Account of surface contribution to the thermodynamic properties of lead selenide films
Being based on the density functional theory (DFT), computer simulation of the surface effect on thermodynamic parameters of lead selenide (PbSe) has been performed in this work. Applying the thermodynamic approach, the choice of model for the plane PbSe [200] preferred orientations has been justifi...
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2019
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| Cite this: | Account of surface contribution to thermodynamic properties of lead selenide films / L.I. Nykyruy, B.P. Naidych, O.M. Voznyak, T.O. Parashchuk, R.V. Ilnytskyi // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2019. — Т. 22, № 2. — С. 156-164. — Бібліогр.: 47 назв. — англ. |
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| author | Nykyruy, L.I. Naidych, B.P. Voznyak, O.M. Parashchuk, T.O. Ilnytskyi, R.V. |
| author_facet | Nykyruy, L.I. Naidych, B.P. Voznyak, O.M. Parashchuk, T.O. Ilnytskyi, R.V. |
| citation_txt | Account of surface contribution to thermodynamic properties of lead selenide films / L.I. Nykyruy, B.P. Naidych, O.M. Voznyak, T.O. Parashchuk, R.V. Ilnytskyi // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2019. — Т. 22, № 2. — С. 156-164. — Бібліогр.: 47 назв. — англ. |
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| description | Being based on the density functional theory (DFT), computer simulation of the surface effect on thermodynamic parameters of lead selenide (PbSe) has been performed in this work. Applying the thermodynamic approach, the choice of model for the plane PbSe [200] preferred orientations has been justified, which indicates domination of the energy of surface states, while minimization of interface energy and deformation are less important in overall changing the free energy. The thermodynamic parameters for the surface of crystals and their temperature dependences in the framework of DFT method and using the hybrid functional B3LYP have been calculated, namely: energy ∆E, enthalpy ∆H, Gibbs’ free energy ∆G, isobaric heat capacities Cᴘ and isovolume heat capacities Cᵥ, entropy ∆S. The analytical expressions of temperature dependences for these thermodynamic parameters approximated using quantum-chemical calculation data have been obtained. The analysis of temperature dependences for the heat capacity corresponds to the experimental data and the Djulong–Pti law.
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ISSN 1560-8034, 1605-6582 (On-line), SPQEO, 2019. V. 22, N 2. P. 156-164.
© 2019, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
156
Semiconductor physics
Account of surface contribution to thermodynamic properties
of lead selenide films
L.I. Nykyruy
1
, B.P. Naidych
1
, O.M. Voznyak
1
, T.O. Parashchuk
2
, R.V. Ilnytskyi
1
1
Vasyl Stefanyk Precarpathian National University,
57, Shevchenko Str., 76018 Ivano-Frankivsk, Ukraine,
E-mail: liubomyr.nykyrui@pu.if.ua, bvolochanska@i.ua
2
The Institute of Advanced Manufacturing Technology,
Wrocławska 37, Krakow 30-011, Poland
E-mail: taras.parashchuk@ios.krakow.pl
Abstract. Being based on the density functional theory (DFT), computer simulation of the
surface effect on thermodynamic parameters of lead selenide (PbSe) has been performed in
this work. Applying the thermodynamic approach, the choice of model for the plane PbSe
[200] preferred orientations has been justified, which indicates domination of the energy of
surface states, while minimization of interface energy and deformation are less important in
overall changing the free energy. The thermodynamic parameters for the surface of crystals
and their temperature dependences in the framework of DFT method and using the hybrid
functional B3LYP have been calculated, namely: energy ∆E, enthalpy ∆H, Gibbs’ free
energy ∆G, isobaric heat capacities CP and isovolume heat capacities CV, entropy ∆S. The
analytical expressions of temperature dependences for these thermodynamic parameters
approximated using quantum-chemical calculation data have been obtained. The analysis of
temperature dependences for the heat capacity corresponds to the experimental data and the
Djulong–Pti law.
https://doi.org/10.15407/spqeo22.02.156
PACS 05.70.Np, 68.35.Md, 71.15.Mb
Keywords: DFT, IV-VI semiconductors, cluster models, quantum-chemical calculations,
thermodynamic properties.
Manuscript received 05.02.19; revised version received 24.04.19; accepted for publication
00.00.19; published online 00.00.19.
