- Email: [email protected]
Ab-initio study of the structural and optoelectronic properties of BaSe1-xSx alloys
Journal Pre-proof Ab-initio study of the structural and optoelectronic properties of BaSe1-xSx alloys S. Gagui, B. Zaidi, Y. Megdoud, B. Hadjoudja, B. Chouial, H. Meradji, S. Ghemid, C. Shekhar PII:
S2352-2143(19)30279-5
DOI:
https://doi.org/10.1016/j.cocom.2019.e00433
Reference:
COCOM 433
To appear in:
Computational Condensed Matter
Received Date: 17 May 2019 Revised Date:
12 July 2019
Accepted Date: 10 September 2019
Please cite this article as: S. Gagui, B. Zaidi, Y. Megdoud, B. Hadjoudja, B. Chouial, H. Meradji, S. Ghemid, C. Shekhar, Ab-initio study of the structural and optoelectronic properties of BaSe1-xSx alloys, Computational Condensed Matter, https://doi.org/10.1016/j.cocom.2019.e00433. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Elsevier B.V. All rights reserved.
Ab-initio study of the structural and optoelectronic properties of BaSe1-xSx alloys S. Gagui1,2, B. Zaidi3, Y. Megdoud1, B. Hadjoudja2, B. Chouial2,H. Meradji1, S. Ghemid1, C. Shekhar4 1
2
Laboratoire de Physique des rayonnements, Université Badji Mokhtar, Annaba, Algeria
Laboratory of Semiconductors, Department of Physics, University of Badji-Mokhtar, Annaba, Algeria 3
Department of Physics, Faculty of Material Sciences, University of Batna 1, Batna, Algeria 4
Department of Applied Physics, Amity University, Gurgaon, India
Abstract Structural and optoelectronic properties of BaSe and BaS compounds and their ternary mixed crystals BaSe1-xSx for 0 ≤ x ≤ 1 which crystallize in NaCl-type structure (B1) have been studied with density functional theory (DFT) based full-potential linearized augmented plane wave (FP-LAPW) methodology. Structural properties of the binary compounds and their ternary alloys have been investigated using both generalized-gradient approximations (WCGGA) developed by Wu-Cohen and (PBE-GGA) developed Perdew-Burke-Ernzerhof. For the electronic properties, in addition to WC-GGA, the recently developed modified Becke and Johnson (mBJ) potential was also used. The concentration dependences of lattice parameter, bulk modulus and band gap for the alloys exhibit nonlinearity. Optical properties of the alloys have been calculated in terms of their respective dielectric function, refractive index, and reflectivity. Keywords: Ternary Alloys, FP-LAPW, WC-GGA, PBE-GGA, mBJ, Structural Properties, optoelectronic Properties.
Corresponding Author: Beddiaf Zaidi Email: [email protected], [email protected] Tel: 00213773261284
1
1. Introduction Among the II–VI wide band gap semiconductors, the barium chalcogenides compounds BaX (X = S, Se and Te) show very interesting properties in the area of catalysts, microelectronics, luminescence, magneto-optical devices, light-emitting diodes (LEDs) and laser diodes (LDs) [1-4]. The structure of the compounds forms a closed-shell ionic system in the NaCl structure at normal conditions. The structure undergoes a first order phase transition at high pressure and transforms to a CsCl type crystal structure prior to metallization [5]. Several experimental research groups have investigated structural phase transition from NaCl type (B1) to CsCl-type (B2) structure and phenomenon of metallization in case barium chalcogenides [5-9]. Also different physical properties of these compounds have been studied experimentally by other several authors [10-16]. In addition, several first-principle based theoretical studies have also been performed so far for BaS, BaSe and BaTe compounds employing a variety of methodologies [17–30] dealing with structural, electronic ,elastic and optical properties of these compounds. Formation of alloys by combining two or more different compounds with different physical properties in their commensurate crystallographic phases is one of the efficient and easiest procedures of fabrication of new materials having intermediate or completely different physical properties. This can be obtained by substitution of atoms with a desired fraction in order to obtain a new class of materials with new searched properties and functionalities adapted to developing new technologies. It should be mentioned in this context that several studies to explore structural, electronic and various other physical properties of ternary alloys, formed by doping of suitable atom(s) from different groups of periodic table into respective unit cells of BaS, BaSe and BaTe at different concentrations, have been performed theoretically [31-34] while no experimental studies for the alloys have been reported so far. In this article, the main properties of BaSe, BaS and their ternary alloy BaSe1-xSx at some specified dopant concentrations x =0.0,0.25, 0.5, 0.75 and 1.0 have been 2
calculated employing the full-potential linearized augmented plane wave method (FPLAPW). The paper is organized as follows: in Section 2 we describe the calculation procedure. The results and a discussion concerning the structural, electronic, and optical properties are presented in Section 3. The paper is concluded in Section 4. 2. Computational details The calculations of the structural, electronic and optical properties of the BaSe1-xSx ternary alloys in their NaCl (B1) phase have been performed for using the density functional theory (DFT) [35, 36] based full-potential linearized augmented plane wave (FP-LAPW) [37] methodology, as implemented in the WIEN2K code [38]. We used both the new form of the generalized gradient approximation proposed by Wu and Cohen (WC-GGA) [39] and that of Perdew–Burke–Ernzerhof (PBE-GGA) [40] to calculate the exchange-correlation potential for the structural properties. To improve further the underestimated band gap results we have also used, Tran-Blaha modified Becke-Johnson (mBJ) exchange potential as it is known to give better results for electronic properties [41, 42]. In the FP-LAPW method the space is divided into an interstitial region (IR) and non-overlapping muffin tin (MT) spheres centered at the atomic sites. In the IR region, the basis set consists of plane waves. Inside the MT spheres, the basis sets are described by radial solutions of the one particle Schrödinger equation (at fixed energy) and their energy derivatives multiplied by spherical harmonics. The maximal l value for the wave function expansion inside the atomic spheres was confined to lmax = 10. The muffin-tin radii were assumed to be 2.5, 2.5 and 2.4 (a.u.) for Ba, Se and S respectively. The plane wave cut-off of Kmax = 8.0/RMT (RMT is the smallest muffin-tin radius in the unit cell) is chosen for the expansion of the wave functions in the interstitial region while the charge density is Fourier expanded up to Gmax = 12 (Ryd)1/2. Special 32 k-points in the irreducible wedge for alloys and 47 for their binary counterparts were considered to perform integration in the reciprocal space over Brillouin zone for our calculations. These values of special k3
points and RMTKmax were ensured by ensuring total energy convergence of the crystal to a lesser amount of 10-4 Ryd. 3. Results and discussion 3.1 Structural properties The calculations of structural properties of the rock-salt structure type (B1) binary compounds and their ternary alloys BaSe1-xSx with different concentrations x = 0.0, 0.25, 0.50, 0.75 and 1.0 have been performed using the volume optimization process. The alloys were modelled at some selected compositions with ordered structures described in terms of periodically repeated supercells with eight atoms per unit cell. The structural optimisation was performed by minimising the total energy of the cell parameters and also the atomic positions. The lattice parameter and bulk modulus are determined from the fitting of total energy versus volume curves using Murnaghan’s equation of state [43]. The obtained results are given in Tables 1 and 2. For the lattice constant, the present WC-GGA and PBE-GGA results agree well with the previous experimental and theoretical reports for the binary compounds. For ternary alloys, we have observed from Table 1 that our computed values for the concentrations x = 0.25, 0.5 and 0.75 are in reasonable agreement with the corresponding available theoretical data. For the bulk modulus, our PBE-GGA values are closer to the previous theoretical ones for the binary compounds whereas the WC-GGA values agree with that obtained experimentally. For the other concentrations (x = 0.25-0.75), on the whole our calculated results compare with the available theoretical data. The variation of the lattice constant and bulk modulus as a function of concentration x is illustrated in Figures 1 and 2. We observe from Figure 1, that as the sulfur concentration increases, the lattice parameter decreases linearly which may be due to the difference in the ionic radius of sulfur (0.37 Å) and that of selenium (0.5 Å). The physical reason behind this weak deviation from linearity would be mainly due to the weak mismatch between the lattice 4
