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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