1. Introduction
The main advantage of lead chalcogenides (PbTe, PbSe,
and PbS) is the small band gap (for example, 0.278 eV
for PbSe at 300 K) [1]. This property is of great
importance in infrared optics, lasers, light emitting
devices, photovoltaics, and medium-temperature
thermoelectric devices [2-5]. Therefore, in recent decades
the purposeful work to find optimal conditions for their
synthesis and application has been done. The areas of
practical use of these compounds are not limited by the
bulk samples. Applied devices were widely used based
on thin films, quantum walls, supercells, nanowires,
colloidal and embedded nanocrystals [6-9].
Application of PbSe in thermoelectricity is justified
by a number of favorable characteristics. Namely, there
are the low thermal conductivity at high temperatures [4],
the minimum values of the band gap close to 0.3 eV at
the L-point [10], the value of the Seebeck coefficient
equal to (222.69 ± 0.02) µV/K and the possibility of its
increase under deviation from stoichiometry in the
direction to selenium [11], and the positive dependence
of its changes with temperature [12]. The high
thermoelectric efficiency is achieved for the combination
of lead chalcogenides in ternary or quaternary solid
solutions [8, 13-16].
At the modern stage of science and technology
development, the lead selenide is used in thermo-
electricity, optoelectronics and spintronic devices,
especially in the long-wave range for production of infra-
red diode lasers and thermo- or photoelectric energy
converters [2, 17, 18]. An in-depth study of the properties
of materials under different external conditions is
associated with a wide spectrum of their application and
sometimes of ambiguity observed in received results.
Simulation of the thermodynamic properties of
crystals by using ab initio calculations is the least
expensive in terms of material resources and duration of
research. These methods have been popular for almost
four decades and have proven themselves in enabling to
SPQEO, 2019. V. 22, N 2. P. 156-164.
Nykyruy L.I., Naidych B.P., Voznyak O.M. et al. Account of surface contribution to thermodynamic properties …
157
obtain the reliable information about properties of
crystalline samples by using the minimum set of input
data, to make their theoretical interpretation. On the other
hand, the computer methods of quantum chemistry are
the best for studying the nanoscale structures, which
should be accompanied by the consideration of the near-
order arrangement of atoms in real crystals, and by the
analysis of its properties. The unconditional advantage of
such approaches is convenience, accuracy and theoretical
justification of research.
In this paper, based on ab initio calculations, using
known crystallographic parameters, new approaches for
determination of the main thermodynamic parameters of
PbSe thin films and their temperature dependences have
been proposed. And the experimental studies of isobaric
heat capacity CP have been carried out. The main
attention is paid to the contribution of surface states to
the values of thermodynamic parameters.
2. Computational details
Modern scientific and technological progress is
dependent on the development of theoretical methods for
researches. However, this success would have been
impossible without the achievements of the novel
computer approaches. First and foremost, they contribute
to the improvement of model research. They are
extremely convenient and satisfy the accuracy
requirements for expanding and deepening information
about the structure and properties of materials.
The value of the obtained results is greatly
enhanced by the use of quantum-chemical methods for
constructing the crystal structural models. The cluster
approximation in the ab initio calculation is the most
suitable and convenient method in this regard. The
Avogadro software was used to simulate geometry of
initial structures. All thermodynamical calculations for
pristine PbSe have been performed using Firefly 8
package within Density Functional Theory (DFT)
formalism [19].
Energy minimization was carried out through self-
consistent field wave function using the Restricted
Hartree–Fock (RHF) calculation. The convergence
criteria for Self-Consistent Field (SCF) method
calculations were chosen as ∆ESCF = 10–4 eV. The
calculations were carried out on the basis of Stevens–
Basch–Krauss–Jasien–Cundari (SBKJC) parameteriza-
tion [20]. DFT calculations were performed using hybrid
DFT GGA with the Becke three-parameter hybrid
method [21] with Lee, Yang, and Parr (B3LYP) gradient
corrected correlation functional [22]. We did not use a
supercell model, however a cluster approach was applied.
The expediency of choosing this set has been proved in
[23-25]. The Chemcraft software was used to visualize
the results.
