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Sep 27, 2017 - The structural, electronic and optical properties of the Li2In2XY6 (X = Si, Ge;. Y = S, Se) compounds, which are scarcely studied by theoretical ...
Journal of ELECTRONIC MATERIALS, Vol. 47, No. 1, 2018

DOI: 10.1007/s11664-017-5805-1 Ó 2017 The Minerals, Metals & Materials Society

Ab Initio Investigation of the Structural, Electronic and Optical Properties of the Li2In2XY6 (X = Si, Ge; Y = S, Se) Compounds KIN MUN WONG ,1,5,6,7 WILAYAT KHAN,2 M. SHOAIB,3 UMAR SHAH,4 SHAH HAIDER KHAN,3 and G. MURTAZA4 1.—American Physical Society, College Park, MD 20740-3844, USA. 2.—New Technologies – Research Center, University of West Bohemia, Univerzitni 8, 306 14 Pilsen, Czech Republic. 3.—Department of Physics, University of Peshawar, Peshawar, KPK, Pakistan. 4.—Materials Modeling Lab, Department of Physics, Islamia College University, Peshawar, Pakistan. 5.—e-mail: [email protected]. 6.—e-mail: [email protected]. 7.—e-mail: [email protected]

The structural, electronic and optical properties of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds, which are scarcely studied by theoretical methods previously, have been investigated by ab initio calculations based on the density functional theory (DFT) in this article by using the full potential linearized augmented plane wave method. The equilibrium structural ground state properties of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds such as the lattice parameters were obtained from the structural optimization process (with the Perdew–Burke–Ernzerhof generalized gradient approximation), and they are in close agreement with the experimental lattice parameters. Conversely, calculations by the modified Becke Johnson exchange potential indicates that the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds are semiconductors with direct energy band gaps. It is clearly observed from the DFT-calculated partial density of states, that there are significant contributions of the S-s and S-p states in the Li2In2SiS6 and Li2In2GeS6 compounds as well as the Se-s and Se-p states in the Li2In2SiSe6 and Li2In2GeSe6 compounds, respectively. The calculated band gaps ranging from 1.92 eV to 3.24 eV of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds are in good agreement with the experimental results, where the calculated band gap values are positioned in the visible region of the electromagnetic spectrum; therefore, these materials can be efficiently used for opto-electronic and optical applications. Furthermore, some general trends are observed in the optical responses of the compounds, which are possibly correlated to the energy band gaps when the X cations changes from Si to Ge and the Y anions changes from S to Se in the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds, respectively. Key words: DFT calculations, direct band gap, non-linear optical materials, semiconductor, density of states, electronic properties, optical properties

INTRODUCTION The search for non-linear optical (NLO) materials has been an active research field due to their

(Received April 11, 2017; accepted September 13, 2017; published online September 27, 2017)

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important industrial and defense applications, which include atmospheric monitoring, laser radar and laser guidance.1 The NLO materials are classified into ultra-violet (UV) NLO materials, visible NLO materials and infra-red (IR) NLO materials, which are dependent on the range of the wavelength that was utilized. In the past, metal oxide NLO,

Ab Initio Investigation of the Structural, Electronic and Optical Properties of the Li2In2XY6 (X = Si, Ge; Y = S, Se) Compounds

