Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the electronic structure of 2H-Sn₂
It was performed the systematic investigation of the chemical modification regularities of electronic structure at the composition changes of “ideal” 2H-SnS₂ crystal was performed by using the self-consistent density functional theory method in the supercell model. The phases obtained during doping...
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| Опубліковано в: : | Semiconductor Physics Quantum Electronics & Optoelectronics |
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| Дата: | 2018 |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2018
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| Цитувати: | Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the electronic structure of 2H-Sn₂ / D.I. Bletskan, V.V. Frolova // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2018. — Т. 21, № 4. — С. 345-359. — Бібліогр.: 36 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860479658875682816 |
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| author | Bletskan, D.I. Frolova, V.V. |
| author_facet | Bletskan, D.I. Frolova, V.V. |
| citation_txt | Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the electronic structure of 2H-Sn₂ / D.I. Bletskan, V.V. Frolova // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2018. — Т. 21, № 4. — С. 345-359. — Бібліогр.: 36 назв. — англ. |
| collection | DSpace DC |
| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | It was performed the systematic investigation of the chemical modification regularities of electronic structure at the composition changes of “ideal” 2H-SnS₂ crystal was performed by using the self-consistent density functional theory method in the supercell model. The phases obtained during doping the sulfur sublattice by substitutional impurity Y→S (Y = Cl, I), as well as during changing tin disulfide structure due to the appearance of atomic vacancies in cation and anion sublattices (non-stoichiometry effects), were analyzed.
|
| first_indexed | 2026-03-23T18:47:46Z |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2018. V. 21, N 4. P. 345-359.
© 2018, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
345
Semiconductor physics
Influence of intrinsic point defects and substitutional impurities
(Cl, I → S) on the electronic structure of 2H-SnS2
D.I. Bletskan, V.V. Frolova
Uzhhorod National University, 54, Voloshin Str., 88000 Uzhhorod, Ukraine
E-mail: crystal_lab457@yahoo.com
Abstract. It was performed the systematic investigation of chemical modification
regularities of electronic structure at the composition changes of “ideal” 2H-SnS2 crystal by
using the self-consistent density functional theory method in the supercell model. It was
analyzed the phases obtained during doping the sulfur sublattice by substitutional impurity
Y→S (Y = Cl, I) as well as during changing tin disulfide structure due to the appearance of
atomic vacancies in cation and anion sublattices (non-stoichiometry effects).
Keywords: tin disulfide, electronic structure, density of states, intrinsic and extrinsic point
defects, photoconductivity.
doi: https://doi.org/10.15407/spqeo21.04.345
PACS 61.72.J-, 61.72.-y, 71.38.-k, 72.40.+w
Manuscript received 17.10.18; revised version received 02.11.18; accepted for publication
29.11.18; published online 03.12.18.
1. Introduction
Tin disulfide (SnS2) belongs to the family of layered
semiconductors, which characteristic feature is the
presence of polytypism. It is known more than 30 various
SnS2 polytypes, among which 2H, 4H and 18R base
structures, are the most stable [1]. Crystal structures of
all tin disulfide polytypes are formed by S–Sn–S three-
layer packets (sandwiches), each of which is constructed
by hexagonal monolayers of S and Sn atoms and has the
trigonal symmetry. The SnS2 polytypes with larger lattice
constants c than for 4H-SnS2 have some laying sequences
of three-layer packets, which are the packing
combinations of 2Н/18R and 4H/18R base structures.
They are not the simple variants of layer packing that
allowed by geometry, but certainly, they are definitely
intermediate ones between the base structures [2, 3].
In early papers, for example Ref. [4], the authors
started description of the crystal structure for various
polytypes of tin disulfide and designation of their space
groups by the packing geometry of completely occupied
hexagonal layers combined in the molecular sandwiches
S–Sn–S. However, it was found that 2H-SnS2 has a
significant difference between the measured and
theoretically calculated density values using X-ray
diffraction data (ρmeas. = 3.4 g/cm3 is much less than ρtheor.
= 4.32 g/cm3) [2]. This difference of the measured and
calculated densities is associated with the fact that only
79% positions of hexagonal Sn-monolayers and only
72% positions of S-monolayers of 2H-polytype crystal
structure are filled. Thereof, it can be concluded that
cation and anion vacancies are the dominant intrinsic
point defects in 2H-SnS2 crystals. Predominant formation
of anion vacancy is caused by lower energy consumption
for the break of only one of six covalent-ionic sulfur-tin
bonds in [SnS6] octahedron, while formation of cation
vacancy requires additional breaks of much more
covalent bonds of removed tin atom with tin atoms of its
second coordination sphere. Consequently, real 2H-SnS2
crystals always contain a large amount of intrinsic point
(zero-dimensional) Schottky defects (anion VS and cation
VSn vacancies). Anion and cation vacancies in 2H-SnS2
SPQEO, 2018. V. 21, N 4. P. 345-359.