The PbSe compound crystallizes in a cubic granular
structure of the type of NaCl (structural type B1) with the
lattice parameter a = 6.12 Å [1, 18, 26], the spatial group
is 53 hOmFm − . This position of atoms can be explained
with account of lead chalcogenide relation to polar
semiconductors characterized by the ionic-covalent type
of bonds. The chosen structure allows the construction of
clusters without involvement of additional atoms for the
purpose to compensate the broken bonds. Crystal
structures of lead sulfide have been investigated using
four models, namely, on the base clusters with 64, 56, 27
and 8 atoms. Constructing the clusters, the main attention
was paid to symmetry and electric charge of clusters to
eliminate structural distortion caused by action of surface
forces. This approach has been successfully used to
creation of the cluster models for II-VI compounds
[27, 28].
In IV-VI semiconductors, the valence electrons of
lead form the sp
3-hybridized bonds with tellurium. Two
s-electrons form deep narrow bands and practically do
not take part in formation of bonding. Therefore, valence
bands and conductive bands should be constructed from
p-orbitals, which cubic symmetry reflects the cubic
structure of bundles in IV-VI semiconductors. If the
atoms of metal and chalcogen are chemically identical,
then their fcc-lattice will turn into a simple cubic with an
odd number of electrons (namely, three) in the cell.
Therefore, under constructing the electronic spectrum of
these compounds, it is necessary to include the
Hamiltonian for the prophase of the ion potential, which
describes the difference between metal atoms and
chalcogen. This potential doubles the period of simple
cubic lattice, and, as a result, even quantity of electrons
(3 × 2 = 6) is available in the new bcc-lattice, and the
spectrum transforms to the dielectric type. By the order
of magnitude, the potential of ion is close to the
difference between the potentials of ionization of metal
atoms and chalcogen [29].
A
B
C
D
Fig. 1. Cluster models for cubic phase of PbSe: А (Pb32Se32),
В (Pb28Se28), C (Pb14Se13), and D (Pb4Se4).
SPQEO, 2019. V. 22, N 2. P. 156-164.
Nykyruy L.I., Naidych B.P., Voznyak O.M. et al. Account of surface contribution to thermodynamic properties …
158
a)
b)
Fig. 2. Models of PbSe films in the cross-section on (200)
plane: front (a) and upper (b) images.
The first of the proposed cluster models (Fig. 1, A –
the general formula is Pb32Se32) is the base for calcu-
lating both the spatial and electronic structure, as well as
thermodynamic parameters. This model consists of 64
atoms and contains 4 pairs of six-coordinated atoms, 12
pairs of five-coordinated atoms, 12 pairs of four-
coordinated atoms and 4 pair of three-coordinated atoms.
The second cluster has the general formula Pb28Se28
(Fig. 1, B) and consists of 56 atoms. It contains 4 pairs of
six-coordinated atoms, 12 pairs of five-coordinated
atoms, and 12 pairs of three-coordinated atoms.
The third cluster model contains 27 atoms and has
the chemical formula Pb14Se13 (Fig. 1, C). This structure
consists of one six-coordinated atom, 6 five-coordinated
atoms, 12 four-coordinated atoms, and 8 three-
coordinated atoms.
The fourth cluster with the formula Pb4Se4
(Fig. 1, D) is composed of 8 three-coordinated atoms.
At the first stage, the crystallographic parameters of
the formed cluster were determined at the minimum
potential energy and corresponded to the real position of
the atoms in crystal. All the calculations began with SCF,
next optimization of the geometry and the subsequent
determination of stable minimum. Then, on the base of
the obtained crystallographic parameters, the frequency
of oscillations of atoms was calculated [30].
Visualization of spatial structures was carried out using
Chemcraft software.
This approach enables to compile a system of
equations for calculation of the thermodynamic values
for selected clusters. As a result, we obtain the values of
these parameters for three-, four-, five- and six-
coordinated atoms, of which the cubic structure of NaCl
forms itself.
Investigation of the films by using model
approaches is based on assumption that real structures are
limited in space, finite and not symmetrical along all
directions.
Model images of the surface according to different
projections are shown in Fig. 2. As our study has
showed, this model corresponds to the experimental data.
