Br6 by DFT method

Materials Science in Semiconductor Processing 112 (2020) 105009

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Probing of mechanical, optical and thermoelectric characteristics of double perovskites Cs2GeCl/Br6 by DFT method Q. Mahmood a, b, *, T. Ghrib a, b, A. Rached a, b, A. Laref c, M.A. Kamran d a

Basic and Applied Scientific Research Center, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, 31441, Dammam, Saudi Arabia Department of Physics, College of Science, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, 31441, City Dammam, Saudi Arabia c Department of Physics and Astronomy, College of Science, King Saud University, Riyadh, 11451, Saudi Arabia d Department of Physics, College of Science, Majmaah University, Al-Majmaah, 11952, Saudi Arabia b

A R T I C L E I N F O

A B S T R A C T

Keywords: Density functional theory Optoelectronic devices Visible region of spectrum Thermal to electrical conductivity ratio Figure of merit

The double perovskites halides are potential materials for renewable energy to meets the demands of the global energy shortage. The structural and thermodynamic stabilities of studied materials are ensured by the Goldsmith tolerance factor (0.86 and 0.91) and negative formation energy. The Poisson and Pugh’s ratios show the ductile behaviour of studied compounds. The electronic band gaps 3.42 eV/2.15 eV for Cs2GeCl/Br6 and maximum absorption of light in ultraviolet and visible regions increased their potential for solar cells and other opto­ electronic applications. The thermoelectric characteristics are analyzed by thermal to electrical conductivity ratio and figure of merit criteria. The studied materials have figure of merit 0.80 and 0.82 for Cs2GeCl6 and Cs2GeBr6 at room temperature.

1. Introduction The increasing demand of energy and shortage of resources in the advanced global world stimulate the searchers to explore new sources of renewable energy. The sunlight and wasted heat are two main sources of renewable energy from which light energy and heat energy can be directly converted into electrical energy by solar cells and thermoelec­ tric generators. The efficiency of optoelectronic and thermoelectric de­ vices depends upon the choice of materials. The perovskites halide with general formula ABX3, where A and B are cations and X is anion, was studied intensively from the last two decade and revolutionized because of their potential applications in the do­ mains; photo catalytic effect [1,2], optoelectronics [3–7] and thermo­ electric [8–13]. The lead-halide perovskites based solar cells have attained record breaking light conversion efficiencies (more than 23%), bettering the state-of-the-art, copper indium gallium selenide solar cell (CIGS) and other thin-film based silicon technologies [14,15]. Further­ more, the primary apprehensions over the stability of devices, fabricated by halide perovskites have been lessened by reaching stabilized device efficiencies up to 20% [16–18]. Regardless, this colossal improvement, it would be necessary to replace Pb with other elements which are envi­ ronment friendly and economical. To meet this aim, double perovskite halides have been explored and synthesized recently by lead-free

substituents [19]. The number of substituents to overcome the problem of instability and toxicity, it has been suggested the Ge and Sn are better alternatives because of same group of periodic table and stable cubic phase [20]. The germanium based double perovskites halides have attracted attention of researchers because of their potential applications in opto­ electronics [21]. The Parrey et al., reported high performance of electro-optical properties of RbGeI3 by density functional theory anal­ ysis [22]. Later on, Zhang et al., calculated the electronic structures and band gaps of CsGeX3 (X ¼ Cl, Br, and I) in the visible region of spectrum [23]. In addition to required stability, the optical properties of Cs2SnI6 are investigated because of electronic band gap 1.6 eV and exceptional alterative for photovoltaic applications [24]. Furthermore, Cs2SnI6 and Cs2TeI6 are elaborated by solid solution method and it was found reduced mobility and defect in tolerance. The structural behavior of Cs2Sn1-xTexI6 by the replacement of Sn with Te reduces the electrical conductivity and carrier mobility [25]. The family of double perovskites A2XY6, where A ¼ Cs, Rb, Tl and X ¼ tetravalent cation, Y ¼ Cl, Br, I are studied by Wang et al., to demonstrate their applicability for solar cell applications [26]. The electronic, optical and transport properties of Cs2PdX6 (X ¼ Cl, Br) are explored for renewable energy by theoretical analysis [27]. Above review ensure the vibrant research predictions and need for suitable solar cell and thermoelectric

* Corresponding author. Basic and Applied Scientific Research Center, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, 31441, Dammam, Saudi Arabia. E-mail address: [email protected] (Q. Mahmood). https://doi.org/10.1016/j.mssp.2020.105009 Received 19 December 2019; Received in revised form 10 February 2020; Accepted 15 February 2020 Available online 20 February 2020 1369-8001/© 2020 Elsevier Ltd. All rights reserved.

