Electronic structure, optical, and photoelectrical properties of crystalline Si₂Te₃
In the framework of the density functional theory (DFT) in the approximation of local density adjusted for the strong correlation (LDA+U method), the band structure, total and partial densities of electronic states, as well as the spatial distribution of the electron density, were calculated. Accord...
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| Опубліковано в: : | Semiconductor Physics Quantum Electronics & Optoelectronics |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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| Цитувати: | Electronic structure, optical, and photoelectrical properties of crystalline Si₂Te₃ / D.I. Bletskan, V.V. Vakulchak, I.P. Studenyak // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2019. — Т. 22, № 3. — С. 267-276. — Бібліогр.: 40 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860480081448665088 |
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| author | Bletskan, D.I. Vakulchak, V.V. Studenyak, I.P. |
| author_facet | Bletskan, D.I. Vakulchak, V.V. Studenyak, I.P. |
| citation_txt | Electronic structure, optical, and photoelectrical properties of crystalline Si₂Te₃ / D.I. Bletskan, V.V. Vakulchak, I.P. Studenyak // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2019. — Т. 22, № 3. — С. 267-276. — Бібліогр.: 40 назв. — англ. |
| collection | DSpace DC |
| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | In the framework of the density functional theory (DFT) in the approximation of local density adjusted for the strong correlation (LDA+U method), the band structure, total and partial densities of electronic states, as well as the spatial distribution of the electron density, were calculated. According to the results of the calculation, Si₂Te₃ is an indirect-gap semiconductor with the calculated band gap Eᶜᵃᶥᶜgi = 2.05 eV, close to the experimentally measured Eᵒᵖᵗg = 2.13 eV. The absorption edge and photoconductivity spectra of the Si₂Te₃ crystal within the temperature range 80...293 K has been measured. It has been shown that the dependence of the absorption coefficient on the photon energy is described by the Urbach rule. The parameter σ₀, associated with the constant of electron-phonon interaction, and the energy of effective phonons ħω₍ph₎, involved in the formation of the absorption edge of crystalline Si₂Te₃, were determined using the temperature dependence of the absorption edge slope. Deviation from the stoichiometric composition in the direction of excess tellurium significantly affects the spectral distribution of the photoconductivity of Si₂Te₃ crystals.
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| first_indexed | 2026-03-23T18:54:29Z |
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ISSN 1560-8034, 1605-6582 (On-line), SPQEO, 2019. V. 22, N 3. P. 267-276.
© 2019, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
267
Semiconductor physics
Electronic structure, optical and photoelectrical properties
of crystalline Si2Te3
D.I. Bletskan, V.V. Vakulchak, I.P. Studenyak
Uzhhorod National University, Faculty of Physics, 54, Voloshyna str.,
88000 Uzhhorod, Ukraine
E-mail: crystal_lab457@yahoo.com
Abstract. In the framework of the density functional theory (DFT) in the approximation of
local density adjusted for the strong correlation (LDA+U method), calculated were the band
structure, total and partial densities of electronic states, as well as the spatial distribution of
the electron density. According to the results of the calculation, Si2Te3 is an indirect-gap
semiconductor with the calculated band gap calc
giE = 2.05 eV, close to the experimentally
measured opt
gE = 2.13 eV. The absorption edge and photoconductivity spectra of Si2Te3
crystal within the temperature range 80...293 K have been measured. It has been shown that
the dependence of the absorption coefficient on the photon energy is described by the
Urbach rule. The parameter σ0, associated with the constant of electron-phonon interaction,
and the energy of effective phonons ħωph, involved in formation of the absorption edge of
crystalline Si2Te3, were determined using the temperature dependence of the absorption
edge slope. Deviation from the stoichiometric composition in the direction of excess
tellurium significantly affects the spectral distribution of the photoconductivity of Si2Te3
crystals.
Keywords: silicon sesquitelluride, electronic structure, electron-phonon interaction,
absorption edge, photoconductivity.
https://doi.org/10.15407/spqeo22.03.267
PACS 31.10.+z, 71.15.Mb, 71.20.-b, 72.40.+w, 78.20.Ci
Manuscript received 22.05.19; revised version received 18.06.19; accepted for publication
04.09.19; published online 16.09.19.
1. Introduction
Silicon sesquitelluride (Si2Te3) is one of binary
compounds, which is characterized by the presence of
natural defects caused by the peculiarities of their crystal
chemistry. Si2Te3 crystals contain a large number of
stoichiometric cationic vacancies (~1027 m3), with two
non-equivalent positions of silicon atoms [1, 2]. The
existence of these vacancies and their presence in the
crystal do not depend on the method and conditions of its
growth. Thus, Si2Te3 belongs to a group of semi-
conductors with positional disordering [3]. It corresponds
to the situation where the number of positions of certain
types of atoms (in this case silicon) is greater than the
number of atoms themselves, and the distribution of
atoms by these positions has a partially (or completely)
random character.