This choice is consistent with other researches and
enables to simulate the effect of surface. In particular, the
plane PbSe (200) is the preferred growth plane, when the
surface energy minimization dominates in the total free
energy variation [31].
3. Theoretical approach of thermodynamic
calculations
3.1. Thermodynamic characteristics of crystals
In approximation of the fixed molecule [32], the enthalpy
H of crystal formation is defined as:
( ) ( ) ( ) ,0 RTTHTHTEHHH transrotvibvibelec +++++≈
(1)
where Hеlec is the electronic component of enthalpy, Hvib
– vibration component of enthalpy, 0
vibH – enthalpy of
zero vibrations, Hrot – rotational component of enthalpy,
Htrans – translational component of enthalpy, R –
universal gas constant, T is absolute temperature in K.
Similarly, the energy of formation was calculated.
In general, the entropy of the crystal is determined
by the sum of components:
( )[ ]1ln 0 −−+++=∆ nNnRSSSSS elecvibrottrans , (2)
where N0 is the Avogadro constant, n is the number of the
mole of molecules.
We can calculate the free Gibbs energy of the crystal at
known temperature T by calculating the contributions of the
energy of zero vibrations and of individual entropy parts of
the reagent molecules A (Pb) and B (Te).
−ν−ν+−=∆ ∑∑
∈∈ Bj
j
Ai
iBA hhHHG
2
1
2
1
( )B
trans
A
trans
B
rot
A
rot
B
vib
A
vib SSSSSST −+−+−− . (3)
To calculate ∆E, ∆H, ∆S, ∆G, CV and СP, used was
the following method taking into account the initial
conditions, on the example of formation energy ∆E.
Initially, the energy of formation ∆EA of the cluster A
(Fig. 1, A) was calculated according to [32]:
SPQEO, 2019. V. 22, N 2. P. 156-164.
Nykyruy L.I., Naidych B.P., Voznyak O.M. et al. Account of surface contribution to thermodynamic properties …
159
∑∑ +−=∆ atelA EEEE , (4)
where E is the total energy of the system, Eel – electron
energy of the atoms forming the system (in the atomic
state), Eat – atomization energy. The total and electronic
energies of the system were used from the calculation
results, and all the other values were taken from references
[33]. Similarly, the formation energies ∆EB, ∆EC and ∆ED
for clusters B, C and D (Fig. 1, B, C, D) were calculated.
The thermodynamic characteristics of PbSe crystals
at different temperatures were calculated on the basis of
computed vibrational spectra (Figs. 3 to 7).
As a result of quantum-chemical calculations, the
values of each thermodynamic quantity for the
corresponding clusters were obtained. Based on the
consideration that these values were obtained as a set of
these values for each individual atom in the cluster, each
equation consists of the sum of contributions of all
atoms, among which there are, respectively, three-, four-,
five-, and six-coordinated atoms:
=
=+++
=++
=+++
,8
,6128
,82424
,824248
3
6543
653
6543
Dx
Cxxxx
Bxxx
Axxxx
(5)
where xi (i = 3, 4, 5, 6) are the contributions of the
corresponding three-, four-, five-, and six-coordinated
atoms to the end value of thermodynamic parameters (in
this case to the end value of formation energy ∆Ei), i is the
number of atomic bonds formed. The factors before the
values xi denote the number of corresponding atoms in the
cluster; ∆EA, ∆EB, ∆EC, and ∆ED – values of
thermodynamic parameters (in this case, for formation
energies under known temperature) for the corresponding
clusters A, B, C, D (Fig. 1).
Having solved this system relatively to x6, we obtain
the following relation:
C
BDA
x −
−
+=
4
5
26 . (6)
Heat capacity at constant volume of CV (similarly to
СP), in accordance with the given approximations is
determined using the following formula:
)()()( vibVrotVtransVV SSSC ++= . (7)
Contributions of translational degrees of freedom were
calculated without data of quantum-chemical calculations,
since they depend on external factors (T, P).
The contribution of the vibration component in the
harmonic approximation, according to which the
symmetry, relatively to the position of the displacement
equilibrium, leads to symmetric change in the potential
energy and is determined by the expression:
( ) ∑
−
=
ν
−
ν
−
i
kT
hc
kT
hc
ii
vibV
i
i
e
evg
kT
hc
RC
2
22
1
. (8)
where gi is the degree of degeneracy of the i-th oscillation.