constants of the initial and terminal binary compounds (BaSe and BaS). The concentration dependence of our calculated bulk modulus for BaSe1-xSx alloys is shown in Figure 2. The computed bulk modulus versus concentration curve for the alloys shows small downward deviation from linearity which is attributed to the weak mismatch between the bulk modulus of the binary compounds BaSe et BaS. It is seen from Figure 2, that the bulk modulus increases with the increase of concentration x, which indicate that the alloy becomes less compressible. 3.2. Electronic properties 3.2.1. Band structures The searches of suitable semiconductors in terms of their electronic band structures as well as energy band gaps are very much important for fabrication of efficient electronic devices. So in the present study, calculations of the band structure of considered alloys at concentrations of 0, 0.25, 0.5, 0.75, and 1 are carried out with the WC-GGA and mBJ approximations. The calculated band structures along the higher-symmetry directions in the Brillouin zone for the binary compounds and the alloys using mBJ are given in Figure 3 as prototype. The overall behavior of the band structures calculated by WC-GGA and mBJ approximations is very similar except for the value of their band gap, which is higher within mBJ as presented in Table 3. The BaSe and BaS compounds have indirect band gaps (Γ→Χ), whereas a direct band gap (Γ → Γ) is observed for BaSe1-xSx. After substituting parts of Se atoms with S atoms in the BaSe compounds, BaSe1-xSx have the direct band-gap character (Γ → Γ). From Table 3, compared to the experimental band gaps, we observe that for the binary compounds the calculated band gaps with mBJ show significant improvement over the calculated band gaps with WC-GGA. The computed band gaps for the initial binary compounds BaSe and BaS with mBJ exchange-correlation potential scheme show fair underestimations of magnitude about 0.378 eV and 0.411 eV, respectively, compared to their corresponding experimental data. For 5
the concentrations x= 0.25, 0.5 and 0.75, the obtained band gaps agree fairly with those obtained theoretically; there is no available experimental data concerning these concentrations. The main problem in electronic property calculations is the band gap. It is well known that the calculated band gaps of semiconductors are systematically too small relative to the experimental values. Main responsibility for this deficiency goes to the selfinteraction error contained in the GGA functionals [51]. Tran and Blaha [41, 51] recently proposed a modified semi-local orbital-independent exchange-correlation potential scheme which improves the local-density approximation (LDA) for a constant electron density. Calculations with this modified Backe Johnson (mBJ) exchange-correlation potential scheme provide band gaps for the insulators and semiconductors with very high degree of accuracy and very good agreement with the experiments. Figure 4 shows the variation in the band gap relative to the concentration according to the WC-GGA, and mBJ schemes along with the experimental results for binary compounds. The band gap varies nonlinearly with the increase in the S content, hence providing a bowing gap. This behavior may be attributed to the difference in the electronegativity mismatch between Ba (0.89), S (2.58) and Se (2.55) atoms. We calculated the total bowing parameter by fitting the nonlinear variation of the calculated band gaps vs. concentration with a quadratic function and the results obey the following variations: −GGA E WC = 2.033 − 0.172 x + 0.353 x 2 g
E gmBJ = 3.023 + 0.156 x + 0.236 x 2 The gap bowings are 0.353 and 0.236 eV using WC-GGA and mBJ schemes respectively. 3.2.2. Charge density The electronic charge density contour plot is a vital tool for investigating the charge distributions as well as exploring the nature of chemical bonds exists between the constituent
6
atoms in a compound. If the electronic charge contours are isolated from each other the bonding will be purely ionic and when there are overlaps in the electronic charge density between the cation and anion, the bonding will be covalent. In the present study, we have computed the charge density contour plots of the binary compounds and ternary alloys systems in their (100) crystallographic plane. As prototype, electron density of BaSe0.5S0.5 is plotted in Figure 5. From this Figure, we observe ionic bonding between barium and chalcogen atoms as there is no overlapping between the charges contours of these constituents due to charge transfer between the cations and anions. 3.3 Optical properties The dielectric function ɛ(ω)=ɛ1(ω)+iɛ2(ω) can be useful in the description of the linear response’ system to electromagnetic radiation, which is related to the interaction of photon with electrons. Kramers–Kronig Relationship is used to calculate the real ɛ1(ω) and imaginary part ɛ2(ω) of the dielectric functions. The complex dielectric function is considered as the main base which is responsible for the production of other optical properties. Expressions are used respectively for the dielectric functions, absorption coefficient α(ω), refractive indexn(ω), and reflectivity R(ω).They are given as the following [53, 54]:
= 1+ =
ħ ² ²
(1)
²
∑$$ |
|!|
× '1 − %
′#| ²%
′ )* +,$ − +,$ − ħ
(2)
where ħ is the energy of the incident photon, p is the momentum operator, ħ// */ *0 , |
> is the eigen function with eigenvalue +,$ and f(kn) is the Fermi distribution
function.
7
The description of the optical properties of a medium requires another important quantity, it is the refractive index "n", which is related to the dielectric function by the following relation [55, 56, 46]: =
√ 45 6
69
7
(3)
7 68
The optical quantity such that, the reflectivity R is defined by the following relation [55]:
:
'$
) 7, 7 ) 7,
= '$
(4)
where K is the extinction coefficient. The absorption coefficient α (ω) is connected to ε2 by the following relation [55]:
;
=
,
<
=
$
(5)
<
At the zero-frequency limit, the static refractive index is calculated by the following expression: 0 =>
0
(6)
In this part, the optical properties of the BaSe1-xSx compounds were calculated using WCGGA approximation. We can notice that all the curves of the dielectric function, absorption coefficients, refractivity, and refraction index for the different spectra of the BaSexS1-x are almost similar in shape. Figure 6 shows the imaginary part of dielectric function ε2(ω) evolution in the energy range [0–40] eV for the BaSe1-xSx (x=0, 0.25, 0.50, 0.75 and 1). It is observed that all the spectra are similar with small differences in details for all the concentrations, and the main peaks which reflect the absorption maximum are located at 5.265, 5.292, 5.293, 5.455 and 5.564 eV for BaSe, BaSe0.75S0.25, BaSe0. 5S0.5, BaSe0.25S0.75 and BaS respectively. The critical energy point
8
of which reflects the fundamental absorption edge, occurs at about 2.041, 2.068, 2.0871, 2.101 and 2.213 eV for the concentrations x= 0, 0.25, 0.5, 0.75 and 1, respectively. The origin of this edge corresponds by identification with the electronic band structure to the threshold for direct optical interband transitions between the highest occupied states of valence band to the lowest unoccupied states of conduction band and therefore is closely related to the obtained WC-GGA band gap values of our studied alloys. Our curves presenting the imaginary part of the dielectric function ε2(ω) are in good agreement on a qualitative point of view with those obtained by A. Pourghazi et al for BaSe and BaS [23]. Figure 7 shows the variation of the real part of the dielectric function ε1(ω), in general, there is a noticeable resemblance of the different spectra related to the different concentrations. ε1(ω) reaches a maximum value of 8.127 at 2.63eV, 7.855 at 2.55eV, 7.621 at 2.42eV, 7.335 at 2.345eV and 7.125 at 2.601eV for x= 0; 0.25;0.5;0.75 and 1, respectively .The magnitude of ε1 (reflecting dispersion) is cancelled at the energies 5.858, 6.140, 6.167,6.353 and 6.433 eV for BaSe, BaSe0.75S0.25, BaSe0.5S0.5, BaSe0.25S0.75 and BaS respectively. For the energy where ε1(ω) = 0 means the absence of dispersion and corresponds to the maximum absorption. ε1(ω has negative minima at 17.308eV, 17.484eV, 17.417eV, 17.398eV and 17.356eV for x= 0; 0.25;0.5;0.75 and 1 respectively. The negative values of ε1(ω) show that in this energy region, the compound exhibits metallic characteristics. The values of the static dielectric constant ε1(0) are reported in Table 4. It can be seen that our results are in good agreement with available theoretical [31, 36] results and are higher than the experimental results for binary compounds. For the other concentrations, our values are slightly higher than that of Drablia et al [31]. A material having ε 1( 0 ) value higher than 5.0 is suitable for fabricating some kind of microelectronics devices.