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Fig. 1. The optimized energy verse volume plots of Cs2GeCl6 and Cs2GeBr6 calculated by.

materials. Therefore, existing literature motivate the possible exploita­ tion of Cesium based halides for large scale energy renewable applications. To the best of knowledge, the double perovskites type compounds Cs2GeX6 (X ¼ Cl, Br), yet not explored in terms of electronic, optical and thermoelectric properties. For the analysis of this unexplored area, we have explained electronic structures in terms of energy band structures and density of states, optical properties in terms of dielectric constants, refraction and absorption coefficient by implementation of TB-mBJ potential. The transport properties are discussed in terms of Seebeck coeffi­ cient, electrical and thermal conductivities and figure of merit for en­ ergy applications.

state properties more accurately but underestimate the electronic band gap. Therefore, to improve the band gap accurately, the TB-mBJ po­ tential has been implemented over PBEsol approximation. The solution of electronic system inside the muffin-tin region is taken spherically harmonic while in interstitial region is plane wave like. The initial pa­ rameters are adjusted by taking angular momentum ℓ ¼ 10, Gaussian parameter Gmax and product of wave vector and muffin-radius KmaxxRMT ¼ 10 in reciprocal lattice. The k-mesh has been selected of the order of 12x12x12 by 2000 k-point at which the energy emitted from the system becomes constant [34]. This is threshold limit of convergence criteria for accuracy of calculated results. The convergence of charge is taken as 0.01mRy. Furthermore, the converged energy and the opti­ mized electronic structures by TB-mBJ have been used to calculate the transport properties through classical Boltzmann transport theory based BoltzTraP code [35].

2. Method of calculations In current article, the electronic, mechanical and optical character­ istics are calculated by density functional theory (DFT) based Wien2k code [28,29]. This all electron based Wien2k code work according to full potential linearized augmented plane wave (FP-LAPW) method [30]. The electronic structures are optimized to reduce interatomic forces and stabilize the structures by PBEsol approximation. The lattice constant, Bulk modulus and ground state energy has been calculated by Murna­ ghan equation of states. The electronic and optical properties are calculated by PBEsol [31,32] and modified Becke Johnson potential of Trans and Blaha (TB-mBJ) [33] because PBEsol analyzed the ground

3. Results and discussion 3.1. Structural behavior and stability The structural study of Cs2GeCl6 and Cs2GeBr6 materials show that they are crystallized into cubic structures with space group Fm3m. The lattice parameters are optimized by PBEsol approximation to remove the strain energies and relax the structures. The optimized crystalline energy verses volume plots are presented in Fig. 1a and Fig. 1b for Cs2GeCl6 and Cs2GeBr6 and their electronic structures are presented on their lift side. The maximum energy released at minimum volume point is noted to elucidate the lattice parameters through Murnaghan equation of states. The calculated lattice constants a0 ¼ 10.61 Å and 11.36 Å are reported for Cs2GeCl6 and Cs2GeBr6 respectively. It is evident that the lattice constant increases by replacement of Cl with Br atom which is due to the increase in atomic radii from 1.75A� (Cl) to 1.85A� (Br). The increasing in cationic size leads to an increase in interatomic distance that make solids less dense and its solidity decreases, therefore, bulk modulus B0 decreases from 22.4 GPa to 17.5 GPa by replacement of Cl with Br. For conformation of structural and thermodynamic stabilities of the studied materials, the Goldsmith’s tolerance (tG) has been calculated by

Table 1 The calculated values of Cs2GeCl6 and Cs2GeBr6 by PBE-GG functional ΔH: enthalpy of formation; Eg(Г-Г): the direct energy band gap (eV), Static dielectric constant ε1(0) and Static refractive index n(0). Parameters