According to [34], the temperature dependence of
the heat capacity of the crystalline structures is
determined by the following function:
253 1010 −−
⋅−⋅+= TcTbaC , (9)
where a, b, c are the constant coefficients, which depend on
the type of crystalline lattice and chemical compound.
3.2. Thermodynamic characteristics of the surface
layers
Created on the surface of the crystal are the bonds
directed inside the structure and along the surface. Thus,
the surface layer of cubic crystal is formed by three-,
four-, and five-coordinated atoms. To define the
thermodynamic characteristics for these atoms, the same
cluster models as for internal atoms can be used, but in
this case the system (5) is solved with regard to x3, x4 and
x5. We obtained the following relations for these atoms:
33
D
x = , (10)
12244
DBA
x +
−
= , (11)
86
262
5
BADC
x +
−−
= . (12)
Fig. 3. Temperature dependences for the isobaric heat capacity
of PbSe: ● – for three-coordinated atoms, ♦ – for four-
coordinated atoms, and ■ – for five-coordinated atoms, ▲ – for
six-coordinated atoms and comparing with experimental data:
○ – [40], × – [42], + – [36], -- – the theoretical curve according
to the Djulong–Pti law.
SPQEO, 2019. V. 22, N 2. P. 156-164.
Nykyruy L.I., Naidych B.P., Voznyak O.M. et al. Account of surface contribution to thermodynamic properties …
160
4. Results and discussion
The changes in the energy of formation ∆E, enthalpy of
formation ∆H, Gibbs free energy ∆G, entropy ∆S,
isovolume heat capacity CV, and isobaric heat capacity
CP for PbSe crystals within the temperature range from
20 up to 1000 K are shown in Figs 3 to 7.
The temperature dependences of the thermo-
dynamic parameters of lead selenide crystals within this
temperature range after approximation by using the
mathematical package Maple 18 yield the following
dependences:
( ) ii bTaTE +=∆ , (13)
( ) ii bTaTH +=∆ , (14)
( ) ( ) ii bTaTS −=∆ ln , (15)
( ) 253 1010 TcTbaTG iii
−−
⋅−⋅+=∆ . (16)
The calculated analytical expressions of the
obtained temperature dependences for the isovolume and
isobaric heat capacities, respectively, approximated using
the quantum-chemical calculation points, are described
by the following equations:
253 1010 −−
⋅−⋅+= TcTbaC iiiP . (17)
Table 1. The coefficients of approximation of the temperature dependences of thermodynamic parameters: energy ∆E, enthalpy
∆H, Gibbs free energy ∆G, entropy ∆S, and isobaric heat capacity CP.
Approximation coefficients
Thermodynamic parameters
аі bi ci
The number of
atomic bonds
0.016 58.742 6
0.0105 104.66 5
0.0173 102.36 4
The energy of formation, ∆E
0.0097 104.76
3
0.0146 58.742 6
0.0162 102.36 5
0.0109 104.66 4
Enthalpy, ∆H
0.0102 104.76
3
20.497 54.11 6
15.622 28.828 5
9.2478 84.726 4
Entropy ∆S
8.4562 91.997
3
60.198 20.3 2 6
6.046 1.6 2 5
4.2496 22.3 1 4
Gibbs free energy, ∆G
4.2099 25.8 1 3
32.784 22.932 0.148 6
45.777 1.784 0.179 5
43.456 4.875 0.144 4
Specific heat capacity, CP
41.945 4.956 0.131 3
Table 2. Experimental data and those calculated in this paper for thermodynamic parameters of PbSe semiconductor at the
temperature 273.15 K.
∆H ∆G ∆S Cp
Reference data
102.58 [35]
105.0 ± 4.0 [36]
106.7 ± 4.0 [37]
83 [41]
–(97.9 ± 7.7) [38]
–101.577 ± 2.092 [39]
–106.4 [40]
102.58 [36]
107.9 ± 4.0 [41]
102.51 ± 2.09 [39]
50.6 ± 1.0 [42]
51.14 [41]
50.21 [40]
Calculation data
(in this paper,
for six-coordinated
atoms)
112.31 100.3 117.67 48.45
SPQEO, 2019. V. 22, N 2. P. 156-164.
