Electronic structure of 2H-SnSe₂: ab initio modeling and comparison with experiment
Energy band structure, total and local partial densities of states, spatial distribution of electronic density of 2H-SnSe₂ have been calculated using the densitym functional theory method in LDA and LDA+U approximations both with and without consideration of spin-orbit interaction. From the band str...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2016
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| Цитувати: | Electronic structure of 2H-SnSe₂: ab initio modeling and comparison with experiment / D.I. Bletskan, K.E. Glukhov, V.V. Frolova // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2016. — Т. 19, № 1. — С. 98-108. — Бібліогр.: 42 назв. — англ. |
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irk-123456789-1215332017-06-15T03:04:58Z Electronic structure of 2H-SnSe₂: ab initio modeling and comparison with experiment Bletskan, D.I. Glukhov, K.E. Frolova, V.V. Energy band structure, total and local partial densities of states, spatial distribution of electronic density of 2H-SnSe₂ have been calculated using the densitym functional theory method in LDA and LDA+U approximations both with and without consideration of spin-orbit interaction. From the band structure calculation results, it follows that 2H-SnSe₂ is an indirect-gap semiconductor. The calculated band structure is compared with the dispersion curves E(k) plotted using the known measurement results of angular dependent photoemission spectra. It has been observed the good agreement between theoretical and experimental dispersion curves. The calculated total and local partial densities of states have been compared with the known experimental data obtained using XPS, UPS, ARXPS, BIS methods. 2016 Article Electronic structure of 2H-SnSe₂: ab initio modeling and comparison with experiment / D.I. Bletskan, K.E. Glukhov, V.V. Frolova // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2016. — Т. 19, № 1. — С. 98-108. — Бібліогр.: 42 назв. — англ. 1560-8034 DOI: 10.15407/spqeo19.01.098 http://dspace.nbuv.gov.ua/handle/123456789/121533 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Energy band structure, total and local partial densities of states, spatial distribution of electronic density of 2H-SnSe₂ have been calculated using the densitym functional theory method in LDA and LDA+U approximations both with and without consideration of spin-orbit interaction. From the band structure calculation results, it follows that 2H-SnSe₂ is an indirect-gap semiconductor. The calculated band structure is compared with the dispersion curves E(k) plotted using the known measurement results of angular dependent photoemission spectra. It has been observed the good agreement between theoretical and experimental dispersion curves. The calculated total and local partial densities of states have been compared with the known experimental data obtained using XPS, UPS, ARXPS, BIS methods. |
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Bletskan, D.I. Glukhov, K.E. Frolova, V.V. |
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Bletskan, D.I. Glukhov, K.E. Frolova, V.V. Electronic structure of 2H-SnSe₂: ab initio modeling and comparison with experiment Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Bletskan, D.I. Glukhov, K.E. Frolova, V.V. |
| author_sort |
Bletskan, D.I. |
| title |
Electronic structure of 2H-SnSe₂: ab initio modeling and comparison with experiment |
| title_short |
Electronic structure of 2H-SnSe₂: ab initio modeling and comparison with experiment |
| title_full |
Electronic structure of 2H-SnSe₂: ab initio modeling and comparison with experiment |
| title_fullStr |
Electronic structure of 2H-SnSe₂: ab initio modeling and comparison with experiment |
| title_full_unstemmed |
Electronic structure of 2H-SnSe₂: ab initio modeling and comparison with experiment |
| title_sort |
electronic structure of 2h-snse₂: ab initio modeling and comparison with experiment |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2016 |
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http://dspace.nbuv.gov.ua/handle/123456789/121533 |
| citation_txt |
Electronic structure of 2H-SnSe₂: ab initio modeling and comparison with experiment / D.I. Bletskan, K.E. Glukhov, V.V. Frolova // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2016. — Т. 19, № 1. — С. 98-108. — Бібліогр.: 42 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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2025-07-08T20:03:29Z |
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| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 1. P. 98-108.
