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RESEARCH ARTICLE
Investigated the structural, optoelectronic, mechanical, and
thermoelectric properties of Sr
2
BTaO
6
(B =Sb, Bi) for solar
cell applications
Mumtaz Manzoor
1
| Debidatta Bahera
2
| Ramesh Sharma
3
| Faisal Tufail
4
|
Muhammad Waqas Iqbal
4
| Sanat Kumar Mukerjee
2
1
Department of Electrical Engineering,
Riphah International University, Lahore,
Pakistan
2
Department of Physics, Birla Institute of
Technology, Mesra, India
3
Department of Applied Science, Feroze
Gandhi Institute of Engineering and
Technology, Raebareli, India
4
Department of Physics, Riphah
International University, Lahore, Pakistan
Correspondence
Ramesh Sharma, Department of Applied
Science, Feroze Gandhi Institute of
Engineering and Technology, Raebareli,
U.P. 229001, India.
Email: sharmadft@gmail.co
Muhammad Waqas Iqbal, Department of
Physics, Riphah International University,
Lahore, Pakistan.
Email: waqa.iqbal@riphah.edu.pk
Summary
Density functional theory was used to investigate the unit structure of
Sr
2
BTaO
6
(B =Sb, Bi) double perovskite oxides. The full-potential linearized
augmented plane wave technique is used to calculate structural, electronic,
electron localization function (ELF), mechanical, optical, and thermoelectric,
properties. We optimized the compounds at ground level by using the Murna-
ghan equation of state. Additionally, the formation, cohesive energy, and Gold-
schmidt tolerance factor were calculated to assure the structure's stability.
With the aid of symmetric lines, we examined the Sr
2
BTaO
6
(B =Sb, Bi) were
found to be semiconductors with indirect band gaps of 2.066 and 0.972 eV, cor-
respondingly. To analyze the bonding in the material and also the magnitude
of charge transformation from inter-band and intra-band, we considered the
electron localization function (ELF). The independent elastic coefficient (C
ij
),
and other parameters were calculated for the material's mechanical stability.
To achieve the maximum absorption coefficient, the optical properties with all
parameters were computed in given double perovskites materials. Lastly, The
BoltzTrap code is also used to compute transport characteristics like as the See-
beck coefficient (S), a figure of merit (ZT), electrical conductivity (σ/τ), power
factor (PF), and thermal conductivity (κ/τ). Sr
2
BiTaO
6
appears to be a more
promising material as compared to Sr
2
SbTaO
6
for thermal devices based on ZT
estimates against chemical potential and carriers' concentrations. All com-
puted properties outcomes advocated that these materials are an attractive
source for thermal devices as well as solar applications.
KEYWORDS
double perovskites, first-principles study, optoelectronic, structure stability, thermoelectric
properties
1|INTRODUCTION
With the shortage of carbon-based fossil fuels, it is essen-
tial to improve the efficiency of existing fossil fuels or find
alternate energy sources.
1
The current energy scenario
requires the conversion of energy sources from fossil fuels
to renewable sources such as solar cells, photovoltaic,
photo-catalyst, piezoelectric, and thermoelectric (TE).
2-4
Received: 31 May 2022 Revised: 11 August 2022 Accepted: 14 August 2022
DOI: 10.1002/er.8669
Int J Energy Res. 2022;1–17. wileyonlinelibrary.com/journal/er © 2022 John Wiley & Sons Ltd. 1
Material scientists are becoming interested in TE mate-
rials because they support effective and efficient methods
of conserving energy in the form of waste heat.
5,6
These
materials can undoubtedly be considered green energy
reservoirs and control mechanisms for addressing the
global energy crisis.
7-9
The ability of materials to convert
waste heat into electrical power is known as the TE phe-
nomenon.
10
TE conversion efficiency is expressed as
ZT =σS
2
T/κ, where, σ,S,T, and κare the electrical con-
ductivity, Seebeck coefficient, absolute temperature, and
total thermal conductivity, respectively.
11
Here, the ther-
mal conductivity (κ) is due to lattice thermal conductivity
(κ
l
) and electronic thermal conductivity (κ
e
).
12
To achieve
an optimum ZT, high TE power factor (S
2
σ) and low ther-
mal conductivity (κ) is the essential tool.
11
On the basis of
a basic understanding of thermoelectricity researchers
worked on improving TE power factor (S
2
σ) and reducing
thermal conductivity (κ).
13
Different strategies have been
considered to improve S
2
σsuch as energy filtering, band
engineering, and rational structure/lattice imperfection
designs that include dislocations, point defects, nano
inclusions, and interfaces considered to reduce κby
improving multi-wavelength phonon scattering. Conse-
quently, new and novel TE materials are developing with
optimum ZT.
14-17
However, perovskite based compounds
have attracted the attention and reported to exhibit out-
standing ZT in recent decades.
18-22
Many scientists and
chemists are interested in these materials because they
have a variety of physical, chemical, and catalytic proper-
ties that can be employed in technological applications.
Simple perovskites (ABX
3
) have a cubic crystal structure
with the space group Fm3m (225).
23
Since, A site cation
has 12 coordination numbers, it forms a 12-fold cubocta-
hedra geometry with its neighbors. By interacting with its
surrounds anions, the B-site cation creates octahedral
geometry.
24
Aside from ordinary perovskites, double
perovskites have gotten a lot of interest because of their
outstanding potential for modern applications.
25,26
The
typical formula for double perovskite is A
2
BB0O
6
, where
the A site is inhabited by a rare-earth or alkaline-earth
metal, and the B and B0sites are occupied by distinct
cations (transition/nontransition metals). Because of its
stunning features, such as electronic, TE, and supercon-
ductivity, oxide-based double perovskites have piqued
attention in a variety of technologically relevant disci-
plines, applied, and fundamental areas of material
research.
