first-principle study of electronic, optical and transport
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First-principle study of electronic, optical and transport propertiesfor (Zn/Cd)Sc2Se4 spinel chalcogenides
HIND ALTHIB1,2, TAHANI H FLEMBAN1,2, A I ALJAMEEL3, ABEER MERA4,5, M G B ASHIQ1,2,Q MAHMOOD1,2,* , BAKHTIAR UL HAQ6 and SYED AWAIS ROUF7
1Basic and Applied Scientific Research Center, Imam Abdulrahman Bin Faisal University,
P.O. Box 1982, Dammam 31441, Saudi Arabia2Department of Physics, College of Science, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 31441,
Saudi Arabia3Department of Physics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11623, Saudi Arabia4Physics Department, College of Arts and Science, Prince Sattam Bin Abdulaziz University, Wadi Addawasir 11991,
Saudi Arabia5Physics Department, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt6Advanced Functional Materials and Optoelectronics Laboratory, Department of Physics, Faculty of Science, King Khalid
University, P.O. Box 9004, Abha, Saudi Arabia7Division of Science and Technology, Department of Physics, University of Education, Lahore 54770, Pakistan
*Author for correspondence (qmmustafa@iau.edu.sa)
MS received 11 April 2021; accepted 12 July 2021
Abstract. The spinel chalcogenides Zn/CdSc2Se4 are evaluated by first-principle approach to compute optoelectronic
and transport characteristics. The formation energy computations favour their thermodynamic stability. The direct
bandgaps 1.0 and 0.80 eV are evaluated of the most versatile modified Becke and Johnson potential. The optical spectra
have been analysed in terms dielectric constants. The absorption region expands from visible to ultraviolet, which is
suitable for optoelectronics. The bandgap-dependent transport characteristics are addressed by classical theory of
Boltzmann using BoltzTraP code, and a high figure of merit was noted. Finally, electron density measures the polar
covalent bond in Sc-Se and Zn/Cd-Se.
Kewords. Density functional theory; optoelectronic; thermoelectric; figure of merits; renewable energy.
1. Introduction
The increasing demand of energy motivates the researchers
to investigate the substitute materials of fossil fuels and
other conventional energy sources, which must be non-
pollutant and environment friendly [1]. To meet these
challenges, scientists are working on a variety of materials
to increases the power. The cycling process of super-ca-
pacitors and energy storage devices depends upon positive
and negative electrodes capability [2,3]. There are many
other fascinating applications of spinels, such as thermal,
magnetic, spintronic, photocatalysis, photoconductors and
optoelectronic devices. It has been observed from experi-
ments that most of these compounds are stable in cubic (227
Fd-3m) structures at room temperature.
Spinel chalcogenides are considered as anode materials
for capacitance, and conductivity [4,5]. The ternary spinels
may have remarkable physical characteristics that rely on
the preparation techniques and manufacturing process [6].
Moreover, spinels are answerable for puzzlement, which get
their best possible properties [7]. Among this diverse class
of spinels, Zn/CdZ2S4 (Z = Y, Se) have gained consider-
able attention. The reported lattice constant is 10.478 and
10.736 A for ZnY2S4 and CdY2S4, respectively [8]. Reil
et al [9] experimentally prepared crystals of CdY2X4
(X = S, Se) compounds for the first time and found crystal
structure is cubic and diamagnetic in nature. They also
reported large optical bandgap through optical analysis of
these compounds. In another study on CdY2S4 by Tressler
et al [10] have been done to measure the hardness and
fracture toughness of these compounds. It is found that the
hardness of the compound is about 3.1 GPa and Young’s
modulus is about 87 GPa. Unfortunately, there are no
experimental or theoretical studies conducted on CdY2S4 to
further explore the hidden applications.
Among these spinel chalcogenides, Pawlak et al [11]
prepared CdSc2S4 and CdSc2Se4 powder samples by evac-
uated quartz ampoules and reported the lattice constant as
10.70 and 11.20 A in cubic phase. Regarding optical and
thermoelectric properties, there is no available experimental
Bull. Mater. Sci. (2021) 44:254 � Indian Academy of Scienceshttps://doi.org/10.1007/s12034-021-02544-w Sadhana(0123456789().,-volV)FT3](0123456789().,-volV)
and theoretical literature on both ZnSc2Se4 and CdSc2Se4spinels. Therefore, our findings provide deep knowledge to
experimentalist to realize their applications for optoelec-
tronics and thermoelectric applications. The electronic
structures and direct bandgaps of ZnSc2Se4 and CdSc2Se4spinels are elaborated by Tran and Blaha (TB)-modified
Becke and Johnson (mBJ) potential [12]. Moreover, the
bandgap-dependent transport characteristics are elaborated
by BoltzTraP code [13].