doi: 10.15407/spqeo19.01.098
© 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
98
PACS 71.15.-m, 71.20.-b
Electronic structure of 2H-SnSe2: ab initio modeling and comparison
with experiment
D.I. Bletskan, K.E. Glukhov, V.V. Frolova
Uzhgorod National University,
54, Voloshin str., 88000 Uzhgorod, Ukraine
E-mail: crystal_lab457@yahoo.com
Abstract. Energy band structure, total and local partial densities of states, spatial
distribution of electronic density of 2H-SnSe2 have been calculated using the density
functional theory method in LDA and LDA+U approximations both with and without
consideration of spin-orbit interaction. From the band structure calculation results, it
follows that 2H-SnSe2 is an indirect-gap semiconductor. The calculated band structure is
compared with the dispersion curves E(k) plotted using the known measurement results
of angular dependent photoemission spectra. It has been observed the good agreement
between theoretical and experimental dispersion curves. The calculated total and local
partial densities of states have been compared with the known experimental data obtained
using XPS, UPS, ARXPS, BIS methods.
Keywords: tin diselenide, electronic structure, density of states.
Manuscript received 18.11.15; revised version received 10.02.16; accepted for
publication 16.03.16; published online 08.04.16.
1. Introduction
Tin diselenide (SnSe2) belongs to the family of layered
semiconductors with the general chemical formula of
MX2 (M – metal, X – chalcogen) [1–3]. Tin diselenide
with a layered structure possesses unique physical and
chemical properties that offer new opportunities for its
practical application as the electrode material for
lithium-ion batteries [4, 5], the memory elements on the
phase change effect [6], the electric keys [7], the field-
effect transistors [8], the SnS2-SnSe2-SnS2 hetero-
structures created by van der Waals epitaxy [9]. Physical
principles for the manufacture and development of
devices and equipment based on tin diselenide are
related with the features of its crystal structure,
electronic energy structure, and the selection rules for
optical transitions. All these reasons stimulate further
studying its physical properties, which is impossible
without the detailed study of its electronic structure.
There is a number of theoretical works devoted to
studying the electronic structure of the simplest 2H-
polytype SnSe2 using different calculation methods of:
the empirical pseudopotential [10-14], a priori
pseudopotential [15], parameterized and semi-empirical
tight-binding method [16, 17]. Table 1 summarizes the
main characteristics of 2H-SnSe2 electronic spectrum
obtained using the specified calculation methods.
Despite acceptable qualitative reproducability of the
main features of electronic structure of the 2H-SnSe2
crystal in the most calculations, there are differences in
the quantitative characteristics of electronic structure:
the total width of the valence bands, values of the direct
and indirect band gaps, sequence and topology of some
energy bands, details of density of states and, most
important, places of localization of the valence band top
and conduction band bottom, and, consequently,
transitions forming direct and indirect gaps. Thus, the
results of different papers are hard to compare with each
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 1. P. 98-108.
doi: 10.15407/spqeo19.01.098
© 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
99
Table 1. The main features and parameters of the 2H-SnSe2 energy spectrum obtained by different calculation methods.
Indirect optical
transitions
Direct optical
transitions Calculation method
Egi, eV Transition
type Egd, eV Transition
type
References
The empirical pseudopotential method 0.81 11 L′→Γ′ 1.78 21 MM ′→′ [10]
The local empirical pseudopotential method 0.91 11 L→Γ′ 1.75 12 MM → [11]
The local empirical pseudopotential method 1.10 12 U→Γ−
1.70 ++ → 12 MM [13]
The a priori pseudopotential method 1.40 14 M→Γ 1.10 14 Γ→Γ [15]
The tight binding method 1.44 +− →Γ 12 L 1.63 +− Γ→Γ 12 [16]
The semi-empirical tight binding method 1.0 ++ Γ→ 12M 1.6 ++ → 12 MM [17]
The density functional method DFT-LDA 0.55 14 U→Γ 0.94 14 Γ→Γ Our calculation
The density functional method DFT-LDA+U 0.99 14 U→Γ 1.26 14 Γ→Γ Our calculation
other due to the differences in the used calculation
methods and because of introducing the empirical
parameters. Besides, the vast majority of available 2H-
SnSe2 band structure calculations are performed without
any consideration of the relativistic effects, and the
group-theoretical analysis results presented in Refs. [10,
11] contain a number of mistakes, which was indicated
by other authors [13]. The significant differences also
observed in the experimental energy values of direct and
indirect band gaps [18-20].