Bletskan D.I., Frolova V.V. Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the …
346
form the defect centers that play the role of electron traps
and recombination centers, and thus they significantly
affect the photoconductivity and photoluminescence of
these crystals. However, the overwhelming majority of
papers did not considered the non-stoichiometric effects
when studying the physicochemical properties of 2H-
SnS2 crystals.
As shown by the authors of Ref. [2, 3], the
important role in formation one or another polytype types
during crystal growth from the gas phase by using the
chemical transport reaction (CTR) method (except of
temperature and vapor pressure in the crystallization
zone) also plays the role of transport agent (carrier),
which generally affects the chemical composition and
first of all on stoichiometry. The growth of tin disulfide
single crystals by CTR method usually leads to the
doping of initial material by transporter atoms. In the vast
majority of cases, halogens (Cl, I) are used as the
transporting agents, and entering into the crystal they
form another type of point defects – substitutional
impurities Cl, I→S that significantly affects the
resistivity [5–8].
Since the basic properties of solids (including
crystals with defects) are determined by their electronic
structure, the better understanding of optical, electrical,
photoelectrical and photoluminescent properties of real
defective 2H-SnS2 crystals requires to ascertain changes
in the band structure of ideal crystal that are caused by
defects generating the localized states in the band gap.
The important role in the study of electronic structure of
defective crystals is played by the computational
modeling, which allows not only to interpret the
experimental data but also to predict them. Thus, it is
evident that electronic structure calculations of real
defective SnS2 crystals can be very useful both for
description of their fundamental electronic properties and
to find the compositions possessing useful practical
perspectives.
By now, the electronic structure and nature of
interatomic interactions for stoichiometric defect-free
SnS2 crystal are fairly well studied [9–20]. As for the
study of influence of intrinsic and impurity point defects
on the electronic structure of tin disulfide, then we are
not aware of this kind of papers.
Fig. 1. Unit cell of 2H-SnS2 (a), 3×3×2 supercells of 2H-SnS2 with tin (b), sulfur (c) vacancies and Y→S (Y = Cl, I) substitutional
impurity (d).
SPQEO, 2018. V. 21, N 4. P. 345-359.
Bletskan D.I., Frolova V.V. Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the …
347
This paper presents electronic structure calculations
of defect-free tin disulfide crystal as well as the crystals
containing intrinsic point defects (cation and anion
vacancies) and isolated substitutional impurity atoms
Y→S (Y = Cl, I), which are performed by ab initio
density functional theory method in the LDA+U
approximation with accounting the single-site Coulomb
correlations.
2. Crystal structure of 2H-SnS2
2H-polytype of SnS2 is characterized by CdI2-type
structure based on the three-layer packets
(“sandwiches”), which are parallel to (001) plane. Each
three-layer packet consists of a tin atom monolayer
sandwiched between two close-packed monolayers of
sulfur atoms (Fig. 1a). In the 2H-SnS2 crystal structure,
tin atoms are centered in the octahedra, which vertices
are occupied by S atoms (Fig. 1a). The [SnS6] octahedra
are linked among themselves by common edges and form
the three-layer –S–Sn–S– packets.
Bonds have the ion-covalent character within three-
layer packets and bonds between three-layer packets are
mainly performed by the van der Waals forces, it causes
the large anisotropy of physical properties of 2H-SnS2
crystals. Formation of various polytypes of tin disulfide
depends on the layered character of three-layer packets
along c axis. The layer packing order of the simplest 2H-
SnS2 structure is [AγB, AγB], where γ designates tin
atom monolayer and A, B – sulfur monolayers. The
symmetry of 2H-polytype crystal lattice is characterized
by the space group
3
3dD (P 3 m1). Experimental
parameters of crystal lattice are a = b = 3.647 Å, c =
5.899 Å, γ = 120° [2]. The equilibrium lattice parameters
a = b = 3.678 Å, c = 5.834 Å, γ = 120° were used in the
calculations, which we obtained at the total energy
minimum of defect-free crystal modeling.
The unit cell of 2H-polytype contains three atoms.
If the usual coordinate system is used, the unit cell of 2H-
SnS2 is described by two vectors a1 and a2 in the XY
plane with the angle 120° between them as well as a3
vector along Z direction, and it contains the Sn atom
located in Wyckoff position a(0, 0, 0) and two sulfur
atoms located in Wyckoff position d(1/3, 2/3, z) with
coordinates (1/3, 2/3, u), (2/3, 1/3, w), where u = 0.25,
w = 0.75 before relaxation and u = 0.25623, w = 0.74377
after relaxation. The symmetry of specified positions is
described by local groups 3m and 3m, respectively.
3. Calculation method
The presence of defects disturbs the translational
symmetry of an ideal crystal. At the present time, the
supercell model with ab initio calculation methods is
most effectively used for the description of electronic
structure of defective crystals.