9
The variation of the refractive index n(ω) as a function of energy at the considered concentrations is shown in Figure 8. From these curves, we can see that by increasing the incident photon energy, from its static value, n(ω) increases to reach a maximum peak at energies 2.87, 2.81, 2.77, 2.70 and 2.67 eV for compounds BaSe, BaSe0.75S0.25, BaSe0.5S0.5, BaSe0.25S0.75 and BaS respectively. The calculated values of the static refractive index n(0) together with other theoretical results are listed in Table 4. Also, for comparison we have used empirical models to calculate the refractive index for these alloys. A few empirical relations [58, 59] relate the refractive index to the energy band gap for a large set of semiconductors.. The following models are used: The Moss formula [58] based on atomic model: Egn4 = k where Eg is the energy band gap and k is a constant with a value of 108 eV. The Ravindra et al. [59] relation, n = α + βE g
with α = 4.084 and β = -0.62 eV-1 The obtained results using these models are given in Table 4. From this Table, we noticed that the values obtained for the static refractive index of the studied alloys by using these empirical models are higher than our calculated ones using FP-LAPW method. The ternary alloys show that the smaller band gap material has a large value of the refractive index as the general behavior of many other semiconductors alloys [61]. In Figure 9 we present the variation of the reflectivity R(ω) of the studied alloys as a function of energy in the (0-45) eV range. From the reflectivity spectrums of the studied materials, we observe that starting from their respective zero-frequency limit, the reflectivity exhibits a bunch of peaks in the lower energy regions 3.0–10.0 eV and another bunch of almost equally intense peaks in the higher energy region 18.0–26.0 eV of incident photon. The reflectivity 10
peaks have the following values 16.37%, 16.32%, 16.20%, 15.53%, and 14.88% for x=0, 0.25, 0.5, 0.75 and 1 respectively. The energies and the maxima of R(ω) are reported in Table 5. Figure 10 shows the variation of the absorption coefficient as a function of energy for the compound BaSe1-xSx. From the Figure, it can be seen that, the fundamental absorption thresholds starts at about 2.000; 2.027; 2.081; 2.190 and 2.272 eV. These values orrespond to the energy gaps for BaSe, BaSe0.75S0.25, BaSe0.5S0.5, BaSe0.25S0.75 and BaS respectively. We also note the appearance of the first absorption peak for the following energy values: 6.081, 6.127, 6.408, 6.462 and 6.489 eV. In addition, absorption maxima at energies 17.320, 17.510, 17.564, 17.592 and 17.619 eV for BaSe, BaSe0.75S0.25, BaSe0.5S0.5, BaSe0.25S0.75 and BaS were obtained. We can conclude that this material is very useful for optoelectronic devices operating in the visible and ultraviolet fields. 4. Conclusion In the present study, the structural and optoelectronic properties of the BaSe1-xSx (x= 0; 0.25; 0.5; 0.75; 1) alloys has been calculated by the FP-LAPW method based on the DFT. The structural parameters obtained by the WC-GGA approximation are in good agreement with the experimental and theoretical values reported in the literature. The lattice parameter has been found to decreases and the bulk modulus increases with increasing concentration x. The electronic properties calculated using the WC-GGA and mBJ approximations, confirm the indirect gap (Γ→X) for the binary compounds and the direct gap (Γ→Γ) for the ternary alloys. In addition, the band gap increases as the concentration x increases. The optical properties of the binary compounds and their ternary alloys, such as dielectric function, refractive index, reflectivity and absorption, were calculated using the WC-GGA approximation. It has been noted that they have a high absorption in the ultraviolet and a part of the visible range.
11
References [1] R. Khenata, H. Baltache, M. Rerat, M. Driz, M. Sahnoun, B. Bouhafs, B. Abbar, Physica B 339 (2003) 208. [2] Y. Nakanishi, T. Ito, Y. Hatanaka, G. Shimaoka, Appl. Surf. Sci. 66 (1992) 515. [3] S. Asano, N. Yamashita, Y. Nakao, Phys. Stat. Sol. 89 (1978) 663. [4] R. Pandey, S. Sivaraman, J. Phys. Chem. Solids 52 (1991) 211. [5] S. Yamaoka, O. Shimomura, H. Nakazawa, O. Fukunaga, Solid State Commun. 33 (1980) 87. [6] T.A. Grzybowski, A.L. Ruoff, Phys. Rev. B 27 (1983) 6502. [7] T.A. Grzybowski, A.L. Ruoff, Phys. Rev. Lett. 53 (1984) 489. [8] A.L. Ruoff, T.A. Grzybowski, in: S. Minomura (Ed.), Solid State Physics under Pressure, Terra Scientific, Tokyo, 1985. [9] S.T. Weir, Y.K. Vohra, A.L. Ruoff, Phys. Rev. B 35 (1987) 874. [10] M.E. Lines, Phys. Rev. B 41 (1990) 3372. [11] T.S. Moss, G.J. Burrel, B. Ellis, Semiconductor Opto-electronics, Butterworths, London, 1973. [12] R.J. Zolweg, Phys. Rev. 11 (1958) 113. [13] P. Bridgman, Proc. Am. Acad. Arts Sci. 74 (1940) 21. [14] S.H. Wei, H. Krakauer, Phys. Rev. Lett. 55 (1985) 1200. [15] G.A. Saum, E.B. Hensley, Phys. Rev. 113 (1959) 1019. [16] K. Syassen, N.E. Christensen, H. Winzen, K. Fischer, J. Evers, Phys. Rev. B 35 (1987) 4052. [17] P. K. Jha, S. P. Sanyal, Phys. Stat. Sol. (b) 212 (1999) 241. [18] A.E. Carlsson, J.W. Wilkins, Phys. Rev. B 29 (1984) 5836. [19] N. Ullah, G. Murtaza, R. Khenata, N. Hassan, S. Naeem, M. N. Khalid, S. B. Omran, Comput. Mater. Sci. 83 (2014) 496. 12
[20] P.K. Jha, U.K. Sakalle, S.P. Sanyal, J. Phys. Chem. Solid. 59 (1998) 1633. [21] N. Boukhris, H. Meradji, S. Ghemid, S Drablia , F. El Haj Hassan, Phys. Scr 83 (2011) 065701. [22] H. Akbarzadeh, M. Dadsetani, M. Mehrani, Comput. Mater. Sci. 17 (2000) 81. [23] A. Pouraghazi, M. Dadestani, Physica B 370 (2005) 35. [24] G.Q. Lin, H. Gong, P. Wu, Phys. Rev. B 71 (2005) 85203. [25] R. Khenata, M. Sahnoun, H. Baltache, M. Rérat, D. Rached, M. Driz, B. Bouhafs, Physica B 371 (2006) 12. [26] F. El Haj Hassan, H. Akbarzadeh, Comput. Mat. Sci. 38 (2006) 362. [27] A. Bouhemadou, R. Khenata, F. Zegrar, M. Sahnoun, H. Baltache, A.H. Reshak Comput, Mat. Sci. 38 (2006) 263. [28] F. Kootstra, P.L. de Boeij, J.G. Snijders, Phys. Rev. B 62 (2000) 7071. [29] M. Dadestani, A. Pouraghazi, Opt. Commun. 266 (2006) 562. [30] S. Drablia, H. Meradji, S. Ghemid, N. Boukhris, B. Bouhafs, G. Nouet, Mod. Phys. Lett. 23 (2009) 3065. [31] S. Drablia, H. Meradji, S. Ghemid, G. Nouet, F. El Haj Hassan, Comput. Mater. Sci. 46 (2009) 376. [32] Z.B. Feng, H.Q. Hu, S.X. Cui, W.J. Wang, Physica B 404 (2009) 2107. [33] M. Ameri, A. Touia, H. Khachai, Z. Mahdjoub, M.Z. Chekroun, A. Slamani, Mat. Sci. Appl. 3 (2012) 612. [34] M. Ameri, K. Boudia, A. Rabhi, S. Benaissa, Y. Al-Douri, A. Rais, D. Hachemane Mat, Sci. Appl. 3 (2012) 861. [35] P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 864. [36] W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) A1133.
13
[37] K. M. Wong, W. Khan, M. Shoaib, U. Shah, S. H. Khan, G. Murtza, J. Electron. Mater. 47 (2018) 566. [38] P. Blaha et al., WIEN2k, An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties (Vienna University of Technology, Vienna, Austria,2001). [39] Z. Wu, R.E. Cohen, Phys. Rev. B 73 (2006) 235116. [40] J.P. Perdew , S. Burke , M. Ernzerhof , Phys. Rev. Lett. 77 (1996) 3865. [41] F. Tran and P. Blaha, Phys. Rev. Lett. 102 (2009) 226401. [42] A. D. Becke and E. R. Johnson, J. Chem. Phys. 124 (2006) 221101. [43] F. D. Murnaghan, Proc. Natl. Acad. Sci USA 30 (1944) 244. [44] Y. Kaneko, K.Morimoto, T. Koda, J. Phys. Soc. Jpn 51 (1982) 2247. [45] S. Drablia, N. Boukhris, R. Boulechfar, H. Meradji, S. Ghemid, R. Ahmed, S. Bin Omran, F. El Haj Hassan, R. Khenata, Phys. Scr. 92 (2017) 105701(8pp). [46] B. Khalfallah, F. Khodja,
F. Saadaoui, M. Khodja, A. Boudali, H. Bendaoud, B.
Bouhafs, J Comput. Electron 17 (2018) 1. [47] S. Chattopadhyaya, R. Bhattacharjee, J Alloy Compd, 694 (2017) 1348. [48] B. Amimour , M. Slimani , C. Sifi , R. Khémissi, H. Meradji, S. Ghemid, S. Bin Omran, R. Khenata, CHINESE J PHYS 55 (2017) 367. [49] I. Benkaddour, H. Khachai, F. Chiker, N. Benosman, Y. Benkaddour, G. Murtaza, S. Bin Omran, R. Khenata, Int J Thermophys.36 (2015) 1640. [50] G. Kalpana, B. Palanivel, M. Rajagopalan, Phys. Rev. B50 (1994) 12318. [51] F. Tran, R. Laskowski, P. Blaha, K. Schwarz, Phys. Rev. B 75 (2007) 115131. [52] R. Dalven, Phys. Rev. B 8 (1973) 6033. [53] F. Wooten, in: Optical Properties of Solids, Academic, New York, 1972. [54] Y. Shena, Z. Zhou, J. Appl. Phys. 103 (2008) 074113.