In this paper, the energy band structure as well as
total and local partial densities of states of the 2H-SnSe2
crystal were calculated using the density functional
theory (DFT) method in the local density approximation
(LDA) and in the approximation supplemented by taking
into account Coulomb interaction (LDA+U). The
character of analyzed chemical bonding is based on
calculations of the spatial distribution of electronic
charge density.
2. Crystal structure
2H-polytype SnSe2 is characterized by the structure of
brucite type based on the three-layer –Se–Sn–Se–
packets (“sandwiches”) that are parallel to the (001)
plane. Each three-layer packet consists of a tin atoms
monolayer enclosed between two close-packed
monolayers of selenium atoms (Fig. 1a). The distance
between three-layer packets (3.08 Å) doubly exceeds the
distance between atomic monolayers within one
“sandwich” (1.53 Å). In the 2H-SnSe2 crystal structure,
tin atoms are centered in the ideal octahedrons with the
vertices on the Se atoms (Fig. 1b). The [SnSe6]
octahedra are related with each other by common edges
and form the three-layer –Se–Sn–Se– packets. Chemical
bonding within three-layer packets has the ion-covalent
character, while chemical bonding between three-layer
packets is mainly provided by van-der-Waals forces
causing large anisotropy of physical properties.
Fig. 1. Crystal structure (a) and the structure projection on XY plane with the highlighted [SnSe6] octahedra (b) of 2H-SnSe2.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 1. P. 98-108.
doi: 10.15407/spqeo19.01.098
© 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
100
In the 2H-SnSe2 structure, an order of the layers
stacking is [AγB, AγB], where γ denotes the tin atom
layer, while A and B – selenium layers. The symmetry
of the 2H-polytype crystal lattice is characterized by
3
3dD ( 13mP ) space group, and the crystalline class
corresponds to the D3d point group. The crystal lattice
parameters are as follows: a = b = 3.811 Å, c = 6.141 Å,
γ = 120° [3].
The unit cell of 2H-polytype contains three atoms
belonging to one three-layer packet only. If the usual
coordinate system is used, the unit cell is described by
two vectors a1 and a2 in the XY plane and makes the
angle 120° between them, as well as c vector along Z
direction, and contains the Sn atom located in Wyckoff
position a(0, 0, 0) and two selenium atoms located in
Wyckoff position d(1/3, 2/3, z) with coordinates of (1/3,
2/3, u), (2/3, 1/3, w) where u = 0.24920, w = 0.75080.
The symmetry of the specified positions is described by
the local groups m3 and 3m, respectively.
3. Calculation method
In this paper, band structure calculations are performed
within DFT using the basis sets of the plane waves (PW)
and the linear combination of atomic orbitals (LCAO),
too; norm-conserving pseudopotentials were used for the
numerical realization of this computational technique by
means of the ABINIT and SIESTA packages [21-24].
The electronic structure calculations were carried out in
the local approximation of the Kohn–Hohenberg–Sham
density functional [25, 26] using the exchange-
correlation potential in the approximation of Ref. [27].
In these calculations, the following electronic configu-
rations were used: for Sn atoms – [Kr] 5s25p2 and for Se
atoms – [Ar] 4s24p4. The influence of core electrons was
considered using the pseudopotentials in parametrization
of Ref. [28].
Calculations of the density of electronic states were
performed using the modified tetrahedra method [29] for
integration by reciprocal space with the 8×8×5 grid for
160 special k-points in the irreducible part of the
Brillouin zone. The basis for the 2H-SnSe2 energy states
calculation counts about 2600 plane waves and has been
limited by the maximum kinetic energy Ecut = 20 Ha.
For a more precise description of the electronic
spectrum, it is necessary to consider Coulomb
interaction, which can be achieved using the methods
based on electronic density functional theory, but taking
into account interatomic Coulomb and exchange
interactions in the framework of the so-called LDA+U
approximation [30, 31]. In the calculations, there were
used the values of Coulomb interaction U = 3 eV and
exchange interaction J = 0.3 eV parameters.
