Simulation of energy states in solid solutions based on the ferroelectrics- semiconductors of Sn₂P₂S₆ type
The energy spectra of charge carriers in several models of the ordered solid solutions and virtual crystal model based on the ferroelectrics of Sn₂P₂S₆ type are calculated by the semiempirical pseudopotential method. It is shown that the band gap depends on the employed model of the solid...
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irk-123456789-1209952017-06-14T03:06:06Z Simulation of energy states in solid solutions based on the ferroelectrics- semiconductors of Sn₂P₂S₆ type Mitin, O.B. Kharkhalis, L.Yu. Mikajlo, O.A. Melnichenko, T.N. Dorogany, V. The energy spectra of charge carriers in several models of the ordered solid solutions and virtual crystal model based on the ferroelectrics of Sn₂P₂S₆ type are calculated by the semiempirical pseudopotential method. It is shown that the band gap depends on the employed model of the solid solution. Методом напівемпіричного псевдопотенціалу розраховані енергетичні спектри носіїв заряду в деяких моделях впорядкованих твердих розчинів і моделі віртуального кристала на основі сегнетоелектриків-напівпровідників типу Sn₂P₂S₆. Показано, що ширина забороненого зони суттєво залежить від вибраної моделі твердого розчину. 2000 Article Simulation of energy states in solid solutions based on the ferroelectrics- semiconductors of Sn₂P₂S₆ type / O.B. Mitin, L.Yu. Kharkhalis, O.A. Mikajlo, T.N. Melnichenko, V. Dorogany // Condensed Matter Physics. — 2000. — Т. 3, № 4(24). — С. 777-786. — Бібліогр.: 15 назв. — англ. 1607-324X DOI:10.5488/CMP.3.4.777 PACS: 71, 07.05.Tp, 71.15.-m, 71.15.Hx, 71.20.Nr http://dspace.nbuv.gov.ua/handle/123456789/120995 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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| description |
The energy spectra of charge carriers in several models of the ordered solid
solutions and virtual crystal model based on the ferroelectrics of Sn₂P₂S₆
type are calculated by the semiempirical pseudopotential method. It is
shown that the band gap depends on the employed model of the solid
solution. |
| format |
Article |
| author |
Mitin, O.B. Kharkhalis, L.Yu. Mikajlo, O.A. Melnichenko, T.N. Dorogany, V. |
| spellingShingle |
Mitin, O.B. Kharkhalis, L.Yu. Mikajlo, O.A. Melnichenko, T.N. Dorogany, V. Simulation of energy states in solid solutions based on the ferroelectrics- semiconductors of Sn₂P₂S₆ type Condensed Matter Physics |
| author_facet |
Mitin, O.B. Kharkhalis, L.Yu. Mikajlo, O.A. Melnichenko, T.N. Dorogany, V. |
| author_sort |
Mitin, O.B. |
| title |
Simulation of energy states in solid solutions based on the ferroelectrics- semiconductors of Sn₂P₂S₆ type |
| title_short |
Simulation of energy states in solid solutions based on the ferroelectrics- semiconductors of Sn₂P₂S₆ type |
| title_full |
Simulation of energy states in solid solutions based on the ferroelectrics- semiconductors of Sn₂P₂S₆ type |
| title_fullStr |
Simulation of energy states in solid solutions based on the ferroelectrics- semiconductors of Sn₂P₂S₆ type |
| title_full_unstemmed |
Simulation of energy states in solid solutions based on the ferroelectrics- semiconductors of Sn₂P₂S₆ type |
| title_sort |
simulation of energy states in solid solutions based on the ferroelectrics- semiconductors of sn₂p₂s₆ type |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2000 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120995 |
| citation_txt |
Simulation of energy states in solid solutions based on the ferroelectrics- semiconductors of Sn₂P₂S₆ type / O.B. Mitin, L.Yu. Kharkhalis, O.A. Mikajlo, T.N. Melnichenko, V. Dorogany // Condensed Matter Physics. — 2000. — Т. 3, № 4(24). — С. 777-786. — Бібліогр.: 15 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
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| first_indexed |
2025-07-08T18:59:24Z |
| last_indexed |
2025-07-08T18:59:24Z |
| _version_ |
1837106374221234176 |
| fulltext |
Condensed Matter Physics, 2000, Vol. 3, No. 4(24), pp. 777–786
Simulation of energy states in solid
solutions based on the ferroelectrics-
semiconductors of Sn2P2S6 type
O.B.Mitin, L.Yu.Kharkhalis∗, O.A.Mikajlo, T.N.Melnichenko,
V. Dorogany
Uzhgorod State University,
54 Voloshin Str., 88000 Uzhgorod, Ukraine
Received November 11, 2000, in final form November 28, 2000
The energy spectra of charge carriers in several models of the ordered solid
solutions and virtual crystal model based on the ferroelectrics of Sn2P2S6
type are calculated by the semiempirical pseudopotential method. It is
shown that the band gap depends on the employed model of the solid
solution.