27,28
Recently, TE behaviors of 3D-metal-based
double perovskites such as La
2
CuMnO
6,29,30
Ba
2
FeMoO
6,31
and Ba
2
MnTaO
632
have been reported.
La
2
CuMnO
6
provides ZT about 0.39 at 800 K.
30
While a
theoretical analysis predicted that Ba
2
FeMoO
6
had a
potential cryogenic TE performance with a high ZT of
1 at 200 K.
31
Furthermore, first-principles calculations
revealed that Sr
2
HoNbO
6
may have a maximum ZT of
0.98 at 250 K, suggesting that it could be useful in low-
temperature TE applications.
4
Lastly, for mechanical sta-
bility in the oxygen based perovskites employing first
principles calculation. Rached et al. reported the phase
stability, electronic, and optical properties of Pb
2
FeMO
6
(M =Mo, Re, W) double perovskite compounds.
33
Mate-
rials scientist are constantly investigating these materials,
both experimentally and theoretically. However, density
functional theory (DFT) has remained a boon in theoreti-
cal studies to explore and analyze the physical and chemi-
cal properties of these compounds.
4
Recently numerous
compounds have been reported under DFT exploring
their structural, electronic, mechanical, and transport
properties. Motivating comes from tuning the bandgap by
replacing the element in the materials from wider to
lower band to attain the maximum efficiency via transi-
tion of electrons, Therefore, we accomplished the above
mentioned properties of Sr
2
BTaO
6
(B =Sb, Bi). We
employed the full-potential linearized augmented plane
wave (FP-LAPW) method by using the multiple approxi-
mations in optimization, electronics parts, and considered
the formation energy, cohesive energy. We computed
structure, tolerance factor, electronic properties, ELF,
optical properties, TE properties against temperature,
chemical potential, and carrier concentration. Finally
spectroscopy limited maximum efficiency (SLME) of the
investigated double perovskite is computed to analyze the
maximum efficiency.
2|COMPUTATIONAL METHOD
The calculation is performed with the WIEN2k
software,
34,35
based on the first-principles DFT approach
with a FP-LAPW approach.
36,37
This method integrates
all electrons in the computational effort, recognized as
the most precise way for determining electronic parame-
ters, including the band structure of crystalline materials.
The structural optimization and elastic parameters were
determined using the Perdew-Burke-Ernzerhof and Gen-
eralized gradient approximations (PBE-GGA).
38
We used
the Tran-Blaha modified Becke-Johnson (TB-mBJ)
exchange potential approximation
39
to achieve the pre-
cise bandgap. Because it offers exact localized electrical
states, this approach appears to be correct. For the inte-
gration of the k-space in Brillouin zone, the modified tet-
rahedron method is used for conserved self-consistency
cycle, 15 15 15 k-mesh was used in the first Brillouin
zone, and the energy cut off was set to 10
5
Ry. To avoid
charge leakage from the core, R
MT
(muffin-tin radii)
values of 2.05, 2.0, 1.92, and 1.73 a.u. are employed in
these computations for Sr, Sb, Ta, and O in Sr
2
SbTaO
6
2MANZOOR ET AL.
and 2.04, 1.98, 1.90, and 1.71 a.u. for Sr, Bi, Ta, and O in
Sr
2
SbTaO
6
, respectively. The matrix size (convergence) is
determined by the convergence parameter R
MT
K
max
=7,
where K
max
is the plane wave-cut-off and RMT is the
smallest of all atomic sphere radii. The G
max
parameter
was taken to be 12. To check the mechanical stability, we
computed the elastic constants using the IRELAST
method, which was employed in the WIEN2k code. The
TE properties of this compound have been studied using
the semi-classical Boltzmann theory as implemented in
the BoltzTrap code.
40
For the transport properties calcu-
lation, we have adopted fine grid mesh (46 46 46).
3|RESULT AND DISCUSSION
3.1 |Structural properties
Each B atom of ABX
3
materials is covered by at least the
closest X atoms, producing an octahedron, whereas “A”
atoms are covered by 12 closest X atoms, making a hexa-
gon. The unit cell of A
2
BB0X
6
is equivalent, with alternat-
ing BX
6
and B0X
6
octahedral. The Sr
2
BTaO
6
(B =Sb, Bi)
crystallizes with the space group Fm3m (#225). Accord-
ing to the Wyckoff rule, the 8c Wyckoff position is occu-
pied by “A,”whereas the 4a and 4b Wyckoff positions are
occupied by B and B0, correspondingly, as well as the 24e
Wyckoff position is occupied by the oxygen atom. For
oxygen based Sr
2
BTaO
6
, Sr, and (B =Sb, Bi) can be +1
sign atoms, Ta can be +3 sign atoms, as well as O can be
1 sign. In this work, we use A =Sr, B =Sb, Bi, B0=Ta,
and X =O atoms for the double perovskites materials as
shown in Figure 1. Two fundamental tolerance condi-
tions must be fulfilled for these chemicals to remain sta-
ble in a high symmetry unit cell. One is Goldschmidt's
tolerance factor,
41,42
t¼RAþRO
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2RBþRO
ðÞ
p, which ought to be
more than 0.8 and near 1. Secondly, the consideration is
the octahedral factor (μ=R
B
/R
X
), which must be greater
than 0.414 for BX
6
octahedral stability. The ionic radii of
the atoms at positions A, (B and B0), and O are repre-
sented by R
A
,R
B
, and R
O
, correspondingly. The initial
round of screening involves selecting currently studied
compounds that meet each of these requirements as
given in Table 1. The size of the Sb, Bi, and Ta atoms are
calculated independently, and the tolerance conditions
are evaluated individually for each octahedral. For struc-
turally stable materials, we parent molecules, we replaced
Sb, Bi atom having an ionic radius of 1.19 Å, which meets
with all tolerance conditions for oxygen. For further veri-
fication of structure stability, we computed the optimiza-
tion by using the Murnaghan equation of state (eos) with
diverse approximations. We employed the PBE, WC, and
PBEsol approximations to attain the most ground states
energy (eV). We observed that the PBE approximations
give us the most optimized results for both materials as
shown in the Figure 2. The most optimized outcomes are
given in the Table 1.
