diffractometer was used (conventional
q
-
q
2
scanning technique, Bragg angle
q
2
(10–60(, Cu Kα, Ni filtered radiation). It is shown that in the Cu7GeS5I–Cu7SiSeI system a row of continuous solid solutions is formed with
m
F
3
4
cubic symmetry at room temperature (Fig. 1).
The measurements of complex electrical conductivity were carried out within the frequency range 1.0(106–1.2(109 Hz and the temperature interval 100–300 K by using a coaxial impedance spectrometer set-up [9].
Spectrometric studies of the optical absorption edge were carried out within the temperature range 77–300 K by using the LOMO KSVU-23 grating monochromator [10]. For these measurements, the samples were oriented at room temperature while being in the cubic phase. For low temperature studies cryostat of UTREX type was used. The relative error in determination of the relative change in the absorption coefficient ((/( did not exceed 10% at 0.3 ( (d ( 3 [11].
3. Results and discussion
It should be noted that measurements of the real bulk conductivity are limited to low frequencies (up to MHz range) due to contact effects. The frequency dependences of the real part of complex electrical conductivity
s
¢
are illustrated for Cu7(Ge0.4Si0.6)S5I mixed crystal and at various temperatures are presented in Fig. 2. Influence of the contact effect is observed at low temperatures within the low-frequency range. With temperature increase, only relaxation dispersion of the electrical conductivity due to bulk conductivity takes place (Fig. 2). Besides, it is shown (Fig. 2) that with the temperature increase the
s
¢
value for Cu7(Ge0.4Si0.6)S5I mixed crystal increases linearly in a semilogarithmic scale and obeys the Arrhenius law:
÷
÷
ø
ö
ç
ç
è
æ
D
-
s
¢
=
s
¢
kT
E
T
a
exp
0
,
(1)
where
a
E
D
is the activation energy,
0
s
¢
is some constant, k is the Boltzmann constant, T is the temperature.
Substitution of Ge atoms with Si atoms leads to decreasing the electrical conductivity
s
¢
(Fig. 3). It should be noted that in comparison with Cu7GeS5I, in Cu7SiSe5I crystals the
s
¢
value decreases by more than an order of magnitude. With the increase of Si content, the
s
¢
value of
(
)
I
Se
S
Ge
Cu
5
x
x
1
7
-
mixed crystals decreases nonlinearly with downward bowing, besides reaches a minimum at x = 0.4. The activation energy
a
E
D
in the mixed crystals under investigation increases within the composition interval 0 < x ( 0.4 achieves its maximum at x = 0.4 and decreases within the composition interval 0.4 < x < 1 (Fig. 3).
Fig. 1. X-ray diffraction patterns for Cu7(Ge1–xSix)S5I mixed crystals: 1 – Cu7GeS5I, 2 – Cu7(Ge0.8Si0.2)S5I, 3 – Cu7(Ge0.6Si0.4)S5I, 4 – Cu7(Ge0.4Si0.6)S5I, 5 – Cu7(Ge0.8Si0.2)S5I, 6 – Cu7SiS5I.
Fig. 2. Frequency dependences of the real part of complex electrical conductivity (( for Cu7(Ge0.4Si0.6)S5I mixed crystal measured at various temperatures T (K): 1 – 180, 2 – 200, 3 – 220, 4 – 240, 5 – 260, 6 – 280. The insert shows the temperature dependence of electrical conductivity (( for Cu7(Ge0.4Si0.6)S5I mixed crystal.
Fig. 3. Compositional dependences of the real part of complex electrical conductivity (( (1) and activation energy (Ea(2) for Cu7(Ge1–xSix)S5I mixed crystals.
Temperature studies of the optical absorption spectra have shown that in the temperature interval 77–300 K, within the range of direct allowed interband transitions, the absorption edge in
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals has an exponential shape, which is described by the Urbach rule [12]
ú
û
ù
ê
ë
é
-
n
×
a
=
n
a
)
(
exp
)
,
(
U
0
0
T
E
E
h
T
h
,
(2)
where
U
E
is the Urbach energy (a reciprocal of the absorption edge slope
)
(
/
)
ln
(
1
U
n
D
a
D
=
-
h
E
),
U
/
E
kT
=
s
is the absorption edge steepness parameter,
0
a
and
0
E
are the convergence point coordinates of the Urbach bundle, h( is the photon energy. Temperature behaviour of the Urbach absorption edge for Cu7(Ge0.4Si0.6)S5I crystal, which is typical for the mixed crystals under investigation, is shown in Fig. 4. The constants (0 and E0 for
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals are given in Table.