All calculations were performed using relaxation of
cell constants and atomic positions with the set of
convergence criteria installed to the maximum residual
stress (tension) 0.1 GPa for each component of the stress
tensor and the maximum component of residual force
0.01 eV/Å. The calculation of optimized structure was
performed within restrictions of fixed symmetry group.
4. Results and discussion
4.1. Band structure and density of electronic
states. Energy bands of the 2H-SnSe2 crystal at all high-
symmetry points and along all corresponding directions
of the Brillouin zone of the hexagonal lattice (Fig. 2)
calculated by the density functional theory method
without account of the spin-orbit interaction in LDA and
LDA+U approximations are shown in Figs. 3a and 3b,
respectively. The energy scale origin is aligned with the
highest occupied state.
The minimum indirect band gap between the empty
and occupied states calculated in the LDA
approximation for 2H-polytype SnSe2 with 16 valence
electrons per unit cell has appeared equal Еgi = 0.55 eV
(transition Γ4→U1). As it follows from the analysis of
experimental spectra of the fundamental absorption of
the SnSe2 single crystals grown by a gas-phase method,
the minimum gap is formed by the indirect forbidden
transitions with the energy gap Egi = 0.98 eV [18],
1.03 eV [19], 0.97 eV [20]. It is known that an ab initio
calculations in the local density approximation in the
framework of the density functional theory describe
precisely the dispersion of valence bands, but always
underestimate the band gap between the valence and the
conduction bands. We performed the band structure
calculation of SnSe2 in the LDA+U approximation
(Fig. 3b) for the agreement between the calculated and
experimental data. The obtained value of the indirect gap
Egi = 0.99 eV in the LDA+U approximation is close to
the experimental one.
Fig. 2. Brillouin zone of hexagonal lattice. kx, ky, kz –
the directions of Cartesian axes in the reciprocal space.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 1. P. 98-108.
doi: 10.15407/spqeo19.01.098
© 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
101
Fig. 3. Electronic structure of 2H-SnSe2 calculated without taking into account the spin-orbit interaction in LDA (a) and LDA+U
(b) approximations.
As for the direct transitions, there are significant
differences in experimental Egd values observed by
different author groups. So, Evans and Hazelwood [19]
indicate the existence of the indirect forbidden
transitions with the energy 1.3 eV and the allowed direct
transitions with the energy 1.97 eV. Two other author
groups [18, 20] give the values for the allowed direct
gap 2.1 eV [18] and for the forbidden direct transitions
1.62 eV [20]. From the energy band calculations in the
LDA+U approximation, it follows that the closest to
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 1. P. 98-108.
doi: 10.15407/spqeo19.01.098
© 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
102
experimental gaps are the calculated direct forbidden
gdE ′ = 1.26 eV (transition Γ4→Γ1) and direct allowed
gdE ′′ = 2.02 eV (transition Γ6→Γ1) transitions.
As shown by the electronic structure calculation
taking into account of the spin-orbit interaction for the
2H-SnSe2 crystal (Fig. 4) leads to the splitting of double-
degenerated states Γ6(∆so ≈ 0.08 eV), Γ5(∆so ≈ 0.23 eV),
А6(∆so ≈ 0.3 eV), А5(∆so ≈ 0.33 eV), H3(∆so ≈ 0.1 eV),
K3(∆so ≈ 0.05 eV), to the removal of degeneracy along
some directions in the Brillouin zone, and it does not
essentially affects the band gap value that is formed by
indirect transition from the point Γ (symmetry Γ11) into
the point along the direction U (symmetry {U3⊕U4}),
i.e., it does not change the localization places of the
valence band maximum and the conduction band
minimum.
