Electronic structure of Ag₈GeS₆
For the first time, the energy band structure, total and partial densities of states of Ag₈GeS₆ crystal were calculated using the ab initio density functional method in LDA and LDA+U approximations. Argyrodite is a direct-gap semiconductor with the calculated band gap width Eᵍᵈ = 1.46 eV in the LDA+...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2017
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| Цитувати: | Electronic structure of Ag₈GeS₆ / D.I. Bletskan, I.P. Studenyak, V.V. Vakulchak, A.V. Lukach // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 1. — С. 19-25. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860272229178146816 |
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| author | Bletskan, D.I. Studenyak, I.P. Vakulchak, V.V. Lukach, A.V. |
| author_facet | Bletskan, D.I. Studenyak, I.P. Vakulchak, V.V. Lukach, A.V. |
| citation_txt | Electronic structure of Ag₈GeS₆ / D.I. Bletskan, I.P. Studenyak, V.V. Vakulchak, A.V. Lukach // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 1. — С. 19-25. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | For the first time, the energy band structure, total and partial densities of states of Ag₈GeS₆ crystal were calculated using the ab initio density functional method in LDA and LDA+U approximations. Argyrodite is a direct-gap semiconductor with the calculated band gap width Eᵍᵈ = 1.46 eV in the LDA+U approximation. The valence band of argyrodite contains four energy-separated groups of occupied subzones. The unique feature of the electron-energy structure of Ag₈GeS₆ crystal is the energy overlapping between the occupied d-states of Ag atoms and the delocalized valence p-states of S atoms in relatively close proximity to the valence band top.
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| first_indexed | 2026-03-21T11:50:46Z |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 19-25.
doi: https://doi.org/10.15407/spqeo20.01.019
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
19
PACS 71.15.Mb, 71.20.-b, 74.20.Pq
Electronic structure of Ag8GeS6
D.I. Bletskan, I.P. Studenyak, V.V. Vakulchak, A.V. Lukach
Uzhhorod National University
54, Voloshin str., 88000 Uzhhorod, Ukraine
E-mail: crystal_lab457@yahoo.com
Abstract. For the first time, the energy band structure, total and partial densities of states
of Ag8GeS6 crystal were calculated using the ab initio density functional method in LDA
and LDA+U approximations. Argyrodite is direct-gap semiconductor with the calculated
band gap width Egd = 1.46 eV in the LDA+U approximation. The valence band of
argyrodite contains four energy separated groups of occupied subzones. The unique
feature of electron-energy structure of Ag8GeS6 crystal is the energy overlapping
between the occupied d-states of Ag atoms and the delocalized valence p-states of S
atoms in relatively close proximity to the valence band top.
Keywords: argyrodite, electronic structure, density of states, density functional theory,
spatial distribution of valence charge, chemical bond.
Manuscript received 21.10.16; revised version received 26.01.17; accepted for
publication 01.03.17; published online 05.04.17.
1. Introduction
Germanium dichalcogenides are base materials for the
synthesis of a wide class of superionic compounds
known in M2X–GeX2 (M = Li, Na, Cu, Ag; X = S, Se)
systems [1–3]. The ternary compound argyrodite
(Ag8GeS6) with the mixed ionic-electronic conductivity
type at room temperature, which transforms to the
superionic state at the phase transition into the high
temperature cubic modification, attracts the heightened
interest among these compounds. The conductivity of
synthesized Ag8GeS6 crystal is ∼10–3 Оhm–1⋅сm–1 at
T = 293 K [4].
From the practical viewpoint, the heightened
interest in argyrodite is caused by the possibility to
obtain it in the nanocrystalline state for use as a major
construction component of the dye-sensitized solar cells
(DSSCs) [5]. The further prospects of practical
application of this compound are determined by the
depth of understanding of formation nature of the
physical and chemical properties as well as finding the
opportunities for their purposeful modification.