Nykyruy L.I., Naidych B.P., Voznyak O.M. et al. Account of surface contribution to thermodynamic properties …
161
Fig. 4. Temperature dependences of energy (∆E) for cubic
PbSe crystals: ● – for three-coordinated atoms, ♦ – for four-
coordinated atoms, ■ – for five-coordinated atoms.
Fig. 6. Temperature dependences of Gibbs free energy (∆G) for
PbSe: ● – for three-coordinated atoms, ♦ – for four-coordinated
atoms, ■ – for five-coordinated atoms.
The obtained values of isovolume heat capacity CV
and isobaric heat capacity CP at different temperatures
are shown in Fig. 3. Good accordance with theoretical
data can be reached by fitting the obtained calculation
data to the classical law by Djulong and Pti. In the low
temperature range, the obtained values are proportional
to T3, which corresponds to the Debye theory. Also,
comparison of the calculation results with the measured
experimental values was performed.
The slight deviations from the rectangular cross-
position of the crystalline planes also were observed in
the modelling of the PbSe structure in [43], using the
GAUSSIAN 03 and SBKJC bases set. These results are
confirmed by the experimental data in [44], as well as by
the structural data in [45].
Fig. 5. The temperature dependences of the entropy (∆S) for
PbSe: ● – for three-coordinated atoms, ♦ – for four-coordinated
atoms, ■ – for five-coordinated atoms.
Fig. 7. Temperature dependences of the enthalpy (∆H) for PbSe
surface atoms: ● – for three-coordinated atoms, ♦ – for four-
coordinated atoms, ■ – for five-coordinated atoms.
The deviation of the theoretically calculated
equilibrium structure from the typical for rock salt lattice
values can be explained by significant deviation of the
lattice spectrum from the Debye spectrum [46]. Ionicity
is the essential phase transition constraining factor. A
similar effect is observed in spin-orbital interaction, since
it violates the congruence of Fermi surface. This value
for lead chalcogenides is large, which explains the lack
of these transitions in respective compounds. However,
the study of the phonon spectrum shows a strong
softening of the optical phonon near the G point [47].
The changes of the formation energy ∆E, enthalpy
∆H, Gibbs free energy ∆G, the entropy ∆S, isovolume heat
capacity CV and isobaric heat capacity CP for the surface of
PbSe films within the temperature range 20…1000 K are
shown in Figs. 3 to 7. Their analytical expressions have
been represented as the dependences (13)–(17).
SPQEO, 2019. V. 22, N 2. P. 156-164.
Nykyruy L.I., Naidych B.P., Voznyak O.M. et al. Account of surface contribution to thermodynamic properties …
162
5. Conclusions
1. The cluster models and boundary conditions for
calculation of thermodynamic parameters have been
proposed as based on the crystalline and electronic
structure of cubic PbSe, as well as its physical and
chemical properties. It has been shown that the
plane PbSe (200) is the preferred growth plane,
when the surface energy minimization dominates
over the total free energy variation.
2. The temperature dependences of thermodynamic
parameters for PbSe crystals and films have been
determined, namely: the energy of formation ∆E,
enthalpy of formation ∆H, entropy ∆S and Gibbs
free energy ∆G, as well as molar isovolume heat
capacity CV and isobaric heat capacity CP.
3. Theoretical models of surface states of PbSe films
have been proposed. The main thermodynamic
parameters have been calculated on the base of this
model. The obtained results are in good agreement
with experimental data, in particular, for heat
capacity at low temperatures [36]. For temperatures
above 500 K, the monotonous growth of
experimental values is observed, and the calculated
values correspond to the law by Djulong and Pti.
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Authors and CV
Lyubomyr Nykyruy, born in 1972,
defended his Ph.D. in Physical and
Mathematical Sciences in 2004.
Docent (Ass. Prof.). Professor of the
Physics and Chemistry of Solids
Department at the Vasyl Stefanyk
Precarpathian National University.
The area of his scientific interests includes the study of
the features of transport phenomena in semiconductors;
thermoelectric and photovoltaic properties of bulk, thin
films and nanocrystalline semiconductor materials.
T.O. Parashchuk, born in 1989,
defended Ph.D. in Physical and
Mathematical Sciences in 2015.