The layered nature of the structure and the presence
of a large number of natural cationic vacancies in Si2Te3
crystals favourably contribute to the intercalation of Li+
and Mg2+ ions inside, which opens the possibilities of
their practical use as energy storage materials [4]. In
addition, silicon sesquitelluride is a thermoelectric
material [5]. The increased interest in the study of Si2Te3
is also reasoned by the fact that nanoplates [4, 6, 7],
nanoribbons [4, 8], nanotapers, and nanowires [8] were
recently synthesized by the chemical vapor deposition
method (CVD process). These nanostructures are
promising materials for use in memory devices [9] and
optoelectronics [10].
The nature of chemical bonds, physical and
physical-chemical properties of crystals are largely
defined by their composition, crystalline and energy
structure, as well as the charge of valence electrons
distribution. Despite the numerous studies of crystalline
structure [1, 2], electrical conductivity, Zeebek coeffi-
cient [11-14], reflection and fundamental absorption
spectra [15, 16], photoconductivity [17, 18], photo-
luminescence [7, 18, 19] and vibrational spectra [20] of
Si2Te3 crystals, the study of their band structure is not
SPQEO, 2019. V. 22, N 3. P. 267-276.
Bletskan D.I., Vakulchak V.V., Studenyak I.P. Electronic structure, optical and photoelectrical properties …
268
Fig. 1. Si2Te3 crystal structure projections on (0001) (а) and
( 0110 ) (b) planes.
numerous [21, 22]. The first results of calculations aimed
at the Si2Te3 crystal electronic structure performed by the
density functional method in the local density
approximation (LDA) are given in [21]. In recent paper
[22], the influence of the character of Si–Si dimers
location in the three-layer package Te–Si–Te on the two-
dimensional electronic structure of Si2Te3 has been
simulated.
This paper presents the results of calculations of
electronic structure, total and partial densities of states,
distribution of valence charge, as well as the study of the
absorption edge and photoconductivity spectra of Si2Te3
crystals grown using the static sublimation method.
2. Preparation and crystal structure of Si2Te3
The easiest way to obtain the polycrystalline Si2Te3 is a
direct fusion of elementary components taken in the
stoichiometric ratio. As initial components, mono-
crystalline silicon and specially purified tellurium were
used. The calculated components were loaded into pre-
cleaned by chemical-thermal treatment silica ampoules of
160...180-mm length and the diameter of 18...20 mm.
Ampoules with the substance were pumped to the
pressure of residual gases 133 Pa and sealed. Because of
the high pressure of telluric vapors at high temperatures,
the synthesis of Si2Te3 substance was carried out in two
stages. In the first stage, the silica ampoule with the
initial mixture was placed in a horizontal tubular resistive
furnace and heated to a temperature of 850...900 K at a
rate of 0.1 to 0.2 K/h with the next ageing at this
temperature for 15...20 hours, whereupon the temperature
in the furnace was raised up to 1200 K at a rate of
0.05...0.1 K/s. At this temperature, the melt was held for
24 h to ensure the melt synthesis and homogenization.
Then, the programmed temperature reduction was
switched on at the set rate 0.2 K/h, and polycrystalline
ingot was obtained.
Si2Te3 single crystals were obtained by static
sublimation method. Crystals were grown in the same
ampoules where the synthesis of substance was
performed. To reach this aim, without opening the
ampoule, the synthesized product was moved by shaking
to one end, whereupon the ampoule was placed into a
two-zone horizontal tubular electric furnace. Optimal
conditions for grown Si2Te3 crystal by using the static
sublimation method were as follows: temperature of
evaporation zone Tev = 1000 K; temperature of
condensation zone Tcon = 900 K; duration of the growth
process 40…50 h. Temperature stabilization in the
process of crystal growth was no worse than ±0.5 K.
Under these conditions, thin plates were grown in the
“cold” zone, the maximum dimensions of which reached
10×10×1 mm. Crystals had natural mirror surfaces (001)
with their c axis perpendicular to the cleavage face.
Silicon sesquitelluride Si2Te3 crystallizes in the
trigonal structure, the symmetry of which is described by
the space group cP 13 with the lattice parameters: a = b
= 7.43 Å, c = 13.482 Å [1]. Projections of the crystalline
structure on the planes (0001) and ( 0110 ) are shown in
Figs. 1a and 1b, respectively. The Si2Te3 structure is
based on hexagonal dense packaging of tellurium atoms
in a two-packet form, each containing two layers of
tellurium atoms, between which there are silicon atoms
in the form of Si2 dumbbells formations. The layered
structure of Si2Te3 is generally similar to GaS and is
characterized by the statistical distribution of Si atoms on
two crystallographically non-equivalent positions in the
layers of Te atoms skeleton forming the densest
hexagonal packaging. Each Si atom is tetrahedrally
coordinated by three Te atoms and one Si atom (Fig. 1).