Our analysis of the absorption edge has shown that the temperature dependence of the absorption edge steepness parameter
(
)
T
s
for
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals is well described by the Mahr formula
÷
÷
ø
ö
ç
ç
è
æ
w
×
÷
÷
ø
ö
ç
ç
è
æ
w
×
s
=
s
kT
kT
T
p
p
2
tanh
2
)
(
0
h
h
,
(3)
where
p
w
h
is the effective phonon energy in the one-oscillator model, describing the electron-phonon interaction (EPI), and
0
s
is a parameter related to the EPI constant
g
as
1
0
)
3
/
2
(
-
=
s
g
[13]. The obtained using Eq. (3) values of the effective phonon energy
p
w
h
and the EPI parameter
0
s
for
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals are listed in Table. For pure Cu7Ge(Si)S5I crystals as well as for Cu7(Ge1–xSix)S5I mixed crystals, the value (0<1 that indicates a strong EPI. It should be noted that EPI in mixed crystals is enhanced (Table).
Temperature dependences of the optical pseudogap
*
g
E
(
*
g
E
is the absorption edge energy position at a fixed value of the absorption coefficient
1
3
cm
10
-
=
a
[10]) and Urbach energy
U
E
for Cu7(Ge0.4Si0.6)S5I crystal are depicted in Fig. 5. It is shown that
*
g
E
value decreases nonlinearly with temperature, and
U
E
value increases nonlinearly without any singularities (Fig. 5). Besides, the temperature dependences of
*
g
E
and
U
E
for
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals are well described in the framework of the Einstein model by the relationships [14, 15]
ú
û
ù
ê
ë
é
-
q
q
-
=
1
)
/
exp(
1
)
0
(
)
(
E
E
*
*
*
T
k
S
E
T
E
g
g
g
,
(4)
(
)
ú
û
ù
ê
ë
é
-
q
+
=
1
)
/
exp(
1
)
(
E
1
U
0
U
U
T
E
E
E
,
(5)
where
*
g
S
is a dimensionless constant of interaction,
E
q
is the Einstein temperature, corresponding to the average frequency of phonon excitations of a system of non-interacting oscillators,
(
)
0
U
E
and
(
)
1
U
E
are constant values. The adjustment parameters
)
0
(
*
g
E
,
*
g
S
,
E
q
,
(
)
0
U
E
and
(
)
1
U
E
are listed in Table.
*
g
E
The compositional studies show that the increase of content for Si atoms in the
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals leads to a nonlinear increase with downward bowing of the optical pseudogap
*
g
E
(Fig. 6). At Ge(Si cationic substitution, the Urbach energy
U
E
in the composition interval 0 ( x ( 0.2 drastically increases (by a factor higher than 5) and at х = 0.6 it reaches the maximum value, then in the composition interval 0.8 ( х ( 1 decreases with x by a factor higher than 3. The significant increase of the Urbach energy
U
E
in
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals is caused by the substantial compositional disordering of their crystal lattice.
It should be noted that the Urbach energy
U
E
characterizes the degree of the edge smearing due to the different types of disordering of the crystal lattice. In
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals, besides the temperature-related (due to the lattice thermal vibrations) and structural (static and dynamical) disordering characteristic for pure Cu7Ge(Si)S5I crystals, compositional disordering should also be revealed. In [16], it was shown that the temperature-related, structural, and compositional disordering affect the Urbach absorption edge shape, i.e. the Urbach energy U
E
is described by the following equation
Fig. 4. Spectral dependences of the Urbach absorption edge for Cu7(Ge0.4Si0.6)S5I mixed crystal at various temperatures Т (K): 1 – 77, 2 – 200, 3 – 250, 4 – 300. The insert shows the temperature dependence of
s
steepness parameter.
Fig. 5. Temperature dependences of the optical pseudogap
*
g
E
(1) and Urbach energy EU (2) for the Cu7(Ge0.4Si0.6)S5I mixed crystal: circles – experiment, curves – calculations.