EVðÞ¼E0þ9V0B0
16
V0
V
2
3
1
"#
3
B0
0
8
<
:
þV0
V
2
3
1
"#
2
64V0
V
2
3
"#
19
=
;
ð1Þ
We estimated the formation energy of the examined
chemical in order to determine its stability. The following
equation bellow used to determine the formation energy
of Sr
2
BTaO
6
(B =Sb, Bi).
EfSr2BTaO6B¼Sb, BiðÞðÞ¼Etot Sr2BTaO6B¼Sb, BiðÞðÞ
ESrðBulkÞ
þEBðBulkÞþETaðBulkÞþEO
where E
tot
(Sr
2
BTaO
6
(B =Sb, Bi)), E
Sr
(Bulk), E
B
(Bulk),
and E
Ta
(Bulk) are equilibrium total energy of Sr
2
BTaO
6
(B =Sb, Bi) and corresponding energies in bulk struc-
ture. The estimated formation energy of Sr
2
BTaO
6
(B =Sb, Bi) is represented in Table 1. The commuted for-
mation energy negative which suggests the investigated
FIGURE 1 Generated the crystal structure of double
perovskites Sr
2
BTaO
6
(B =Sb, Bi) compounds
MANZOOR ET AL.3
compound is thermodynamically stable and cannot
decomposed once synthesized.
3.2 |Electronic properties
The electronic properties of the compound can be charac-
terized by the energy band structure and the density of
states (DOS) to analyze the material nature.
28
The elec-
tronic band structure of Sr
2
BTaO
6
(B =Sb, Bi) double
perovskite computed along the high symmetry lines in
the Brillouin zone and presented in Figure 3A,B.We have
computed the electronic band structure of Sr
2
BTaO
6
(B =Sb, Bi) using different potentials Perdew-Burke-
Ernzerhof (PBE), Wu-Cohen (WC), Perdew-Burke-
Ernzerhof solid (PBEsol), 1 new modified Becke-Johnson
(1nmBJ), 2 new modified Becke-Johnson (2nmBJ), 1 non-
magnetic modified Becke-Johnson (1nmmBJ), modified
Becke-Johnson plus spin orbital coupling (mBJ +SOC),
and new modified Becke-Johnson plus spin orbital cou-
pling (nmBJ +SOC).as presented in the Table 2. Using
2nmBJ potential indirect band gap 0.97, 2.066 eV
obtained for Sr
2
BTaO
6
(B =Sb, Bi) double perovskite,
respectively. Figure 3A,B illustrates the combined TDOS
and PDOS of Sr
2
BTaO
6
(B =Sb, Bi) double perovskite. The
plot provides comprehensive information regarding ele-
mental contribution. The DOS contour indicates that the
upper region of the valence band extending from 0 to 4 eV
TABLE 1 Calculated lattice parameter a(A), bulk modulus B, its derivative B
P
, the minimum total energy E
tot
, energy of cohesion E
coh
,
enthalpy of formation E
f
, and bond length (Å) for properties 10 * 10 * 10 mesh used
XC a(Å) V(a.u
3
)B(GPa) B
P
E
tot
(Ry) E
f
(eV/atom) Bond length (Å)
Sr
2
SbTaO
6
PBE-GGA 8.444 1015.76 143.04 4.30 57 842.842806 2.886 Sr Sb =3.5955
Sr Ta =3.5955
Sr O=2.9367
WC-GGA 8.357 984.72 153.93 4.31 57 835.377493
PBEsol-GGA 8.354 983.60 153.31 4.25 57 817.282449
Sr
2
BiTaO
6
PBE-GGA 8.555 1056.34 140.25 4.66 88 038.641525 2.798 Sr Bi =3.5843
Sr Ta =3.5843
Sr O=2.9369
WC-GGA 8.466 1023.72 153.92 4.79 88 030.087901
PBEsol-GGA 8.465 1023.52 153.32 4.74 88 007.373752
Ba
2
ReFeO
643
8.192 980.14 49 604.71
Note: Yellow colour demonstrated that we attained the most optimized value of double perovskites's lattice parameters after employing the diverse exchange-
functions and red colour presented the modified values after revision.
FIGURE 2 Accomplished the optimization plots with diverse approaches (PBE, WC, and PBEsol) to get the utmost optimized energy vs
volume (a.u)
3
of double perovskites Sr
2
BTaO
6
(B =Sb, Bi) compounds, respectively
4MANZOOR ET AL.
is predominantly occupied due to O p states with aggrega-
tion of Bi/Sb atoms, while the bands in the energy range of
0to4eVareduetotheSratomforSr
2
BTaO
6
(B =Sb, Bi).
In the conduction band, the Taatomisresponsibleforthe
bands in the region of 2.5 to 4 eV. The bands occurring
inside the higher energy level of the conduction band are
due to the hybridization between the Sb/Bi atoms with a
small aggregate of Sr atom.
3.3 |ELF and Bader charge
The charge density and its spatial distribution can be
used to calculate the bonding characteristic.
44
Ionic
bonding has no charge between its constituents, whereas
metallic and covalent bonding has atoms that share a
charge. Charge sharing is directed in a covalent bond,
whereas charge distribution is homogeneous throughout
a metallic bond.
45
Along the body diagonal plane,
Figure 4A,B depicts the spatial charge configuration for
the O-based double perovskite. The charge distributions
of the Sr and Sb/Bi atoms are perfectly spherical, with
no charge contours overlapping those of the O atom.