Cs2GeCl6

Cs2GeBr6

ΔH (eV/unit cell) tG Eg (Г-Г) ε1(0) n(0)

1.80 0.86 3.42 2.61 1.61

1.95 0.91 2.15 2.70 1.64

2

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Table 2 The calculated elastic constants (GPa) (C11, C12 and C44); G: shear modulus (GPa); E: Young’s modulus (GPa); B: bulk modulus ν: Poisson ratio; B0/G: Pugh’s; A: anisotropy factor (dimensionless); V: average sound velocity; ϴD: Debye temperature. Parameters

Cs2GeCl6

Cs2GeBr6

C11 C12 C44 B G E Υ B/G A V ϴD

39.6 13.7 12.2 22.4 12.5 31.6 0.26 1.79 0.94 1496 181.9

33.4 9.5 7.2 17.5 8.8 22.6 0.28 1.89 0.60 1395 158.8

Fig. 2. The energy band structure of Cs2GeCl6 and Cs2GeBr6calculated by TBmBJ potential.

pffiffiffi using formula t ¼ ðrCs þrO Þ= 2ðrCl=Br þrO Þ where rCs , rCl=Br and rO are atomic radii of Cs, Ge and Cl/Br atoms [36]. The Goldsmith’s criteria for stable cubic perovskite structures approach to unity for ideal case. However, the range between 0.8-1.4 is considered for stable structures. Our reported values in Table 1, assure the studied materials structures are stable. The comparative analysis shows the Cs2GeBr6 is more near to the ideal limit than Cs2GeCl6. Furthermore, thermodynamic stability has been reported by formation energy through chemical equation ΔHf ¼ ETotal ðCsa Cl = Brb Oc Þ

aECs

bECl=Br

cEGe

Debye temperature is presented in Table 2, has greater value for Cs2GeCl6 as compared to Cs2GeBr6. The Debye temperature is directly proportional to specific heat capacity. Therefore, Cs2GeCl6 has more capacity to withstand against heat produced by lattice vibration [42,43]. Moreover, the increasing heat is directly associated with thermody­ namic stability of the material.

(1)

3.3. Energy bands and density of states

Where ETotal ðCsa Cl =Brb Gec Þ is the total energy of compound, ECs energy of Cs, EGe is the energy of Ge and ECl=Br energy of Cl/Br atoms [37]. The negative value of formation energy shows energy release during com­ pound formation that stabilizes it. The calculated values of formation energy presented in Table 1, confirm the thermodynamic stability of studied materials. The Cs2GeBr6 is comparatively more stable than Cs2GeCl6.

The band structures (BS) of two compounds Cs2GeCl6 and Cs2GeBr6 are shown in Fig. 2 (a, b). The compounds have direct band gap Eg (Γ- Γ) 3.42 eV (Cs2GeCl6) and 2.15 eV (Cs2GeBr6) in near ultraviolet and visible region which increases their importance for solar cell and other optoelectronic applications. Moreover, inter-band transition occurs at Γ-symmetry point directly and at other symmetry points indirectly. To understand the electronic contribution, total density of states (TDOS), partial density of states (PDOS) are plotted in Fig. 3 (a, b). The TDOS shows the total contribution of individual states in valence and con­ duction bands which is similar like band structures. The individual Cs, Ge, Cl and Br atoms have electronic configuration as Cs [Xe] 6s1, Ge [Ar] 4s2 3d10 4p2, Cl [Ne] 3s2 3p5 and Br [Ar] 4s2 3d10 4p5. Only valence electrons contribute to hybridization and inter-band transitions and their contribution at valence and conduction bands are shown in Fig. 3 (a, b). At valence band edge the major contribution comes from Cs-6s1 and Cl/Br3/4p5, and electrons make transitions from valence band to conduction band when carriers get energy.