The values of Si–Si (~2.3 Å) distances provide with the
opportunity to assert formation of fragments in the form
of dumbbells (dimers) Si–Si (Si2) located, thus, in the
centers of slightly distorted [Te6] octahedra (Fig. 1a).
Unlike GaS, where all Ga–Ga (Ga2) dimers are
oriented parallelly to the trigonal axis, in Si2Te3 only 1/4
of Si–Si (Si2) dimers formed by Si atoms at the position
4e are oriented in parallel to c axis (vertical Si–Si
dimers). The distances of Si–Si in these “vertical” dimers
constitute 2.269 Å аnd six shortest Si–Te bonds in
[Si2Te6] octahedra, within which they are located at the
distances equal to 2.533 Å. Te–Te distances in triangular
faces perpendicular to “vertical” Si2 dimers is 4.243 Å,
the angles Te–Te–Te are equal to 60°. The remaining 3/4
of Si–Si dimers formed by Si atoms in two different
positions 12і are located in planes that are approximately
SPQEO, 2019. V. 22, N 3. P. 267-276.
Bletskan D.I., Vakulchak V.V., Studenyak I.P. Electronic structure, optical and photoelectrical properties …
269
Fig. 2. Elementary cell of Si2Te3.
perpendicular to c axis with planes (with an angle of
inclination equal to approximately 18°) and are oriented
by three different ways in such a manner that six Si
atoms on average form a six-member cycle. The lengths
of Si–Te bonds in containing these “horizontal” Si–Si
dimers in weakly distorted [Si2Te6] octahedra constitute
2.451 to 2.662 Å. The distances Te–Te in triangular faces
perpendicular to the “horizontal” Si2 dimers constitute
4.36...4.37 Å, and the angles Te–Te–Te are ~60°. The
shortest Te–Te interlayer distance is 4.016 Å.
Thus, the most important feature of Si2Te3
crystalline structure is the statistical placement of 8
silicon atoms in two positions 12i and one – 4e. These
positions are filled with a deficit of 71 percent, because
instead of 28 silicon atoms, only 8 are placed in them. In
the first position 12i 4 atoms are placed, in the second 12i
only 2 atoms and finally in the position 4е also 2 atoms
are located. Therefore, both 12i positions are occupied by
1/3 or 1/6, respectively, and position 4e is filled by 50%.
As a result, Si2 dimers inside Si2Te3 structure are
separated into the “vertical” and “horizontal” ones in the
ratio 1:3. The elementary cell taking into account this
filling of the Si and Te atoms is shown in Fig. 2.
3. Results and discussion
3.1. Electronic structure and density of states
The electronic structure of Si2Te3 crystal was calculated
within the framework of density functional theory in
LDA and LDA+U approximations [23] by using the
software package SIESTA [24]. The values of the
parameters of direct Coulomb and exchange interactions
constituted U = 7 eV and J = 0.7 eV. The band structure
and state density of Si2Te3 calculated by LDA+U method
without taking into account the spin-orbital interaction at
all points of high symmetry and along all symmetrical
directions in irreducible parts of the Brillouin zone
(Fig. 3) are shown in Figs. 4 and 5, respectively.
Fig. 3. Brillouin zone of hexagonal Si2Te3.
The last filled state is taken for zero energy. The
Si2Te3 crystal valence complex consists of 52 dispersion
branches grouped into three bundles of bands in the
energy intervals –12.88…–10.81, –9.26…–5.63 and
–5.02…0 eV separated by forbidden gaps. The total
width of the occupied bands is 12.88 eV. The top of the
valence band is located in the center of the Brillouin
zone, and the bottom of the conductivity band is
localized at the point K. Thus, silicon sesquitelluride is
the indirect-gap semiconductor with the calculated
energy gap Egi = 2.05 eV.
Analysis of partial contributions to the total density
of states N(E) (Fig. 5) allows identifying the genetic
origin of different subzones of the valence band and the
conductivity band of Si2Te3. The relationships between
the intensities of maxima in partial densities of states for
various types of symmetry are different. In the depth of
the valence band of this compound in the total density of
electronic states N(E), the contribution of 5s tellurium
state dominates, whereas in the upper part of the valence
band the contribution of 5р-states of Te atoms is
dominating. The lowest valence subband located within
the energy range from –12.88 to –10.81 eV is mainly
formed by 5s-states of tellurium. Despite the prevailing
nature of Te 5s-states, the effects of hybridization of
silicon and tellurium atoms states are significant for this
subband, leading to the appearance of silicon atoms
3s-states contributions that are mostly localized at the
bottom of this subband, and Si s-, р-, d-states – at its top.