At this point, the physical properties of argyrodite
are poorly studied. In literature, there are only data on
the study of fundamental absorption edge [6, 7],
photoconductivity [8] and electrical conductivity [4] of
Ag8GeS6 crystals.
It is also very important to study electronic
structure and chemical bonds in this silver-containing
compound. The crystal structure complexity of this
orthorhombic phase, the low lattice symmetry and the
large number of atoms (60) in the unit cell make
calculation of Ag8GeS6 electronic structure difficult.
This paper presents calculations of the energy band
structure, total and local partial densities of states as well
as spatial distribution of electronic charge density of
Ag8GeS6 crystal performed using the density functional
theory method in the local density approximation (LDA)
based on the LDA and LDA+U exchange-correlation
functionals.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 19-25.
doi: https://doi.org/10.15407/spqeo20.01.019
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
20
2. Crystal structure of Ag8GeS6
Synthetic argyrodite melts congruently (with open peak)
at 1221 K [3] and 1223 K [2] and undergoes a
polymorphic transformation at 488 K [9], 500 K [2]. The
low-temperature modification of Ag8GeS6 crystallizes in
the orthorhombic lattice. Its unit cell contains four Ge
atoms, thirty two Ag atoms and twenty four S atoms.
The symmetry corresponds to Pna21 space group. The
experimental unit cell parameters are: a = 15.149 Å,
b = 7.476 Å, c = 10.589 Å, Z = 4 [10]. Our calculated
equilibrium parameters are slightly larger: a = 15.339 Å,
b = 7.582 Å, c = 10.798 Å.
Ag atoms have three types of coordination in
Ag8GeS6 crystal structure: distorted tetrahedral (Аg–S
2.56–2.94 Å), flat triangular (Аg–S 2.49–2.76 Å) and linear
(S–Аg–S). Germanium atoms are located at the centers of
isolated [GeS4] tetrahedra (Ge–S 2.200–2.227 Å). All sulfur
atoms in Ag8GeS6 structure are bridged. Therefore, a
complex three-dimensional structure carcass is formed by
vertex-linked [GeS4], [AgS4] tetrahedra and [AgS3]
triangles. Ag atoms with linear coordination are
additionally introduced into the voids of this carcass,
thereby it is realized the short contacts Ag–Ag (2.93–
3.11 Å) in the structure similar in magnitude to the
interatomic distances typical for elementary Ag (2.889 Å).
3. Calculation method
The energy band structure calculations were carried out
in the framework of density functional theory [11, 12]
using the local density approximation (LDA) as the
exchange-correlation potential. As known, the
calculations with the LDA approximation give the
underestimated band gap values. The electronic
spectrum can be described more correctly with account
of the Coulomb interaction, which can be achieved in the
methods based on density functional theory, but taking
into account the interatomic Coulomb and exchange
interactions in the framework of the so-called LDA+U
approximation [13]. The magnitude of the Coulomb
parameter U was calculated using the linear response
described in [14]. The calculations were performed using
the SIESTA software package [15, 16].
Total and partial densities of electronic states were
determined using the modified tetrahedra method, for
which the energy spectrum and the wave functions were
calculated on the k-grid containing 15 points. The
integration over the irreducible part of Brillouin zone
was carried out using the method of special k-points [17,
18]. The total valence charge density ρ(r) was calculated
using the integration circuit at special points [18].
4. Electronic structure of Ag8GeS6
The electronic structure calculation of Ag8GeS6 crystal
was performed in the high symmetry points and
directions of Brillouin zone (BZ) for the orthorhombic
cell shown in Fig. 2. The energy band structure, total and
partial densities of states of Ag8GeS6 crystal calculated
in the LDA+U approximation without considering the
spin-orbital interaction are shown in Figs. 3 and 4,
respectively. The top of valence band is accepted as the
energy zero. The calculations in the LDA approximation
qualitatively repeat the calculation results in the LDA+U
approximation. According to our calculations, the
argyrodite is a direct-gap semiconductor with the
dispersion law extremes at the center of Brillouin zone
with the band gap width Egd = 1.46 eV calculated in the
LDA+U approximation.