3.2. Mechanical properties For cubic crystalline structures of the studied double perovskites, mechanical properties are elaborated by tensor analysis of nonlinear differential equations by Chapin method. The three elastic constants C11, C12 and C44 are enough to explain complete mechanical behavior for cubic symmetry. The calculated elastic constants are according to Born mechanical stability criteria C11–C12>0, C44 > 0, C11 þ 2C12 > 0 and C12 < Bo < C11) [38]. The values of elastic constants of Cs2GeBr6 are smaller than Cs2GeCl6 which shows Cs2GeCl6 is mechanically more stable than Cs2GeBr6. The calculated bulk modulus (B), Young modulus (Y) and shear modulus (G) are presented in Table 2, show higher values of moduli for Cs2GeCl6 that make it rigid. The critical limit 1.75 of Pugh’s ratio (B/G) distinguish the brittle (B/G < 1.75) and ductile (B/G > 1.75) behavior of the studied materials. The reported values in Table 2, show ductile behavior which is further ensured by Poisson ratio (υ) whose critical limit for ductile materials is υ > 0.26 [39]. The comparison shows the Cs2GeBr6 is more ductile than Cs2GeCl6 because of large values of Pugh’s and Poisson ratios. Furthermore, the sound velocity is calculated as average of longitudinal and transverse parts of sound ve­ locities by solving Navier equation of states [40,41]. Its value is high for Cs2GeCl6 as compared to Cs2GeBr6 which directly affect the Debye temperature. The Debye temperature has been calculated from the equation θD ¼

� �1 h 3n NA ρ 3 υm κB 4π M

3.4. Optical properties Our studied compounds are direct band gap semiconductors with band gap 3.42 eV and 2.15 eV, therefore, these materials are best suited for optical applications. The optical applications are analyzed in terms of complex dielectric constant, refractive and absorption coefficient as plotted in Fig. 4(a-d). As we discussed above, the studied materials are crystallized in cubic structure, therefore, the unique non-zero compo­ nent of dielectric tensor directly relate band structures with imaginary part of dielectric tensor which is evaluated by dispersion band theory using following equation [44]. Z � 4π2 e2 X i ε2 ðwÞ ¼ 2 2 jijMjjj2 fi ð1 fi Þδ Ej Ei ℏω d3 k (3) m ω i;j V

(2)

Where m and e represent mass and charge of electrons respectively and

ω denotes the angular frequency of electromagnetic radiations. V de­

Where θD is the Debye temperature, M molar mass, NA, Avogadro number, ρ density and υm is average sound velocity. The calculated

scribes a unit-cell volume, ‘ijMjj‘ represents the components of dipole moment matrix, fi is Fermi distribution function and Ei is the electron

3

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Fig. 3. The total density of states (TDOS) and partial density of states (PDOS). of Cs2GeCl6 and Cs2GeBr6calculated by TB-mBJ potential.

energy of state ‘i’. This product jijMjjj2 fi ð1 fi Þ denotes the probability of transition from state ‘i’ of VB to state j of CB. The conservation of total energy during transitions is guaranteed by Dirac function δðEj Ei ℏωÞ. The real part of dielectric function ε1 ðωÞ is illustrated in Fig. 4a, represent the dispersion of light is maximum at resonance frequency for energies 4 eV/3.7eV and 6.3 eV/5.7 eV for Cs2GeCl/Br6. After reso­ nance, the peaks sharply drop to minimum value. The static dielectric constant (zero frequency limit, ω ¼ 0) ε1 ð0Þ which increases from 2.61 to 2.70 by replacement of Cl with Br has inverse relation with band gap and in agreement with Penn’s model [45].

� pffiffi ω qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ε21 ðωÞ þ ε22 ðωÞ C

αðωÞ ¼ 2

Furthermore, real part of dielectric function ε1 ðωÞ is obtained from ε2 ðωÞ using the Kramers-Kronig transformation [46]. 2

ε1 ðωÞ ¼ 1 þ P π

Z 0

∝

ω’ ε2 ðω’ Þ ’ dω ω’2 ω2

(5)