The presence of an ionic link between the Sr and Sb/Bi
atoms and the O atom was demonstrated. The charge
distribution of the Ta, on the other hand, fluctuates from
perfect spherical to deformed, resulting in covalent
bonding with the O atom (dumb-bell type). This is cor-
roborated by the Bader charge analysis, the results of
which are listed in Table 3. Due to covalent properties, it
has been confirmed that O takes electrons from the Ta
network.
FIGURE 3 Accomplished the
combined the electronic band structure
and density of states to analyzed the
material nature of double perovskites
Sr
2
BTaO
6
(B =Sb, Bi) compounds,
respectively
TABLE 2 Calculated energy bandgap (in eV) by different potentials PBE, WC, PBEsol, mBJ, nmBJ, unmBJ, and mBJ +SOC
Properties PBE WC PBEsol mBJ 1nmBJ 2nmBJ unmBJ mBJ +SOC nmBJ +SOC
Sr
2
SbTaO
6
0.371 0.160 0.125 0.798 0.863 0.972 0.457 0.652 0.818
Sr
2
BiTaO
6
1.077 0.895 0.889 1.837 1.913 2.066 1.282 1.793
Reference 43 0.40 2.20
Note: Red coulor presence the modified word after revision.
MANZOOR ET AL.5
3.4 |Elastic properties
Mechanical properties are essential when designing
solids for commercial manufacturing for various applica-
tions with the IRELAST method by using the WIEN2k
code. Second-order elastic constants (C
ij
) were calculated,
including Young's modulus (Y), Poisson's ratio (v), bulk
modulus (B), shear modulus (G), brittleness, ductility,
anisotropy, elastic wave propagation, Debye temperature,
average velocity, longitudinal and transverse waves, and
brittleness, ductility, anisotropy, elastic wave propaga-
tion, Debye temperature, average velocity, longitudinal
For cubic systems, and the three independent elastic
constants C
11
,C
12
, and C
44
are used to determine the
dimensional strength of each structure. These parameters
were calculated using the matrix of equations, and we
also have to meet the born elastic solidity conditions,
which are (C
11
C
12
)/2 > 0, (C
11
+2C
12
)>0, C
11
>0,
and C
44
>0.
46
Table 4presents our calculated elastic con-
stants for Sr
2
AsBO
6
(B =Sb, Bi) compounds in GPa.
These findings meet the requirement for born elastic sta-
bility, showing that these molecules are mechanically sta-
ble. Furthermore, the values of Cauchy pressure, which
is the difference between C
11
,C
12
, and C
44
, are positive
for both compounds investigated.
48
This demonstrated
that our structures have a metal nature. The elastic con-
stants for cubic structure are used to compute the bulk
modulus (B), shear modulus (G), Young modulus (Y),
Poisson's ratio (ν), and anisotropy (A), using the below
formulae.
B¼C11 þ2C12
3ð2Þ
G¼C11 C12
2ð3Þ
Y¼9GB
3BþGð4Þ
FIGURE 4 Accomplished electron localized function (ELF) to
check the transformation of electron in double perovskites
Sr
2
BTaO
6
(B =Sb, Bi) compounds, respectively
TABLE 3 Bader charge analysis of for Sr
2
BTaO
6
(B =Sb, Bi)
compounds
Bader charges
Sr =1.6264 Sr =1.6207
Sb =2.008 Bi =1.9918
Ta =2.6760 Ta =2.6854
O=1.3218 O =1.3198
TABLE 4 Calculated values of elastic constants C
11
,C
12
,C
44
in
(GPa), bulk modulus B(GPa), shear modulus G(GPa), Young's
modulus Y(GPa), Poisson's ratio ν, Zener anisotropy factor (A), B/
Gratio, Cauchy pressure (C
12
-C
44
) and melting temperature T
m
(K),
effective mass of holes, and electrons m*
h
,m*
e
for Sr
2
BTaO
6
(B =Sb, Bi)
Parameters Sr
2
SbTaO
6
Sr
2
BiTaO
6
Other study
47
C
11
334.14 409.56 339.87
C
12
92.46 94.99 96.96
C
44
27.17 5.20 98.04
B173.02 199.84 178
G64.64 66.03 107.05
Y172.45 178.45 267.52
ν0.333 0.6512 0.25
B/G2.6 3.02 1.66
A0.22 0.03 0.081
Θ
D
389.5 310.6
V
tran
2870 2294
V
long
6196 5937
V
avg.
3233 2601
T
m
2126.7 1586.3 2561
m*
h
3.1958 2.0579
m*
e
0.2943 0.2474
6MANZOOR ET AL.
ν¼3B2G
23BþGðÞ ð5Þ
A¼2C44
C11 C12 ð6Þ
Bulk modulus determines the crystal strength against
compression strain. The large bulk modulus (B) value
suggests high crystal strength. The crystal resistance to
deformation by plastic forces is described by the shear
modulus (modulus of rigidity).Shear modulus values are
higher in stiff materials. Young's modulus (Y) determines
the stiffness of a composite. Another parameter, Pugh's
ratio (B/G), validates if the material is brittle or ductile.
49
If the B/Gratio exceeds 1.75, the crystal is ductile; other-
wise, it is brittle. The computed B/Gfor Sr
2
BTaO
6
(B =Sb, Bi) compounds are shown in the Table 4sug-
gesting that investigated compounds are ductile. Frantse-
vich et al. distinguish brittleness and ductility using
Poisson's ratio; 0.26 is the critical value for both brittle
and ductile qualities.