(
)
(
)
(
)
C
X
T
E
E
E
E
U
U
U
U
+
+
=
,
(6)
where
(
)
T
U
E
,
(
)
X
U
E
, and
(
)
C
U
E
are contributions of temperature-related and structural disordering to
U
E
, respectively. The first term in the right-hand side of Eq. (5) represents the static structural disordering for pure crystals or sum of static structural disordering and compositional disordering for mixed crystals, and the second one – the temperature-related types of disordering: temperature disordering due to thermal lattice vibrations and dynamic structural disordering due to presence of mobile ions in superionic conductors. The calculations have shown that the contribution of static structural disordering into the Urbach energy
U
E
at T = 300 K for Cu7GeS5I crystals is 51%, while for Cu7SiSe5I it is 69%. Within the framework of the procedure, described in [17], the relative contributions of different type disordering into the Urbach energy were estimated and adduced in Fig. 7. It is shown for
(
)
I
Se
S
Ge
Cu
5
x
x
1
7
-
mixed crystals that Ge(Si cation
Fig. 6. Compositional dependences of the optical pseudogap
*
g
E
(1) and Urbach energy EU (2) for the Cu7(Ge1–xSix)S5I mixed crystals.
Fig. 7. Relative contributions of static structural disordering
(
)
U
stat
X
U
E
E
,
(1), temperature-related disordering
(
)
U
T
U
E
E
(2) and compositional disordering
(
)
U
C
U
E
E
(3) into EU at Т = 300 K for Cu7(Ge1–xSix)S5I mixed crystals.
substitution results in a linear decrease of the relative contribution of the static structural disordering
(
)
U
stat
X
U
E
E
,
, a nonlinear decrease with a downward bowing of the temperature-related disordering
(
)
U
T
U
E
E
, and a nonlinear increase with an upward bowing of the compositional disordering
(
)
U
C
U
E
E
into
U
E
at 300 K.
4. Conclusions
The linear increase of electrical conductivity with temperature, which obeys the Arrhenius law, is observed in
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals. The Ge(Si cationic substitution results in a nonlinear decrease of the electrical conductivity by more than an order of magnitude. It is noted that (
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals are characterized by rather high electric conductivity and low activation energy what puts them in line with the most efficient solid electrolytes.
It is shown that the Urbach absorption edge is observed in
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals within the temperature interval 77–300 K. Urbach behaviour of the absorption edge is related to the electron-phonon interaction that is strong for
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals. It should be noted that the temperature dependences of optical pseudogap and Urbach energy for
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals are well described in the framework of the Einstein model.
A nonlinear increase of the optical pseudogap in
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals at Ge(Si cationic substitution is revealed while the compositional dependence of the Urbach energy exhibits typical behaviour for mixed crystals. The Urbach energy in
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed crystals is shown to be determined by the effect of the temperature-related, structural and compositional disordering.
References
1.
W.F. Kuhs, R. Nitsche, K. Scheunemann, The argyrodites – a new family of the tetrahedrally close-packed srtuctures // Mater. Res. Bull. 14, p. 24-248 (1979).
2.
A. Dziaugys, J. Banys, A. Kezionis, V. Samulionis, I. Studenyak, Conductivity investigations of Cu7GeS5I family fast-ion conductors // Solid State Ionics, 179, p. 168-171 (2008).
3.
I.P. Studenyak, M. Kranjčec, Gy.Sh. Kovacs, I.D. Desnica-Frankovic, A.A. Molnar, V.V. Panko, V.Yu. Slivka, Electrical and optical absoprtion studies of Cu7GeS5I fast-ion conductor // J. Phys. Chem. Solids, 63, p. 267-271 (2002).
4.
I.P. Studenyak, O.P. Kokhan, M. Kranjčec, V.V. Bilanchuk, V.V. Panko, Influence of S(Se substitution on chemical and physical properties of (
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
superionic solid solutions // J. Phys. Chem. Solids, 68, p. 1881-1884 (2007).
5.
I.P. Studenyak, V.V. Bilanchuk, O.P. Kokhan, Yu.M. Stasyuk, A.F. Orliukas, A. Kezionis, E. Kazakevicius, T. Salkus, Electrical conductivity, electrochemical and optical properties of Cu7GeS5I-Cu7GeSe5I superionic solid solutions // Lit. J. Phys. 49, p. 203-208 (2009).
6.
I.P. Studenyak, M. Kranj(ec, V.V. Bilanchuk, O.P. Kokhan, A.F. Orliukas, E. Kazakevicius, A. Kezionis, T. Salkus, Temperature variation of electrical conductivity and absorption edge in Cu7GeSe5I advanced superionic conductor // J. Phys. Chem. Solids, 70, p. 1478-1481 (2009).
7.
I.P. Studenyak, M. Kranj(ec, V.V. Bilanchuk, O.P. Kokhan, A.F. Orliukas, A. Kezionis, E. Kazakevicius, T. Salkus, Temperature and compositional behaviour of electrical conductivity and optical absorption edge in
(
)
I
S
Si
Ge
Cu
5
x
x
1
7
-
mixed superionic crystals // Solid State Ionics, 181, p. 1596-1600 (2010).