3.5. Thermoelectric properties

Where, P is the principal value of integral. In Fig. 4b, the graphs have similar type of absorption spectra. It starts increasing from threshold limits 3.42eV/2.15eV for Cs2GeCl/Br6 and reaches to peaks at A (4.17 eV) and B (6.46 eV) for Cs2GeCl6 and at C(4.01eV) and D(5.89 eV) for Cs2GeBr6 respectively. The peak (A) recorded due to transition of elec­ trons from Cl-3p and Cs-5s states of VB to Cl-3p states in CB and tran­ sition from Ge-4p and Cl-3p states of VB to Cl-3p states of CB is responsible of peak (B). For Cs2GeBr6, peak (C) correspond to transition of electrons from Br-4p and Cs-5s states of the VB to the Br-4p states in the CB and peak (D) is due to the transition of electrons from Ge-4p and Br-4p states of VB to Br-4p states in CB. The absorption peaks A (4.17 eV)/C (4.0 eV) lies at visible region edge while the peaks B (6.4 eV)/D (5.9 eV) lies in the ultraviolet region. Therefore, the studied materials are suitable for solar cell and other optoelectronic applications. Furthermore, refractive index nðωÞ and absorption coefficients αðωÞ are calculated from ε1 ðωÞ and ε2 ðωÞ by using following equations [47]. "

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi#12 ε1 ðωÞ ε21 ðωÞ þ ε22 ðωÞ nðωÞ ¼ ​ þ 2 2

(7)

The refractive index nðωÞ measures the transparency of material and dispersion of light. The reported values of nðωÞ are plotted in Fig. 4c which is replica of ε1 ðωÞ. The zero energy values of refractive indices nð0Þ 1.61/1.64 for Cs2GeCl/Br6 are in accordance to the relation nð0Þ ¼ pffiffiffiffiffiffiffiffiffiffiffi ε1 ð0Þ. The absorption coefficient αðωÞ measures the attenuation of light energy per centimeter in to material. Its calculated values are presented in Fig. 4d; illustrate the threshold limits 3.42 eV/2.15 eV of αðωÞ are consistent with ε2 ðωÞ that shows the reliability of our reported results. The maximum absorption peaks are found in visible and ultra­ violet region. The peaks also show the ultraviolet region has more in­ tensity than visible region that is suitable for optoelectronic devices functional in ultraviolet light.

(4)

ε1(0) � 1þ (ħωp/Eg) 2

�1=2

ε1 ðωÞ

The thermoelectric properties of Cs2GeCl6and Cs2GeBr6 are calcu­ lated by classical Boltzmann transport theory (CBT) as implemented in BoltzTraP code explained above. The electrical conductivity, Seebeck coefficient and thermal conductivity are expressed in mathematical expression of quantum integral � � Z ∂fμ ðT; εÞ 1 Σ αβ ðεÞ σ αβ ðT; μÞ ¼ (8) dε Ω ∂ε Sαβ ðT; μÞ ¼

keαβ ðT; μÞ ¼

1 e ​ T ​ Ω ​ σ αβ ​ ​ 1 e2 ​ T ​ Ω ​ ​ ​

Z X ðεÞðε

�

μÞ

αβ

Z X ðεÞðε αβ

�

μÞ2

�

∂fμ ðT; εÞ dε ∂ε

(9)

�

∂fμ ðT; εÞ dε ∂ε

(10)

Where Ω is the volume of unit cell, α and β represent independent indices, μ is the chemical potential and f is Fermi-Dirac function. The calculated electrical conductivity versus temperature plots for Cs2GeCl6 and Cs2GeBr6 are shown in Fig. 5a. It measures how many

=

(6)

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Fig. 4. (a) The real part ε1 (ω) and (b) imaginary part ε2 (ω) of complex dielectric constant, (c) refractive index n (ω) and (d) absorption coefficient α (ω) of Cs2GeCl6and Cs2GeBr6 Calculated by TB-mBJ potential.

electrons/holes are available for conduction. The value of electrical conductivity at 50 K is 0.89/0.45 � 1018 (Ω m)-1 and reaches to 8.20/ 7.17 � 1018 (Ω m)-1 at 800 K for Cs2GeCl/Br6 because at high temper­ ature more electrons are produced by bond breaking and have high ki­ netic energy. The electrical energy of Cs2GeCl6 is comparatively higher than Cs2GeBr6 at each point because electrons have to face less collusion. The thermal conduction phenomena can be assured by two modes; electrons mode and phonons mode that can be expressed as k ¼ keþ kph which ke and kph are electrons and phonons thermal conductivities, respectively. In our present calculations, only electronic part is calcu­ lated and ignored phonons contribution because of limitation of classical theory based BoltzTraP code. The calculated thermal conductivity is presented in Fig. 5b. Its value increases from 0.025/0.019 � 1014 (W/m. K) at 50 K linearly up to 400 k for both Cs2GeCl/Br6. After 400 K, it increases up to 800 k (1.22 � 1014 W/m.K) for Cs2GeCl6 while for Cs2GeBr6 it becomes almost constant (2.09 � 1014 W/m.K). The reason of less increasing thermal conductivity of Cs2GeBr6 may be associated with its small band gap as compared to Cs2GeCl6. The Seebeck coefficient (S) measures potential difference with