This modeling was performed within the frames of
density functional theory (DFT) method [21, 22] with the
local density approximation (LDA) as an exchange-
correlation functional. It is known that first-principle
calculations within the density functional theory in the
local density approximation for exchange-correlation
potential give the underestimated values of bang gap
widths and defect centers depths. The LDA+U method
[23, 24] is used for more correct description of electronic
correlation in comparison with LDA calculations. It is
known that the magnitude of direct Coulomb single-site
interaction U can significantly affect the depth of defect
states in the band gap, and also the charge localization
degree.
Calculations were performed using SIESTA
software package [25, 26], which has a powerful and
effective mechanism for the model manipulations of
crystal unit cells: introduction and removal of atoms,
formation of defects, introduction of distortions into the
lattice, supercell construction and their relaxation, etc. In
the supercell model, the infinite crystal is considered by
introduction of periodic boundary conditions and a quasi-
molecule is considered in the form of extended unit cell
constructed using several primitive unit cells. This
approach combines the advantages of molecular model
(not all one-electron states of a crystal are considered but
their finite number) with the correct consideration of the
symmetry of object and does not create the problems
associated with an extraction of fragment from the
crystalline environment. Being mainly aimed at the
electronic structure calculation of defective crystals, this
method is also useful for the studying of band structures
of defect-free crystals. The 54-atom supercell (Sn18S36)
was produced for the modeling of stoichiometric tin
disulfide as well as anion and cation vacancies. It was
received by 3×3×2 translation of 2H-SnS2 unit cell, then
the appearance of cation (VSn) or anion (VS) vacancies
was simulated by removing one of Sn or S atoms,
respectively. Such cell {Sn17VSnS36} corresponds to a
cation-defective tin disulfide with a formal stoichiometry
of Sn0.944S2. It must be emphasized that the supercell
model supposed the ordered vacancy distribution in the
crystal volume, given by the regular translation of
supercell.
SPQEO, 2018. V. 21, N 4. P. 345-359.
Bletskan D.I., Frolova V.V. Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the …
348
The geometry optimization procedure to minimize
the supercell mechanical tensions was performed, which
was considered as full-performed, when the force acting
on each individual ion appeared is less than 0.01 eV/Å.
Displacements caused by the presence of tin and/or sulfur
vacancies change the bond lengths, but do not change the
shape of local arrangement of the nearest and following
upon the nearest atoms. So, in the case of cation vacancy
presence, all six sulfur ions of the nearest vacancy
environment undergo the significant shifts, moving from
their regular positions in the direction from vacancy. The
shift of S atoms from cation vacancy is explained by the
fact that tin ion removal leads to the repulsion between S
ions nearest to the vacancy and by Coulomb attraction of
these sulfur ions toward tin ions of the second
coordination sphere. The removal of S atom causes the
shifts of surrounding Sn atoms in the direction from the
vacancy.
4. Results and discussion
4.1. Electronic structure of defect-free 2H-SnS2
As the first step of study, we performed the electronic
structure calculations of defect-free SnS2 crystal. The
electronic structure of defect-free 2H-SnS2 calculated
using the density functional method without regard for
the spin-orbital interaction in the LDA+U approximation
in all high-symmetry points and directions of the
Brillouin zone (Fig. 2) of hexagonal lattice is shown in
Fig. 3a. The energy origin is set to the upper occupied
level.
The valence band of defect-free 2H-SnS2 (total
width 13.11 eV) includes eight occupied bands. Layered
character of 2H-SnS2 crystal is reflected in the energy
spectrum structure. It is observed the significant
anisotropy of dispersion law for individual bands along
and across three-layer packets. So, the dispersion of most
of upper valence bands in the Γ→M, Γ→K directions
(along three-layer packet) exceeds the dispersion in the
Γ→A direction (across layers). Weak dispersion E(k)
along the c axis of 2H-SnS2 crystal (i.e., along the Γ–∆–
A direction, which is perpendicular to the monolayers
formed by Sn and S atoms) indicates the layered nature
of compound and the relatively weak influence of
interaction between three-layer packets on the electronic
structure. The noticeable dispersion of bands along the
directions parallel to the three-layer packets indicates the
strong interaction in the structural [SnS6] units, which
form the sandwiches. These structure features of layered
2H-SnS2 allow to tell about quasi-two-dimensional
character of electronic energy spectrum.
Fig. 2. Brillouin zone of 2H-SnS2.
The calculations of total and local partial densities
of states give information on the atomic orbital
contributions into the crystal states of 2H-SnS2. The
spectra of total N(E) and local partial nat (E) densities of
electronic states (DOS) obtained on the basis of band
calculation are shown in Fig. 3b. It is possible to identify
the genetic origin of various subbands of occupied states
by the analysis of partial contributions into the electronic
density of states. The relationships between intensities of
maxima in partial densities of states with various
symmetry types are different. Partial sulfur s-, p-states
predominate in the valence band of tin disulfide, and also
their energy positions are significantly different. The
coincidence of energy positions for the main maxima in
the partial spectra of sulfur s-, p-states with the positions
of corresponding maxima of tin s-, p-states indicates their
strong hybridization.