2. Method of calculations
The ZnSc2Se4 and CdSc2Se4 have been depicted by Wien2k
through full-potential linearized augmented planewave
method [14,15]. The PBEsol describes the structural prop-
erties precisely but differs in electronic bandgap. Therefore,
to make the bandgap accurate, TB-mBJ is implemented
over PBEsol calculations [12]. TB-mBJ potential improves
the bandgap accurately, given below is the mathematical
expression.
VmBJx;r rð Þ ¼ cVBR
x;r rð Þ þ 3c� 2ð Þ 1p
ffiffiffi
5p
12
ffiffiffiffiffiffiffiffiffiffiffiffi
2tr rð Þp
qr rð Þ ð1Þ
Here c is important that measures the convergence of
charge,
c ¼ aþ b1
Vcell
Z
d3rrq rð Þj jq rð Þ
� �1=2
; ð2Þ
where a and b are constant parameters adjusted in Wien2k
code. Furthermore, the product RMT 9 Kmax = 8 constants,
where RMT is muffin-tin radius and Kmax the maximum of
wave vectors. The other inputs are lmax = 10 and
Gmax = 16. The most important is the choice of k-mesh,
which is taken as the order of 20 9 20 9 20 through the
iteration process. The optical characteristics have been
explained by dielectric constants and Kramer–Kronig
relation.
e1 xð Þ ¼ 1þ 2
pP
Z
1
0
x0e2 x0ð Þx02 � x2
dx0 ð3Þ
e2 xð Þ ¼ e2h0
pm2x2
X
v;c
Z
1
BZ
Mcv kð Þj j2d xcv kð Þ � x½ �d3k ð4Þ
The other optical properties are measured by absorption
coefficient and refractive index and reflection. The transport
properties are evaluated by Boltzmann transport-dependent
BoltzTraP Code [13]. The electrical conductivity is calcu-
lated through the relation.
rab eð Þ ¼ 1
N
X
i;k
rab i; kð Þd e� ei;k� �
d eð Þ ; ð5Þ
rab i; kð Þ ¼ e2si;kta i; k~� �
tb i; k~� �
; ð6Þ
where s is 10-14 s set inside the BoltzTraP code. Seebeck
coefficient and electrical conductivity with respect to tem-
perature is illustrated as
rab a; lð Þ ¼ 1
X
Z
rab eð Þ � of0 T ; e; lð Þoe
de; ð7Þ
Sab T ; lð Þ ¼ 1
eTXrab T ; lð Þ
�Z
rab eð Þ e� lð Þ � of0 T ; e; lð Þoe
de ð8Þ
The Seebeck coefficient is impartial of the relaxation time,
while electrical and thermal conductivities are dependent on
relaxation time.
3. Results and discussion
3.1 Structral and electronic properties
To investigate the characteristics of studied compounds,
stable structural parameters are estimated. For this purpose,
structural optimization has been performed using the Mur-
naghan equation of states under PBEsol functional [15]. It is
found that studied compounds exhibit stable cubic structure
and belong to the space group 227 Fd-3m. Our calculated
cubic lattice constant (a0) and bulk modulus (B0) have
shown excellent agreement with previous results, as listed
in table 1. The crystal structure of studied compounds is
shown in figure 1, which has been used to estimate all
density functional theory calculations in this study. By
changing Zn with a Cd atom in the crystal structure,
noticeable increase in lattice constant and decrease in bulk
modulus are observed. This is due to change in atomic radii
of Zn (1.35 A) and Cd (1.55 A) atoms. We have also
computed enthalpy of formation (DH) of these compounds
to check the structural stability in crystal structure. The
Table 1. The calculated parameters for ZnSc2Se4 and CdSc2Se4.
Compounds ZnSc2Se4 CdSc2Se4
ParametersLattice constant (a0) 10.87 11.16
Other cal. (GGA) 11.06a 11.36a
Exp. 11.21b
B (GPa) 74.52 67.51
Formation energy (DHf) –1.64 –1.60
Bandgap, Eg (eV) 1.0 0.80
e1 (0) 7.60 7.72
n (0) 2.75 2.80
aRef. [33] and bRef. [11].
254 Page 2 of 6 Bull. Mater. Sci. (2021) 44:254
following expression has been used in this study. The
negative values show thermodynamic stability [16,17].