The middle part of the valence bands in the energy
range from –9.26 to –5.63 eV can be separated into four
subgroups of relatively isolated subbands, each
containing two dispersion branches. The two lower
subgroups of four valence bands (–9.26…–5.84 eV) are
formed by the hybridized Si 3s-, 3р- – Te 5s-states. The
next two upper subgroups have a mixed character
with involving 5s- and 5р-states of Te and 3s- and 3р-
states of Si.
SPQEO, 2019. V. 22, N 3. P. 267-276.
Bletskan D.I., Vakulchak V.V., Studenyak I.P. Electronic structure, optical and photoelectrical properties …
270
Fig. 4. The electronic structure of Si2Te3 calculated in LDA+U
approximation.
Fig. 5. Full and local partial densities of electronic states of
Si2Te3 crystal, calculated in the approximation of LDA+U.
The most complicated is the upper subband of the
occupied states (–5.02…0 eV) consisting of 32 dispersion
branches. The very top of this subband, located directly
near the top of the valence band (–1.60…0 eV), is mainly
formed by 5p-states of tellurium with a slight admixture
of 3р-, 3d-states of silicon. The lower part of this
subband (–5.02…–1.60 eV) is formed by the hybridized
5p-states of tellurium and 3p-states of silicon.
The electronic low-energy structure of unfilled
electronic states in silicon sesquitelluride is mainly
formed by kneading free Te p-, d- and Si s-, р-, d-states,
with predominant contribution of p-states inherent to
both atoms. Thus, the analysis of full and partial densities
of states indicates significant hybridization of s- and р-
states of Si and Te atoms, which evidences for strongly
covalent nature of chemical bond Si–Te in [Si2Te6]
coordination octahedron (structural unit of Si2Te3), and
the main role in the optical interband transitions should
be performed by the transfer of charge between Te 5p
occupied states and Te p + Si s, p free states in the
conductivity band.
3.2. Electronic density distribution
To analyze the chemical bond in crystals, it is convenient
to use the spatial distribution of charge (electronic)
density ρ(r). As an example, Fig. 6 shows electron
density distribution maps in four different planes: (а) the
plane passing along the links lines Te–Si–Te in [SiTe3Si]
tetrahedron (Fig. 2); (b) and (c) in the plane
perpendicular to the four-layer packets Te–Si–Si–Te,
passing through the “horizontal” (b) and “vertical” (c) Si2
dimers; (d) in the plane of the tellurium monolayer.
The shape of contour maps of electronic density
clearly indicates that in its composition the contributions
of tellurium atoms occupy a noticeably greater part of
space than those of silicon atoms. The general contours
ρ(r) covering silicon and tellurium atoms in [SiTe3Si]
tetrahedra indicate the existence of a covalent component
of the chemical bond, formation of which is the
responsibility for Si 3s-, 3p- and Te 5s-, 5p-states
hybridization. Polarization of the charge density in the
direction Si→Te indicates the presence of an ion
component in addition to the covalent one. Thus, the
nature of the electron density distribution indicates the
mixed ion-covalent bond type in four-layer packages
Te–Si–Te. A characteristic feature of chemical binding in
Si2Te3 is the presence of common contours ρ(r) between
three tellurium atoms in the tellurium monolayer
(Fig. 6d) belonging to a separate [Si2Te6] octahedron,
which is not typical for other layered crystals
crystallizing in CdI2 structure, for example SnSе2 [25].
Found in [14] strong anisotropy of electrical
properties of the Si2Te3 layered crystals becomes clear
from the density distribution map of valence electrons
carried out in a plane that intersects two four-layer
packages, as it is shown in Fig. 6c. The electronic density
within the four-layer packets, reflecting the chemical
bond of silicon atoms with the nearest neighbors
(tellurium atoms) in [Si2Te6] octahedral, is much higher
than at their boundaries. There are no common level ρ(r)
lines for adjacent tellurium atoms belonging to two
different adjacent four-layer packets, indicating a weak
overlap of their wave functions. This spatial anisotropy
of electron density and energy distribution of electron 5р-
states of tellurium is the cause of quasi-two-dimensional
nature of silicon sesquitelluride.
3.3. Spectra of the fundamental absorption edge of
Si2Te3 crystal
Spectral dependences of the absorption coefficient of
crystalline Si2Te3, measured at various temperatures
within the range 80...293 K, are shown in Fig. 7. The
absorption coefficient was calculated according to the
standard method of two thicknesses [26]. Experimental
absorption edge spectra show two characteristic areas,
formation of which is caused by different mechanisms of
light interaction with Si2Te3 crystalline lattice. In the
long-wave part of spectra, the absorption coefficient α is
weakly dependent on the photon energy, and various
samples have the values within the range 30...100 сm–1.