Two lowest quasi-core bands (forming the valence
band bottom) in the energy range from –13.11 to
–10.38 eV are mainly formed by S 3s-atomic orbitals
with the insignificant impurities of tin 5s-, 5p-states. The
next subband in the energy range from –7.18 to –4.22 eV
is formed by hybridized Sn 5s- and S 3p-orbitals, and
contributions of these states are comparable in their
magnitude. Formation of an intermolecular chemical
bond is genetically associated with these bands. The
energy gap between the middle of the occupied band and
two bottom valence bands is 3.2 eV. The upper bunch of
5 occupied bands with 5.02 eV width has a mixed
character involving the hybridized 3p-states of sulfur and
5p-states of tin. The uppermost part of this occupied
SPQEO, 2018. V. 21, N 4. P. 345-359.
Bletskan D.I., Frolova V.V. Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the …
349
Fig. 3. Electronic structure (a), total and partial densities of states (b) of 2H-SnS2 calculated using the LDA+U approximation.
SPQEO, 2018. V. 21, N 4. P. 345-359.
Bletskan D.I., Frolova V.V. Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the …
350
Fig. 4. Experimental XPS (1486 eV) [30] (1), UPS (22 eV) [31]
(2) spectra of 2H-SnS2; calculated 2H-SnS2 total density of
valence states in the unit cell (3) and supercell (4) models;
partial densities of valence electronic pz- (5) pxy- (6) states of
sulfur.
subband (1.5 eV width) has mainly anionic character, and
sulfur pz-states form its top.
The characteristic feature of 2H-SnS2 electronic
structure is the presence of forbidden gap with 1.51 eV
width in the conduction band separating the isolated low-
energy unoccupied subband from the continuous
spectrum of free states. This isolated subband of
conduction band has significant dispersion and contains
contributions of free Sn s-, S p-states. Free p-states of tin
are dominating in the continuous spectrum of conduction
band with the admixing of sulfur p-states.
According to the calculation results, 2H-SnS2 is an
indirect-gap semiconductor with the valence band top
located in the Γ point (Γ4 symmetry) formed primarily by
sulfur pz-states. The conduction band bottom is localized
in U direction (U1 symmetry) of Brillouin zone. Our
results are in good agreement with previously calculation
data performed by the local pseudopotential method [14].
The value of indirect gap calculated in the LDA+U
approximation is Egi = 2.21 eV (transition Γ4→U1), and it
is close to the experimental values Egi = 2.21 [27], 2.22
[28], 2.29 eV [29] obtained from the analysis of
fundamental absorption spectra of 2H-SnS2 single
crystals grown from the gas phase.
A necessary condition to compare the results of
“defective” supercells is the reliable transfer of bulk
properties of a defect-free crystal by the supercell model.
For this purpose, we performed the electronic structure
calculations of defect-free 2H-SnS2 crystal in the
supercell model in the LDA+U approximation (Fig. 5a).
The energy band structure of defect-free 2H-SnS2
crystal calculated by the density functional method in the
3×3×2 supercell model is shown in Fig. 5a where the
Fermi level is taken as the zero energy. For the band
structure calculations of defect-free and defective crystals
in the supercell model, we used only four high-
symmetric points of the Brillouin zone, namely: Γ(0, 0,
0), M (0.5, 0, 0), L(0.5, 0, 0.5), K(0.33, 0.33, 0),
however, in order to ascertain the reliability of the
results, some calculations were tested using six points. It
follows from the comparison of electronic structures and
density of states of defect-free 2H-SnS2 crystal calculated
using the unit-cell (Figs. 3a and 3b) and by supercell
(Figs. 5a and 5b) models that they do not significantly
differ both by quantity of subbands as well as by their
formation genesis.
The adequacy of the model description of electronic
structure of defect-free 2H-SnS2 in the supercell
approximation is determined by the similarity of
calculated spectra of total density of states and
experimental photoelectron spectra. The smoothed
spectrum of total density of states N(E) of defect-free tin
disulfide calculated using the supercell model is
compared in Fig. 4 in the unified energy scale with the
known experimental X-ray and ultraviolet photoelectron
spectra of 2H-SnS2 crystal taken from Refs. [30, 31]. It
can be seen from this figure that the calculated N(E)
spectrum well reproduces the positions of gravity centers
(centroids) of energy bands in the experimental XPS and
UPS spectra. It is conditionally possible to allocate the
А1, А2, А3 subbands having the symmetry of p-orbital of
sulfur in the binding energy range from 0 to 5 eV. The
energy distribution of chalcogen px,y,z-states in the
occupied part of valence band is anisotropic (curves 5, 6,
Fig. 4) which is the reflection of two-dimensional nature
of 2H-SnS2 crystal structure.