respect to temperature difference between the contacts of two dissimilar metals. Its calculated values are presented in Fig. 5c. The positive value of Seebeck coefficient shows the majority carriers are electrons and studied materials are n-type semiconductors. Its value starts from 237/ 264 μV/k at 50 K and reaches to 74/125 μV/k at 800 k for Cs2GeCl/Br6, respectively. The Seebeck coefficient of Cs2GeBr6 is greater than Cs2GeCl6 because of its small electrical conductivity. The power factor defined as P ¼ σS2 whose variation versus temperature for Cs2GeCl6 and Cs2GeBr6 is shown in Fig. 5d. It is denoted that the power factor in­ creases with increasing temperature up to 1.5 � 1011 (W/mk2) at 300 k for Cs2GeCl6 and 1.8 � 1011 (W/mk2) at 400 K for Cs2GeBr6. After 400 K, it decreases to 0.40/1.6 � 1011 (W/mk2) at 800 K for Cs2GeCl/Br6. Therefore, PF’s increasing rate of the two compounds is the same at low temperature, but at high temperature decreasing rate is smaller for Cs2GeBr6 as compared to Cs2GeCl6 which indicates two materials may find opportunity in thermoelectric applications at low temperatures. The complicated effect of electrical and thermal conductivities can be easily understand by thermal to electrical conductivity ratio (κ/σ) because it is difficult to separate the electronic part of thermal con­ ductivity from total thermal conductivity. The heat conduction 5

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Fig. 5. (a) The electrical conductivity (σ/τ) and (b) thermal conductivity (κ/τ), (c) Seebeck coefficient (S)and (d) power factor (σS2/τ) of Cs2GeCl6and Cs2GeBr6 calculated by BoltzTraP code.

compared to Cs2GeCl6 because it has less electrical conductivity as plotted in Fig. 6a. The figure of merit variation versus temperature is given in Fig. 6b. Its value for Cs2GeCl6 increases in (50 K–200 K) temperature range and then gradually decreasing in (200 K–800 K) temperature range. For Cs2GeBr6; it keeps approximately the same magnitude during all the temperature range (50 K–800 K). This is due to more Seebeck coefficient and less thermal conductivity for Cs2GeBr6. Form the above analysis of optical and thermoelectric properties, it is concluded that the studied double perovskites are potential materials for renewable optical and thermoelectric energies.

Table 3 Coefficients of k/σ expansion for Cs2GeCl6and Cs2GeBr6. Cs2 GeCl6 A0 A1 A2 A3 A4

Cs2 GeBr6

3:959 � 10

7

9:158 � 10

7

6:399 � 10

8

7:308 � 10

8

1:122 � 10 1:592 � 10

10

13

8:673 � 10

17

1:088 � 10 4:998 � 10

14

3:969 � 10

18

10

phenomenon involves lattice vibration and charge carriers. The ratio of thermal to electrical conductivity can be expressed in terms of polynomial � ke σ ¼ A0 þ A1 T þ A2 T 2 þ A3 T 3 þ A4 T 4 (11)

4. Conclusion In current paper, mechanical, optical and thermoelectric properties are analyzed for renewable energy. The structural and thermodynamic stabilities have been confirmed by the tolerance factor, 0.86 for Cs2GeCl6 and 0.91 for Cs2GeBr6 and negative formation energy. The ductile behavior of Cs2GeCl/Br6 has been ensured by Pugh’s ratio (1.79/ 1.89) and Poisson ratio (0.26/0.28). The reported band gap 3.42 eV show the maximum absorption in ultraviolet region which is shifted to visible region by replacement of Cl with Br and reduction of band gap 2.15 eV. The variation of refractive index in region between 6 eV and 7