DH ¼ Etotal Zn=CdaScbSecð Þ � aEZn=Cd � bESc � cESe
To perform electronic band structure calculations TB-
mBJ potential is used. In this way, we can best estimate the
electronic band structure as depicted in figure 2a and b. The
calculations of electronic band structure are highly accurate.
Moreover, from band structures, we can find the nature of
bandgap. In direct bandgap, transition of carriers must lie at
the same symmetry point. Any deviation from this direct
bandgap configuration results in the formation of an indirect
bandgap [18]. The bandgaps reported in table 1 are appro-
priate for optical characteristics. The density of states are
plotted for explanation of individual involvements of sub-
atomic states as depicted in figure 3a and b. The transitions
form conduction band Sc-p and valence band Se-p leading
to the direct bandgaps.
3.2 Optical properties
The transitions occur due to light in contact with materials,
which is important considerations during the evaluation of
optical properties. Intra-band and inter-band transitions are
two main types of electronic transitions. This makes inter-
band transitions dominant over intra-band transitions
[19–21]. The complex dielectric constant (x) = e1(x) ?ie2(x) has two parts; real part e1(x) measures the dispersion
Figure 1. Structre of Zn/CdSc2Se4 formed by VESTA software in atomic (right) and polyhedra (left)
formats.
Figure 2. Electronic band strucutres (right) and density of states
(left) of (a) ZnSc2Se4 and (b) ZnSc2Se4.Figure 3. Partial density of states of Zn/Cd, Sc and Se:
(a) ZnSc2Se4 and (b) ZnSc2Se4.
Bull. Mater. Sci. (2021) 44:254 Page 3 of 6 254
and imaginary part e2(x) measures the absorption of light.
The other significant parameters are evaluated from the
e1(x) and e2(x) in terms of reflectivity R(x), absorptiona(x) and refractive index n(x) according to reference [22].
The computed characteristics are depicted in figure 4a–d.
The real dielectric constant e1(x) shown in figure 4a
has the peak values at 2.1 and 2.0 eV for ZnSc2Se4 and
CdSc2Se4, respectively. After the resonance frequency,
graph sharply drops to minimum values and becomes neg-
ative between 5 and 6 eV. The negative values depict the
metallic response of this specified region and all the elec-
tromagnetic radiations are reflected. In addition, the static
dielectric constant e1(0) has been evaluated for both the
compounds, from which it becomes clear that our computed
results are quite in line with that of Penn’s rule
e1(0) & 1 ? (�hxp/Eg)2 (see table 1) [23]. To calculate the
optical absorption for the studied spinels, the e2(x) has beendetermined for the permitted electronic transitions as
depicted in figure 3a. The value of the bandgap for
CdSc2Se4 is 0.80 eV, and for ZnSc2Se4 is 1.0 eV. It has
been observed that both compounds absorb light in visible
and ultraviolet regions. Refraction shows n(x) and k(x),which are replica of e1(x) and e2(x). Therefore, k(x) andn(x) are related with e1(x) and e2(x) through the following
expressions [24].
n2�k2 ¼ e1 xð Þ ð9Þ2nk ¼ e2 xð Þ ð10Þ
The static values of the refractive index n(0) for ZnSc2Se4and CdSc2Se4 are very close, as shown in figure 4b. The
peak values of ZnSc2Se4 and CdSc2Se4 have intensity 3.5,
which exists as photon’s energy 2.0 eV. The extinction
coefficient has a similar trend as the imaginary dielectric
constant, which shows the accuracy of results. The results
show that the studied compounds are suitable for photo-
voltaic applications [25].
The reflection of light described in figure 4c shows the
surface morphology of the studied materials. The CdSc2Se4has greater value of reflection (0.23) than ZnSc2Se4 (0.22).
The absorption coefficient a(x) also measures the attenua-
tions of light like an imaginary dielectric constant and
extinction coefficient. The values of absorption coefficients
are little bit overestimated because of density functional
theory-based approximations. The zero absorption has been
noted for the energies lower than the bandgaps of studied
spinels, which indicates that the light energy should be
greater than the bandgap for the absorption process.
3.3 Thermoelectric properties
The thermoelectric properties of ZnSc2Se4 and CdSc2Se4have been evaluated by BoltzTraP code [26,27]. The
T(K) from 200 to 800 K has been fixed for the intended
investigation. The abundance of electrons in conduction
bands increases electrical conductivity (r/s). The r/s in
metals is maximum due to richness of mobile electrons in
them as compared to the semiconductors, where the value of
r/s can be tuned by bandgap [28]. Furthermore, energy is
needed to electrons to make transitions. In fact, the value of
bandgaps should be small for thermoelectric systems. It has
been also observed that r/s increases with the increase in
T(K) (200–800 K), as shown in figure 5a and b. The free
carriers and the lattice vibrations of phonons are responsible
for thermal conductivity (j/s) in semiconductors [16,29].