which are the KTiOPO4 (KTP), KH2PO4 (KDP), LiNbO3 (LNO), BaB2O4 (BBO) and LiB3O5 (LBO) have been developed in the UV, and the visible electromagnetic spectrum for practical applications, but these materials are generally unsuitable for IR broad band applications.2–6 Conversely, about more than 40 years ago (1970s), the chalcopyrite-type AgGaX2 (X = S, Se) and ZnGeP2 compounds were utilized as IR NLO materials. However, these compounds have some serious problems such as relatively low-induced damage thresholds (LIDTs), phase match ability and two photon absorption (TPA), which limits their capability for high power applications.7–9 On the other hand, the organic materials and polymers also possess high non-linear optical properties but these materials lack sufficient transparency and have poor thermal stability and low LIDTs.10 Consequently, this promotes the recent active search of new materials for non-linear optical applications where the most important purpose in finding good IR NLO materials is to increase the LIDTs and to avoid the two photons absorption problem. In this aspect, large band gaps of IR NLO materials play an important role to achieve the above two objectives. Hence, the incorporation of alkaline earth metals or alkali in the fabrication of the IR NLO materials is an effective method to increase their energy band gaps and to further increase the laser induced damage thresholds.1 Many researchers have experimentally studied the different properties of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds where Jiyong et al.11 had prepared the Li2In2SiS6 compound by using the solid phase reaction. They have also prepared nonlinear optical crystal of the Li2In2SiS6 compound by using the spontaneous crystallization method or the Bridgman–Stokbargar method. Furthermore, it was noted that the non-linear optical crystal of the Li2In2SiS6 compound has stable mechanical properties, is hard and possesses wide light wave band.11 The above properties clearly show that the nonlinear optical Li2In2SiS6 crystal is suitable to be considered for manufacturing a non-linear optical component. Conversely, Yin et al.1 have produced four types of iso-structural Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds. According to their work, these compounds crystallize in the monoclinic phase with the Cc space group. Although the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds have been studied experimentally by using different techniques, however, to the best of my knowledge, the theoretical aspect of these important compounds are scarcely reported. Therefore, in this work, the electronic band structures and optical properties of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds are thoroughly investigated with the selfconsistent calculations based on the density functional theory (DFT) where additional information such as the density of states can be obtained from the DFT calculations. Although the electronic structure of solid state materials at room temperature can be

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obtained from the experimental spectroscopic scanning capacitance microscopy techniques12–14 as demonstrated by Kin Mun Wong; however, it is expected that the DFT calculations carried out in the present work will provide additional theoretical background and insights to the experimental results of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds that were investigated earlier.1 COMPUTATIONAL DETAILS In this work, the DFT-based full potential linearized augmented plane wave (FP-LAPW) method utilized in the Wien2K code15 was used to study the physical properties of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds. This method is very useful for obtaining reliable results to determine the ground state properties of the materials based on the DFT16–18 as demonstrated by Kin Mun Wong et al. The Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds are experimentally observed to exist in the monoclinic phase with the Cc symmetry space group.1 The structural optimization of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds were performed by optimizing the unit cell volume and relaxing the lattice parameters (e.g., c/a ratio) of the compounds (details are provided in the next subsection). Furthermore, the structural parameters used for the calculation of the electronic structure and optical properties of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds in the unit cell as represented in Fig. 1, were initially obtained from the experimental x-ray diffraction results on the compounds in Ref. 1. This is due to the very slight differences between the DFT calculated equilibrium ground state monoclinic lattice parameters with the experimental lattice parameters of the compounds as described in the next subsection. The Tran and Blaha modified Becke Johnson (TB-mBJ)19 potential was used to treat the exchange and correlation

Fig. 1. Crystal structure of the iso-structural Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds.

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functional for determining the electronic and optical properties of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds. The unit cell of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds is separated into two regions,which consist of the non-overlapping muffin-tin (MT) spheres enveloping each atom and the interstitial space between the various atoms. Suitable muffintin radii (RMT) for the Li, In, Si, Ge, S and Se atoms are selected together with a mesh of 1000 k-points

in the full Brillouin zone (BZ). Inside the spherical MT region, the wave function is expanded by spherical harmonics up to lmax = 10.0, and the charge density is Fourier expanded up to Gmax = 12.0. The expansion of the wave function in the interstitial region of constant potential is by the plane wave basis set, and the RMT * Kmax value at 7.0 was used for the plane wave cut-off in the interstitial region. The self-consistent calculations of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds are considered to be converged, when the total energy in the computations is less than 103 Ry. RESULTS AND DISCUSSION Structural Properties

Fig. 2. Structural optimization plots of the (a) Li2In2XS6 (X = Si, Ge) and (b) Li2In2XSe6 (X = Si, Ge) compounds as a function of the unit cell volume.

The equilibrium structural ground state properties of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds, such as the lattice parameters, were obtained from the structural optimization process in the WIEN2K code with the Perdew–Burke– Ernzerhof generalized gradient approximation (PBE-GGA) as the exchange–correlation functional.20 Initially, the experimental lattice parameters of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds1 are used as the reference for the structural optimization tool in the WIEN2K code, where the simulated unit cell of the compounds is optimized for the total energy as a function of the unit cell volume. The self-consistent calculated total energy of the unit cell in the compounds are varied due to the variation of the unit cell volume during structural optimization. Additionally, the unit cell lattice parameters and the atomic positions are fully relaxed, where the total energy calculations are considered to be converged, when the energy is stabilized within 0.001 Ry. Figure 2a and b show the structurally optimized plots of the minimum total energies as a function of the unit cell volumes of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds.