The layered character of the crystal is reflected in
its band spectrum structure. Considerable anisotropy of
dispersion law for insulated bands along and across the
three-layer packets is observed. The weak dispersion
E(k) is observed along c axis of the crystal, i.e., along
the direction ΓΔA that is perpendicular to the
monolayers formed by Sn and Se atoms; it testifies to the
layered nature of compound as well as to the relatively
weak influence of interaction between the three-layer
packets on the electronic structure. A significant disper-
sion of the bands along the directions parallel to the
three-layer packets (Sn and Se monolayers) indicates
strong interaction in the structural units [SnSe6] that
form the sandwiches. These features of 2H-SnSe2 band
structure allow speaking about the two-dimensional
character of energy bands.
The information about contributions of atomic
orbitals into 2H-SnSe2 crystalline states can be obtained
from the calculations of total and local partial densities
of states. Fig. 5 shows the spectra of total N(E) and local
partial nat(E) densities of electronic states (DOS)
obtained from the band calculation. Selenium 4s- and
4p-states make the main contribution to the valence band
of this polytype, they are not mixed in the electronic
spectrum and are separated by the forbidden energy
interval. From the analysis of total and local partial
densities of states for the 2H-SnSe2 crystal, it follows
that the most low-energy bunch of two valence branches
located in the range from –14.14 eV to –11.87 eV below
the latter occupied state is mainly created by selenium
4s-orbitals with an insignificant impurity of tin 5s- and
5p-orbitals. The middle divided valence subband (from
–7.69 to –5.35 eV) separated from the lowest valence
subband by the energy interval 4.17 eV and formed by
hybridized Sn5s- and Se4p-states, which are responsible
for the covalent component of chemical bonding in the
[SnSe6] octahedra.
Fig. 4. Electronic structure of 2H-SnSe2 calculated with account of the spin-orbit interaction in LDA approximation.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 1. P. 98-108.
doi: 10.15407/spqeo19.01.098
© 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
103
Fig. 5. Total and local partial densities of electronic states of 2H-SnSe2 calculated in LDA (a) and LDA+U (b) approximations.
The upper valence subband (from –5.05 to 0 eV) is
the most difficult, and it has the mixed character
involving Se 4p-states and Sn 5p-states. It is virtually
separated into two parts by composition: the lower part
(from –5.05 to –2.0 eV) mainly formed by Se 4p- and Sn
5p-orbitals, which are responsible for the p-p covalent
bonds Sn–Se and the upper part (from –2.0 to 0 eV)
formed mainly by selenium 4p-orbitals, providing the
weak bonds between the neighbor three-layer packets.
The dominant contribution to formation of the upper part
of the valence band is given by selenium 4p-orbitals
with a negligible impurity of the virtual d-states of tin.
The lower part of upper valence subband is formed by
the bonding Se4p–Sn5p-orbitals. The characteristic
feature of the 2H-SnSe2 electronic structure is
availability of forbidden interval in the conduction band,
which separates the isolated low-energy unoccupied
subband from the continuous spectrum of unbound
states. The lowest unoccupied subband of 2H-SnSe2 is
separated from the other unoccupied subbands by the
forbidden interval 0.41 eV. Hybridization of tin 5s-states
with selenium 4p-orbitals is a characteristic feature of
the bottom conduction band. Sn 5s-states are localized at
the bottom of the conduction band, and further the Sn
5p-states are dominating with the energy increasing. The
performed above analysis of the nature of crystalline
orbitals in LDA approximation (Fig. 5a) remains valid
for the calculation results in LDA+U approximation
(Fig. 5b).
4.2. Comparison of the theory and experiment.
Among the number of experimental methods studying
the electronic structure of layered crystals, there are the
mutually complementary spectroscopic methods such as
ultraviolet (UPS) and X-ray (XPS) photoelectron
spectroscopy, angle-resolved ultraviolet photoelectron
spectroscopy (ARPES), angle-resolved X-ray photo-
electron spectroscopy (ARXPS) and bremsstrahlung
isochromatic spectroscopy (BIS). The surface state of
studied crystals is very important for the photoemission
studies because the thickness of an analyzed surface
layer is very small and amounts to tens angstroms [32].