Postdoctoral Fellowship in the
Institute of Advanced Manufacturing
Technology, Krakow (Poland). The
area of his scientific interests includes
semiconductor materials for thermo-
electricity, calculations of structural and electronic
properties of semiconductors by the DFT method.
B.P. Naidych, born in 1990, Ph.D.
student, researcher. The area of her
scientific interests includes the tech-
nology of obtaining semiconductor
materials, quantum-chemical calcu-
lations of thermodynamic properties
of semiconductor crystals, tempe-
rature dependences of thermodynamic
properties, temperature of phase
transitions of binary semiconductor
materials II-VI and IV-VI.
O.M. Vozniak, born in 1949, devoted
PhD in Physical and Mathematical
Sciences in 1975. Docent (Ass. Prof.)
of the Physics and Chemistry of
Solids Department at the Vasyl
Stefanyk Precarpathian National
University. The area of his scientific
interests includes the theoretical
studies concerning the properties of two- dimensional
electron gas, the spectrum of electronic excitations of
disordered systems and their localization, the study of
transport phenomena in semiconductor materials with a
narrow band gap by the variational method.
R.V. Ilnitskyi, born in 1977,
defended his Dr. Sc. degree in 2017.
Doctor of the Physical and
Mathematical Sciences, Professor,
Head of Postgraduate and Doctoral
Department at the Vasyl Stefanyk
Precarpathian National University.
The area of his scientific interests
includes the methods for modifying of the surface in
materials for energy, research of the nano-dispersed
titanium dioxide properties, etc.
|
| id | nasplib_isofts_kiev_ua-123456789-215470 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-23T18:52:48Z |
| publishDate | 2019 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Nykyruy, L.I. Naidych, B.P. Voznyak, O.M. Parashchuk, T.O. Ilnytskyi, R.V. 2026-03-18T11:40:31Z 2019 Account of surface contribution to thermodynamic properties of lead selenide films / L.I. Nykyruy, B.P. Naidych, O.M. Voznyak, T.O. Parashchuk, R.V. Ilnytskyi // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2019. — Т. 22, № 2. — С. 156-164. — Бібліогр.: 47 назв. — англ. 1560-8034 PACS: 05.70.Np, 68.35.Md, 71.15.Mb https://nasplib.isofts.kiev.ua/handle/123456789/215470 https://doi.org/10.15407/spqeo22.02.156 Being based on the density functional theory (DFT), computer simulation of the surface effect on thermodynamic parameters of lead selenide (PbSe) has been performed in this work. Applying the thermodynamic approach, the choice of model for the plane PbSe [200] preferred orientations has been justified, which indicates domination of the energy of surface states, while minimization of interface energy and deformation are less important in overall changing the free energy. The thermodynamic parameters for the surface of crystals and their temperature dependences in the framework of DFT method and using the hybrid functional B3LYP have been calculated, namely: energy ∆E, enthalpy ∆H, Gibbs’ free energy ∆G, isobaric heat capacities Cᴘ and isovolume heat capacities Cᵥ, entropy ∆S. The analytical expressions of temperature dependences for these thermodynamic parameters approximated using quantum-chemical calculation data have been obtained. The analysis of temperature dependences for the heat capacity corresponds to the experimental data and the Djulong–Pti law. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Semiconductor physics Account of surface contribution to the thermodynamic properties of lead selenide films Article published earlier |
| spellingShingle | Account of surface contribution to the thermodynamic properties of lead selenide films Nykyruy, L.I. Naidych, B.P. Voznyak, O.M. Parashchuk, T.O. Ilnytskyi, R.V. Semiconductor physics |
| title | Account of surface contribution to the thermodynamic properties of lead selenide films |
| title_full | Account of surface contribution to the thermodynamic properties of lead selenide films |
| title_fullStr | Account of surface contribution to the thermodynamic properties of lead selenide films |
| title_full_unstemmed | Account of surface contribution to the thermodynamic properties of lead selenide films |
| title_short | Account of surface contribution to the thermodynamic properties of lead selenide films |
| title_sort | account of surface contribution to the thermodynamic properties of lead selenide films |
| topic | Semiconductor physics |
| topic_facet | Semiconductor physics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/215470 |
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