14
[55] R. Khemici, Z. Chouahda, L. Tairi, F. Semari, B. Amimoura, S. Benlamari, H. Meradji, S. Ghemid, CHINESE J PHYS 56 (2018) 1033. [56] N. Ullah, G. Murtaza, R. Khenata, J. Rehman, H. U. Din, S. B. Omran, Mat. Sci. Semicon. Proc. 26 (2014) 681. [57] M. Dadsetani, A. Pourghazi, Opt Commun. 266 (2006) 562. [58] V.P. Gupta, N.M. Ravindra, Phys. Stat. Sol. b 10 (1980) 715. [59] N.M. Ravindra, S. Auluck, V.K. Srivastava, Phys. Stat. Sol. b 93 (1979) 155. [60] S. Adachi, J. Appl. Phys. 61 (1987) 4869. [61] M. Drofenik, A.Ažman, J. Phys. Chem. Solids 33(1972) 761.
15
Table 1: Calculated lattice constant a(Å)using WC-GGA and PBE-GGA approximations for BaSe1-xSx alloys compared with experimental results and other works.
Lattice constant a(Å) BaSe1-xSx
This work
Exp
Other work
WC-GGA
PBE-GGA
LDA
GGA
BaSe
6.5515
6.6628
6.6[44]
6.477[32],6.677[32],6.668[45],6.657[46],6.561[47]
BaSe0.75S0.25
6.5014
6.6091
-
6.428[32],6.632[32],
BaSe0.5S0.5
6.4482
6.5531
-
6.378[32],6.559[32],
BaSe0.25S0.75
6.3930
6.4947
-
6.327[32],6.496[32],
BaS
6.3354
6.4356
6.384[44]
6.273[32],6.444[32],6.435[48], 6.343[47], 6.391 [49]
Table 2; Calculated Bulk modulus B (GPa) using WC-GGA and PBE-GGA approximations for BeSexS1-x alloys compared with experimental results and other works.
Bulk modulus B(GPa) BaSe1-xSx
This work
Exp
Other work
WC-GGA
PBE-GGA
LDA
GGA
BaSe
40.1223
35.4666
43.42[50]
44.38[32],32.82[32],34.00[45],34.9[46],38.667[47]
BaSe0.75S0.25
41.4618
36.7284
-
45.69[32],34.88[32],
BaSe0.5S0.5
42.8934
38.0906
-
47.52[32],36.48[32],
BaSe0.25S0.75
44.5818
39.5739
-
49.18[32],37.80[32],
BaS
45.7628
41.1540
39.42[50]
51.13[32],39.37[32],40.8031[48], 44.399[47] ,42.79[49]
Table 3: Band gap energy calculated by WC-GGA and mBJ approximations for BaSe1-xSx alloys. Band gap energy (Eg) / eV Our calculations WC-GGA
Exp
Other calculations GGA[50]
mBJ
BaSe
2.0335
3.04177
3.42[52]
2.12[50], 2.75[31], 1.66[30]
BaSe0.75S0.25
2.0154
3.09853
-
2.14[50]
BaSe0.5S0.5
2.02126
3.17387
-
2.17[50]
BaSe0.25S0.75
2.11697
3.29726
-
2.23[50]
BaS
2.20909
3.39881
3.81[52]
2.25[50], 2.235[48],3.00[31],1.85[30],3.731[49]
Table 4: Calculated static values for both real part ε1(0) and refractive index n(0) using WCGGA schemes.
ε1(0)
n(0) Empirical
BaSe1-xSx
Present
Exp
Other works
Present
Other
models
works BaSe
5.56
4.48[41]
5.54[56], 6.07[30]
2.36
2. 46[30]
Moss 2.69
5.555[31]
Ravindra 2.82
BaSe0.75S0.25
5.54
5.026[31],
2.35
2.70
2.83
BaSe0. 5S0.5
5.48
5.017[31]
2.34
2.70
2.83
BaSe0.25S0.75
5.32
4.968[31]
2.31
2.67
2.77
BaS
5.11
5.01[56] 5.58[30]
2.26
2.64
2.71
4.26[41],4.60[60]
5.076[31]
2.36[30]
Table 5: Peaks maxima of reflectivity of BaSe1-xSx using WC-GGA schemes. Reflectivity peaks R(ω) %
Position (eV)
R(ω) %
Position (eV)
BaSe
40.3
7.41
39.5
18.45
BaSe0.75S0.25
39.9
7.46
38.9
22.08
BaSe0.5 S0.5
39.37
7.10
39.8
22.10
BaSe0.25 S0.75
37.93
7.16
41.83
22.34
BaS
37.13
7.12
42.70
22.34
Figure captions Figure 1: Variation of lattice constant a (Å) as a function of concentration x for BaSe1-xSx alloys. Figure 2: Variation of bulk modulus B(GPa) as a function of concentration x for BaSe1-xSx alloys. Figure 3: Calculated band structures of BaSexS1-x using mBJ approximation. Figure 4: Composition dependence of the calculated band gap energy within the WC-GGA and mBJ of BaSe1-xSx alloys compared with the experimental data. Figure 5: Electron density plots in (100) plane for BaSe0.5S0.5 Figure 6: Variation of imaginary part of the dielectric function versus energy of BaSe1-xSx alloys. Figure 7: Variation of real part of the dielectric function versus energy of BaSe1-xSx alloys. Figure 8: Variation of refractive index versus energy of BaSe1-xSx alloys. Figure 9: Variation of reflectivity versus energy of BaSe1-xSx alloys. Figure 10: Variation of absorption coefficient as a function of energy for BaSe1-xSx alloys.
6.70 6.65
WC-GGA Expt PBE-GGA
0
Lattice parameter (Α )
6.60 6.55 6.50 6.45 6.40 6.35 6.30 0.0
0.2
0.4
0.6
0.8
1.0
0.8
1.0
Composition x
Figure 1
46
Expt PBE-GGA WC-GGA
45
Bulk modulus (GPa)
44 43 42 41 40 39 38 37 36 35 0.0
0.2
0.4
0.6
Composition x
Figure 2
Figure 3
mBJ Expt WC-GGA
3.8 3.6
Band gap (eV)
3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0 0.0
0.2
0.4
0.6
Composition x
Figure 4
0.8
1.0
Figure 5
BaSe BaSe0,75S0,25
8
BaSe0,5S0,5
6
BaSe0,25S0,75
5
BaS
4 3 2 1 0
5
10
15
20
25
30
35
Energy (eV)
Figure 6
40
ε2(ω)
7
BaSe0,5S0,5 BaSe0,25S0,75
8 6 4
BaS 2
ε1(ω)
BaSe BaSe0,75S0,25
0 -2
5
10
15
20
25
30
35
40
Energy (eV)
Figure 7
2.5
BaSe0,5S0,5
2.0
BaSe0,25S0,75 BaS
1.5 1.0 0.5 0.0
5
10
15
20
25
30
35
Energy (eV)
Figure 8
40
n(ω ω)
3.0
BaSe BaSe0,75S0,25
0.45
BaSe BaSe0,75S0,25
0.40
BaSe0,5S0,5
0.30
BaSe0,25S0,75
0.25
BaS
0.20 0.15
R(ω)
0.35
0.10 0.05 0.00
5
10
15
20
25
30
35
40
Energy (eV)
200
BaSe0,5S0,5
150
BaS
100 50
0
5
10
15
20
25
30
35
Energy (eV)
Figure 10
40
(
BaSe0,25S0,75
−4 -1 α(ω) 10 cm
BaSe BaSe0,75S0,25
)
Figure 9
S2352-2143(19)30279-5
DOI:
https://doi.org/10.1016/j.cocom.2019.e00433
Reference:
COCOM 433
To appear in:
Computational Condensed Matter
Received Date: 17 May 2019 Revised Date:
12 July 2019
Accepted Date: 10 September 2019
Please cite this article as: S. Gagui, B. Zaidi, Y. Megdoud, B. Hadjoudja, B. Chouial, H. Meradji, S. Ghemid, C. Shekhar, Ab-initio study of the structural and optoelectronic properties of BaSe1-xSx alloys, Computational Condensed Matter, https://doi.org/10.1016/j.cocom.2019.e00433. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Elsevier B.V. All rights reserved.