Key words: pseudopotential method, ordered solution, energy states,
simulation, virtual crystal, ferroelectrics-semiconductors.
PACS: 71, 07.05.Tp, 71.15.-m, 71.15.Hx, 71.20.Nr
The physical property investigations of the ferroelectrics of the
(PbySn1−y)2P2(SxSe1−x)6 system [1,2] are relevant since one can look after the
change of the crystal structure anisotropy and the effect of the anion and cation
replacement on both the property anomalies in the critical region and the energy
and phonon spectra. It was established [2,3] that the replacement of Sn by Pb in
(PbySn1−y)2P2S6 leads to the decrease of the temperature of the ferroelectric phase
transition and this transition does not change its character. The replacement of the
S atom by Se in the system Sn2P2(SxSe1−x)6 leads to the splitting of the phase tran-
sition line [4]. The evolution of the phase transition peculiarities for the considered
systems has been analyzed based on the investigations of temperature dependency
of the heat conduction and the dielectric function [5]. The absorption edge studies
of the ferroelectric solid solutions (PbySn1−y)2P2(SxSe1−x)6 helped to establish the
main conformities in the variation of the optical parameters (see table 1 from [2]).
In particular, the change of the band gap with the concentration of the replacement
atoms and the thermal and baric coefficients of the band gap changes were deter-
mined. Further, these important experimental characteristics can be used to compare
∗E-mail: kharkhalis@univ.uzhgorod.ua, Tel.: (803122) 3-23-39
c© O.B.Mitin, L.Yu.Kharkhalis, O.A.Mikajlo, T.N.Melnichenko, V. Dorogany 777
O.B.Mitin et al.
the theoretical values obtained from the calculations of the energy structure under
the pressure and temperature. We have already investigated the band structure of
the Sn2P2S6, Sn2P2Se6 [6,7], Pb2P2S6 and Pb2P2Se6 crystals. The similarity of the
crystal structures and the observed similarity of the band structures, the essential
difference in the energy gap of the above mentioned crystals make it possible to
create heterostructures based on them. Therefore, the theoretical simulation of the
energy states in the solid solutions should precede the experimental fabrication of
such heterostructures.
1. The models of the solid solution based on the Sn2P2S6
crystals
In the paper [8] we discussed several models of the solid solution based on the
CdSb and ZnSb crystals and investigated the energy states of the charge carriers.
We considered the model of the virtual crystal [9] with the averaged lattice param-
eters and atomic positions or parameters of pseudopotential form, i.e., factors. As
it is known, such a model overcomes the difficulties connected with the breaking
of translational symmetry. We also proposed the model of the ordered solid solu-
tion [9,10], in which the periodic structure remains. Both models are utilized in the
pseudopotential calculations. Our simulation of the energy states showed that the
behaviour of the dispersion curve E(k) slightly changes and depends on the consid-
ered model. The shift of the local extrema is possible too, but the band gap changes
considerably.