The energy spectrum of valence electrons directly
determines such an important characteristic of the crystal
as the spectral dependence of absorption coefficient.
There are two papers [7, 8] devoted to the experimental
study of fundamental absorption edge of Ag8GeS6
crystals grown by the Bridgman method. It follows from
the analysis of fundamental absorption edge that
argyrodite realy is direct-gap semiconductor with the
band gap width opt
gdE = 1.48 ± 0.05 eV [6] and
opt
gdE = 1.41 eV [7]. The band gap estimated from the
red border of photoconductivity is Eg = 1.39 eV [8].
Thus, the account of Hubbard correction in the LDA-
Hamiltonian allowed to obtain the band gap value close
to the experimental one. Calculation of the argyrodite
electronic structure in the LDA approximation gives the
value of direct band gap width (direct transition Гv→Гc)
Egd = 0.44 eV, i.e. it is significantly underestimated in
comparison with the experimental values.
Fig. 1. Crystal structure (a) and the structure projection onto
[010] plane (b) of Ag8GeS6.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 19-25.
doi: https://doi.org/10.15407/spqeo20.01.019
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
21
Fig. 2. Brillouin zone of orthorhombic Ag8GeS6.
Fig. 3. Electronic structure of Ag8GeS6 calculated in the
LDA+U approximation.
Fig. 4. Total and local partial densities of states in Ag8GeS6
calculated using LDA+U approximation.
The valence band energy spectrum E(k) consists of
256 dispersion branches forming four energy separated
valence subbands with a total width 15.3 eV (from the
lower edge of S3s-band to the valence band top). The
analysis of partial contributions to the total density of
electronic states N(E) (Fig. 4) allows one to identify the
genetic nature of the various subbands of occupied
states.
From the ion transport viewpoint, the greatest
interest is attracted by the formation nature of upper
subband of occupied states consisted of 228 dispersion
branches and located inside the energy range from 6.47
to 0 eV. This section of the density of electronic states
N(E) spectrum (Fig. 4) is formed by S3s- and Ag4d-
atomic orbitals with a small impurity of Ge4р-states.
The special feature of this electron spectrum section is
the splitting of sulfur 3р-band into two components and
the repulsion of the last ones on both sides of the
position of silver 4d-band with a strongly marked peak
at –3.24 eV. Consequently, the upper valence subband
can be separated into three parts. The lower part inside
the energy range from –6.47 to –4.44 eV is formed by
hybridized Ag4d–S3p-states with an insignificant
impurity of germanium 4р-states. Silver 4d-states make
the dominant contribution into the middle part (from
–4.44 to –2.72 eV) of this subband. The electronic states
in the vicinity of the valence band top have mixed anion-
cation nature with roughly equal contributions of Ag4d-
and S3p-states.
The lowest bunch (from –15.3 to –14.35 eV) of
four dispersion branches is formed mostly by sulfur 3s-
states with admixing the germanium 4s-states. Next
subband (from –13.31 to –12.32 eV) of 20 dispersion
branches has very low dispersion, and it is also formed
mainly by sulfur 3s-states, but with an insignificant
impurity of germanium 4p-states. These two quasi S3s-
subbands are separated by a gap 3.73 eV from the
second subband (–8.6 ÷ –7.84 eV) consisted of four
dispersion branches and formed by hybridized sulfur
3s-, 3р-states and germanium 4s-states. Thus, the
analysis of total and partial densities of S3s-, 3p- and
Ge4s-, 4p-states indicates the significant impurity of
germanium and sulfur s-, p-states to each other, which
is indicative of the strong covalent nature of chemical
bond between Ge and S atoms in the coordination
[GeS4] tetrahedron that is one of the structural unit in
Ag8GeS6.