Ab-initio study of the structural and optoelectronic properties of BaSe1-xSx alloys S. Gagui1,2, B. Zaidi3, Y. Megdoud1, B. Hadjoudja2, B. Chouial2,H. Meradji1, S. Ghemid1, C. Shekhar4 1
2
Laboratoire de Physique des rayonnements, Université Badji Mokhtar, Annaba, Algeria
Laboratory of Semiconductors, Department of Physics, University of Badji-Mokhtar, Annaba, Algeria 3
Department of Physics, Faculty of Material Sciences, University of Batna 1, Batna, Algeria 4
Department of Applied Physics, Amity University, Gurgaon, India
Abstract Structural and optoelectronic properties of BaSe and BaS compounds and their ternary mixed crystals BaSe1-xSx for 0 ≤ x ≤ 1 which crystallize in NaCl-type structure (B1) have been studied with density functional theory (DFT) based full-potential linearized augmented plane wave (FP-LAPW) methodology. Structural properties of the binary compounds and their ternary alloys have been investigated using both generalized-gradient approximations (WCGGA) developed by Wu-Cohen and (PBE-GGA) developed Perdew-Burke-Ernzerhof. For the electronic properties, in addition to WC-GGA, the recently developed modified Becke and Johnson (mBJ) potential was also used. The concentration dependences of lattice parameter, bulk modulus and band gap for the alloys exhibit nonlinearity. Optical properties of the alloys have been calculated in terms of their respective dielectric function, refractive index, and reflectivity. Keywords: Ternary Alloys, FP-LAPW, WC-GGA, PBE-GGA, mBJ, Structural Properties, optoelectronic Properties.
Corresponding Author: Beddiaf Zaidi Email: [email protected], [email protected] Tel: 00213773261284
1
1. Introduction Among the II–VI wide band gap semiconductors, the barium chalcogenides compounds BaX (X = S, Se and Te) show very interesting properties in the area of catalysts, microelectronics, luminescence, magneto-optical devices, light-emitting diodes (LEDs) and laser diodes (LDs) [1-4]. The structure of the compounds forms a closed-shell ionic system in the NaCl structure at normal conditions. The structure undergoes a first order phase transition at high pressure and transforms to a CsCl type crystal structure prior to metallization [5]. Several experimental research groups have investigated structural phase transition from NaCl type (B1) to CsCl-type (B2) structure and phenomenon of metallization in case barium chalcogenides [5-9]. Also different physical properties of these compounds have been studied experimentally by other several authors [10-16]. In addition, several first-principle based theoretical studies have also been performed so far for BaS, BaSe and BaTe compounds employing a variety of methodologies [17–30] dealing with structural, electronic ,elastic and optical properties of these compounds. Formation of alloys by combining two or more different compounds with different physical properties in their commensurate crystallographic phases is one of the efficient and easiest procedures of fabrication of new materials having intermediate or completely different physical properties. This can be obtained by substitution of atoms with a desired fraction in order to obtain a new class of materials with new searched properties and functionalities adapted to developing new technologies. It should be mentioned in this context that several studies to explore structural, electronic and various other physical properties of ternary alloys, formed by doping of suitable atom(s) from different groups of periodic table into respective unit cells of BaS, BaSe and BaTe at different concentrations, have been performed theoretically [31-34] while no experimental studies for the alloys have been reported so far. In this article, the main properties of BaSe, BaS and their ternary alloy BaSe1-xSx at some specified dopant concentrations x =0.0,0.25, 0.5, 0.75 and 1.0 have been 2
calculated employing the full-potential linearized augmented plane wave method (FPLAPW). The paper is organized as follows: in Section 2 we describe the calculation procedure. The results and a discussion concerning the structural, electronic, and optical properties are presented in Section 3. The paper is concluded in Section 4. 2. Computational details The calculations of the structural, electronic and optical properties of the BaSe1-xSx ternary alloys in their NaCl (B1) phase have been performed for using the density functional theory (DFT) [35, 36] based full-potential linearized augmented plane wave (FP-LAPW) [37] methodology, as implemented in the WIEN2K code [38]. We used both the new form of the generalized gradient approximation proposed by Wu and Cohen (WC-GGA) [39] and that of Perdew–Burke–Ernzerhof (PBE-GGA) [40] to calculate the exchange-correlation potential for the structural properties. To improve further the underestimated band gap results we have also used, Tran-Blaha modified Becke-Johnson (mBJ) exchange potential as it is known to give better results for electronic properties [41, 42]. In the FP-LAPW method the space is divided into an interstitial region (IR) and non-overlapping muffin tin (MT) spheres centered at the atomic sites. In the IR region, the basis set consists of plane waves. Inside the MT spheres, the basis sets are described by radial solutions of the one particle Schrödinger equation (at fixed energy) and their energy derivatives multiplied by spherical harmonics. The maximal l value for the wave function expansion inside the atomic spheres was confined to lmax = 10. The muffin-tin radii were assumed to be 2.5, 2.5 and 2.4 (a.u.) for Ba, Se and S respectively. The plane wave cut-off of Kmax = 8.0/RMT (RMT is the smallest muffin-tin radius in the unit cell) is chosen for the expansion of the wave functions in the interstitial region while the charge density is Fourier expanded up to Gmax = 12 (Ryd)1/2. Special 32 k-points in the irreducible wedge for alloys and 47 for their binary counterparts were considered to perform integration in the reciprocal space over Brillouin zone for our calculations. These values of special k3
points and RMTKmax were ensured by ensuring total energy convergence of the crystal to a lesser amount of 10-4 Ryd. 3. Results and discussion 3.1 Structural properties The calculations of structural properties of the rock-salt structure type (B1) binary compounds and their ternary alloys BaSe1-xSx with different concentrations x = 0.0, 0.25, 0.50, 0.75 and 1.0 have been performed using the volume optimization process. The alloys were modelled at some selected compositions with ordered structures described in terms of periodically repeated supercells with eight atoms per unit cell. The structural optimisation was performed by minimising the total energy of the cell parameters and also the atomic positions. The lattice parameter and bulk modulus are determined from the fitting of total energy versus volume curves using Murnaghan’s equation of state [43]. The obtained results are given in Tables 1 and 2. For the lattice constant, the present WC-GGA and PBE-GGA results agree well with the previous experimental and theoretical reports for the binary compounds. For ternary alloys, we have observed from Table 1 that our computed values for the concentrations x = 0.25, 0.5 and 0.75 are in reasonable agreement with the corresponding available theoretical data. For the bulk modulus, our PBE-GGA values are closer to the previous theoretical ones for the binary compounds whereas the WC-GGA values agree with that obtained experimentally. For the other concentrations (x = 0.25-0.75), on the whole our calculated results compare with the available theoretical data. The variation of the lattice constant and bulk modulus as a function of concentration x is illustrated in Figures 1 and 2. We observe from Figure 1, that as the sulfur concentration increases, the lattice parameter decreases linearly which may be due to the difference in the ionic radius of sulfur (0.37 Å) and that of selenium (0.5 Å). The physical reason behind this weak deviation from linearity would be mainly due to the weak mismatch between the lattice 4