Table I. Monoclinic lattice parameters (ao, bo and co), Vo and Eo of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds obtained from the structural optimization procedure as compared with the experimental results Compounds Parameters

Li2In2SiS6

˚) ao (A

12.0727 12.07411 7.0213 7.02211 12.0788 12.08021 983.06 962.091 57868.57

˚) bo (A ˚) co (A ˚ 3) Vo (A Eo (Ry) Ref. 1.

Li2In2GeS6

Li2In2SiSe6

Li2In2GeSe6

12.1609 12.16501 7.0816 7.08401 12.1296 12.13101 1007.98 980.701 65104.97

12.6195 12.62101 7.3779 7.37881 12.5786 12.58001 1132.89 1102.951 106613.35

12.7183 12.72261 7.4518 7.45271 12.6684 12.66981 1160.09 1130.121 113849.66

Ab Initio Investigation of the Structural, Electronic and Optical Properties of the Li2In2XY6 (X = Si, Ge; Y = S, Se) Compounds

Conversely, Table I lists the calculated equilibrium monoclinic lattice parameters (ao, bo and co) as well as the optimized ground state volume of the unit cell (Vo) in the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds at the lowest ground state energy, Eo (minimum of the parabolic energy-volume curves as shown in Fig. 2a and b). From Table I, it is clearly observed that the optimized ground state structural properties of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds obtained with the PBE-GGA functional in the WIEN2k code are in close agreement with the experimental results,1 where very slight differences are observed between the structurally optimized monoclinic lattice parameters with the corresponding experimental parameters of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds that are obtained from the x-ray diffraction measurements. In addition, the variance between the calculated and experimental Vo values differ by about 1.9–2.7% across the four compounds. Conversely, it is similarly reasonable to use the structural parameters that were obtained from the experimental x-ray diffraction results on the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds1 (due to the very slight differences between the DFT calculated equilibrium ground state monoclinic lattice parameters with the experimental lattice parameters of the compounds as shown in Table I), for the subsequent calculations of the electronic structure and optical properties of the compounds with the TB-mBJ potential19 (to treat the exchange and correlation functional). By setting the convergence criteria of the total energy calculations of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds to be smaller than 0.001 Ry, the reduction of the resultant variation between the optimized lattice parameters with the experimental results of the compounds (as compared to the results in Table I) is almost negligible. Hence, this confirms the convergence of the DFT calculated optimized ground state monoclinic lattice parameters of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds as shown in Table I. In addition, the lattice parameters of the Li2In2XS6 (X = Si, Ge) compounds increase when the X cation changes from Si to Ge and further increase for the Li2In2SiSe6 and Li2In2GeSe6 compounds, when the Y anion (Y = S, Se) changes from S to Se. This is due to the increase of the atomic ˚ ) to Ge (1.25 A ˚ ) atoms (for radii21 from the Si (1.11 A the same Y = S anion) and similarly from the ˚) increase of the atomic radii21 from the S (0.88 A ˚ ) atoms (for the same X = Si and Ge to Se (1.03 A cations, respectively). This also increases the corresponding lattice constants in the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds. Hence, the lattice parameters, L of the compounds increase in the following order: L(Li2In2SiS6) > L(Li2In2GeS6) > L(Li2In2SiSe6) > L(Li2In2GeSe6).

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Electronic Properties It is important to investigate the electronic structure of a compound for its possible applications in optical and optoelectronics devices. The band structure of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds are shown in Fig. 3a, b, c, and d where the maxima of the valance band and the minima of the conduction band lies at the same symmetry point G. This indicates that these compounds have direct energy band gaps. The calculated band gaps for the Li2In2SiS6, Li2In2SiSe6, Li2In2GeS6 and Li2In2GeSe6 compounds are 3.24 eV, 2.35 eV, 2.99 eV and 1.92 eV, respectively. These band gaps calculated with the TB-mBJ potential are in good agreement with the experimental band gaps of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds as shown in Table II, which were obtained by using the UV–visible-near-IR diffuse-reflectance spectra.1 The small discrepancies/incompatibilities observed between the DFT calculated and the experimental band gap values of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds are commonly ascribed to some physical aspects. Firstly, the wellknown limitation of the DFT is the use of approximations to treat the exchange–correlation energies in the DFT calculations (where the approximations do not fully replicate the real exchange–correlation interactions in the compounds).22 However, the TB-mBJ potential19 has been utilized for the subsequent calculations of the electronic structure and optical properties of the compounds. The TB-mBJ potential has been repeatedly demonstrated in providing an accurate description of the band gaps of semiconductors and insulators as well as reproducing the band gap trends as observed in more complicated hybrid functional methods.23,24 However, it was observed that the TB-mBJ potential would still underestimate the experimental band gaps in some compounds, which contain the sulfide anions.25,26 Hence, this could possibly lead to the small computational discrepancies/incompatibilities between the DFT calculated and the experimental band gap values of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds, which contain the S anions as shown in Fig. 3a, b, c, and d (though the exact physical mechanism for this discrepancy is beyond the scope of this article). On the other hand, very slight differences are observed between the structurally optimized monoclinic lattice parameters that are acquired from the WIEN2K code, with the corresponding experimental parameters of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds that are obtained from the x-ray diffraction measurements1 (as shown in Table I). Hence, this could be a relatively marginal contribution to the discrepancies/incompatibilities between the DFT calculated