4.2. Influence of intrinsic point defects on the electronic
structure and density of states of 2H-SnS2 crystal
The electronic structure of 2H-SnS2 crystal with intrinsic
point defects (tin (VSn) and sulfur (VS) vacancies) is
presented by the band diagram in Fig. 5. It is important
for the analysis of electronic structure of defective crystal
to separate the states related with the presence of defects
from the states typical for the crystal matrix.
SPQEO, 2018. V. 21, N 4. P. 345-359.
Bletskan D.I., Frolova V.V. Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the …
351
Fig. 5. Electronic structure, total and partial densities of states of defect-free 2H-SnS2 (a, b) as well as 2H-SnS2 with cation (c, d) and
anion (e, f) vacancies calculated in 3×3×2 supercell model.
SPQEO, 2018. V. 21, N 4. P. 345-359.
Bletskan D.I., Frolova V.V. Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the …
352
Fig. 6. Photoconductivity spectra of 2H-SnS2 crystal.
T = 293 K.
The presence of cation vacancy in 2H-SnS2 crystal
leads not only to modification of crystal local geometry,
but it also primarily reflects the electronic properties of
whole crystal system as well as, in particular, of ions near
the defect. Cation vacancies in 2H-SnS2 induce the
appearance of an intense peak of density of states in the
depth of valence band in the pseudo-gap region above the
quasi-core sulfur 3s-subband. The genesis of these cation
vacancy states (generally of sulfur s-symmetry) is caused
by restructuring the electronic states of matrix, where the
wave functions of sulfur atoms nearest to the cation
vacancy play the decisive role. Important changes also
occur in the middle subband of occupied states, where
S 3p–Sn 5s-hybridization takes place. The nature of these
changes is manifested in restructuring the peak intensities
in the partial DOS-spectrum of tin 5s-states which is a
reflection of bond changes (more precisely their breaks,
absence) in that part of [SnS6] octahedra that have no tin
atoms, i.e., there are cation vacancies. Besides, in the
band spectrum of non-stoichiometric 2H-SnS2 above the
valence band top there is the acceptor level, which nature
is associated with sulfur 3p-states.
The coordination number of tin atom in 2H-SnS2 is
greater than that of sulfur atom. Consequently, formation
of anion vacancies in 2H-SnS2 crystals is caused by the
lower energy costs of the breaking one of six ion-
covalent sulfur-tin bonds in the [SnS6] octahedron in
comparison with the energy costs for formation of cation
vacancy. Therefore, in the case of non-stoichiometric 2H-
SnS2 with anion vacancies the density of occupied states
practically does not undergo the significant changes in
comparison with a defect-free crystal; at the same time,
the donor level appears in the fundamental gap of band
spectrum, its nature is related with the mixed S 3p- and
Sn 5p-states (Fig. 5f). In the case of LDA modeling, the
donor level practically overlaps with the conduction band
bottom, whereas accounting the Hubbard correlation (U)
within the LDA approximation gives the defective level
by 0.47 eV away from the bottom of conduction band
(Fig. 5f). The approximately flat form of dispersion law
curve for the donor level indicates the strong localization
in the real space. Thus, it can be concluded from the
obtained calculation data that anion vacancy plays a role
of deep donor in tin disulfide.
Intrinsic point defects, being electrically charged,
significantly affect the electrical, photoelectrical and
photoluminescent properties of 2H-SnS2 crystals. Since
VSn vacancies create the acceptor levels in the band gap
and VS – donor levels, the crystals grow up the self-
compensated, and they are high-resistance by this reason;
the concentration of anion vacancies in 2H-SnS2 crystals
prevails over the concentration of cation vacancies, in
vast majority of cases they have the n-type conductivity.
The intensive impurity band with a maximum 875 nm
(1.42 eV), observed in the photoconductivity spectrum
(Fig. 6) behind the intrinsic absorption edge, testifies the
presence of high concentration of intrinsic point defects
in 2H-SnS2 crystals, which we grown by the sublimation
method. Besides, two more intrinsic high-energy bands
are observed in the photoconductivity spectra, which
nature is related with the band-to-band transitions. So,
the band with a maximum 2.25 eV (550 nm) is caused by
the indirect transitions Г4→U1 from the valence band to
the conduction band (Fig. 3) and the more high-energy
maximum 2.55 eV (485 nm) is caused by the direct
optical transitions Г4→Г1. These results of studying the
PC spectra of 2H-SnS2 crystals well agree with the
spectra given in Ref. [32, 33], which in addition to the
intrinsic bands also contain the intense impurity band
near 900 nm [32] (865 nm [33]).
4.3. Influence of Cl, I→S substitutional impurities on the
electronic structure of 2H-SnS2.