Similar to [8], let us carry out the calculation of the energy spectra of the ordered
solid solutions based on the crystals of Sn2P2S6 type. We will consider the replace-
ment solutions where the atoms of different types distribute only in the positions of
the crystal lattice. The presence of many atoms in the unit cell (two formula units,
20 atoms [1]) makes it possible to choose different versions of placing the replacement
atoms. The strains are known to appear in these cases. They could be compensated
by the deformation of the unit cell and by the change of the atom positions. But the
problem of determining the energy of the internal strains is quite complicated since
these strains are defined not only by the crystallographic peculiarities but also by
the magnitudes of the elastic module. So, as far as we have no information about the
deformation change of the lattice parameters from the concentration of the replace-
ment atoms we will consider several versions of the solid solution models, assuming
that the replacement of the atoms of one type by the atoms of another type causes
no changes in the lattice either the changes do occur, and the lattice parameters are
regarded as the mean parameters.
To choose the solid solution model, we utilize the investigation data of the concen-
tration rearrangement of vibrational spectra for the mixed crystals Sn2P2(SexS1−x)6.
Authors of [11,12] showed that the increase of x leads to the decrease of a number
of anions [P2S6]
4−. It corresponds to the appearance of the additional bands in the
vibrational spectra. The intensity of these bands is proportional to the probability
of the appearance of the structure group P2[SekS6−k]
4− (k=1...6) type. The analysis
778
Simulation of energy states in solid solutions. . .
Table 1. The atomic coordinates of the Sn2P2S6 crystal (P21/n).
Atom number Atom X Y Z
1 Sn 0.2574 –0.3691 0.0410
2 Sn 0.2426 0.1309 0.4590
3 P –0.0674 –0.1087 0.0605
4 P 0.4326 –0.3913 –0.4395
5 S –0.2630 –0.0021 0.1013
6 S 0.0325 –0.1913 0.3229
7 S 0.0569 0.3023 0.1560
8 S 0.2370 –0.4979 –0.3987
9 S 0.4431 –0.1977 0.3440
10 S 0.4675 0.3087 0.1771
of the frequency of P-S(Se) valence vibrations and the calculations of the probability
show us that a lot of the mixed anions in the solid solutions of Sn2P2(SexS1−x)6 are
realized at x = 0.5, especially in the complex consisting of three atoms of S and of
three atoms of Se. Besides it was shown that other configurations of the complexes
P2[SekS6−k]
4− are possible too.
Let’s consider the following models of the solid solution similar to the investiga-
tions of [11,12]:
Model 1: Pb atoms replace half of Sn atoms in Sn2P2S6.
Model 2: one atom of S is replaced by Se in Sn2P2S6 crystal. It corresponds to
the presence of a structure group of PS2Se–PS3 type.
Model 3: the third of S atoms is replaced by Se atoms. The structure complexes
PS2Se–PS2Se and PSSe2–PS3 are realized in this case.
Model 4: half of S atoms are replaced by Se atoms. It corresponds to the presence
of the structure groups of PS3–PSe3 and PSSe2–PS2Se type, and besides the complex
PS3–PSe3 is less probable according to the calculation [12].
Note that the lattice parameters of the Sn2P2S6 crystal remain the parameters of
the above mentioned models of the solid solutions: a=9.318 Å, b=7.463 Å, c=6.518 Å,
γ = 91.15◦ [13]. In these models, the unit cell contains the same number of atoms
as in the constituent materials and the replacement is performed in such a manner
that the space symmetry of the resulting crystal does not change.
Model 5: the virtual crystal.
The atomic coordinates for the Sn2P2S6 crystal (space group P21/n, the origin
is replaced on the value r0 = (a+ b+ c) /4 [7,13]) are presented in table 1. The
atoms with their coordinates are denoted as 1–10 and the atoms with the invariant
coordinates are denoted as 1′ − 10′ accordingly.