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Fig. 3. The calculated band structures of the (a) Li2In2SiS6, (b) Li2In2SiSe6, (c) Li2In2GeS6 and (d) Li2In2GeSe6 compounds.

and the experimentally measured band gaps of the compounds. Furthermore, due to the pre-conditions adopted in the DFT formalism where the ground state structural, electronic and optical properties calculations of the compounds are performed at temperature, T = 0 K, which is much lower than the temperatures at which the

Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds were experimentally measured.1 Hence, this may possibly lead to additional discrepancies or incompatibilities that are observed between the DFT calculated and the experimental band gap values of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds as shown in Fig. 3a, b, c, and d.

Ab Initio Investigation of the Structural, Electronic and Optical Properties of the Li2In2XY6 (X = Si, Ge; Y = S, Se) Compounds

It is observed from the calculations that the band gaps of the Li2In2SiY6 (Y = S, Se) and Li2In2GeY6 (Y = S, Se) compounds decrease when the Y anion changes from S to Se. Moreover, the calculated band gaps of the Li2In2SiY6 (Y = S, Se) compounds are larger than that of the Li2In2GeY6 (Y = S, Se) compounds. This indicates that the Li2In2SiY6 (Y = S, Se) compounds can perform a better role when selected as new IR NLO materials by Table II. The calculated band gap energies (in eV) of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds together with the experimental results Bandgap (eV) Compounds

TB-mBJ

Exp.

Li2In2SiS6 Li2In2SiSe6 Li2In2GeS6 Li2In2GeSe6

3.24 2.35 2.99 1.92

3.611 2.541 3.451 2.301

Ref. 1.

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decreasing the LITDs.10 The energy band gaps of the investigated Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds lie in the visible region of the electromagnetic spectrum; therefore, these materials can be efficiently utilized for different opto-electronic applications. The partial density of states (PDOS) of the isostructural Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds are calculated through the TB-mBJ potential as shown in Fig. 4a, b, c, and d. The PDOS plots in Fig. 4a, b, c, and d clearly show that there exists an energy range (above EF and below the conduction band) where the density of states (DOS) remains at zero, hence, confirming that the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds are semiconductors. In addition, the PDOS plots in Fig. 4a, b, c, and d show three main regions [(15 eV to 10 eV), (10 eV to 5 eV) and 5 eV to 0 eV)] in the valence band of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds. The first region in the valence band (15 eV to 10 eV) consists of the contributions by the S-s, Si-p, In-s, In-p and In-d states in the Li2In2SiS6 compound (Fig. 4a), by the Se-s, Si-p, In-s, In-p and In-d states in the

Fig. 4. The calculated partial density of states of the (a) Li2In2SiS6, (b) Li2In2SiSe6, (c) Li2In2GeS6 and (d) Li2In2GeSe6 compounds.

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clearly observed that there are significant contributions of the S-s and S-p states in the Li2In2SiS6 and Li2In2GeS6 compounds as well as the Se-s and Se-p states in the Li2In2SiSe6 and Li2In2GeSe6 compounds, respectively, in the valence band. Therefore, the DOS plots provide additional information such as the degree of the various contributions from the different states due to the different elements in the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds, which can complement the experimental results of the compounds that were previously studied. Optical Properties The dielectric function shows the optical response of a medium at all photon energies where it is given by: eðxÞ ¼ e1 ðxÞ þ ie2 ðxÞ:

Fig. 5. The calculated (a) real and (b) imaginary parts of the dielectric function of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds.