50
If the Poisson's ratio is less than
0.26, the compound is brittle; if it is greater than 0.26, the
compound is ductile. Poisson's ratio is 0.33 (Sr
2
SbTaO
6
)
and 0.65 (Sr
2
BiTaO
6
), indicating that these compounds
are ductile in nature. A=1 suggests isotropic crystals,
whereas 1 < A< 1 indicates anisotropic crystals. The
computed values of Aare 0.22 (Sr
2
SbTaO
6
) and 0.03
(Sr
2
BiTaO
6
), indicating that these compounds are aniso-
tropic. Except for these, we computed the Debye temper-
ature, melting temperature, and effective mass for holes
and electrons for both compounds. Debye temperature
(389.5 and 310.6) and melting temperature (2126.7
and1586.3) of Sr
2
BTaO
6
(B =Sb, Bi) are respectively.
Here, Debye temperature and melting temperature of
Sr
2
SbTaO
6
are greater than Sr
2
BiTaO
6
compound. Lastly,
we have an effective mass for holes are 3.1958 and 2.0579
of Sr
2
BTaO
6
(B =Sb, Bi), respectively. Similarly, effective
mass for holes of Sr
2
SbTaO
6
is greater than Sr
2
BiTaO
6
compound. Electrons effective mass are 0.2943 and
0.2474 for Sr
2
BTaO
6
(B =Sb, Bi) are respectively.
3.5 |Optical properties
Motivated by the prospect of using its interesting elec-
tronic structure for optoelectronic semiconductor applica-
tions, the optical and electronic transport properties of
the double perovskite oxide of Sr
2
BTaO
6
(B =Sb, Bi)
were studied.
44,51
The energy-dependent optical proper-
ties were studied and calculated through the dielectric
functions. It was realized that the optical properties of a
solid can be portrayed by the complex dielectric work
ε(ω), which has two sections, real and imaginary,
11,52
and
can be communicated as:
ε¼ε1ωðÞþiε2ωðÞ ð7Þ
The imaginary part ε
2
(ω), which arises from inter-
band and intra-band transitions, shows the possible tran-
sitions from the occupied to unoccupied states with fixed
(k-vectors) over the Brillouin zone (BZ), which are depen-
dent on DOS and the momentum matrix P; it can be
mathematically defined as:
ε2ωðÞ¼ e2ℏ
πm2ω2XZMν,ckðÞ
jj
2δω
νckðÞω½d3kð8Þ
where prepresents the moment matric element between
the states of band αand βwithin the crystal momentum
k, while c
k
and v
k
are the crystal wave functions corre-
sponding to the conduction and valence bands with the
crystal wave vector kfrom the imaginary part using the
Kramers-Kronig relationship,
53,54
which provides the real
part ε
1
(ω) of the dielectric function
ε1ωðÞ¼1þ2
πPZ∞
0
ω0ε2ω0
ðÞdω0
ω02ω2
ð9Þ
The knowledge of both the real and imaginary parts
of the dielectric function allow the calculation of impor-
tant optical functions such as, refractive index nωðÞ,
extinction coefficient kωðÞ, reflectivity RωðÞ, optical
absorption coefficient αωðÞ, and optical conductivity σωðÞ
using the following expression
55
:
nωðÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ε2
1ωðÞþε2
2ωðÞ
pþε1ωðÞ
2
"#
1
=
2
ð10Þ
Extinction coefficient kωðÞcan be determined by
using calculated values of ε1ωðÞand ε2ωðÞfor the afore-
said double perovskite with the help of relation given
below
kωðÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ε2
1ωðÞþε2
2ωðÞ
p2ε1ωðÞ
2
"#
1
=
2
ð11Þ
Figure 5A,B shows the real and imaginary compo-
nents of a dielectric matrix as a function of photon energy
for both materials (0-10 eV). The dielectric permittivity of
Sr
2
BTaO
6
(B =Sb, Bi) compounds began about 4.8 and
3.2, respectively, according to Table 4.The static constant
ε
1
(0) for Sr
2
BTaO
6
(B =Sb, Bi) is 4.8 and 3.2,
MANZOOR ET AL.7
respectively, according to the Penn model.
56,57
Further-
more, increasing the energy in the form of photon energy
(eV) enhanced the transition of electrons from valence to
conduction till the visible region for Sr
2
AsSbO
6
, but
increased in the ultraviolet region for Sr
2
BiTaO
6
.Figde-
picts an imagined dielectric function that is used to calcu-
late the absorption factor by increasing the photon
energy (eV). The static point values of ε
2
(0) are evaluated
at zero for both substances. Meanwhile, we discovered
absorption in the visible area for both compounds, as
shown in Figure 5B. These variations are caused by
numerous inter-band transitions between the valence
and conduction bands. The values nearest to the bandgap
are called fundamental absorption edge values. The main
absorption edges correspond to the optical transitions
between valence band maxima and conduction band
minima. In the UV, on the other hand, there is a signifi-
cant increase in absorption. In comparison, of both mate-
rials, the Sr
2
AsSbO
6
has maximum absorption rather
than Sr
2
BiTaO
6
compound. Understanding a material's
refractive index n(ω) and extinction coefficient K(ω) aids
in understanding its optoelectronic capabilities, which
are critical for practical applications. The variations of n
(ω) vs photon energy (eV) for both Sr
2
BTaO
6
(B =Sb, Bi)
materials are shown in Figure 5C. The refractive index of
Sr
2
BTaO
6
(B =Sb, Bi) compounds at 0 eV energy is listed
in Table 5, however, at 3.1 and 4.2 eV, the greatest values
of n(ω) for Sr
2
BTaO
6
(B =Sb, Bi) are around 2.7 and 2.5.
In Figure 5D, we estimated the energy-related extinction
coefficient, k(ω), which represents the damping of the
incoming electric field's oscillation amplitude. At zero,
there is no oscillation; however, by increasing the energy
(eV), the oscillations in the visible zone are revealed. The
variation in optical conductivity for the materials studied
is plotted against photon energy (eV) from 0 to 10 eV pre-
sented Figure 6A. The σ(ω) for Sr
2
BTaO
6
(B =Sb, Bi)
compounds starts about 1.9 and 3.3 eV, respectively, and
increases to 5000 and 6200 (cm)
1
around 5.9 and 6.2 eV
as shown in Figure 6A. According to our findings, these
materials can be used in a number of optoelectronic
applications. Another important optical measure is the
material's absorption coefficient α(ω), which indicates
how much light is absorbed by the compound.