In the first model of the solid solution, the choice of the versions is digit: 1, 1’ or
2, 2’atoms (Sn) are replaced by Pb atoms. In the second model we considered such
distribution of the atoms: 5, 6, 8 and 5’, 6’, 8’ atoms are the S atoms and the 7, 7’
779
O.B.Mitin et al.
atoms are the Se atoms. Model 3 assumes the following versions: the first version –
5, 6, 8, 9 and 5’, 6’, 8’, 9’ atoms are S atoms; 7, 10 and 7’, 10’ are the Se atoms;
the second version: 5, 8, 9, 10 and 5’, 8’, 9’, 10’ atoms are the S atoms and 6, 7,
6’, 7’ atoms are Se atoms. We chose different versions in the fourth model of the
Sn2P2(S0.5Se0.5)6 solid solution: the first version – 5, 6, 7 and 5’, 6’, 7’ atoms are the
S atoms; 8, 9, 10 and 8’, 9’, 10’ atoms are the Se atoms; the second version – 5, 8,
9 and 5’, 8’, 9’ atoms are the S atoms; 6, 7, 10 and 6’, 7’, 10’ atoms are Se atoms.
Since the latter is the most probable, we consider different cycle rearrangements of
the atoms.
2. The analysis of the dispersion curves for different models of
the solid solutions based on the Sn2P2S6 crystals
Now we analyze the changes which take place in the vicinity of the extrema of
valence and conduction band in the resulting solid solutions based on the Sn2P2S6
crystals at the replacement of Sn and S atoms.
As it is shown in our work [7], the band structure of the crystal Sn2P2S6 is char-
acterized by many valleys. The absolute extremum of the valence band is localized
in the vicinity of Y point and displaces on the kxky plane in the Brillouin zone. The
additional extremum of the valence is localized in the vicinity of R point The abso-
lute and additional extrema for the conduction band are localized on the R-U and
Γ-Y symmetry lines [7]. More detailed calculations showed that ∆k, corresponding
to the difference between the localization points of the conduction band minimum
and valence band maximum in the Γ-Y direction, is equal to 0.03 π/b. Energy ∆E,
corresponding to this ∆k, is equal to ∼ 0.02 eV for the conduction band and is
equal to 0.004 eV for the valence band (matrix order N ∼ 400). The value of ∆E
slightly increases with the decrease of the plane wave number. Therefore, one can
consider that direct transitions are realized in the vicinity of Y point if the pseu-
dopotential calculations are inaccurate. The direct transitions are also confirmed by
the optical investigations [1]. To calculate the energy spectra in the solid solutions
we will take into account only the Γ-Y and R-U directions of the Brillouin zone. We
denote the first minimum forbidden gap as Eg1 and the second minimum forbidden
energy interval, connected with the additional valley in the conduction band, as Eg2.
To calculate the energy states in the solid solutions we used the semiempirical
pseudopotential method. The form-factors for different ions of α type are described
by the analytical expression [9]:
vα (q) = β × vα0 (q) ;
vα
0
(q) = Aα
1
(
q2 − Aα
2
)
/
(
1 + expAα
3
(
q2 −Aα
4
))
,
where β = Ωα/Ωc is the normalizing parameter, Ωα is the atomic volume of the type
α: ΩSn = 181.5, ΩPb = 203.4, ΩS = 173.6, ΩSe = 181.6 atomic unit [9]; Ωc is the
volume of the unit cell; Aα
i (i = 1 − 4) are the pseudopotential parameters. For the
Sn, Pb, S, Se and P atoms, these parameters are listed in table 2. The form-factors
780
Simulation of energy states in solid solutions. . .
Table 2. The values of Aα
i parameters for the Sn, Pb, P, S and Se atoms.
Atom A1 A2 A3 A4
Sn 0.4 1.916 1.05 0.6
Pb 0.33 2.16 1.05 0.6
P 0.9 2.6 0.664 –1.44
S 0.2 3.13 2.5 3.0
Se 0.155 3.13 3.1 3.2
were selected so that, on the one hand, they coincided with the form- factors of
the model pseudopotential in the actual region of the wave vectors [14] and, on the
other hand, they gave the real value of the energy gap. We used the same program of
calculation and kept the same order of the secular matrix ( ∼ 400) as in calculation
of the band structure of the Sn2P2S6 crystal [7].