Li2In2SiSe6 compound (Fig. 4b), by the S-s, Ge-p, Ge-d, In-s, In-p and In-d states in the Li2In2GeS6 compound (Fig. 4c), as well as by the Se-s, Ge-p, Ged, In-s, In-p and In-d states in the Li2In2GeSe6 compound (Fig. 4d), respectively. The second region from (10 eV to 5 eV) is mainly contributed by the Si-s, In-s states in the Li2In2SiS6 and the Li2In2SiSe6 compounds (Fig. 4a and b), by the Ge-s, In-s states in the Li2In2GeS6 and the Li2In2GeSe6 compounds (Fig. 4c and d), respectively. The third region (5 eV to 0 eV) is composed of the Li-s, S-p, Si-p, In-s, In-p and In-d states in the Li2In2SiS6 compound (Fig. 4a), of the Li-s, Se-p, Si-p, In-s, In-p and In-d states in the Li2In2SiSe6 compound (Fig. 4b), of the Li-s, S-p, Ge-p, In-s, In-p and In-d states in the Li2In2GeS6 compound (Fig. 4c) and by the Li-s, Se-p, Ge-p, In-s, In-p and In-d states in the Li2In2GeSe6 compound (Fig. 4d). The conduction band is composed of the Li-s, S-p, Si-s, Si-p, In-s, In-p and In-d states in the Li2In2SiS6 compound (Fig. 4a), composed of the Li-s, Se-p, Se-d, Si-s, Si-p, In-s, In-p and In-d states in the Li2In2SiSe6 compound (Fig. 4b), composed of the Li-s, S-p, Ge-s, Ge-p, In-s, In-p and In-d states in the Li2In2GeS6 compound (Fig. 4c) and composed of the Li-s, Se-p, Se-d, Ge-s, Ge-p, In-s, In-p and In-d states in the Li2In2GeSe6 compound (Fig. 4d), respectively. Importantly, the mixed nature of the density of states suggests strong hybridization among the states of cations and anions. From Fig. 4a, b, c, and d, it can be

ð1Þ

The first term in the above equation is the real part, [e1(x)] of the dielectric function, which shows the energy stored in a medium. Conversely, the second term in Eq. 1 represents the imaginary part [e2(x)] which is related to the absorption behavior of the materials as well as the electronic band structure27 of the compounds. Figure 5a and b show the variation of the real and imaginary part of the complex dielectric function of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds with photon energy. At low frequency (x = 0), the values of e1(0) for each compound are listed in Table III. Beyond the low frequency, the magnitude of e1(x) increases with increasing photon energy, and the photon energies where the peak of the e1(x) spectra occur and the corresponding maximum values of e1(x) for the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds are also listed in Table III. In addition, within the energy ranges of 8.422–18.300 eV, 7.252–16.994 eV, 8.068–18.164 eV, and 6.953–16.885 eV, the spectra of e1(x) are negative for the Li2In2SiS6, Li2In2SiSe6, Li2In2GeS6 and Li2In2GeSe6 compounds, respectively. Hence, the materials show metallic behavior in these photon energy ranges, which become reflective towards the incoming photons.16 Figure 5b shows the variation of the frequency dependent absorptive part of the dielectric function with photon energy and the threshold energy (or adsorption edges) of the e2(x) spectra for the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds given in Table III. Above the threshold energy, the magnitude of the e2(x) spectra increases with energy for each compound. Importantly, the different peaks in the imaginary part of the dielectric function [i.e., e2(x)] are due to the electronic interband transitions where the origin of the different peaks in the e2(x) spectra can be related to the PDOS plots of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds as shown in Fig. 4a, b, c, and d. To better illustrate this relationship, certain features of the e2(x) spectra of the compounds are labeled in Fig. 5b. The peak A

Ab Initio Investigation of the Structural, Electronic and Optical Properties of the Li2In2XY6 (X = Si, Ge; Y = S, Se) Compounds

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Table III. This table shows the calculated static components of the real part of the dielectric function [e1(0)], refractive indices [n(0)] and the reflectivity [R(0)] of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds Compounds Parameters e1(0) (arb. unit) e1(x)max (arb. unit) Energy at e1(x)max (eV) e1(x)min (arb. unit) Energy at e1(x)min (eV) e2(x)max (arb. unit) Energy at e2(x)max (eV) e2(x) energy threshold (eV) n(0) (arb. unit) n(x)max (arb. unit) Energy at n(x)max (eV) Energy value at n(x)< 1 (eV) k(x)max (arb. unit) Energy at k(x)max (eV) k(x) energy threshold (eV) r(x)max (X1 cm1) Energy at r(x)max (eV) r(x) energy threshold (eV) R(0) (arb. unit) R(x)max (arb. unit) Energy at R(x)max (eV)