SPQEO, 2019. V. 22, N 3. P. 267-276.
Bletskan D.I., Vakulchak V.V., Studenyak I.P. Electronic structure, optical and photoelectrical properties …
271
This long-wave part of spectra, as a rule, is
associated with the presence of static defects of the lattice
with different nature (uncontrolled residual impurities,
pores, dislocations, cracks, etc.) [27, 28].
In the short-wave part of spectra (absorption
coefficient takes values in the interval of 102...103 сm–1),
the spectral dependence of absorption edge is described
by the empirical Urbach rule [29, 30]:
( )
−ν
⋅α=
−νσ
⋅α=να
)(
expexp),(
U
0
0
0
0
TE
Eh
kT
Eh
Th , (1)
where α0, Е0 are the coordinates of the convergence point
of the Urbach “bundle”; σ is a steepness parameter of the
absorption edge, EU = kT/σ is Urbach energy (energy
width of the absorption edge), k – Boltzmann constant,
T – temperature, hν – photon energy. Fig. 7 shows that
Fig. 6. Electronic density distribution maps in Si2Te3 crystal: (a) in the plane passing along the links lines Te–Si–Te in [SiTe3Si]
tetrahedron; (b) and (c) in the plane perpendicular to the four-layer packets Te–Si–Si–Te, passing through the “horizontal” (b) and
“vertical” (c) dimers Si2; (d) in the plane of the tellurium monolayer.
SPQEO, 2019. V. 22, N 3. P. 267-276.
Bletskan D.I., Vakulchak V.V., Studenyak I.P. Electronic structure, optical and photoelectrical properties …
272
Fig. 7. Spectral dependence of the boundary absorption of the
Si2Te3 crystal at various temperatures, K: 80 (1), 100 (2), 150
(3), 200 (4), 250 (5), and 293 (6). The insert shows the
temperature dependence of the absorption edge slope.
high-energy parts of the absorption edge spectra
of crystalline Si2Te3 within the investigated tempe-
rature range 80...293 K form the characteristic
temperature “bundle” with coordinates of convergence
α0 = 9.6·106
сm–1 and Е0 = 2.510 eV (Table).
With increasing the temperature from 80 up to
293 K, the absorption edge is shifted to low energies
(Fig. 7), which reflects a decrease in the energy band gap.
The temperature dependence of absorption edge slope is
described by the equation [31]:
ω
⋅
ω
⋅σ=σ
kT
kT
T
2
th
2
)( 0
0
0
h
h
, (2)
where σ0 is the parameter associated with the constant of
exciton(electron)-phonon interaction g by the relation
σ0 = (2/3)g–1, ħωph – characteristic energy of phonons that
most effectively interact with electrons (excitons). For
the most crystals, ħωph is close to the energy of the most
high-energy LO-phonon [31]. Analysis of Toyazawa
criterion [32] indicates that in Si2Te3 crystals there is a
strong electron-phonon interaction (EPI) (σ0 < 0.61 < 1).
Fig. 8. Temperature dependences of the optical pseudogap
*
gE (1) and Urbach energy EU (2) of Si2Te3 crystal.
The analysis of the absorption edge spectra (Fig. 7)
allowed us to determine the value of the effective phonon
energy (frequency) ħωph = 38.8 meV (313 cm–1). The
comparison of above mentioned value with the real
values of vibrational frequencies of Si2Te3 crystal lattice
allows to find out what type of phonons is involved into
formation of the absorption edge. The obtained ħωph
value is close to the frequency of the longitudinal optical
LO-phonon (335 cm–1) which appear in the Raman
spectra of Si2Te3 [20]. Thus, the exponential shape of
Si2Te3 absorption edge is determined not only by the
influence of charged impurities, but also by longitudinal
optical LO-phonons.
Due to the fact that indirect optical transitions in
Si2Te3 crystals are masked by long-wave Urbach
absorption “tails”, it is difficult to determine the true
value of the energy band gap [31]. In this case, often the
energy band gap is taken as the value, which corresponds
to the energy position of the absorption edge at a fixed
absorption level α = 103 сm–1. The optical pseudogap *
gE
(Fig. 8) determined in this manner is described within the
Einstein model using the equation [33]:
( )
−θ
θ−=
1exp
1
)0()(
E
E
***
T
kSETE ggg , (3)
Parameters of Urbach absorption edge and EPI for Si2Te3 crystal.