constants of the initial and terminal binary compounds (BaSe and BaS). The concentration dependence of our calculated bulk modulus for BaSe1-xSx alloys is shown in Figure 2. The computed bulk modulus versus concentration curve for the alloys shows small downward deviation from linearity which is attributed to the weak mismatch between the bulk modulus of the binary compounds BaSe et BaS. It is seen from Figure 2, that the bulk modulus increases with the increase of concentration x, which indicate that the alloy becomes less compressible. 3.2. Electronic properties 3.2.1. Band structures The searches of suitable semiconductors in terms of their electronic band structures as well as energy band gaps are very much important for fabrication of efficient electronic devices. So in the present study, calculations of the band structure of considered alloys at concentrations of 0, 0.25, 0.5, 0.75, and 1 are carried out with the WC-GGA and mBJ approximations. The calculated band structures along the higher-symmetry directions in the Brillouin zone for the binary compounds and the alloys using mBJ are given in Figure 3 as prototype. The overall behavior of the band structures calculated by WC-GGA and mBJ approximations is very similar except for the value of their band gap, which is higher within mBJ as presented in Table 3. The BaSe and BaS compounds have indirect band gaps (Γ→Χ), whereas a direct band gap (Γ → Γ) is observed for BaSe1-xSx. After substituting parts of Se atoms with S atoms in the BaSe compounds, BaSe1-xSx have the direct band-gap character (Γ → Γ). From Table 3, compared to the experimental band gaps, we observe that for the binary compounds the calculated band gaps with mBJ show significant improvement over the calculated band gaps with WC-GGA. The computed band gaps for the initial binary compounds BaSe and BaS with mBJ exchange-correlation potential scheme show fair underestimations of magnitude about 0.378 eV and 0.411 eV, respectively, compared to their corresponding experimental data. For 5
the concentrations x= 0.25, 0.5 and 0.75, the obtained band gaps agree fairly with those obtained theoretically; there is no available experimental data concerning these concentrations. The main problem in electronic property calculations is the band gap. It is well known that the calculated band gaps of semiconductors are systematically too small relative to the experimental values. Main responsibility for this deficiency goes to the selfinteraction error contained in the GGA functionals [51]. Tran and Blaha [41, 51] recently proposed a modified semi-local orbital-independent exchange-correlation potential scheme which improves the local-density approximation (LDA) for a constant electron density. Calculations with this modified Backe Johnson (mBJ) exchange-correlation potential scheme provide band gaps for the insulators and semiconductors with very high degree of accuracy and very good agreement with the experiments. Figure 4 shows the variation in the band gap relative to the concentration according to the WC-GGA, and mBJ schemes along with the experimental results for binary compounds. The band gap varies nonlinearly with the increase in the S content, hence providing a bowing gap. This behavior may be attributed to the difference in the electronegativity mismatch between Ba (0.89), S (2.58) and Se (2.55) atoms. We calculated the total bowing parameter by fitting the nonlinear variation of the calculated band gaps vs. concentration with a quadratic function and the results obey the following variations: −GGA E WC = 2.033 − 0.172 x + 0.353 x 2 g
E gmBJ = 3.023 + 0.156 x + 0.236 x 2 The gap bowings are 0.353 and 0.236 eV using WC-GGA and mBJ schemes respectively. 3.2.2. Charge density The electronic charge density contour plot is a vital tool for investigating the charge distributions as well as exploring the nature of chemical bonds exists between the constituent
6
atoms in a compound. If the electronic charge contours are isolated from each other the bonding will be purely ionic and when there are overlaps in the electronic charge density between the cation and anion, the bonding will be covalent. In the present study, we have computed the charge density contour plots of the binary compounds and ternary alloys systems in their (100) crystallographic plane. As prototype, electron density of BaSe0.5S0.5 is plotted in Figure 5. From this Figure, we observe ionic bonding between barium and chalcogen atoms as there is no overlapping between the charges contours of these constituents due to charge transfer between the cations and anions. 3.3 Optical properties The dielectric function ɛ(ω)=ɛ1(ω)+iɛ2(ω) can be useful in the description of the linear response’ system to electromagnetic radiation, which is related to the interaction of photon with electrons. Kramers–Kronig Relationship is used to calculate the real ɛ1(ω) and imaginary part ɛ2(ω) of the dielectric functions. The complex dielectric function is considered as the main base which is responsible for the production of other optical properties. Expressions are used respectively for the dielectric functions, absorption coefficient α(ω), refractive indexn(ω), and reflectivity R(ω).They are given as the following [53, 54]:
= 1+ =
ħ ² ²
(1)
²
∑$$ |
|!|
× '1 − %
′#| ²%
′ )* +,$ − +,$ − ħ
(2)
where ħ is the energy of the incident photon, p is the momentum operator, ħ// */ *0 , |
> is the eigen function with eigenvalue +,$ and f(kn) is the Fermi distribution
function.
7
The description of the optical properties of a medium requires another important quantity, it is the refractive index "n", which is related to the dielectric function by the following relation [55, 56, 46]: =
√ 45 6
69
7
(3)
7 68
The optical quantity such that, the reflectivity R is defined by the following relation [55]:
:
'$
) 7, 7 ) 7,
= '$
(4)
where K is the extinction coefficient. The absorption coefficient α (ω) is connected to ε2 by the following relation [55]:
;
=
,
<
=
$
(5)
<
At the zero-frequency limit, the static refractive index is calculated by the following expression: 0 =>
0
(6)
In this part, the optical properties of the BaSe1-xSx compounds were calculated using WCGGA approximation. We can notice that all the curves of the dielectric function, absorption coefficients, refractivity, and refraction index for the different spectra of the BaSexS1-x are almost similar in shape. Figure 6 shows the imaginary part of dielectric function ε2(ω) evolution in the energy range [0–40] eV for the BaSe1-xSx (x=0, 0.25, 0.50, 0.75 and 1). It is observed that all the spectra are similar with small differences in details for all the concentrations, and the main peaks which reflect the absorption maximum are located at 5.265, 5.292, 5.293, 5.455 and 5.564 eV for BaSe, BaSe0.75S0.25, BaSe0. 5S0.5, BaSe0.25S0.75 and BaS respectively. The critical energy point
8
of which reflects the fundamental absorption edge, occurs at about 2.041, 2.068, 2.0871, 2.101 and 2.213 eV for the concentrations x= 0, 0.25, 0.5, 0.75 and 1, respectively. The origin of this edge corresponds by identification with the electronic band structure to the threshold for direct optical interband transitions between the highest occupied states of valence band to the lowest unoccupied states of conduction band and therefore is closely related to the obtained WC-GGA band gap values of our studied alloys. Our curves presenting the imaginary part of the dielectric function ε2(ω) are in good agreement on a qualitative point of view with those obtained by A. Pourghazi et al for BaSe and BaS [23]. Figure 7 shows the variation of the real part of the dielectric function ε1(ω), in general, there is a noticeable resemblance of the different spectra related to the different concentrations. ε1(ω) reaches a maximum value of 8.127 at 2.63eV, 7.855 at 2.55eV, 7.621 at 2.42eV, 7.335 at 2.345eV and 7.125 at 2.601eV for x= 0; 0.25;0.5;0.75 and 1, respectively .The magnitude of ε1 (reflecting dispersion) is cancelled at the energies 5.858, 6.140, 6.167,6.353 and 6.433 eV for BaSe, BaSe0.75S0.25, BaSe0.5S0.5, BaSe0.25S0.75 and BaS respectively. For the energy where ε1(ω) = 0 means the absence of dispersion and corresponds to the maximum absorption. ε1(ω has negative minima at 17.308eV, 17.484eV, 17.417eV, 17.398eV and 17.356eV for x= 0; 0.25;0.5;0.75 and 1 respectively. The negative values of ε1(ω) show that in this energy region, the compound exhibits metallic characteristics. The values of the static dielectric constant ε1(0) are reported in Table 4. It can be seen that our results are in good agreement with available theoretical [31, 36] results and are higher than the experimental results for binary compounds. For the other concentrations, our values are slightly higher than that of Drablia et al [31]. A material having ε 1( 0 ) value higher than 5.0 is suitable for fabricating some kind of microelectronics devices.