8
I.P. Studenyak, O.P. Kokhan, M. Kranjčec, M.I. Hrechyn, V.V. Panko, Crystal growth and phase interaction studies in Cu7GeS5I–Cu7SiS5I superionic system // J. Cryst. Growth, 306, p. 326-329 (2007).
9.
A.F. Orliukas, A. Kežionis, and E. Kazakevičius, Impedance spectroscopy of solid electrolytes in the radio frequency range // Solid State Ionics, 176, p. 2037-2043 (2005).
10.
I.P. Studenyak, M. Kranjčec, Gy.Sh. Kovacs, V.V. Panko, D.I. Desnica, A.G. Slivka, P.P. Guranich, The effect of temperature and pressure on the optical absorption edge in Cu6PS5X (X = Cl, Br, I) crystals // J. Phys. Chem. Solids, 60, p. 1897-1904 (1999).
11.
F. Oswald, Zur me(genauigkeit bei der bestimmung der absorptionskonstanten von halbleitern im infraroten spektralbereich // Optik, 16, p. 527-537 (1959).
12.
F. Urbach, The long-wavelength edge of photographic sensitivity and electronic absorption of solids // Phys. Rev. 92, p. 1324-1326 (1953).
13.
M.V. Kurik, Urbach rule (Review) // Phys. Status Solidi (a), 8, p. 9-30 (1971).
14.
M. Beaudoin, A.J.G. DeVries, S.R. Johnson, H. Laman, T. Tiedje, Optical absorption edge of semi-insulating GaAs and InP at high temperatures // Appl. Phys. Lett. 70, p. 3540-3542 (1997).
15.
Z. Yang, K.P. Homewood, M.S. Finney, M.A. Harry, K.J. Reeson, Optical absorption study of ion beam synthesized polycrystalline semiconducting FeSi2 // J. Appl. Phys. 78, p. 1958-1963 (1995).
16.
G.D. Cody, T. Tiedje, B. Abeles, B. Brooks, Y. Goldstein, Disorder and the optical-absorption edge of hydrogenated amorphous silicon // Phys. Rev. Lett. 47, p. 1480-1483 (1981).
17.
I.P. Studenyak, M. Kranjčec, M.V. Kurik, Urbach rule and disordering processes in
(
)
y
y
-
1
5
x
x
1
6
I
Br
Se
S
P
Cu
-
superionic conductors // J. Phys. Chem. Solids, 67, p. 807-817 (2006).
Table. Urbach edge parameters and EPI parameters of Cu7(Ge1–xSix)S5I mixed crystals.
Crystal�
x = 0�
x = 0.2�
x = 0.4�
x = 0.6�
x = 0.8�
x = 1�
�
(0 (cm–1)�
1.1(106�
2.6(104�
8.3(104�
6.2(104�
8.3(104�
7.8(105�
�
E0 (eV)�
2.371�
2.801�
3.146�
3.128�
3.034�
2.593�
�
�EMBED Equation.3��� (300 K) (eV)�
2.125�
2.136�
2.148�
2.171�
2.207�
2.250�
�
EU(300 K) (meV)�
35�
206�
228.6�
235�
190�
52�
�
(0�
0.81�
0.199�
0.187�
0.185�
0.213�
0.60�
�
�EMBED Unknown��� (meV)�
28.7�
73.7�
77.2�
78.6�
71.0�
43.1�
�
(E (K)�
333�
855�
896�
912�
824�
511�
�
(EU)0 (meV)�
17.8�
185.4�
206.9�
213.3�
167.1�
35.9�
�
(EU)1 (meV)�
35.1�
365.8�
403.5�
425.6�
327.2�
75.1�
�
�EMBED Equation.3��� (eV)�
2.247�
2.200�
2.228�
2.251�
2.271�
2.365�
�
�EMBED Equation.3����
8.5�
14.2�
19.8�
20.4�
13.2�
12.3�
�
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
227
p
w
h
)
0
(
*
g
E
*
g
S
_1408783242.unknown
_1408783275.unknown
_1408783309.unknown
_1413295478.unknown
_1413295546.unknown
_1413295618.unknown
_1413295696.unknown
_1413295701.unknown
_1413295705.unknown
_1413295661.unknown
_1413295612.unknown
_1413295495.unknown
_1413295500.unknown
_1413295485.unknown
_1408785469.unknown
_1408785899.unknown
_1408785939.unknown
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