At such low values of electrons escape depth, it is
necessary to prepare ultrapure surface for obtaining
reliable information from measurements of these
photoelectron spectra. The special studies performed
using the methods of diffraction of slow electrons and
Auger spectroscopy showed that basic (001) surfaces of
SnSe2 layered crystals obtained by the cleavage in
ultrahigh vacuum possessed the exceptional inertness in
relation to the absorption of gasses [33].
4.2.1. Comparison of the calculated total density of
states with X-ray and ultraviolet photoelectron spectra.
The electronic states of valence band can be
experimentally studied using X-ray and ultraviolet
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2016. V. 19, N 1. P. 98-108.
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© 2016, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
104
photoelectron spectroscopies. Fig. 6 shows UPS [34, 35]
and XPS [36, 37] spectra of 2H-SnSe2 crystal combined
in a single energy scale with the calculated spectra of the
total density of states N(E) in LDA and LDA+U
approximations. The valence band top is taken as the
zero energy position. The shape of overall valence band
spectra depends on contribution of electronic states of
different orbital symmetry as well as on their photo-
ionization cross-section (at a given excitation energy) for
atoms of chemical elements belonging to the compound.
The photoionization cross-section of electron excitation
from the valence band into the vacuum depends on the
symmetry of electron wave functions and on the energy
of exciting quantum [38]. It is this fact, i.e., the
dependence of photoionization cross-section of electrons
at the emission into vacuum on the energy of the
exciting quantum is the main reason that the shape of
valence band photoelectron spectra depends on the
excitation energy (compare XPS and UPS curves). Since
the photoionization cross-section of selenium
4p-electrons exceeds the photoionization cross-section
of tin p- and d-states, the main part of photoelectron
spectra in the energy range from –5 to 0 eV is formed by
selenium 4p-states. It can be conditionally separated by
three subbands A, B and C within this energy range
(Fig. 6), which genetic origin is clearly visible when
studying the polarized XPS spectra (Fig. 8).
4.2.2. Comparison of the calculated and
experimental band structures. We have discussed above
the photoelectron XPS and UPS spectra, in which only
the energy of emitted electrons was fixed. These
characteristics make it possible to define only some
average characteristics of the occupied bands. In the case
of angle-resolved photoemission spectroscopy (ARPES)
[32], there performed are the measurements of not only
the kinetic energy of photoelectron but also its
distribution direction that is defined by polar and
azimuthal angles, which allows finding out the complete
spectrum of elementary excitations, i.e., the magnitude
E(k). Really, under these conditions the experimenter
automatically establishes not only the magnitude of the
impulse of emitted photoelectron Ki, since
Ekin = ħ2K2/2m, but also its direction. Photoelectron
emission with angular resolution allows finding the
dispersion law E(k) by tracing the energy of spectral
peaks depending on the components of the electron wave
vector parallel to the crystal (001) surface of k||.
Therefore, the results obtained using the method of
ultraviolet photoelectron spectroscopy with angular
resolution are quite enough for comparison with
theoretically calculated electronic spectrum. This is
especially justified in the case of 2H-SnSe2 layered
crystals that have weak dispersion in one of the
directions.
For the first time, the angular dependence of
electron photoemission spectra from the (001) surface of
SnSe2 single crystals with the exciting photon energy
21.2 eV (He I) was studied in Ref. [36]. However, usage
of synchrotron radiation (high intensity, total polariza-
tion, continuous spectrum) for the excitation of electrons
allows to more accurately determine the electron level
positions, which is very important for comparison of
experimental results with the band structure calculations.
The angular dependence of electron photoemission
spectra of 2H-SnSe2 layered crystals at excitation by
synchrotron radiation was studied in two modes [40]:
1) the changing of polar angle within the range from
θ = –10° up to θ = 67.5° relatively to the normal of (001)
surface at the constant energy of incident photons
hν = 21 eV; 2) the changing of an incident photon
energy within the range from hν = 19 eV up to hν =
24 eV at the constant polar angle θ = 45°.
Fig. 6. 1, 2 – theoretical calculated smoothed total density of
states of 2H-SnSe2 in LDA+U and LDA; 3 – HeI UPS
hν = 21.2 eV [34]; 4 – HeII UPS hν = 23.09 eV [35]; 5 – XPS
hν = 1486 eV [36]; 6 – XPS hν = 1486 eV [37]; 7 – BIS
hν = 1486.6 eV [39].