9
The variation of the refractive index n(ω) as a function of energy at the considered concentrations is shown in Figure 8. From these curves, we can see that by increasing the incident photon energy, from its static value, n(ω) increases to reach a maximum peak at energies 2.87, 2.81, 2.77, 2.70 and 2.67 eV for compounds BaSe, BaSe0.75S0.25, BaSe0.5S0.5, BaSe0.25S0.75 and BaS respectively. The calculated values of the static refractive index n(0) together with other theoretical results are listed in Table 4. Also, for comparison we have used empirical models to calculate the refractive index for these alloys. A few empirical relations [58, 59] relate the refractive index to the energy band gap for a large set of semiconductors.. The following models are used: The Moss formula [58] based on atomic model: Egn4 = k where Eg is the energy band gap and k is a constant with a value of 108 eV. The Ravindra et al. [59] relation, n = α + βE g
with α = 4.084 and β = -0.62 eV-1 The obtained results using these models are given in Table 4. From this Table, we noticed that the values obtained for the static refractive index of the studied alloys by using these empirical models are higher than our calculated ones using FP-LAPW method. The ternary alloys show that the smaller band gap material has a large value of the refractive index as the general behavior of many other semiconductors alloys [61]. In Figure 9 we present the variation of the reflectivity R(ω) of the studied alloys as a function of energy in the (0-45) eV range. From the reflectivity spectrums of the studied materials, we observe that starting from their respective zero-frequency limit, the reflectivity exhibits a bunch of peaks in the lower energy regions 3.0–10.0 eV and another bunch of almost equally intense peaks in the higher energy region 18.0–26.0 eV of incident photon. The reflectivity 10
peaks have the following values 16.37%, 16.32%, 16.20%, 15.53%, and 14.88% for x=0, 0.25, 0.5, 0.75 and 1 respectively. The energies and the maxima of R(ω) are reported in Table 5. Figure 10 shows the variation of the absorption coefficient as a function of energy for the compound BaSe1-xSx. From the Figure, it can be seen that, the fundamental absorption thresholds starts at about 2.000; 2.027; 2.081; 2.190 and 2.272 eV. These values orrespond to the energy gaps for BaSe, BaSe0.75S0.25, BaSe0.5S0.5, BaSe0.25S0.75 and BaS respectively. We also note the appearance of the first absorption peak for the following energy values: 6.081, 6.127, 6.408, 6.462 and 6.489 eV. In addition, absorption maxima at energies 17.320, 17.510, 17.564, 17.592 and 17.619 eV for BaSe, BaSe0.75S0.25, BaSe0.5S0.5, BaSe0.25S0.75 and BaS were obtained. We can conclude that this material is very useful for optoelectronic devices operating in the visible and ultraviolet fields. 4. Conclusion In the present study, the structural and optoelectronic properties of the BaSe1-xSx (x= 0; 0.25; 0.5; 0.75; 1) alloys has been calculated by the FP-LAPW method based on the DFT. The structural parameters obtained by the WC-GGA approximation are in good agreement with the experimental and theoretical values reported in the literature. The lattice parameter has been found to decreases and the bulk modulus increases with increasing concentration x. The electronic properties calculated using the WC-GGA and mBJ approximations, confirm the indirect gap (Γ→X) for the binary compounds and the direct gap (Γ→Γ) for the ternary alloys. In addition, the band gap increases as the concentration x increases. The optical properties of the binary compounds and their ternary alloys, such as dielectric function, refractive index, reflectivity and absorption, were calculated using the WC-GGA approximation. It has been noted that they have a high absorption in the ultraviolet and a part of the visible range.
11
References [1] R. Khenata, H. Baltache, M. Rerat, M. Driz, M. Sahnoun, B. Bouhafs, B. Abbar, Physica B 339 (2003) 208. [2] Y. Nakanishi, T. Ito, Y. Hatanaka, G. Shimaoka, Appl. Surf. Sci. 66 (1992) 515. [3] S. Asano, N. Yamashita, Y. Nakao, Phys. Stat. Sol. 89 (1978) 663. [4] R. Pandey, S. Sivaraman, J. Phys. Chem. Solids 52 (1991) 211. [5] S. Yamaoka, O. Shimomura, H. Nakazawa, O. Fukunaga, Solid State Commun. 33 (1980) 87. [6] T.A. Grzybowski, A.L. Ruoff, Phys. Rev. B 27 (1983) 6502. [7] T.A. Grzybowski, A.L. Ruoff, Phys. Rev. Lett. 53 (1984) 489. [8] A.L. Ruoff, T.A. Grzybowski, in: S. Minomura (Ed.), Solid State Physics under Pressure, Terra Scientific, Tokyo, 1985. [9] S.T. Weir, Y.K. Vohra, A.L. Ruoff, Phys. Rev. B 35 (1987) 874. [10] M.E. Lines, Phys. Rev. B 41 (1990) 3372. [11] T.S. Moss, G.J. Burrel, B. Ellis, Semiconductor Opto-electronics, Butterworths, London, 1973. [12] R.J. Zolweg, Phys. Rev. 11 (1958) 113. [13] P. Bridgman, Proc. Am. Acad. Arts Sci. 74 (1940) 21. [14] S.H. Wei, H. Krakauer, Phys. Rev. Lett. 55 (1985) 1200. [15] G.A. Saum, E.B. Hensley, Phys. Rev. 113 (1959) 1019. [16] K. Syassen, N.E. Christensen, H. Winzen, K. Fischer, J. Evers, Phys. Rev. B 35 (1987) 4052. [17] P. K. Jha, S. P. Sanyal, Phys. Stat. Sol. (b) 212 (1999) 241. [18] A.E. Carlsson, J.W. Wilkins, Phys. Rev. B 29 (1984) 5836. [19] N. Ullah, G. Murtaza, R. Khenata, N. Hassan, S. Naeem, M. N. Khalid, S. B. Omran, Comput. Mater. Sci. 83 (2014) 496. 12
[20] P.K. Jha, U.K. Sakalle, S.P. Sanyal, J. Phys. Chem. Solid. 59 (1998) 1633. [21] N. Boukhris, H. Meradji, S. Ghemid, S Drablia , F. El Haj Hassan, Phys. Scr 83 (2011) 065701. [22] H. Akbarzadeh, M. Dadsetani, M. Mehrani, Comput. Mater. Sci. 17 (2000) 81. [23] A. Pouraghazi, M. Dadestani, Physica B 370 (2005) 35. [24] G.Q. Lin, H. Gong, P. Wu, Phys. Rev. B 71 (2005) 85203. [25] R. Khenata, M. Sahnoun, H. Baltache, M. Rérat, D. Rached, M. Driz, B. Bouhafs, Physica B 371 (2006) 12. [26] F. El Haj Hassan, H. Akbarzadeh, Comput. Mat. Sci. 38 (2006) 362. [27] A. Bouhemadou, R. Khenata, F. Zegrar, M. Sahnoun, H. Baltache, A.H. Reshak Comput, Mat. Sci. 38 (2006) 263. [28] F. Kootstra, P.L. de Boeij, J.G. Snijders, Phys. Rev. B 62 (2000) 7071. [29] M. Dadestani, A. Pouraghazi, Opt. Commun. 266 (2006) 562. [30] S. Drablia, H. Meradji, S. Ghemid, N. Boukhris, B. Bouhafs, G. Nouet, Mod. Phys. Lett. 23 (2009) 3065. [31] S. Drablia, H. Meradji, S. Ghemid, G. Nouet, F. El Haj Hassan, Comput. Mater. Sci. 46 (2009) 376. [32] Z.B. Feng, H.Q. Hu, S.X. Cui, W.J. Wang, Physica B 404 (2009) 2107. [33] M. Ameri, A. Touia, H. Khachai, Z. Mahdjoub, M.Z. Chekroun, A. Slamani, Mat. Sci. Appl. 3 (2012) 612. [34] M. Ameri, K. Boudia, A. Rabhi, S. Benaissa, Y. Al-Douri, A. Rais, D. Hachemane Mat, Sci. Appl. 3 (2012) 861. [35] P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 864. [36] W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) A1133.
13
[37] K. M. Wong, W. Khan, M. Shoaib, U. Shah, S. H. Khan, G. Murtza, J. Electron. Mater. 47 (2018) 566. [38] P. Blaha et al., WIEN2k, An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties (Vienna University of Technology, Vienna, Austria,2001). [39] Z. Wu, R.E. Cohen, Phys. Rev. B 73 (2006) 235116. [40] J.P. Perdew , S. Burke , M. Ernzerhof , Phys. Rev. Lett. 77 (1996) 3865. [41] F. Tran and P. Blaha, Phys. Rev. Lett. 102 (2009) 226401. [42] A. D. Becke and E. R. Johnson, J. Chem. Phys. 124 (2006) 221101. [43] F. D. Murnaghan, Proc. Natl. Acad. Sci USA 30 (1944) 244. [44] Y. Kaneko, K.Morimoto, T. Koda, J. Phys. Soc. Jpn 51 (1982) 2247. [45] S. Drablia, N. Boukhris, R. Boulechfar, H. Meradji, S. Ghemid, R. Ahmed, S. Bin Omran, F. El Haj Hassan, R. Khenata, Phys. Scr. 92 (2017) 105701(8pp). [46] B. Khalfallah, F. Khodja,
F. Saadaoui, M. Khodja, A. Boudali, H. Bendaoud, B.
Bouhafs, J Comput. Electron 17 (2018) 1. [47] S. Chattopadhyaya, R. Bhattacharjee, J Alloy Compd, 694 (2017) 1348. [48] B. Amimour , M. Slimani , C. Sifi , R. Khémissi, H. Meradji, S. Ghemid, S. Bin Omran, R. Khenata, CHINESE J PHYS 55 (2017) 367. [49] I. Benkaddour, H. Khachai, F. Chiker, N. Benosman, Y. Benkaddour, G. Murtaza, S. Bin Omran, R. Khenata, Int J Thermophys.36 (2015) 1640. [50] G. Kalpana, B. Palanivel, M. Rajagopalan, Phys. Rev. B50 (1994) 12318. [51] F. Tran, R. Laskowski, P. Blaha, K. Schwarz, Phys. Rev. B 75 (2007) 115131. [52] R. Dalven, Phys. Rev. B 8 (1973) 6033. [53] F. Wooten, in: Optical Properties of Solids, Academic, New York, 1972. [54] Y. Shena, Z. Zhou, J. Appl. Phys. 103 (2008) 074113.