The calculated values of thermal conductivities for the
studied compounds are reported in figure 5c and d. When
temperature increases, the thermal conductivity also
increases due to increase in the kinetic energy of electrons.
Figure 4. (a) e1(x) and e1(x), (b) n(x) and k(x), (c) R(x) and(d) a(x) of ZnSc2Se4 and CdSc2Se4. Figure 5. (a, b) r/s, (c, d) j/s and (e, f) S of ZnCdSc2Se4.
254 Page 4 of 6 Bull. Mater. Sci. (2021) 44:254
The lattice vibration also increases due to increase in the
movement of electrons and moves in the material like
elastic waves. Therefore, phonons and the free carriers lying
in the compounds are responsible for conductivity but
ignore the lattice contribution. Because thermal conductiv-
ity is exceedingly small as compared to electrical conduc-
tivity, which does not affect the results at large.
The potential difference developed by the temperature
gradient across the ends of two dissimilar conductors is
named as Seebeck coefficients, whose calculated values vs.temperature are plotted in figure 5e and f. The compounds
having high S are used for thermoelectric applications. The
positive or negative values of S show the nature of charge
carriers as either holes or electrons, which discriminates the
p-type and n-type semiconductors. The values of S are notedas -1.5 and 250 mK V-1 at 300 K for ZnSc2Se4 and
CdSc2Se4, respectively. The multiplication of r/s with the
square of S provided us with a power factor (P). Its value
increases with increase in temperature as described in
figure 6a and b. We only considered the electric conduction
originated by free carriers and neglected the phonon con-
tribution during power factor (PF) readings [30]. Moreover,
ZT (see figure 6c and d) has been evaluated through rS2/jTrelation with increasing temperature. The values of ZT are
0.98 and 0.76 for ZnSc2Se4 and CdSc2Se4 at 300 K. The
increasing temperature causes an increase in the value of
ZT. In conclusion, both ZnSc2Se4 and CdSc2Se4 have been
proved suitable for optoelectronic as well as thermoelectric
applications.
3.4 Electron charge density
The charge density of electrons for ZnSc2Se4 and CdSc2Se4elaborate the charge transfer rate in two-dimensional plane
(101), see figure 7. The distribution of charge exists
between Sc-Se and Zn/Cd-Se, which shows the partial polar
covalent bonding. The core region has more charge, and it
decreases towards corners. Core has dense yellow, then
purple and brown colours. The outer region has blue and
green colours, which is the indication of less charge. This
concept of bonding nature is analysed by electronegativity
divergence (D). For D\ 0.5, 0.5\D\ 1.5 and D[ 1.5
decimate nonpolar, polar and the ionic bond. In our com-
puted results, the D for Sc-Se is 1.19 and Zn/Cd-Se is 0.86/
0.82, which show the polar covalent bonding [31–33].
Furthermore, the charge transfer indicates that the electron
spin plays a dominant role in Sc and changes its spherical
symmetry.
4. Conclusions
In summary, we have elaborated the bandgap-dependent
properties of ZnSc2Se4 and CdSc2Se4 by Wien2K and
BoltzTraP codes. The optimized lattice constants and bulk
modulus are consistent with literature. The bandgap 1.0 and
0.80 eV have been noted. The maximum absorption visible
region and minimum dispersion of light make them
important for optoelectronic applications. Moreover, the
small bandgap and ultralow thermal conductivity increase
their potential for thermoelectric generators. The thermal to
electrical conductivity ratio is exceedingly small. ZT is
verified as 0.99 and 0.76 for ZnSc2Se4 and CdSc2Se4,
respectively. Finally, the partial polar covalent bonding is
observed in both the compounds, which also help to
increase the device feasibility.
Acknowledgement
We extend our appreciation to the Deanship of Scientific
Research at King Khalid University for funding this study
through Research Groups Program under Grant No. R.G.P.
2./126/42.Figure 6. (a, b) rS2 and (c, d) ZT of ZnCdSc2Se4.
Figure 7. Electron charge density plots of (a) ZnSc2Se4 and
(b) ZnSc2Se4.
Bull. Mater. Sci. (2021) 44:254 Page 5 of 6 254
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