Besides, the investigations of the energy spectra were carried out for different
parameters β.We consider the cases when α is Pb or Sn for the Pb “impurity atoms”
in the crystal Sn2P2S6 or Pb2P2S6, and α is Se or S for the Se “impurity atoms” in
the Sn2P2S6 or Sn2P2Se6 crystal. The values of β are presented in the table 3 only for
the cases: β = ΩSn/ΩSn2P2S6 = 0.059, β = ΩPb/ΩPb2P2S6 = 0.065, β = ΩS/ΩSn2P2S6 =
0.057, β = ΩSe/ΩSn2P2Se6 = 0.053.
The obtained dispersion curves E(k) for both the valence and the conduc-
tion bands in the extrema vicinity for the solid solutions of (Pb0.5Sn0.5)2P2S6 and
Sn2P2(SexS1−x)6 are presented in figures 1–3. For the purpose of revealing the
changes in the energy spectrum we also present the fragment of the energy structure
in the Γ–Y and R–U directions in the Brillouin zone for the Sn2P2S6 crystal.
0,30 0,35 0,40
10,75
11,00
13,25
13,30
13,35
13,40
13,45
Sn2P2S6
(Pb0.5Sn0.5)2P2S6 (β=0.065)
(Pb0.5Sn0.5)2P2S6 (β=0.059)
E
,
eV
k
y
0,40 0,42 0,44 0,46 0,48 0,50
10,80
10,85
10,90
10,95
13,10
13,15
13,20
13,25
Sn2P2S6
(Pb0.5Sn0.5)2P2S6 (β=0.065)
(Pb0.5Sn0.5)2P2S6 (β=0.059)
E
,
e
V
R-U
Figure 1. Dispersion curves E(k) in the vicinity of the absolute extrema for the
model 1 and for Sn2P2S6 crystal.
781
O.B.Mitin et al.
0,30 0,32 0,34 0,36 0,38 0,40
10,0
10,5
11,0
12,5
13,0
13,5
Sn2P2S6
Virtual crystal
Virtual crystal
E
,
eV
k
y
0,40 0,42 0,44 0,46 0,48 0,50
10,0
10,5
11,0
12,5
13,0
Sn2P2S6
Virtual crystal
Virtual crystal
E
,
eV
R-U
Figure 2. Dispersion curves E(k) in the vicinity of the absolute extrema for the
virtual crystal model.
The results of our calculations show that the replacement of Sn by Pb (inde-
pendently on the position of Sn atom in the cell) in the Sn2P2S6 crystal does
not lead to essential changes in the energy spectrum (figure 1). The localization
points of the absolute and additional extrema in the solid solution of the first model
(PbSn)P2S6 coincide with those for the Sn2P2S6 crystal. The deviation of Eg1 for
the case β = 0.0653 (α is Pb) equals ∼ 0,4% and for the parameter β=0.059 this
deviation equals ∼ 5% (α is Sn). Note that the second subband, localized in the
R-U direction, is more sensitive to atomic replacements. An insignificant change
takes place for Eg2 as well (figure 1). The experimental investigations regarding the
fundamental absorption of the Sn2P2S6 materials at the cation replacement suggest
a small change of the energy gap in the crystals (PbxSn1−x)2P2S6 [2].
The calculations of the energy structure for the virtual crystal model are pre-
sented in figure 2. We used the form-factors of the pseudopotentials averaged over
the pseudopotential parameters Ai. The lattice parameters, atomic coordinates and
angles were also averaged over Sn2P2S6 and Pb2P2S6 crystals (model 5, the first
version) and Sn2P2S6 and Sn2P2Se6 crystals (model 5, the second version). As fol-
lows from the analysis of the dispersion curves E(k) in figure 2, the Eg2 changes
unessentially in comparison with the ideal crystal Sn2P2S6 and equals 2.35 eV, be-
sides the shift of the local extremum for the valence band toward the little wave
vector k in the Γ-Y direction of the Brillouin zone is observed. The value of Eg1
equals 2.45 eV for the second version of the virtual crystal. A slight shift of the
bottom of the conduction band takes place in this case.