*
gE (293 K)
(eV)
EU (293 K)
(meV)
α0
(сm–1)
E0
(eV)
σ0
ħω0
(meV)
θE
(K)
( )0UE
(meV)
( )1UE
(meV)
)0(*
gE
(eV)
α
gS
2.083 46.6 9.6×106 2.510 0.61 38.8 381 26.3 54.4 2.270 15.2
SPQEO, 2019. V. 22, N 3. P. 267-276.
Bletskan D.I., Vakulchak V.V., Studenyak I.P. Electronic structure, optical and photoelectrical properties …
273
Fig. 9. Photoconductivity (1–4) and absorption edge (5, 6)
spectra of Si2Te3 single crystals at various temperatures, K:
293 (1), 350 (2), 410 (3), and 440 (4) (5 – current measure-
ments, 6 taken from [16]).
where )0(*
gE and *
gS are, respectively, the optical
pseudogap at 0 K and dimensionless constant; Eθ is the
Einstein temperature that corresponds to the average
frequency of phonon excitations of the system of non-
interacting oscillators. )0(*
gE , *
gS and Eθ parameters
obtained during the description of ( )TEg
* dependence by
Eq. (3) are given in Table.
Despite the fact that there is currently no single
universal interpretation of the Urbach rule, there is no
doubt that the exponential form of the Urbach absorption
edge is caused by the influence of disordering processes.
In the case of crystals, it is a dynamic (temperature)
disorder, the source of which is EPI caused by lattice
fluctuations, and static (structural) disorder caused by the
small scale violations of the periodic potential of the
crystal lattice due to the presence of point charged
defects in the crystal [34–36]. The contribution of each of
these factors depends on the concentration of charged
impurities in material under investigation and its
temperature, which determines the concentration of
equilibrium phonons. With the temperature decrease, the
phonons freeze, but the tails of the absorption coefficient
do not disappear. Their existence is related with the
heterogeneity of the crystal caused by the presence of its
proper point defects. In the case of Si2Te3 crystals, this is
primarily a high concentration of stoichiometric cationic
vacancies.
The Urbach energy EU (Fig. 8) can serve as a
measure of the absorption edge smearing, and
accordingly, the measure of disorder degree [37],
which, as indicated above, is determined by
dynamic (temperature) and static (structural) disordering
[34, 38]:
( ) ( )
TX
EEE UUU += , (4)
Fig. 10. Photoconductivity (1, 2) and absorption edge (3, 4)
spectra of Si2Te3 single crystals at Т = 293 K. (3 – current
measurements, 4 taken from [16]).
where ( )
X
EU and ( )
T
EU are, respectively, the contri-
butions of structural (static) and temperature (dynamic)
disordering into EU, they are considered as independent,
equivalent and additive. To separate contributions of
different types of disordering into EU, the methodology
proposed by the authors was used [31]. To perform this,
the known equation, well describing the temperature
dependence of the Urbach energy EU within the Einstein
model, was used [34, 35]:
( ) ( ) ( )
( )
−θ
+=
1exp
1
E
1U0UU
T
EEE , (5)
where ( )0UE and ( )1UE are constant values. The values
of the parameters ( )0UE and ( )1UE obtained during
describing the experimental temperature dependences EU
by Eq. (4) are given in Table. Comparing the equations
(4) and (5), we find the values ( )
T
EU = 20.3 meV
(43.6% from EU) and ( )
X
EU = 26.3 meV (56.4% from
EU) at T = 293 K.
3.4. Photoconductivity spectra of Si2Te3 crystals
Another independent method of studying the band
structure is the spectral distribution of the
photosensitivity of the crystal, which in general reflects
the presence of two photo effects: proper and impurity
ones. In the first case, there is a band-to-band bipolar
generation of free carriers, in the second one, it is
generation of free carriers of the same type, i.e.,
monopolar generation related with impurity centers.
Since Si2Te3 crystals have significant integrated
photosensitivity (σf /σt = 102–103, where σf is the
electrical conductivity at illumination of 104 lux) without
special additional heat treatments, it allowed performing
SPQEO, 2019. V. 22, N 3. P. 267-276.
Bletskan D.I., Vakulchak V.V., Studenyak I.P. Electronic structure, optical and photoelectrical properties …
274
studies of their photoconductivity spectra. To measure
photoconductivity, gold contacts were applied to natural
faces of crystalline samples, so that coplanar geometry
was realized, that is, between the contacts there was a
gap of 5-6 mm, through which illumination of the sample
was performed.
Given that silicon sesquitelluride has a two-sided
homogeneity region [39], it is important to study the
influence of deviation degree of the crystal composition
from stoichiometric on the spectral photosensitivity
distribution. With this aim in mind, we have studied the
photoconductivity spectra of Si2Te3 crystals grown from
both stoichiometric and tellurium-surplus mixtures.