Fig. 7. Experimental (dashed lines) [40] and calculated
LDA+U (solid lines) dispersion curves E(k||) of 2H-SnSe2
along the direction Γ–M–Γ of Brillouin zone.
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Fig. 8. XPS spectra (θ = 22°(1), 82°(2)) [41] and the calculated
partial density of selenium px,y- (3), pz-states (4) of 2H-SnSe2.
The obtained data of peak positions in the spectrum
as a function of the polar angle θ was used by authors of
the work [40] for the construction of dispersion curves
of six upper valence bands of 2H-SnSe2 in the direction
Γ–M–Γ of Brillouin zone, which we compared with the
calculation results of E(k) by density functional method
(Fig. 7). The radiation energy 21 eV was insufficient to
examine the two lowest valence branches located at
12…15 eV below the valence band top. Usage of
polarized synchrotron excitation radiation showed the
weak dispersion of peaks in 2H-SnSe2 energy
distribution curves of normal emission relatively to the
changes in the photon energy, which indicates weak
interlayer interaction in tin diselenide.
In contrast to ARPES with the low excitation
energy (hν = 21 eV) where the angular dependence of
photoelectron spectra is mainly associated with the
dispersion of energy bands, the angle-resolved X-ray
photoelectron spectroscopy (ARXPS) method with the
excitation photon energy hν =1500 eV allows to directly
study spatial symmetry of the structure of valence bands
[41]. The photoelectron spectra of valence states of 2H-
SnSe2 layered crystals measured at the excitation by
X-ray radiation with the photon energy hν = 1500 eV for
two values of the polar angles θ = 22° and 82° taken
from Ref. [41] are combined in Fig. 8 in a single energy
scale with our calculated local partial selenium px,y- and
pz-states of tin diselenide. As seen from this figure, the
agreement between the calculated and experimental
results is satisfactory for all bands except that the bands
of experimental spectrum are more broadened. There
observed are six distinct maxima in XPS spectrum in the
energy range from 0 to 16 eV below the valence band
top (Fig. 8, curves 1, 2). The intensive wide peak D at
the valence band bottom is mainly caused by selenium
4s-electrons, while at the valence band top (A, B and B′
maxima), where selenium and tin p-electrons are
localized, contribution of the former ones into the
photoelectron spectrum is dominating. The intensities of
separated bands in the spectra are redistributed with
changing the electron emission angle; it allows to
analyze the energy distribution of Se 4p-states with the
different spatial symmetry. So, the density of Se 4p-
states reaches the maximum value (peak A) within the
energy range from 0 to –2 eV, the density of pz-states are
higher than that of px,y-states, and the valence band top
of 2H-SnSe2 in the Γ point (symmetry Γ4) is formed by
pz-states. The px,y-orbitals lie in the basal plane and they
are responsible for formation of peaks B′ and C′.
4.2.3. Comparison of the calculated density of
states with BIS spectrum. Among X-ray spectroscopic
methods, the bremsstrahlung isochromatic spectroscopy
method [39] is very informative for studying the
conduction band structure of tin diselenide. The
bremsstrahlung isochromatic spectrum measured on the
surface (001) cleaved in ultrahigh vacuum at the energy
quanta 1486.6 eV is shown in Fig. 6 (curve 7). The BIS
spectra contain four maxima which nature can be
identified by comparison with the calculated total and
partial densities of states of conduction band (Fig. 5). So,
the peak a is mainly formed by unoccupied selenium
p-states with an admixture of tin s- and p-states; free tin
p-states and selenium p- and d-orbitals make the main
contribution into the peak b; the nature of the following
two peaks c and d is similar, and it is formed by identical
contribution of anion and cation p-, d-states, however,
the total selenium contribution about twice exceeds the
tin contribution.