The lower edge of conduction band has a
significant dispersion. The electronic low-energy
structure of unoccupied electron states of argyrodite is
mainly formed by mixing the empty p-states of sulfur
and s, p-states of germanium and silver.
The comparison of the calculated total densities of
states N(E) with the experimental X-ray photoelectron
spectra (XPS) of GeS2, Ag2S and Ag8GeS6 (Fig. 5)
allows to observe the changes of electronic structure,
which occur with the silver introduction into germanium
disulfide at alloying it with Ag2S and formation of the
ternary Ag8GeS6 compound. The introduction of silver
atoms into GeS2 leads to increasing the total valence
band width, to splitting the bottom S3s-like subband on
two subbands as well as to changing topology of the
upper valence subband. Fig. 5 shows that the location,
width and intensity of the major structural features in the
XPS spectra related with silver 4d-states are close to the
calculated values in N(E) spectra of Ag2S and Ag8GeS6.
Thus, the theoretical calculation gives the well observed
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 19-25.
doi: https://doi.org/10.15407/spqeo20.01.019
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
22
admixing the sulfur 3p-states to silver 4d-states, which is
understandable in the formation of Ag–S chemical bonds
in Ag8GeS6.
5. The effective masses of electrons and holes
The effective masses of charge carriers depend on the
same matrix elements of the momentum operator
between energy bands that determine the value of the
optical absorption due to the direct transitions. In this
case, it was taken into account that the tensor
components of reciprocal effective masses are
determined by the second-order derivatives from the
energy of one-electron states on the wave vector
Cartesian coordinates k = (kx, ky, kz) at the extremum
point:
( )
βααβ ∂∂
∂
=
kk
kE
m
0
2
2
11
h
. (1)
The effective masses of electrons ( ∗
em ) and holes
( ∗
hm ) in argyrodite crystal were received by the
quadratic approximation of calculated dispersion law
E(k) at the extrema vicinity in the center of Brillouin
zone using the Eq. (1). Table shows the values of
effective masses of electrons and holes with the
corresponding directions in the reciprocal space
calculated in the LDA and LDA+U approximations. The
table shows that the effective masses of electrons and
holes obtained in the LDA+U calculations become
larger. By now, the experimentally effective masses of
electrons and holes in crystalline Ag8GeS6 are not
determined.
Fig. 5. Comparison of the smoothed calculated total densities
of states (1, 3, 4) in the valence band of crystalline Ag2S (1),
Ag8GeS6 (3) and GeS2 (4) with the experimental XPS spectra
of crystalline Ag2S (2) [19] and GeS2 (5) [20].
Table. The values of effective masses of electrons ∗
em and
holes ∗
hm in Ag8GeS6. They are given in units m0.
Calculation
type Direction Г→X Г→Z Г→Y
0mme
∗ 0.12 0.15 0.17
LDA
0mmh
∗ –0.26 –1.07 –1.07
0mme
∗ 0.24 0.28 0.29
LDA+U
0mmh
∗ –0.41 –1.49 –1.42
6. Spatial distribution of valence charge density
Formation of main interparticle interactions in the
orthorhombic Ag8GeS6 phase can be clearly observed
using the distribution of total charge density ρ(r). The
complex crystal structure of argyrodite complicates
representation of contour maps in the available 2D
format. In this case, it is the most convenient to present
the electronic configurations in the planes that pass
through two sulfur atoms and one Ge(Ag) atom in
[GeS4], [AgS4] tetrahedra and [AgS3] triangle (Figs. 6a–
6c), along linear coordination S–Ag–S (Fig. 7), along
plane passing through two [AgS3] triangles linked
together by the [GeS4] tetrahedron (Fig. 8) and along
plane passing through linked to each other the [GeS4]
tetrahedron, [AgS3] triangle and S–Ag–S (Fig. 9).
The contour maps clear show that the charge
density is concentrated mainly in the indicated structural
units and the silver atom contributions occupy more
noticeable part of the space than sulfur atom
contributions and even more than germanium atoms.