Where, the coefficients A0, A1, A2, A3, A4 are presented in Table 3. The coefficient of linear term A1 is in the same order as Weidman-Franz law [48] ke =σ ¼ L0 T where L0 ¼ 2:44 � 10 8 ða:u:Þ: Therefore, thermal to electrical conductivity ratio is very small of the order of (10-6) which increases the interest of materials for thermoelectric applications (Fig. 6a). Comparatively, the slope of graph for Cs2GeBr6 is less as

Fig. 6. (a) Thermal to electrical conductivity ratio and (b) Figure of merit (ZT) of Cs2GeCl6and Cs2GeBr6 calculated byBoltzTraP code. 6

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eV polarized/disperse the light in to its constituent colors at resonance frequency. The thermal conductivity to electrical conductivity is of the order of 10-5 which satisfied the Weidman Franz law. Moreover, the figures of merits at 300 k are 0.80 and 0.82 for Cs2GeCl6 and Cs2GeBr6 which decrease with increasing temperature for Cs2GeCl6 and remain almost constant for Cs2GeBr6. Therefore, the maximum absorption in visible region and more ZT for Cs2GeBr6 shows more potential for solar cells thermoelectric refrigeration applications.

[12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]

Declaration of competing interest We have no conflict of interest; we abide by the policy of Journal.

[23] [24]

Acknowledgement

[25]

The author (A. Laref) acknowledges the financial support by a grant from the “Research Center of the Female Scientific and Medical Col­ leges”, Deanship of Scientific Research, King Saud University. The authors gratefully acknowledge use of the services and facilities of the Basic and Applied Scientific Research Center at Imam Abdulrah­ man Bin Faisal University.

[26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36]

Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.mssp.2020.105009.

[37]

References

[38] [39]

[1] L. Zhou, Y.F. Xu, B.X. Chen, D.B. Kuang, C.Y. Su, Small 14 (2018) 1703762. [2] A.H. Reshak, Phys. Chem. Chem. Phys. 16 (2014) 10558. [3] H.S. Kim, C.R. Lee, J.H. Im, K.B. Lee, T. Moehl, A. Marchioro, S.J. Moon, R. H. Baker, J.H. Yum, J.E. Moser, M. Gratzel, N.G. Park, Sci. Rep. 2 (2012) 591. [4] G. Wang, D. Wang, X. Shi, AIP Adv. 5 (2015) 127224. [5] Z. Xiao, H. Lei, X. Zhang, Y. Zhou, H. Hosono, T. Kamiya, Bull. Chem. Soc. Jpn. 88 (2015) 1250–1255. [6] X. Qiu, B. Cao, S. Yuan, X. Chen, Z. Qiu, Y. Jiang, Q. Ye, H. Wang, H. Zeng, J. Liu, M.G. Kanatzidis, Sol. Energy Mater. Sol. Cell. 159 (2017) 227–234. [7] N. Guechi, A. Bouhemadou, S.B. Omran, A. Bourzami, L. Louail, J. Electron. Mater. 47 (2017) 1533–1545. [8] T. Ishibe, A. Tomeda, K. Watanabe, Y. Kamakura, N. Mori, N. Naruse, Y. Mera, Y. Yamashita, Y. Nakamura, ACS Appl. Mater. Interfaces 10 (2018) 37709–37716. [9] E. Haque, M.A. Hossain, Comp. Cond. Matt. 16 (2019), 00374. [10] Y. Zhang, C.Y. Tso, J.S. I~ nigo, S. Liu, H. Miyazaki, C.Y.H. Chao, K.M. Yu, Appl. Energy 254 (2019) 113690. [11] L. Peedikakkandy, J. Naduvath, S. Mallick, P. Bhargava, Mater. Res. Bull. 108 (2018) 113–119.