59
Figure 6B shows the energy-dependent absorption spec-
tra of both Sr
2
BTaO
6
(B =Sb, Bi) compounds against
photon energy (eV). The absorption edges of Sr
2
BTaO
6
FIGURE 5 Accomplished the optical properties with real and imaginary dielectric, refractive index, and extinction coefficient to
analyzed the material nature by fall the light of double perovskites Sr
2
BTaO
6
(B =Sb, Bi) compounds, respectively
8MANZOOR ET AL.
(B =Sb, Bi) compounds are 2.5 and 3.5 eV, respectively.
For energy levels greater than 3 eV, a significant intensity
of α(ω) is observed, indicating that the examined com-
pounds may absorb visible and UV radiations. The reflec-
tance R(ω) of the investigated Sr
2
AsBO
6
(B =Sb, Bi)
compounds has also been investigated and depicted in
Figure 6C within the energy spectrum of 0 to 10 eV.
The reflectance of Sr
2
BTaO
6
(B =Sb, Bi) compounds at
0 eV energy is 0.9 and 0.12, indicating typical semicon-
ductor characteristics. The reflectance coefficient of
Sr
2
BTaO
6
(B =Sb, Bi) increases with increasing photon
energy, peaking at 3.2 and 4.1 eV, respectively. L(ω)is
another important optical constant for determining the
optical characteristics of substances. It gives informa-
tion on the plasma frequencies of the compounds as
well as the scattering of electrons traveling through
themasshowninFigure6D.
60
At energies above and
below plasma frequency, compounds have dielectric
and semiconducting characteristics, respectively. The
highest peaks in Sr
2
BTaO
6
(B =Sb, Bi) compounds are
TABLE 5 Calculated optical and transport properties by nmBJ potential
Material property Sr
2
SbTaO
6
Other works
58
Sr
2
BiTaO
6
Other work
58
Optical properties ε
1
(0) 4.15 2.30 3.32 2.74
R(0) 0.11 0.042 0.08 0.061
n(0) 2.04 1.52 1.82 1.66
Transport properties (300 K) σ/τ(Ωms)
1
(10
18
) 1.04 1.772 1.27 1.7720
S(μVK) 249 147.36 241 158.59
k/τ(W/mKs) (10
15
) 0.025211 0.39 0.0292 0.433
PF (10
10
) (W/K
2
ms) 6.45 3.84 7.34 4.33
ZT
e
0.768 0.753
FIGURE 6 Accomplished the optical properties with electrical conductivity, absorption, reflection, and energy loss to analyzed the
material nature by fall the light of double perovskites Sr
2
BTaO
6
(B =Sb, Bi) compounds, respectively
MANZOOR ET AL.9
around 6.9 and 7.2 eV, respectively. The transition sites
of Sr
2
BTaO
6
(B =Sb, Bi) from semiconducting to dielec-
tric properties correspond with the peaks in electron
energy loss.
3.6 |Transport properties
The BoltzTrap software
40
was used to calculate the trans-
port properties of oxygen based double perovskites
Sr
2
BTaO
6
(B =Sb, Bi) compounds. The attained out-
comes were plotted against temperature, chemical poten-
tial, and carrier concentrations. We elaborated the
Sr
2
AsBO
6
(B =Sb, Bi) compounds vs temperature to find
out the material's nature with the majority of holes or
electrons. Lastly, we proved the Sr
2
BTaO
6
(B =Sb, Bi)
compounds nature against μE
f
(eV) and N(e/a.u) and
have categorized a p-type as well as an n-type.
24
We have
computed the different parameters such as electrical con-
ductivity (σ/τ), and Seebeck coefficient (S). Thermal con-
ductivity (κ/τ), power factor (PF), and figure of merits
(ZT). Individually elaborated the transport properties and
relate the effects in the materials by T,μ(eV), and N(e/a.
u). We considered the transport properties against
temperature with S,κ/τ,σ/τ, and PF for both compounds
presented in Figure 7A-D, and here we just let the
300 and 1200 K to check the thermal behavior of the
materials.
The Seebeck coefficient formula S=rV/rKis given
and the induced voltage was examined at 300 and 1200 K
are 249.8, 242.5, 240.5, and 240 μV/K for both com-
pounds, respectively as demonstrated in Figure 7A.We
examined by increasing the temperature in these mate-
rials the induced voltages decreased due to increasing the
vibration of carriers. Figure 7B presents the σ/τ,at
300 and 1200 K the electrical conductivity gradually
increased by surging the temperature having the values
0.9 10
18
, 8.5 10
18
,110
18
, and 10 10
18
(Ω.m.s)
1
.
Furthermore, we considered the thermal conductivity at
300 and 1200 K with achieved values in the double perov-
skites are 0.01 10
15
, 0.8 10
15
, 0.02 10
15
, and
0.81 10
15
W/K.m.s. we observed by increasing the tem-
perature thermal conductivity increased as shown in
Figure 7C. PF examined 0.6 10
11
, 5,0 10
11
,
6.1 10
11
, and 5.5 10
11
W/K
2
.m.s as shown in
Figure 7D.
Furthermore, n-type or p-type system vs μ
(eV) associated to eradicate or accumulation of carriers
FIGURE 7 Accomplished the transport properties with S,σ/τ,κ/τ, and PF against temperature of double perovskites Sr
2
BTaO
6
(B =Sb,
Bi) compounds, respectively
10 MANZOOR ET AL.
from materials.