The valence electron charge in [GeS4] tetrahedra is
distributed primarily on the sulfur atom with strong
contour deformations in the direction to germanium
atoms. It can also be seen from the maps that there are
the localized maximums on the Ge–S bonds in [GeS4]
tetrahedra, and they are combined by the common
contours. The strongly pronounced deformation of
contours ρ(r) in the direction from the sulfur atoms to
the germanium ones along Ge–S bond line and the
presence of the overall contours covering the electron
density maximums in the cation-anion bonds (Fig. 6a)
reflect the covalent component of the chemical bond in
[GeS4] tetrahedra caused by hybridization of Ge4s-, 4p-
and S3p-states (Fig. 4). The ionic chemical bond
component in [GeS4] tetrahedra is caused by the partial
transfer of charge density from germanium atoms to
more electronegative sulfur atoms. It is reflected on the
electron density maps by a higher density of valence
electrons near the localization places of sulfur atoms.
The main charge in the structural units formed with
participation of Ag atoms is concentrated on the silver
atoms, and it has the form of closed and almost spherical
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 19-25.
doi: https://doi.org/10.15407/spqeo20.01.019
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
23
contours with very small polarization (Figs. 6b and 6c).
The charge transfer from the noble metal atoms to sulfur
atoms leads to electrostatic interactions and creates an
ionic component of the interatomic bond. In addition,
there are several types of bonding and antibonding
covalent interactions. The most important of those are
bonds of silver d-electrons and sulfur p-electrons.
Overall contours covering cation Ag and anion S atoms
precisely characterize the covalent component of
chemical bond in this compound, which although is
small but nevertheless occurs.
Furthermore, Figs. 8 and 9 clearly show that the
valence electron density has the overall contours for
various structural units linked to each other through the
bridged sulfur atoms. However, the deformation nature
of contours on anion-cation bond lines around common
sulfur atoms connecting neighbor [GeS4], [AgS4]
tetrahedra and [AgS3] triangles differs significantly.
Thus, the contours around a chalcogen are stronger
deformed in the direction to germanium atom along
S–Ge bond line, than along S–Ag bond line (Figs. 8, 9).
Fig. 7. Electronic density distribution map in the plane passing
along the linear coordination S–Ag–S.
Fig. 8. Electronic density distribution map in the plane passing
parallel to the b-axis of Ag8GeS6 crystal.
Fig. 6. Electronic density maps in the planes passing along Ge–S bond line in [GeS4] tetrahedron (a), along Ag–S in [AgS4]
tetrahedron (b) and [AgS3] triangle (c).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 19-25.
doi: https://doi.org/10.15407/spqeo20.01.019
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
24
Fig. 9. Electronic density map along the plane passing
through linked together [GeS4] tetrahedron, [AgS3]
triangle and S–Ag–S bond line.
Fig. 10. The radial charge density distribution in [GeS4] (a)
and [AgS4] (b) tetrahedra.
Thus, the nature of total electron density contours
ρ(r) in Ag8GeS6 crystal shows the ion-covalent type of
bonding. The difference of chemical nature of Ag and
Ge atoms determines the difference of Ag–S and Ge–S
chemical bonds. The Ag–S bond is more ionic than the
Ge–S one, at the same time, the Ag–S bond is weaker
than the Ge–S one.
The character of formed interatomic bonds in the
specific structural units of Ag8GeS6 crystal can be also
illustrated using the spatial distribution of the radial
charge densities (4πnr2). Fig. 10 presents the 4πnr2
values of atoms in [GeS4] and [AgS4] tetrahedra. It is
seen that the anion charge density in [GeS4] tetrahedron
has a pronounced local maximum near the nucleus,
whereas it is less pronounced near the cation (Ge).
Conversely, the charge density in [AgS4] tetrahedron is
minimal near the anion, and it is mainly concentrated in
the vicinity of silver atoms.