Let’s analyze the dispersion curves E(k) for the models 2–4 of the solid solution
Sn2P2(SexS1−x)6 (figure 3). Note that the following replacement of S atoms by the
Se atoms from 1 to 3 in the structure complex [SekS6−k]
4− leads to the decrease of
Eg1 and Eg2. The most sharp changes are observed at the parameter β=0.053 (α is
Se). It is interesting that the energy gap Eg1 is equal to 0.6 eV for the solid solution
782
Simulation of energy states in solid solutions. . .
0,28 0,30 0,32 0,34 0,36 0,38 0,40 0,42
11,0
11,2
11,4
11,6
11,8
12,0
13,0
13,2
13,4
Sn
2
P
2
S
6
Sn
2
P
2
(Se
x
S
1-x
)
6
2 Model (β=0.053)
Sn
2
P
2
(Se
x
S
1-x
)
6
2 Model (β=0.057)E
,
e
V
Γ-Y
0,40 0,42 0,44 0,46 0,48 0,50 0,52
11,0
11,5
12,0
13,0
13,2
Sn
2
P
2
S
6
Sn
2
P
2
(Se
x
S
1-x
)
6
2 Model (β=0.053)
Sn
2
P
2
(Se
x
S
1-x
)
6
2 Model (β=0.057)E
,
e
V
R-U
0,28 0,30 0,32 0,34 0,36 0,38 0,40 0,42
11,0
11,2
11,4
11,6
11,8
12,0
13,0
13,2
13,4
Sn
2
P
2
S
6
Sn
2
P
2
(Se
x
S
1-x
)
6
3 Model 1Ver (β=0.053)
Sn
2
P
2
(Se
x
S
1-x
)
6
3 Model 1Ver (β=0.057)
E
,
e
V
Γ-Y
0,40 0,42 0,44 0,46 0,48 0,50 0,52
11,0
11,5
13,0
Sn
2
P
2
S
6
Sn
2
P
2
(Se
x
S
1-x
)
6
3 Model 1Ver (β=0.053)
Sn
2
P
2
(Se
x
S
1-x
)
6
3 Model 1Ver (β=0.057)
E
,
eV
R-U
0,28 0,30 0,32 0,34 0,36 0,38 0,40 0,42
11,0
11,2
11,4
11,6
11,8
12,0
12,2
12,4
12,6
12,8
13,0
13,2
13,4
Sn
2
P
2
S
6
Sn
2
P
2
(Se
x
S
1-x
)
6
4 Model 1 Ver (β=0.053)
Sn
2
P
2
(Se
x
S
1-x
)
6
4 Model 1 Ver (β=0.057)
E
,
e
V
Γ-Y
0,40 0,42 0,44 0,46 0,48 0,50 0,52
11,0
11,5
12,0
12,5
13,0
Sn
2
P
2
S
6
Sn
2
P
2
(Se
x
S
1-x
)
6
4 Model 1 Ver (β=0.053)
Sn
2
P
2
(Se
x
S
1-x
)
6
4 Model 1 Ver (β=0.057)
E
,
e
V
R-U
Figure 3. Dispersion curves E(k) in the vicinity of the extrema for the solid
solutions of the models 2–4.
783
O.B.Mitin et al.
Table 3. The results of the band structure calculations in the different models
of the ordered solid solution and the virtual crystal model on the base of the
ferroelectrics of the Sn2P2S6 type.