61,62
We considered the transport proper-
ties with diverse temperatures like 300, 600, 900, and
1200 K as a function of chemical potential. To observe
the variation in the Sfor double perovskites materials
Sr
2
BTaO
6
(B =Sb, Bi) compounds, we plotted the Swith
diverse temperatures as exhibited in Figure 8A,B. The
highest temperature (1200 K) provided the Sin up-side
up to 250 μV/K and downside 500 μV/K at 0.25 μE
f
(eV) and 0.5 μE
f
(eV). For 700 and 300 K the
Sexamined under 750 μV/K and approximately 780,
1600, and 1750 μV/K at 0.3 and 0.4 μE
f
(eV), respec-
tively, as shown in Figure 8A. Similarly, For theSr
2
Sb-
TaO
6
compound, the Svalues at 1200, 700, and 300 K are
900 μV/K at 0.8 μE
f
(eV), 1050 μV/K at 0.7 μE
f
(eV),
2800 μV/K at 0.5 μE
f
(eV), 1000 μV/K at 1.1 μE
f
(eV), 1060 μV/K at 1.20 μE
f
(eV), and 3000 μV/K at
1.25 μE
f
(eV) for up and downside, respectively as
demonstrated in Figure 8B. We concluded that by
increasing the external temperature the S gradually
increased up and downside with positive chemical poten-
tial. Figure 9A,B presents the σ/τfor both materials, there
are no specifically fluctuations in σ/τvalues by increasing
the temperature as well as chemical potentials values
however we examined the thermal bandgap which is
approximately equal to the optoelectronics band gap. For
Sr
2
BTaO
6
(B =Sb, Bi) compounds, from 0 to 1.4 μE
f
(eV) and 0 μE
f
(eV), to up to 2 μE
f
(eV) the electri-
cal conductivity lines remains constant which is advo-
cates these band gaps values are comparable with
optoelectronic band gaps values. We found 3.5 10
15
,
2.5 10
15
, and 1.2 10
15
W/mKs κ/τwith 1200 K,
700 K, 300 K 1.0 μE
f
(eV), 0.99 μE
f
(eV), and
0.93 μE
f
(eV) but in positive chemical potential side
there was minor values of for the Sr
2
SbTaO
6
compound
as shown in Figure 9A. In the same way, We found
3.4 10
15
, 2.4 10
15
, and 1.1 10
15
W/mKs κ/τwith
1200 K, 700 K, 300 K 1.0 μE
f
(eV), 0.99 μE
f
(eV), and 0.93 μE
f
(eV) but in positive chemical poten-
tial side there were minor values of for the Sr
2
TaSbO
6
compound as exposed in Figure 9B. By comparison of
materials, the Sr
2
SbTaO
6
compound has maximum ther-
mal conductivity as the Sr
2
BiTaO
6
compound. Figure 9C,
Dpresents the power factor of double perovskites
Sr
2
BTaO
6
(B =Sb, Bi) compounds which advocates for
Sr
2
SbTaO
6
having maximum PF on the positive side than
the negative side. By increasing the temperature PF step
FIGURE 8 Accomplished the transport properties with Sand σ/τ, against chemical potential of double perovskites Sr
2
BTaO
6
(B =Sb,
Bi) compounds, respectively
MANZOOR ET AL.11
by step surged. With the 300, 700, and 1200 K, there are
PF values are around about 3.9 10
11
, 6.9 10
11
, and
7.2 10
11
W/mK
2
s at 1.65 μE
f
(eV) as illustrated in
Figure 9C. Figure 9D presents the maximum PF at
0.2 μE
f
(eV) with different temperatures of 300, 700,
and 1200 K having the values are 0.31 10
11
, 5.0 10
11
,
and 7. 0 10
11
W/mK
2
s but at 1 there is no PF as shown
in Figure 9D. We have calculated the figure of merits
ZT ¼S2σ
KeþKL
ðÞ
63
for both compounds. Figure 10A,B demon-
strates the ZT value of oxygen-based perovskites with
values 1, and 1.1 with 300 K at 0.5 μE
f
(eV) and
1μE
f
(eV), and these values are allowed to use in ther-
mal devices.
Figure 11A-D presents the S,σ/τagainst N(e/u.c)
with positive and negative doping in the materials, and
in graphs of the Seebeck coefficient, there is no change
FIGURE 9 Accomplished the transport properties with κ/τ, and PF against chemical potential of double perovskites Sr
2
BTaO
6
(B =Sb,
Bi) compounds, respectively
FIGURE 10 Accomplished the
transport properties with ZT against
chemical potential of double perovskites
Sr
2
BTaO
6
(B =Sb, Bi) compounds,
respectively
12 MANZOOR ET AL.
by increasing the doping and temperature (K) and also in
σ/τ. Overall, we analyzed that in Sr
2
BiTaO
6
compound
has major variation in n-type doping from 0 to 0.5 as
shown in Figure 11A,B. Additionally, at 1 N(e/u.c) there
is a maximum achievement in σ/τfor both studied com-
pounds. However, Sr
2
SbTaO
6
has the highest σ/τas com-
pared to the Sr
2
BiTaO
6
compound. Electronic thermal
conductivity (κ
e
/τ) for both compounds has been com-
puted to examine the induced heat energy from the mate-
rials. We studied these materials with 300, 700, and
1200 K temperatures against n-type and p-type doping.
We attained the maximum value with 300, 700, and
1200 K are 1 10
15
, 2.6 10
15
, and 4.1 10
15
W/mKs at
1N(e/u.c) for Sr
2
SbTaO
6
compound. Similarly, Sr
2
Bi-
TaO
6
compounds with 300, 700, and 1200 K are
1.3 10
15
, 3.8 10
15
, 4.6 10
15
W/mKs at 1.3 N(e/u.c).