The main changes of energy spectrum associated with the
structural vacancies have been already considered above.
The Cl, I→S substitutional impurities are another type of
zero-dimensional defects in 2H-SnS2 crystals, grown
using CTR method. The concentrations of these
mentioned defects in the anion sublattice depending on
the growing conditions and the concentrations of
transporting agent in the growth ampoule can reach the
very significant values in real crystals (up to 1017 cm–3),
which can significantly change the physical properties
[7]. It requires to study the influence of these impurities
on the energy spectrum of an initial matrix.
SPQEO, 2018. V. 21, N 4. P. 345-359.
Bletskan D.I., Frolova V.V. Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the …
353
Fig. 7. Electronic structure, total and partial densities of states of 2H-SnS2 crystal with anion substitutional impurity Cl (a, b), I (c, d)
in 3×3×2 supercell model.
SPQEO, 2018. V. 21, N 4. P. 345-359.
Bletskan D.I., Frolova V.V. Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the …
354
Fig. 8. Electronic density distribution maps of defect-free 2H-SnS2 crystal (a, c) as well as 2H-SnS2 with cation (b), anion (d)
vacancies and Cl, I → S substitutional impuritites (e, f) in the cation (a, b) and anion (c–f) sublattice planes.
SPQEO, 2018. V. 21, N 4. P. 345-359.
Bletskan D.I., Frolova V.V. Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the …
355
Fig. 9. Electronic density distribution maps of defect-free 2H-SnS2 crystal (a) as well as 2H-SnS2 with VSn cation (b), VS anion (c)
vacancies and Cl, I → S substitutional impurities (d, e) in the (110) plane.
SPQEO, 2018. V. 21, N 4. P. 345-359.
Bletskan D.I., Frolova V.V. Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the …
356
In the vast majority of cases, the interaction of
impurity atoms with the matrix lattice leads to
modification of impurity atom potential and to formation
of deep levels in the energy spectrum of crystal. The
energy positions of impurity levels depend on how well
the impurity atoms entered into the electronic and
geometrical structure of the main lattice, i.e., it is
determined by the impurity atom locations in the lattice,
their dimensions and structures of electronic shells. The
same factors determine the limited solubility of
impurities in these crystals [34]. From the
crystallochemical point of view, with account of atom
sizes (the covalent radii are 1.40 Å for Sn, 1.03 Å for S,
1.07 Å for Cl, 1.345 Å for I [35]) and electronegativities,
chlorine and iodine should preferably occupy the sites in
the S sublattice. It strongly depends on the number of
valence electrons in the impurity and substituted atoms,
whether the substitutional impurity will behave as a
donor or as an acceptor. Halogen atoms (Cl, I) with seven
electrons in the external shell replacing sulfur with six
electrons exhibit a donor action; the doping of tin
disulfide by these impurities during crystal growth by
using the CTR method leads to formation of crystals with
a high concentration of electrons ∼1020 cm–3 [36]. The
losses of chlorine (iodine) during the post-growth
annealing do not change the initial n-type of
conductivity, since sulfur vacancies represent the donor
centers.
The hybridization degree of wave functions of
single impurity centers with the crystal valence states is
determined by their mutual energy position. Electronic
structure calculations in the Sn18S35Y1 supercell (Fig. 7)
show that substitution of sulfur atoms with the halogen
ones leads to appearance of deep energy levels in the
energy spectrum below the S 3s-band that corresponds to
the electronic s-states localized on the chlorine (iodine)
atoms as well as on the nearest tin atoms. The analysis of
spectra of local partial states of impurity atoms shows
that p-states of halogen atoms participate in formation of
middle and upper valence subbands. It testifies
appearance of chemical bonds between impurity and tin
atoms. It is possible to destiny on the nature of this bond
from the spatial distribution of electronic charge density
between tin and impurity atoms (Figs. 9d and 9e).
Besides, introduction of substitutional impurity
atoms (Y→S, Y = Cl, I) leads to appearance of local
donor-type levels in the band gap of 2H-SnS2 crystal near
the conduction band bottom (Fig. 7); their depth
increases in the Cl→I series, which qualitatively agree
with the values obtained from the temperature
dependence of electrical conductivity of crystals grown
using the CTR method (Cl, I transporter) [36]. In the
same impurity series, it is observed the systematic
decrease of static Mulliken charge value on the halogen
atom, which correlates with the electronegativity value
decrease during the transition from chlorine to iodine.