[40] [41] [42] [43] [44] [45] [46] [47] [48]

7

E. Haque, M.A. Hossain, J. Alloys Compd. 748 (2018) 63–72. M.A. Green, A.H. Baillie, H.J. Snaith, Nat. Photon. 8 (2014) 506–514. G.E. Eperon, et al., Science 354 (2016) 861–865. S.H.T. Cruz, A. Hagfeldt, M. Saliba, Science 362 (2018) 449–453. G. Volonakis, M.R. Filip, A.A. Haghighirad, N. Sakai, B. Wenger, H.J. Snaith, F. Giustino, J. Phys. Chem. Lett. 7 (2016) 1254–1259. A.H. Slavney, T. Hu, A.M. Lindenberg, H.I. Karunadasa, J. Am. Chem. Soc. 138 (2016) 2138–2141. M. Roknuzzaman, et al., Org. Electron. 59 (2018) 99–106. Y.Q. Zhao, X. Wang, B. Liu, Z.L. Yu, P.B. He, Q. Wan, M.Q. Cai, H.L. Yu, Org. Electron. 53 (2018) 50–56. J.Y. Qian, B. Xu, W.J. Tian, Org. Electron. 37 (2016) 61–73. M.G. Ju, J. Dai, L. Ma, X.C. Zeng, J. Am. Chem. Soc. 139 (2017) 8038–8043. K.A. Parrey, T. Farooq, S.A. Khandy, U. Farooq, A. Gupta, Comput. Condens. Matter 16 (2019) 381. Q. Zhang, H. Mushahali, H. Duan, M.H. Lee, Q. Jing, Optik 179 (2019) 89–98. B. Saparov, J.P. Sun, W. Meng, Z. Xiao, H.S. Duan, O. Gunawan, D. Shin, I.G. Hill, Y. Yan, D.B. Mitzi, Chem. Mater. 28 (2016) 2315–2322. A.E. Maughan, A.M. Ganose, M.M. Bordelon, E.M. Miller, D.O. Scanlon, J.R. Neilson, J. Am. Chem. Soc. 138 (2016) 8453–8464. M.G. Brik, I.V. Kityk, J. Phys. Chem. Solid. 72 (2011) 1256–1260. K.C. Bhamu, A. Soni, J. Sahariya, Sol. Energy 162 (2018) 336–343. P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, Techn. An Augmented Plane Waveþ Local Orbitals Program for Calculating Crystal Properties, 2001. K. Schwarz, P. Blaha, G.K.H. Madsen, Comput. Phys. Commun. 147 (2002) 71. P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864. J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L. A. Constantin, X. Zhou, K. Burke, Phys. Rev. Lett. 100 (2008) 136406. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. A.D. Becke, E.R. Johnson, J. Chem. Phys. 124 (2006) 221101. P. Blochl, O. Jepsen, O.K. Andersen, Phys. Rev. B 49 (1994) 16223. G.K. Madsen, D.J. Singh, Comput. Phys. Commun. 175 (2006) 67. A.E. Fedorovskiy, N.A. Drigo, M.K. Nazeeruddin, Small. Methods 1 (2019) 1900426. Q. Mahmood, M. Rashid, M. Hassan, M. Yaseen, A. Laref, B.U. Haq, Phys. Scripta 94 (2019) 105812. X. Ji, Y. Yu, J. Ji, J. Long, J. Chen, D. Liu, J. Alloys Compd. 623 (2015) 304. M. Roknuzzaman, K. Ostrikov, H. Wang, A. Du, T. Tesfamichael, Sci. Rep. 7 (2017) 14025. Y.O. Ciftci, K. Colakoglu, E. Deligoz, H. Ozissk, Mater. Chem. Phys. 108 (2008) 120–123. Y.J. Hao, X.R. Chen, H.L. Cui, Y.L. Bai, Phys. B Condens. Matter 382 (2006) 118–122. R. Singh, G. Balasubramanian, RSC Adv. 7 (2017) 37015. M. Marathe, A. Grunebohm, T. Nishimatsu, P. Entel, C. Ederer, Phys. Rev. B 93 (2016), 054110. H. Ehrenreichand, H.R. Philipp, Phys. Rev. 128 (1962) 1622. D. Penn, Phys. Rev. 128 (1962) 2093. F. Wooten, Optical Properties of Solids, Academic Press, New York, 1972. Q. Mahmood, M. Hassan, S.H.A. Ahmad, A. Shahid, A. Laref, J. Phys. Chem. Solid. 120 (2018) 87–95. Q. Mahmood, M. Hassan, M. Rashid, B.H. Haq, A. Laref, Phys. B Condens. Matter 571 (2019) 87–92.