In both cases, there was a blue shift for p-type doping by
increasing the temperature. The PF is the product of elec-
trical conductivity and the square of the Seebeck coeffi-
cient and evaluates the material's performance to use in
thermal devices.
64,65
Figure 12C,D illustrates the PF for
both double perovskites with diverse temperatures such
as 300, 700, and 1200 K at 1 N(e/u.c) for p-type doping
there is no PF but near to the Fermi-level for both mate-
rials attained 7.8 10
11
and 5 10
11
W/mK
2
s at 1200 K
for both Sr
2
AsBO
6
(B =Sb, Bi) materials, respectively.
Figure 13A,B demonstrated the ZT values at 0 N(e/u.c) is
1 for both compounds but by increasing the p-type dop-
ing sharply decreases, and for n-type doping ZT value lin-
early deceased by increasing the temperature values are
increased.
3.7 |SLME analysis
The performance of a photo-voltaic (PV) device is deter-
mined by the Transport as well as optical characteristics
of the PVA materials. Additionally, the device manufac-
tures process and solid impurities. The SLME was pre-
sented by Yu et al
66
as an effective detection technique
for identifying acceptable PVA materials. It is the greatest
simulated projected performance supplied by a solitary
junction solar cell manufactured from a certain PVA
solid as well as assessed with respect to the ratio of
FIGURE 11 Accomplished the transport properties with Sand σ/τagainst carriers concentrations of double perovskites Sr
2
BTaO
6
(B =Sb, Bi) compounds, respectively
MANZOOR ET AL.13
maximum output power P
m
generated to total incident
solar power P
in
. We used relation
66-68
to replicate the
optimal current density J
V
features of an activated
PV cell.
J¼JSC J0eeV
kBT1
Tis the external temperature, eis the electron charge,
and k
B
is the Boltzmann constant, J
SC
and J
0
are the
short-circuit and reverse-saturation current densities,
respectively.
67
We can measure the absorption efficiency,
electronic bandgap, and solids sheet thickness. For the
normal AM 1.5G visible radiation at 25C, the P
m
is deter-
mined by maximizing power P=J
V
with respect to volt-
age V. Figure 14 shows the influence of SLME on the
thickness of the Sr
2
BTaO
6
(B =Sb, Bi) double perovskite
materials at multiple temperatures in the current investi-
gation. With 293.15 K the SLME values are 1.2%, 30%,
2.1%, and 22.5% at 10
2
and 10
2
μm for Sr
2
SbTaO
6
(solid
FIGURE 12 Accomplished the transport properties with κ/τand PF against carriers concentration of double perovskites Sr
2
BTaO
6
(B =Sb, Bi) compounds, respectively
FIGURE 13 Accomplished the
transport properties with ZT against
carriers concentrations of double
perovskites Sr
2
BTaO
6
(B =Sb, Bi)
compounds, respectively
14 MANZOOR ET AL.
line) Sr
2
BiTaO
6
(dotted line) compounds, respectively.
Further, with 1000 K the SLME values are 0%, 10.8%, 0%,
and 7.6% at 10
2
and 10
2
μm for Sr
2
SbTaO
6
(solid line)
Sr
2
BiTaO
6
(dotted line) compounds, respectively. The
graph demonstrates that a PVA solids film with a thick-
ness of about 1 m has the maximum effectiveness. The
computed SLME ofSr
2
SbTaO
6
(solid line) perovskite is
somewhat higher than Sr
2
BiTaO
6
(dotted line). This
shows keenly theSr
2
SbTaO
6
(solid line) perovskite mate-
rial's capability for harvesting solar energy via reliable
and expensive PV systems at 293.15 K.
4|CONCLUSION
We investigated the Sr
2
BTaO
6
(B =Sb, Bi) compounds
by using the WIEN2k code with diverse approximations.
We computed the structural, mechanical, ELF electron-
ics, optical, SLME, and transport features of oxygen-
based double perovskite Sr
2
BTaO
6
(B =Sb, Bi) com-
pounds. The stability of the Sr
2
BTaO
6
(B =Sb, Bi) struc-
ture was confirmed by optimization, formation, and
cohesive energy. ELF elaborated on the transformation
of electrons from one state to another or from one band
to another band. The calculated electronic structure of
Sr
2
BTaO
6
(B =Sb, Bi) materials reveals that both are
indirect bandgap semiconducting, with energy gaps of
0.972 and 2.066 eV for Sr
2
BTaO
6
(B =Sb, Bi) com-
pounds, respectively. The mechanical properties of the
investigated compounds were analyzed to emphasize
their stability, ductility, and anisotropy, suggesting their
potential for device fabrication. We investigated at the
optical properties of both compounds and found that
they have high absorption power and little reflections for
visible and UV radiation. The maximum absorptions for
both materials were revealed using SLME. Using the
BoltzTraP software, we calculated the power factor and
figure of merit for the transport properties. At 300 K, the
computed ZT values for both compounds are 0.76, indi-
cating that electrons are more effective than holes. The
potential applicability of Sr
2
BTaO
6
(B =Sb, Bi) com-
pounds in optoelectronic and TE applications is demon-
strated by the appropriate values of estimated
parameters such as indirect band gap, absorption spec-
tra, power factor, and figure of merit. Sr
2
BTaO
6
(B =Sb,
Bi) have a PEC of 30% indicating its suitability for solar
devices.
DATA AVAILABILITY STATEMENT
Data available will be available on reasonable request by
the corresponding author.
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How to cite this article: Manzoor M, Bahera D,
Sharma R, Tufail F, Iqbal MW, Mukerjee SK.
Investigated the structural, optoelectronic,
mechanical, and thermoelectric properties of
Sr
2
BTaO
6
(B =Sb, Bi) for solar cell applications.
Int J Energy Res. 2022;1‐17. doi:10.1002/er.8669
MANZOOR ET AL.17