Li2In2SiS6

Li2In2SiSe6

Li2In2GeS6

Li2In2GeSe6

4.657 8.031 4.395 1.956 10.327 7.144 7.034 3.225 2.158 2.875 4.422 10.300 1.796 9.755 3.140 7277.953 8.204 2.844 0.134 0.428 10.381

5.684 9.632 3.606 1.941 9.075 7.654 6.871 2.301 2.384 3.158 3.633 9.429 1.940 7.470 2.218 7173.483 7.143 2.109 0.167 0.438 10.082

4.801 8.729 4.286 1.729 10.463 7.836 7.388 2.968 2.191 2.998 4.313 10.272 1.811 7.442 2.967 7787.543 7.415 2.708 0.139 0.414 10.572

5.907 9.838 3.252 1.725 9.755 8.047 6.354 1.891 2.430 3.195 3.388 9.429 1.908 7.388 1.825 7098.187 6.599 1.864 0.174 0.418 10.136

The maximum values of the e1(x)max, e2(x)max, n(x)max, k(x)max, r(x)max, R(x)max spectra, and the energy values where the peaks occur in the e1(x), e2(x), n(x), k(x), r(x) and R(x) spectra are also included. In addition, the threshold energy of the e2(x), k(x) and the r(x) spectra as well as the minimum negative values of e1(x)min, energy values at which e1(x)min occur, and the energy values where the magnitude of the n(x) spectra begins to decrease below 1 are also listed in the Table for the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds.

for the Li2In2SiS6 compound is due to the transition of the electrons from the S-p state to the In-s state. Conversely, the peak B for the Li2In2SiSe6 compound is due to the electrons transition from the Sep state to the In-s state. The peaks C, D and E in the e2(x) spectra of the Li2In2GeS6 compound are due to the electrons transition from the S-p state to the Ins, Ge-s and Ge-p states. Similarly, the peaks F, G and H in the e2(x) spectra of the Li2In2GeSe6 compound are due to the electrons transition from the Se-p state to the In-s, Ge-s and Ge-p states. The photon energy at the peak e2(x) spectra and the corresponding peak e2(x) value of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds are listed in Table III. The complex refractive index is defined as N*(x) = n(x) + ik(x) where n(x) represents the ordinary refractive index while k(x) is the extinction coefficient.27 From Fig. 6a, it is clear that for each Li2In2XY6 (X = Si, Ge; Y = S, Se) compound, the magnitude of the n(x) spectra gradually increases with energy from the static refractive index n(0) and reaches their maximum values at varying energies as tabulated in Table III. Physically, values of n(x) greater than 1 indicates that the photons entering the compounds are slowed down by the interactions with the electrons in the materials. In addition for these values of n(x), the

phase velocity of light within the compounds is smaller as compared to the speed of light in vacuum. This is followed by the decrease of the refractive index for each compound with further increase in energy and the magnitude of n(x) goes below unity at high photon energies. It is observed that the peaks of the n(x) spectra for the Li2In2SiY6 (Y = S, Se) compounds are red shifted when the Y anions change from S to Se due to the decrease of their band gap (as shown in Fig. 3a and b) and the Li2In2GeY6 (Y = S, Se) compounds also show similar behavior (when the Y anions change from S to Se). The static real part of the dielectric and refractive indexes, e1(0) and n(0) indicate the real part of the dielectric and refractive indexes, e1(x) and n(x) in Figs. 5a and 6a, respectively, at the zero frequency. They are listed in Table III where it is observed from the first and the ninth row in Table III that the Li2In2XY6 (X = Si, Ge; Y = S) compounds pffiffiffiffiffiffiffiffiffiffiffi obey the following relationship of [nð0Þ ¼ e1 ð0Þ] between the two static parameters at x = 0. Figure 6b represents the variation of the extinction [k(x)] coefficient with energy for the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds. The threshold energy of each compound are listed in Table III and above these limits, the extinction coefficient gradually increases with energy. In addition, Table III also lists the energies where the sharp peaks of the