4.4. Electronic density distribution in 2H-SnS2 crystals
with intrinsic and impurity point defects
The mechanism of chemical bonding formation in the
defect-free and defective tin disulfide can be analyzed in
detail by consideration of electronic density contour
maps constructed on the basis of DFT calculations in the
supercell model. Electronic charge distribution between
different tin (sulfur) atoms belonging to the same cation
(anion) monolayer in a three-layer packet is presented by
the maps shown in Figs. 8a and 8c. Solid lines on contour
maps describe the surfaces of constant electronic density,
and the density of lines in the figures describes the
gradient of electronic density. The positions of S atoms
in the monolayer located above (the distance 1.49 Å or
1/4c) the tin monolayer plane are designated in Fig. 8a by
the points, and S atoms located below this plane are
designated by the circles. The nearest neighbors of S
atom are three Sn atoms (designated by the points in
Fig. 8c) which are at the equal distances. It can be seen
from Figs. 8a and 8c that there are no common lines of
ρ(r) level for the neighboring cations (anions) in tin
(sulfur) monoatomic layers, which indicates a weak
overlap of their wave functions.
Fig. 9 shows the electronic density maps inside the
three-layer packets, reflecting the chemical bonding of
tin atoms with the nearest neighbor sulfur atoms in
[SnS6] octahedra. Valence density distribution in the
anion-cation plane passing along Sn–S bonds in [SnS6]
octahedra (Fig. 9) reveals the presence of common
contour lines between cation (Sn) and anion (S) (it
indicates hybridization of Sn 5s-, 5p- and S 3s-, 3p-
states). At the same time, it is observed the polarization
of an electronic cloud in the direction from S atom to Sn
atom. The electronic density gradient is directed along
Sn–S bonds with primary density localization on sulfur
atoms due to their higher electronegativity. The strongly
pronounced deformation of ρ(r) contours from sulfur
atoms toward tin atoms along the Sn–S bond line as well
as the presence of common contours encompassing the
maxima of electron density over the cation-anion bonds
characterize the covalent component of the chemical
bond in three-layer packets. The presence of covalent
component in SnS2 is caused by hybridization of sulfur
3p-states and tin 5s-, 5p-states (Fig. 5). The charge of
covalent bond is responsible for the stability of [SnS6]
octahedral structural units in this compound.
SPQEO, 2018. V. 21, N 4. P. 345-359.
Bletskan D.I., Frolova V.V. Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the …
357
Ionic component of chemical bond is caused by the
partial transfer of charge density between tin and sulfur
atoms due to the difference of their electronegativities
(ENSn = 1.96, ENS = 2.58). It is reflected on the
electronic density maps by the greater density of valence
electrons near the localization places of sulfur atoms as
well as by the charge reduction on the covalent bond
between sulfur and tin atoms.
It can be seen from Fig. 9 that the electronic density
within the three-layer packets is much higher than near
their boundaries. The charge distribution in a single
three-layer packet forms an almost closed shell that
indicates a weak interpacket van der Waals interaction
caused by sulfur pz-states that partially enter into the
interlayer space. This spatial anisotropy of electronic
density and energy distribution of electronic sulfur 3p-
states is the reason for quasi-two-dimensionality of tin
disulfide crystals.
Thus, the interatomic interactions in the defect-free
SnS2 have the combined character and include covalent,
ionic and van der Waals components of chemical bond.
Since deviation from the stoichiometric
composition and the presence of impurity Cl, I atoms
affect the physical and chemical properties of layered
2H-SnS2 crystals, so it is important to ascertain the
chemical bond features in this compound with the
presence of anion and/or cation vacancies as well as
Cl, I → S substitutional impurity. Changes of total charge
density distribution caused by the anion (cation) removal
and formation of vacancies or introduction of foreign
substitutional atoms are also convenient to study with the
charge density maps.
The presence of tin (sulfur) vacancies in 2H-SnS2
layered crystals is illustrated by the ρ(r) charge density
distribution maps in tin (sulfur) atomic grids (Figs. 8b
and 8d). It can be seen that ρ(r) distribution in the
vacancy (VSn, VS) localization places has the delocalized
character. Charge density deformation in the defective
SnS2 is visible in Figs. 8, 9: there are no new Sn–Sn
(S–S) bonds passing through the vacancy center, and the
charge density contour deformations reflect its growth
along Sn–Sn bond line near the defect.
According to the form of total charge distribution, it
is possible to note that the electronic density perturbation
in the presence of (VSn, VS) cation (anion) vacancies is
experienced by the atoms at least of two its coordination
spheres. This effect is demonstrated by the isoelectronic
maps of non-stoichiometric SnS2 (Fig. 9). The vacancy
perturbing the acting mechanism is associated with the
changes of electronic states of sulfur atoms nearest to
VSn. It occurs the transfer of a part of S 3p-states to the
region of non-bonding states. As a result of the presence
of tin vacancies, it occurs the “emptying” of the parts of
bonding states, the Fermi level shifts down on the energy
scale, and the density of states near EF increases.
Introduction of chlorine and iodine atoms into
sulfur position of tin disulfide does not lead to the
changes in the general mechanism of interatomic
interactions. Contours ρ(r) near impurity Cl (I) atoms
testify the presence of covalent component of Sn–Cl(I)
bond (Fig. 9). The main role of covalent bond effects
between Cl(I) impurity and nearest tin atoms is played by
Cl(I) p–Sn p-interactions. The defining one is the
bonding between tin and introduction Cl, I elements,
having p–p-type.