It is also possible to estimate the type of chemical
bonds in the crystal by using the atomic charge values
and the valence electronic density redistribution. The
atomic charges of Ag8GeS6 crystal calculated using the
Mulliken model have the following values (in e units):
10.580–10.704 for Ag atoms, 3.922 for Ge atoms,
6.368–6.694 for S atoms; and they well correlate with
the atomic electronegative values: 2.58 for S, 2.01 for
Ge, 1.93 for Ag. It is well known that the bond polarity
is greater when the electronegativity difference of
bonding atoms is larger. If the difference is higher than
two units, then the ionic component is almost always
predominant. It is known that the lower charge, the
higher polarizability of electron shell, and the radius
close to 1 Å of silver-cation allows to designate it to
the category of the so-called “magic ions”, which are
typical for the compounds with high ionic conductivity
[21].
7. Conclusions
For the first time, the energy band structure, total and
partial densities of states for Ag8GeS6 crystal were
calculated using the ab initio density functional method
in the LDA and LDA+U approximations. According to
the calculation results, the argyrodite is a direct-gap
semiconductor with the localization of valence band top
and the conduction band bottom at the Γ point of
Brillouin zone. The band gap width Egd is 1.46 eV in the
LDA+U approximation, which agrees well with the
experimental values obtained from the analysis of
fundamental absorption edge of Ag8GeS6 crystal.
The electronic density ρ(r) was calculated, and the
spatial distribution maps of valence electronic charge in
the plane passing along Ge(Ag)–S bond lines in the
different structural units of Ag8GeS6 crystal structure
were plotted, which allowed to describe the formation
features of chemical bonds between atoms forming this
crystal. The effective mass values for electrons and holes
in Ag8GeS6 were estimated.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 1. P. 19-25.
doi: https://doi.org/10.15407/spqeo20.01.019
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
25
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| id | nasplib_isofts_kiev_ua-123456789-214917 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-21T11:50:46Z |
| publishDate | 2017 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Bletskan, D.I. Studenyak, I.P. Vakulchak, V.V. Lukach, A.V. 2026-03-03T11:10:42Z 2017 Electronic structure of Ag₈GeS₆ / D.I. Bletskan, I.P. Studenyak, V.V. Vakulchak, A.V. Lukach // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 1. — С. 19-25. — Бібліогр.: 21 назв. — англ. 1560-8034 PACS: 71.15.Mb, 71.20.-b, 74.20.Pq https://nasplib.isofts.kiev.ua/handle/123456789/214917 https://doi.org/10.15407/spqeo20.01.019 For the first time, the energy band structure, total and partial densities of states of Ag₈GeS₆ crystal were calculated using the ab initio density functional method in LDA and LDA+U approximations. Argyrodite is a direct-gap semiconductor with the calculated band gap width Eᵍᵈ = 1.46 eV in the LDA+U approximation. The valence band of argyrodite contains four energy-separated groups of occupied subzones. The unique feature of the electron-energy structure of Ag₈GeS₆ crystal is the energy overlapping between the occupied d-states of Ag atoms and the delocalized valence p-states of S atoms in relatively close proximity to the valence band top. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Electronic structure of Ag₈GeS₆ Article published earlier |
| spellingShingle | Electronic structure of Ag₈GeS₆ Bletskan, D.I. Studenyak, I.P. Vakulchak, V.V. Lukach, A.V. |
| title | Electronic structure of Ag₈GeS₆ |
| title_full | Electronic structure of Ag₈GeS₆ |
| title_fullStr | Electronic structure of Ag₈GeS₆ |
| title_full_unstemmed | Electronic structure of Ag₈GeS₆ |
| title_short | Electronic structure of Ag₈GeS₆ |
| title_sort | electronic structure of ag₈ges₆ |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214917 |
| work_keys_str_mv | AT bletskandi electronicstructureofag8ges6 AT studenyakip electronicstructureofag8ges6 AT vakulchakvv electronicstructureofag8ges6 AT lukachav electronicstructureofag8ges6 |