4.3. Spatial distribution of electronic density.
The properties of material are determined by the spatial
and energy electronic structures. At the same time, the
electronic structure of valence electrons represents the
particular interest, and it characteristically changes at
occurrence of the chemical bond between atoms. It is
necessary to know the overall picture of spatial
distribution of electronic density for the exact descript-
tion of chemical bonding in 2H-SnSe2 layered crystals
[42]. We performed the self-consistent calculations of
2H-SnSe2 electronic density ρ(r) including hybridization
effects between all atoms in four planes: (110) and
( 011 ) located perpendicular to the three-layer packets;
(001) through tin and selenium monolayers (Fig. 9). The
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.
It is seen from Figs. 9a, 9b that the electronic den-
sity is much higher within the three-layer packet (sand-
wich) than at its border, which reflects the chemical
bonding of tin atoms with the nearest neighbors in
[SnSe6] octahedron. The analysis of total electronic
density distribution maps shows that the electronic den-
sity distribution in 2H-SnSe2 layered crystal is aniso-
tropic due to the difference of the nature of interatomic
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106
interactions having the combined character and includes
covalent, ionic and van-der-Waals components. As can
be seen from Fig. 9a, the primary charge is concentrated
on the anions (Se) and the minimum charge – in the
interlayer van-der-Waals space. At the same time, it is
observed the polarization of an electronic cloud in the
direction from Se atom to Sn atom. The covalent
component of chemical bond in the three-layer packets is
reflected by the strongly pronounced deformation of ρ(r)
contours from selenium atoms toward tin atoms along
the Sn–Se bond line as well as by the presence of overall
contours that cover the electronic density maxima on the
cation-anion bonds. The presence of covalent component
in 2H-SnSe2 is caused by hybridization of selenium
4p-states and tin 5s-, 5p-states (Fig. 5). Exactly, the
charge of covalent bond is responsible for stability of
[SnSe6] octahedral structural formations in this polytype.
The ionic component is determined by the partial
transfer of charge density from tin atoms to more
electronegative selenium atoms. It reflects on the
electronic density maps by the higher density of valence
electrons near the localization places of selenium atoms
and by the charge reduction in the covalent bond
between selenium and tin atoms. The analysis of
calculations also shows that the proportion of covalent
interatomic bond in the three-layer packets is greater
than the ionic because contribution of the s-partial
density is less than p-component.
Fig. 9. Maps of total electronic density distribution for 2H-SnSe2 crystal in (110) (a), ( 011 ) (b), (001) of cation (c) (points and
circles mark the locations of Sе ions being in two different anion monolayers of a three-layer packet) and anion (d) planes.
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107
The maps in Figs. 9c, 9d show the electron charge
distribution between different selenium (tin) atoms
belonging to one anion (cation) monolayer in the three-
layer packet. It is seen that no overall lines for the ρ(r)
level for neighboring anions (cations) in monoatomic
layers of selenium (tin) are observed, which testifies to
the weak overlapping of their wave functions. The
charge distribution in one three-layer packet forms the
almost closed shell that indicates weak interpacket inter-
action caused by selenium pz-states that partially enter
into the interlayer space. From the density distribution
contours of valence electrons presented in Fig. 9, aniso-
tropy of electrical, optical and mechanical properties of
tin diselenide layered crystals becomes understandable.
5. Conclusions
The detailed study of the 2H-polytype SnSe2 electronic
structure has been performed including calculations of
the band structure with and without account of spin-orbit
interaction, total and local partial densities of states as
well as spatial distribution of electronic density. The
calculated 2H-SnSe2 band structure has been compared
with the known dispersion curves E(k) constructed by
the measurement results of angle-dependent photo-
emission spectra. A good agreement between the
theoretical and experimental dispersion curves is
observed, especially in the range of the top subbands of
the valence band. The total density of states N(E)
calculated in the whole Brillouin zone for the valence
band is compared with the known experimental X-ray
and ultraviolet photoelectron spectra as well as for the
conduction band – with the bremsstrahlung isochromatic
spectra. It has been shown that the band positions and its
nature in 2H-SnSe2 electronic energy spectrum in the
LDA+U approximation agree well with the data of
photoelectron spectroscopy, which confirms the
correctness of the chosen exchange and correlation
parameters.
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