It is observed the systematic decrease of static
Mulliken charge on the halogen atom (Cl – 7.350 e, I –
7.189 e) in the impurity Cl→I series, which correlates
with the decrease of electronegativity values during the
transition from chlorine to iodine (Cl – 3.16, I – 2.66).
When sulfur is replaced with chlorine (iodine), the length
of RSn–Cl(I) = 2.76 Å (2.96 Å) regularly increases in
comparison with RSn–S = 2.60 Å. It should be noted that
the difference in sizes of impurity and tin atoms leads to
the appearance of local elastic deformations in the
vicinity of crystalline lattice sites occupied by the
impurity atoms.
Estimates of population changes of separate bond
types (Sn–Sn, Sn–S) allow to confirm that the near
covalent Sn–S bonds of s, p–p-type remain as the main
interaction type in both complete (stoichiometric) and
defective compositions.
5. Conclusions
For the first time within the density functional theory, it
was study the influence of tin (VSn) and sulfur (VS) lattice
vacancies as well as substitutional impurities (Y→S, Y =
Cl, I) on the electronic spectrum and chemical bonding of
2H-SnS2. Quantum-chemical calculations have shown
that the presence of vacancies in tin disulfide crystal
structure leads to changes of its electronic structure and
formation of defective states in the band gap. Thus, in the
case of VSn cation vacancy it occurs the acceptor level in
the band gap separated from the valence band top on
0.3 eV; in the case of VS sulfur vacancy it occurs the
donor level separated from the conduction band bottom
on 0.47 eV. Introduction of chlorine and iodine atoms
into tin disulfide does not lead to changes in the general
mechanism of interatomic interactions in this compound.
Bonding between tin and introduction elements (Cl, I)
remains crucial and are s, p–p-type. Bonding between
non-metallic components (S–Cl, S–I) is absent.
SPQEO, 2018. V. 21, N 4. P. 345-359.
Bletskan D.I., Frolova V.V. Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the …
358
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Authors and CV
Dmytro I. Bletskan. Doctor in
Physics and Mathematics Sciences,
Professor, professor of the department
physics of semiconductors at
Uzhhorod National University,
Ukraine. Authored over 260 scientific
publications, 86 patents, 2 textbooks,
2 monographs. The area of his
scientific interests – technology and physics of highly
anisotropic layered crystals, chalcogenide glassy
semiconductors and superionics.
Uzhhorod National University
Viola V. Frolova. Researcher of the
Institute for Solid State Physics and
Chemistry (INPCSS) at Uzhhorod
National University, Ukraine.
Authored 30 scientific publications
and 2 patents. The area of scientific
interests is electronic structure and
optical properties of layered crystals.
Uzhhorod National University
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| id | nasplib_isofts_kiev_ua-123456789-215327 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-23T18:47:46Z |
| publishDate | 2018 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Bletskan, D.I. Frolova, V.V. 2026-03-12T08:55:56Z 2018 Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the electronic structure of 2H-Sn₂ / D.I. Bletskan, V.V. Frolova // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2018. — Т. 21, № 4. — С. 345-359. — Бібліогр.: 36 назв. — англ. 1560-8034 PACS: 61.72.J-, 61.72.-y, 71.38.-k, 72.40.+w https://nasplib.isofts.kiev.ua/handle/123456789/215327 https://doi.org/10.15407/spqeo21.04.345 It was performed the systematic investigation of the chemical modification regularities of electronic structure at the composition changes of “ideal” 2H-SnS₂ crystal was performed by using the self-consistent density functional theory method in the supercell model. The phases obtained during doping the sulfur sublattice by substitutional impurity Y→S (Y = Cl, I), as well as during changing tin disulfide structure due to the appearance of atomic vacancies in cation and anion sublattices (non-stoichiometry effects), were analyzed. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Semiconductor physics Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the electronic structure of 2H-Sn₂ Article published earlier |
| spellingShingle | Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the electronic structure of 2H-Sn₂ Bletskan, D.I. Frolova, V.V. Semiconductor physics |
| title | Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the electronic structure of 2H-Sn₂ |
| title_full | Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the electronic structure of 2H-Sn₂ |
| title_fullStr | Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the electronic structure of 2H-Sn₂ |
| title_full_unstemmed | Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the electronic structure of 2H-Sn₂ |
| title_short | Influence of intrinsic point defects and substitutional impurities (Cl, I → S) on the electronic structure of 2H-Sn₂ |
| title_sort | influence of intrinsic point defects and substitutional impurities (cl, i → s) on the electronic structure of 2h-sn₂ |
| topic | Semiconductor physics |
| topic_facet | Semiconductor physics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/215327 |
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