Substance β Eg1, eV Eg2, eV
Sn2P2S6 – 2.15 2.25
Model 1 0.065 2.14 2.24
(SnPb)P2S6 0.059 2.25 2.34
Model 2 0.053 1.26 1.43
0.057 1.65 1.79
Model 3
Version 1 0.053 1.18 1.30
0.057 1.62 1.74
Version 2 0.053 0.80 0.96
0.057 1.36 1.48
Model 4
Version 1 0.053 0.59 0.84
0.057 1.17 1.37
Version 2 0.053 0.91; 0.88 1.19; 1.10
0.057 1.41; 1.31 1.55; 1.57
Virtual crystal
(model 5)
Version 1 2.35 2.48
Version 2 2.45 2.60
Sn2P2(Se0.5S0.5)6 where the structure complex P[SekS3−k] consists of the Se atoms
in one trigonal pyramid (such groups are less real according to the calculations [11]).
The maximum for the valence band is localized in the point R of the Brillouin zone.
The rapprochement of the certain and additional valleys in the model 4 of the solid
solution is observed as well.
The estimations of the values Eg1 and Eg2 for the above mentioned ordered solid
solutions of the Sn2P2(SexS1−x)6 system are listed in table 3.
3. Conclusion
Thus the pseudopotential calculations of the energy states in different ordered
solid solutions based on the Sn2P2S6 crystals show that the energy gap essentially
changes depending on the model employed. In spite of the simplicity of the above
considered models we obtain (at a fixed value of β) that the replacement of S atom
by Se in the anion sublattice of the Sn2P2S6 crystal leads to a decrease of the energy
gap Eg, simultaneously the replacement Sn→ Pb increases Eg (at β = 0.059).
Analogical results have been obtained for the solid solutions of Sn2P2(SexS1−x)6 and
(PbxSn1−x)2P2S6 in the paraelectric phase [15] but the concentration dependencies
784
Simulation of energy states in solid solutions. . .
of Eg (as it is follows from figure 1, table 1 [15]) have got a less sharp character
in comparison with our calculations. One can explain the unessential change of the
minimum forbidden gaps at the replacement Sn→ Pb and more essential changes
at the replacement S→ Se using the functional dependencies of the form-factor of
the pseudopotentials (see formula) for the atoms Sn and Pb and the atoms S and
Se. It has been found that the values of the normalizing form-factors for Sn and
Pb atoms at β = 0.059 almost coincide in the actual region of the wave vectors q.
The normalizing form-factors for atoms S and Se have got different values in the
same region of the wave vectors, and as a consequence the change of the extrema of
the conduction band and of the valence band occurs. Varying the parameter β we
change the value vα (q) and obtain different values for Eg1 and Eg2. It is possible
that the oscillated character of the change of the energy gap (see table 3) testifies
that the considered models are only the extreme limits of all variations, which really
take place in the ordered solid solution in comparison with the pure crystals. Such a
simulation of the energy states in the solid solutions based on the Sn2P2S6 crystals
may stimulate the investigations and fabrication of the heterostructures and the
materials with the control physical properties.
4. Acknowledgement
Authors are very grateful to Prof. Dr. D.M.Bercha for her help in the analysis
of the results obtained.
References
1. Vysochanskii Yu.M., Slivka V.Yu. Ferroelectrics of the Sn2P2S6 family. Properties in
the vicinity of Lifshits point. Lviv, Oriana–Nova, 1984.
2. Gerzanich E.I, Slivka A.G., Guranich P.P, Shusta V.S. The influence of anion and
cation replacement on the fundamental absorption of the Sn2P2S6 crystals. // Mate-
rialy optoelectroniky. Izd. Tecknika, 199, p. 31–38.
3. Vysochanskii Yu.M., Gurzan M.I, Mayor M.M. The concentration dependen-
cies of the temperatures and phase transition character in (PbySn1−y)2P2S6 and
(PbySn1−y)2P2Se6. // Fizika tverdogo tela, 1983, vol. 25, No. 1, p. 858–864 (in Rus-
sian).
4. Gomonaj A.V., Grabar A.A., Vysochanskii Yu.M. The splitting of the phase transition
in the ferroelectric solid solutions. // Fizika tverdogo tela, 1981, vol. 23, No. 12,
p. 3602–3606 (in Russian).