Typical non-polarized photoconductivity spectra of the
first type of crystals measured within the temperature
range 293...440 K at a constant current and modulated
illumination of the sample under study are shown in
Fig. 9. As can be seen from Fig. 9, in the photo-
conductivity spectra of Si2Te3 crystals grown from the
stoichiometric mixture, one wide band is observed, the
energy position of the maximum of which shifts to the
low-energy region with an increase of the temperature,
which reflects a decrease of the energy gap value. To
identify the nature of the maximum in the photo-
conductivity spectrum, Fig. 9 also shows the absorption
edge spectra of the Si2Te3 crystal, measured by us
(curve 5) and taken from the Ref. [16] (curve 6). It
follows from the comparison of photoconductivity and
fundamental absorption spectra that the energy position
of the maximum hωmax = 2.13 eV in the spectrum of
photoconductivity is located in the area of its proper
absorption and meets value α ≈ 2·103 сm–1. Thus, the
nature of this maximum is caused by generation of non-
equilibrium carriers caused by optical band-to-band
transitions (G→K) from the top of valence band formed
by 5р-states of the tellurium lone pair to the bottom of
the conductivity band formed by kneading of free
р-states of tellurium and silicon (Figs. 4 and 5).
This naturally raises the question, what is the exact
way to determine the value of the energy gap from the
photoconductivity spectra of the Si2Te3 crystal? In the
study of homopolar semiconductor (Si, Ge, etc.)
photoconductivity, the fundamental absorption edge is
sharply pronounced, and Eg is determined beyond the
threshold of photoconductivity (Moss rule). However, in
the case of Si2Te3 crystals, the frequency dependence of
the absorption coefficient α(ω) in the region of
fundamental absorption edge at α ≤ 103
сm–3 (Fig. 7) is
not a root one, as in the case of direct optical transitions
in ideal semiconductors. In this case, as shown in Ref.
[40], in wide-band crystals with the exponential
dependence of the long-wave absorption edge in wide
range of the thickness of samples and velocities of
surface recombination, the effective value of energy gap
can be determined with great accuracy by the effective
position of the intrinsic maximum in the spectrum of
photoconductivity. Thus, if the energy of interband
transitions is estimated by the spectral position of the
intrinsic maximum of photoconductivity, then it follows
from the photoconductivity spectra given in Fig. 9 that
the energy gap value of Si2Te3 crystal equals
Eg = 2.13 eV at room temperature.
It should be noted that even when Si2Te3 crystals
are grown from a stoichiometric mixture, in the same
ampoule, the crystals grow with a different from the
above-described photoconductivity spectrum (curve 1,
Fig. 10). As can be seen from Fig. 10, the photo-
sensitivity of these crystals manifests itself in a wider
spectral range of 1.0…2.5 eV, and the photoconductivity
spectrum is complex and contains a pronounced intense
peak at 2.02 eV, one feature in the form of an influx
at 2.12 eV at a high energy downturn of the main peak
and two features at 1.7 and 1.32 eV at a long-wave
downturn.
The authors of Refs [17, 18] give close in their form
photoconductivity spectra of Si2Te3 crystals, in which at
T = 93 K there is an intense band with a maximum at
2.2 eV in the range of fundamental absorption, a feature
in the form of an inflection at 1.9 eV on the long-wave
decline of the main band and a wide long-wave band
with the maximum close to 1 eV.
The photoconductivity spectrum of non-
stoichiometric Si2Te3 crystals, grown from the original
mixture containing the excess of tellurium, is undergoing
even greater changes (curve 2, Fig. 10). It can be seen
from Fig. 10 that impurity bands with the maxima at 1.65
and 1.33 eV are dominant in the photoconductivity
spectrum, while the intensity of its intrinsic maximum
sharply decreases, and it manifests itself in the form of
inflection at ~2.1 eV. Given that non-stoichiometric
Si2Te3 crystals contain both silicon vacancies (by the
nature of the substance itself) and excess tellurium
atoms, additional complex studies of stationary and
kinetic characteristics of photoconductivity are necessary
to establish the nature of impurity bands in the
photoconductivity spectra.
4. Conclusions
Calculations of the electronic structure, the total and
partial densities of states, and the spatial distribution of
the electron charge density of a Si2Te3 crystal are
performed for an optimized structure by using ab initio
the density functional theory method in the LDA+U
approximation. The calculation and analysis of the total
and partial densities of the electron states of the N(E)
silicon sesquitelluride made it possible to determine the
genesis of the individual subbands and their band
structure as a whole.
It is shown that the dependence of the absorption
coefficient on the photon energy is described by the
Urbach rule. An estimation of the contribution of
structural and dynamic disorder to the smearing of the
absorption edge of a Si2Te3 crystal has been performed.
The parameters of the Urbach absorption edge and the
electron-phonon interaction have been determined.