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Fig. 6. The calculated (a) real and (b) imaginary parts of the complex refractive index for the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds.

k(x) spectra are observed and their corresponding peak values. The physical interpretation of the peak k(x) values for the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds indicate the maximum absorption behavior of the materials, where further increase in the photon energy brings a considerable decrease in the magnitude of the k(x) spectra. Figure 7a shows the variation of the frequency dependent optical conductivity, r(x) for the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds with energy. From Fig. 7a, it is clear that the threshold energy of the optical conductivity is the largest for the Li2In2SiS6 compound, and these values together with the maximum values of the optical conductivity for the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds are listed in Table III. Similarly, the optical conductivity gradually increases with further increase of the energy above the threshold limits. Figure 7b represents the variation of the frequency dependent optical reflectivity, R(x) with energy. Table III lists the magnitude of the static reflectivity, R(0), the peak R(x) as well as the corresponding energies where the maximum values of reflectivity are attained for each compound. Importantly, it is observed that the peaks of the R(x) spectra coincide with the region where the e1(x) spectra is negative as shown in Fig. 5a and could be due to the interband transitions. The zero crossing of the e1(x) spectra (returning to the

Wong, W. Khan, Shoaib, Shah, S.H. Khan, and Murtaza

Fig. 7. The variation of the (a) optical conductivity and (b) reflectivity with energy for the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds.

positive e1(x) values in Fig. 5a) correspond to the screened plasma frequency (xp) which is located at approximately 18.3 eV for the Li2In2XS6 (X = Si, Ge) compounds and at approximately 17.0 eV for the Li2In2XSe6 (X = Si, Ge) compounds, respectively. At higher energies beyond xp,28 it is also observed from Fig. 7b that the magnitude of R(x) of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds begins to decrease steeply. On the other hand, it is also observed that the magnitude of the R(x) spectra is the lowest at 10.3% for the Li2In2XSe6 (X = Si, Ge) compounds at the high frequency region. Hence, this indicates that the Li2In2XSe6 (X = Si, Ge) compounds could be possibly utilized as an UV anti-reflecting coating material. The calculations of the various optical properties [e1(x), e2(x), n(x), k(x), r(x) and R(x)] of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds with a finer k-points mesh, from 0 eV to 20 eV, did not result in any appreciable or significant change in the general feature, magnitude or trends as compared to the spectra of the corresponding optical properties as shown in Figs. 5, 6, and 7 for the compounds. Hence, this confirms the reliability and convergence of the calculated optical parameters [e1(x), e2(x), n(x), k(x), r(x) and R(x)] in the same energy region, as illustrated in Figs. 5, 6, and 7 that are associated with the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds. From the different graphs in Figs. 5, 6, and 7, it is observed that the peak magnitude of the e1(x), e2(x), n(x), k(x) and r(x)

Ab Initio Investigation of the Structural, Electronic and Optical Properties of the Li2In2XY6 (X = Si, Ge; Y = S, Se) Compounds

spectra of the Li2In2XS6 (X = Si, Ge) compounds increases when the X cation changes from Si to Ge except for the R(x) spectra. Conversely, the peak magnitude of the e1(x), e2(x) and n(x) spectra of the Li2In2XSe6 (X = Si, Ge) compounds increases when the X cation changes from Si to Ge, whereas the peak magnitude of the k(x), r(x) and R(x) spectra of the Li2In2XSe6 (X = Si, Ge) compounds decreases when the X cation changes from Si to Ge. On the other hand, when the Y anion changes from S to Se, the peak magnitude of the e1(x), e2(x), n(x), k(x) and R(x) spectra of the Li2In2SiY6 (Y = S, Se) compounds increases [except for the r(x) spectra which decreases when the Y anion changes from S to Se]. Similarly, the peak magnitude of the e1(x), e2(x), n(x), k(x) and R(x) spectra of the Li2In2GeY6 (Y = S, Se) compounds increases when the Y anion changes from S to Se [except for the r(x) spectra, which decreases when the Y anion changes from S to Se]. Importantly, a consistent trend is observed for the threshold energies corresponding to e2(x), k(x) and r(x) spectra, which increases from the Li2In2XSe6 (X = Ge, Si) compounds to the Li2In2XS6 (X = Ge, Si) compounds (when the X cation changes from Ge to Si). It is observed that the threshold energy of the e2(x) spectra in Fig. 5b is closely correlated with the energy band gap of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds as shown in Table II. This could be due to the energy band gap, which determines the threshold of the allowed electronic interband transitions in the compounds from the absorption of photons. In contrast, the magnitude of the static e1(x), n(x) and R(x) spectra at low frequency [e1(0), n(0) and R(0)] increases from the Li2In2XS6 (X = Si, Ge) compounds to the Li2In2XSe6 (X = Si, Ge) compounds (when the X cation changes from Si to Ge). CONCLUSIONS In this article, the structural, electronic and optical properties of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds are studied by using the DFT calculations with the FP-LAPW method in the WIEN2 K program. The unit cell of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds is optimized by optimizing the unit cell volume and relaxing the unit cell lattice parameters with the PBE-GGA functional. Importantly, the structural optimization studies indicate very slight differences between the structurally optimized monoclinic lattice parameters with the corresponding experimental parameters of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds that are obtained from the x-ray diffraction measurements. On the contrary, the electronic band structure of the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds are calculated by using the TB-mBJ potential. From the band structure calculations, it is observed that all the four compounds are semiconductors with direct band gaps. Furthermore, the PDOS states from the DFT calculations identify the