5. Vysochanskii Yu.M., Slivka V.Yu. Lifshits point on the state diagrams of the ferro-
electrics. // Uspechi fizicheskich nauk, 1992, vol. 2, p. 139–160.
6. Bercha D.M., Kharkhalis L.Yu, Mitin O.B., Melnic R. Relation of Sn2P2S6 ferro-
electrics electron and phonon spectra peculiarities connected and unconnected with
Fedorov symmetry. // Ferroelectrics, 1997, vol. 192, p. 135–136.
7. Bercha D.M., Grabar A.A., Kharkhalis L.Yu., Mitin O.B., Bercha A.I. Band spectrum
and protostructure model of Sn2P2S6 crystal. // Fizika tverdogo tela, 1997, vol. 39,
No. 7, p. 1219–1222 (in Russian).
785
O.B.Mitin et al.
8. Bercha D.M., Mitin O.B., Kharkhalis L.Yu. Models of the Cd0.5Zn0.5Sb solid solution
and the energy spectrum of current carriers. // Inorganic Materials, 1997, vol. 33,
No. 3, p. 230–234.
9. Heine V., Cohen M., Weaire D. The Pseudopotential Concept; The Fitting of pseu-
dopotentials to Experimental Data and Their Subsequent Application; Pseudopoten-
tial Theory of Cohesion and Structure. New York, McGraw-Hill, 1970 (Russian trans-
lation: Teoriya Pseudopotentsiala. Moscow, Mir, 1973).
10. Khachaturyan A.G. Theory of Phase Transformations and Structure of Solid Solutions.
Moscow, Nauka, 1974 (in Russian).
11. Vysochanskii Yu.M., Grabar A.A., Mikajlo O.A., Rizak V.M. Spectroscopic presence
of replacement character in Sn2P2(SxSe1−x)6 and the concentration transformation of
interatomic interactions. – In: Abstracts of IV Conference on the spectroscopy of the
light raman scattering, Uzhgorod, 1989, p. 164.
12. Mikajlo O.A. PhD Thesis. Uzhgorod, 1993.
13. Ditmar G, Schafeer H. Die structur des Di–Zinn–Hexathiohypodiphoshats Sn2P2S6.
// Zs. Naturforsch, 1974, vol. 29b, No. 5–6, p. 312–317.
14. Harrison U. Pseudopotentials in the Theory of the Metals. Moscow, Mir, 1968.
15. Slivka G.A., Gerzanich E.I., Shusta V.S., Guranich P.P. Influence of the isomorphic
replacement and external pressure on the edge of fundamental absorption by the
crystals Sn(Pb)2P2S(Se)6. // Izvestiya vuzov RAN, Seriya fizicheskaya, 1999, No. 9,
p. 23–2 (in Russian).
Моделювання енергетичних станів у твердих
розчинах на основі сегнетоелектриків-
напівпровідників типу Sn2P2S6
О.Б.Мітін, Л.Ю.Хархаліс, О.А.Микайло, Т.Мельниченко,
В.Дорогань
Інститутфізики і хімії твердого тіла,
Ужгородський державний університет,
88000 Ужгород, вул. Волошина, 54
Отримано 11 листопада 2000 р., в остаточному виглядi –
28 листопада 2000 р.
Методом напівемпіричного псевдопотенціалу розраховані енерге-
тичні спектри носіїв заряду в деяких моделях впорядкованих твердих
розчинів і моделі віртуального кристала на основі сегнетоелектриків-
напівпровідників типу Sn2P2S6. Показано, що ширина забороненого
зони суттєво залежить від вибраної моделі твердого розчину.
Ключові слова: метод псевдопотенціалу, енергетичні стани,
впорядковані тверді розчини, віртуальний кристал, моделювання,
сегнетоелектрики-напівпровідники
PACS: 71, 07.05.Tp, 71.15.-m, 71.15.Hx, 71.20.Nr
786
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