The effect of deviation of the composition from the
stoichiometric one on the photoconductivity spectra of
layered Si2Te3 crystals has been studied.
SPQEO, 2019. V. 22, N 3. P. 267-276.
Bletskan D.I., Vakulchak V.V., Studenyak I.P. Electronic structure, optical and photoelectrical properties …
275
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Authors and CV
Dmytro I. Bletskan, born in 1946,
defended his Doctoral Dissertation in
Physics and Mathematics in 1985 and
became full professor in 1988.
Professor of the Department physics
of semiconductors at the Uzhhorod
National University, Ukraine.
Authored over 260 scientific publi-
cations, 86 patents, 2 textbooks, 2
monographs. The area of his scientific
interests – technology and physics of highly anisotropic
layered crystals, physical properties of chalcogenide
glassy semiconductors and superionics.
Vasyl V. Vakulchak, born in 1986,
defended his PhD thesis in Physics
and Mathematics in 2015. Senior
researcher of the Department of
Applied Physics at the Uzhhorod
National University, Ukraine.
Authored of 60 scientific publications
and 1 patent. The area of scientific
interests is ab initio calculation of the
electronic structure, physical
properties of semiconductors.
Ihor P. Studenyak, born in 1960,
defended his Dr. Sc. degree in Physics
and Mathematics in 2003 and became
full professor in 2004. Vice-rector for
research at the Uzhhorod National
University, Ukraine. Authored over
200 publications, 120 patents, 15 text-
books. The area of his scientific inte-
rests includes physical properties of semiconductors,
ferroics and superionic conductors.
|
| id | nasplib_isofts_kiev_ua-123456789-215501 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-23T18:54:29Z |
| publishDate | 2019 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Bletskan, D.I. Vakulchak, V.V. Studenyak, I.P. 2026-03-19T10:44:27Z 2019 Electronic structure, optical, and photoelectrical properties of crystalline Si₂Te₃ / D.I. Bletskan, V.V. Vakulchak, I.P. Studenyak // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2019. — Т. 22, № 3. — С. 267-276. — Бібліогр.: 40 назв. — англ. 1560-8034 PACS: 31.10.+z, 71.15.Mb, 71.20.-b, 72.40.+w, 78.20.Ci https://nasplib.isofts.kiev.ua/handle/123456789/215501 https://doi.org/10.15407/spqeo22.03.267 In the framework of the density functional theory (DFT) in the approximation of local density adjusted for the strong correlation (LDA+U method), the band structure, total and partial densities of electronic states, as well as the spatial distribution of the electron density, were calculated. According to the results of the calculation, Si₂Te₃ is an indirect-gap semiconductor with the calculated band gap Eᶜᵃᶥᶜgi = 2.05 eV, close to the experimentally measured Eᵒᵖᵗg = 2.13 eV. The absorption edge and photoconductivity spectra of the Si₂Te₃ crystal within the temperature range 80...293 K has been measured. It has been shown that the dependence of the absorption coefficient on the photon energy is described by the Urbach rule. The parameter σ₀, associated with the constant of electron-phonon interaction, and the energy of effective phonons ħω₍ph₎, involved in the formation of the absorption edge of crystalline Si₂Te₃, were determined using the temperature dependence of the absorption edge slope. Deviation from the stoichiometric composition in the direction of excess tellurium significantly affects the spectral distribution of the photoconductivity of Si₂Te₃ crystals. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Semiconductor physics Electronic structure, optical, and photoelectrical properties of crystalline Si₂Te₃ Article published earlier |
| spellingShingle | Electronic structure, optical, and photoelectrical properties of crystalline Si₂Te₃ Bletskan, D.I. Vakulchak, V.V. Studenyak, I.P. Semiconductor physics |
| title | Electronic structure, optical, and photoelectrical properties of crystalline Si₂Te₃ |
| title_full | Electronic structure, optical, and photoelectrical properties of crystalline Si₂Te₃ |
| title_fullStr | Electronic structure, optical, and photoelectrical properties of crystalline Si₂Te₃ |
| title_full_unstemmed | Electronic structure, optical, and photoelectrical properties of crystalline Si₂Te₃ |
| title_short | Electronic structure, optical, and photoelectrical properties of crystalline Si₂Te₃ |
| title_sort | electronic structure, optical, and photoelectrical properties of crystalline si₂te₃ |
| topic | Semiconductor physics |
| topic_facet | Semiconductor physics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/215501 |
| work_keys_str_mv | AT bletskandi electronicstructureopticalandphotoelectricalpropertiesofcrystallinesi2te3 AT vakulchakvv electronicstructureopticalandphotoelectricalpropertiesofcrystallinesi2te3 AT studenyakip electronicstructureopticalandphotoelectricalpropertiesofcrystallinesi2te3 |