14
[55] R. Khemici, Z. Chouahda, L. Tairi, F. Semari, B. Amimoura, S. Benlamari, H. Meradji, S. Ghemid, CHINESE J PHYS 56 (2018) 1033. [56] N. Ullah, G. Murtaza, R. Khenata, J. Rehman, H. U. Din, S. B. Omran, Mat. Sci. Semicon. Proc. 26 (2014) 681. [57] M. Dadsetani, A. Pourghazi, Opt Commun. 266 (2006) 562. [58] V.P. Gupta, N.M. Ravindra, Phys. Stat. Sol. b 10 (1980) 715. [59] N.M. Ravindra, S. Auluck, V.K. Srivastava, Phys. Stat. Sol. b 93 (1979) 155. [60] S. Adachi, J. Appl. Phys. 61 (1987) 4869. [61] M. Drofenik, A.Ažman, J. Phys. Chem. Solids 33(1972) 761.
15
Table 1: Calculated lattice constant a(Å)using WC-GGA and PBE-GGA approximations for BaSe1-xSx alloys compared with experimental results and other works.
Lattice constant a(Å) BaSe1-xSx
This work
Exp
Other work
WC-GGA
PBE-GGA
LDA
GGA
BaSe
6.5515
6.6628
6.6[44]
6.477[32],6.677[32],6.668[45],6.657[46],6.561[47]
BaSe0.75S0.25
6.5014
6.6091
-
6.428[32],6.632[32],
BaSe0.5S0.5
6.4482
6.5531
-
6.378[32],6.559[32],
BaSe0.25S0.75
6.3930
6.4947
-
6.327[32],6.496[32],
BaS
6.3354
6.4356
6.384[44]
6.273[32],6.444[32],6.435[48], 6.343[47], 6.391 [49]
Table 2; Calculated Bulk modulus B (GPa) using WC-GGA and PBE-GGA approximations for BeSexS1-x alloys compared with experimental results and other works.
Bulk modulus B(GPa) BaSe1-xSx
This work
Exp
Other work
WC-GGA
PBE-GGA
LDA
GGA
BaSe
40.1223
35.4666
43.42[50]
44.38[32],32.82[32],34.00[45],34.9[46],38.667[47]
BaSe0.75S0.25
41.4618
36.7284
-
45.69[32],34.88[32],
BaSe0.5S0.5
42.8934
38.0906
-
47.52[32],36.48[32],
BaSe0.25S0.75
44.5818
39.5739
-
49.18[32],37.80[32],
BaS
45.7628
41.1540
39.42[50]
51.13[32],39.37[32],40.8031[48], 44.399[47] ,42.79[49]
Table 3: Band gap energy calculated by WC-GGA and mBJ approximations for BaSe1-xSx alloys. Band gap energy (Eg) / eV Our calculations WC-GGA
Exp
Other calculations GGA[50]
mBJ
BaSe
2.0335
3.04177
3.42[52]
2.12[50], 2.75[31], 1.66[30]
BaSe0.75S0.25
2.0154
3.09853
-
2.14[50]
BaSe0.5S0.5
2.02126
3.17387
-
2.17[50]
BaSe0.25S0.75
2.11697
3.29726
-
2.23[50]
BaS
2.20909
3.39881
3.81[52]
2.25[50], 2.235[48],3.00[31],1.85[30],3.731[49]
Table 4: Calculated static values for both real part ε1(0) and refractive index n(0) using WCGGA schemes.
ε1(0)
n(0) Empirical
BaSe1-xSx
Present
Exp
Other works
Present
Other
models
works BaSe
5.56
4.48[41]
5.54[56], 6.07[30]
2.36
2. 46[30]
Moss 2.69
5.555[31]
Ravindra 2.82
BaSe0.75S0.25
5.54
5.026[31],
2.35
2.70
2.83
BaSe0. 5S0.5
5.48
5.017[31]
2.34
2.70
2.83
BaSe0.25S0.75
5.32
4.968[31]
2.31
2.67
2.77
BaS
5.11
5.01[56] 5.58[30]
2.26
2.64
2.71
4.26[41],4.60[60]
5.076[31]
2.36[30]
Table 5: Peaks maxima of reflectivity of BaSe1-xSx using WC-GGA schemes. Reflectivity peaks R(ω) %
Position (eV)
R(ω) %
Position (eV)
BaSe
40.3
7.41
39.5
18.45
BaSe0.75S0.25
39.9
7.46
38.9
22.08
BaSe0.5 S0.5
39.37
7.10
39.8
22.10
BaSe0.25 S0.75
37.93
7.16
41.83
22.34
BaS
37.13
7.12
42.70
22.34
Figure captions Figure 1: Variation of lattice constant a (Å) as a function of concentration x for BaSe1-xSx alloys. Figure 2: Variation of bulk modulus B(GPa) as a function of concentration x for BaSe1-xSx alloys. Figure 3: Calculated band structures of BaSexS1-x using mBJ approximation. Figure 4: Composition dependence of the calculated band gap energy within the WC-GGA and mBJ of BaSe1-xSx alloys compared with the experimental data. Figure 5: Electron density plots in (100) plane for BaSe0.5S0.5 Figure 6: Variation of imaginary part of the dielectric function versus energy of BaSe1-xSx alloys. Figure 7: Variation of real part of the dielectric function versus energy of BaSe1-xSx alloys. Figure 8: Variation of refractive index versus energy of BaSe1-xSx alloys. Figure 9: Variation of reflectivity versus energy of BaSe1-xSx alloys. Figure 10: Variation of absorption coefficient as a function of energy for BaSe1-xSx alloys.
6.70 6.65
WC-GGA Expt PBE-GGA
0
Lattice parameter (Α )
6.60 6.55 6.50 6.45 6.40 6.35 6.30 0.0
0.2
0.4
0.6
0.8
1.0
0.8
1.0
Composition x
Figure 1
46
Expt PBE-GGA WC-GGA
45
Bulk modulus (GPa)
44 43 42 41 40 39 38 37 36 35 0.0
0.2
0.4
0.6
Composition x
Figure 2
Figure 3
mBJ Expt WC-GGA
3.8 3.6
Band gap (eV)
3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0 0.0
0.2
0.4
0.6
Composition x
Figure 4
0.8
1.0
Figure 5
BaSe BaSe0,75S0,25
8
BaSe0,5S0,5
6
BaSe0,25S0,75
5
BaS
4 3 2 1 0
5
10
15
20
25
30
35
Energy (eV)
Figure 6
40
ε2(ω)
7
BaSe0,5S0,5 BaSe0,25S0,75
8 6 4
BaS 2
ε1(ω)
BaSe BaSe0,75S0,25
0 -2
5
10
15
20
25
30
35
40
Energy (eV)
Figure 7
2.5
BaSe0,5S0,5
2.0
BaSe0,25S0,75 BaS
1.5 1.0 0.5 0.0
5
10
15
20
25
30
35
Energy (eV)
Figure 8
40
n(ω ω)
3.0
BaSe BaSe0,75S0,25
0.45
BaSe BaSe0,75S0,25
0.40
BaSe0,5S0,5
0.30
BaSe0,25S0,75
0.25
BaS
0.20 0.15
R(ω)
0.35
0.10 0.05 0.00
5
10
15
20
25
30
35
40
Energy (eV)
200
BaSe0,5S0,5
150
BaS
100 50
0
5
10
15
20
25
30
35
Energy (eV)
Figure 10
40
(
BaSe0,25S0,75
−4 -1 α(ω) 10 cm
BaSe BaSe0,75S0,25
)
Figure 9