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important contributions of certain electronic states in the different regions of the electronic band structures of the compounds. On the other hand, some general trends for the threshold (or adsorption edges) and peak values of the optical properties of the compounds are observed when the X cations changes from Si to Ge, and the Y anions changes from S to Se in the Li2In2XY6 (X = Si, Ge; Y = S, Se) compounds, respectively. The direct band gap nature of the compounds in the visible energy spectrum and the high absorption ability of these compounds make them potential candidates for the optoelectronic applications. ACKNOWLEDGEMENTS Dr. Kin Mun Wong is an independent researcher/ scientist who is a member of the American Physical Society did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Dr. Kin Mun Wong is the corresponding author of Refs. 12–14 and 16 and the co-corresponding author of Refs. 17 and 18 respectively. Furthermore, Dr. Kin Mun Wong was previously (formerly) a research scientist at the Technische Universita¨t Ilmenau in Germany, but he is currently an independent researcher/scientist. His research interests includes computational condensed matter physics and the application of scanning probe microscopy and confocal microscopy for the characterization of materials. In addition, Dr. Kin Mun Wong can be contacted at the following email addresses: [email protected], [email protected], kmwong@kinmunwong. me. W. Khan acknowledges project VEDPMNF (CZ.02.1.01/15.003/358) of Czech ministerium MSMT, which was supported by the European Regional Development Fund (ERDF), project CEDAMNF, Reg. No. CZ.02.1.01/0.0/0.0/15_003/0000358 and CZ LD15 147 of the Ministry of Education, Youth and Sports. REFERENCES 1. W. Yin, K. Feng, W. Hao, J. Yao, and Y. Wu, Inorg. Chem. 51, 5839 (2012). 2. T.A. Driscoll, H.J. Hoffman, R.E. Stone, and P.E. Perkins, J. Opt. Soc. Am. B 3, 683 (1986). 3. J.F. Ward and P.A. Franken, Phys. Rev. 133, A183 (1964). 4. R.C. Miller and W.A. Nordland, Phys. Rev. B 2, 4896 (1970). 5. C. Chen, B. Wu, A. Jiang, and G. You, Sci. Sin. B 28, 235 (1985). 6. C. Chen, Y. Wu, A. Jiang, B. Wu, G. You, R. Li, and S. Lin, J. Opt. Soc. Am. B 6, 616 (1989). 7. D.S. Chemla, P.J. Kupecek, D.S. Robertson, and R.C. Smith, Opt. Commun. 3, 29 (1971). 8. G.D. Boyd, H.M. Kasper, J.H. McFee, and F.G. Storz, IEEE J. Quant. Electron. 8, 900 (1972). 9. G.D. Boyd, E. Buehler, and F.G. Storz, Appl. Phys. Lett. 18, 301 (1971). 10. L.R. Dalton, P.A. Sullivan, and D.H. Bale, Chem. Rev. 110, 25 (2010). 11. J. Yao, W. Yin, K. Feng, W. Hao, P. Fu, and Y. Wu, Li2In2SiS6 compound and Li2In2GSiS6 nonlinear optical crystal as well as preparation methods and applications thereof (CN Patent: 103290480 A, 2013). https://google. com/patents/CN103290480A?cl=es. Accessed 11 September 2013. 12. K.M. Wong, Results Phys. 7, 1308 (2017).

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