O. Tahiri et al. Electronic and optical properties of Ba(1-x)Ca(x)TiO3 and Ba(1-x)Sr(x)TiO3 (x=0.4, 0.6) OAJ Materials and Devices, Vol 3 #1, 2004 (2018) – DOI: 10.23647/ca.md20182004 Article type: A-Regular research paper First principles calculations of electronic and optical properties for mixed perovskites: Ba(1-x)Ca(x)TiO3 and Ba(1-x)Sr(x)TiO3 (x=0.4, 0.6) O. Tahiri, S. Kassou, R. El Mrabet & A. Belaaraj Laboratoire Physique des Matériaux et Modélisation des Systèmes, CNRST-URAC08, Département de physique, Faculté des Sciences, Université Moulay Ismail, 50000-Meknes, Maroc. Corresponding author: a.belaaraj@fs-umi.ac.ma RECEIVED: 23 February 2018 / RECEIVED IN FINAL FORM: 20 April 2018 / ACCEPTED: 23 April 2018 Abstract: The effect of Ca and Sr-doping on the structural electronic and optical properties of the cubic Ba1- xCaxTiO3 and Ba1-xSrxTiO3 (x=0.4, 0.6) mixed crystals was investigated using first-principles calculations based on density functional theory (DFT). The calculated band structures based on the optimized geometry of the cell for the solid solutions show an indirect band gap character at M-points, with low energy dispersion along height symmetry directions in the Brillouin zone. The band gaps increase with Ca and Sr concentrations. The total and partial densities of states were analyzed to examine the contribution of different orbitals to the maximum of valence band and the minimum of the conduction band. The optical properties such as reflectivity, energy loss, refractive index and extinction coefficient were studied. Keywords: DFT CALCULATIONS, BAND GAP, DENSITY OF STATE, OPTICAL PROPERTIES. Introduction The interest carried in perovskites (ATiO3) and their dielectric properties did not stop growing. The technico-economics requirements, directed essentially to the miniaturization and the production at a lower cost, are at the origin of the discovery of new successful materials. The most recent fields of application are the ones of the aeronautics, the antennas guides of waves, filters, satellite links, the processing and storage of the information [1-3].The titanate of barium is certainly the material most studied among compounds ferroelectrics [4] due to their chemical and mechanical stability. At room temperature it exhibit a ferroelectric properties in tetragonal phase with space group P4mm, over this temperature the BaTiO3 becomes a cubic phase Pm-3m. The integration of ions isovalents as, Ca2+, Sr2+ and Pb2+ in Ba sites and the substitution of tetravalent ions Ti4+ by Zr4+, Sn4+ and Hf4+ can influences the properties of the BaTiO3, such as the phase transition temperature and tailor these properties to performance requirements. The investigations in this domain were mainly concentrated on the systems (Ba, Sr)TiO3 characterized by high dielectric constant. Increasing content of Sr2+on the Ba2+ site, leads to decrease the temperature transition with an expansion of the constant dielectric, low leakage current, low dielectric dispersion against frequency and can be implanted in electroluminescent devices as a high transparency insulator layer [5]. The major problems of these compounds seem of dielectric losses and its relative variation, according to the temperature [6,7]. In order to reduce this inconvenient, we have considered the good dielectric properties and the relaxor nature of (Ba, Ca) TiO3 materials which are expected as alternative candidates fortunable microwave dielectric materials with low dielectric loss and temperature dependence. The aim of this work is to carry out the electronic and optical properties; O. Tahiri et al. Electronic and optical properties of Ba(1-x)Ca(x)TiO3 and Ba(1-x)Sr(x)TiO3 (x=0.4, 0.6) OAJ Materials and Devices, Vol 3 #1, 2004 (2018) – DOI: 10.23647/ca.md20182004 such as reflectivity, energy loss, refractive index and extinction coefficient of Ba1-xCaxTiO3 and Ba1-xSrxTiO3, where x = 0.4 and 0.6, using the first principle calculations. Computation detail We used for our calculations ABINIT ab initio software package [8-10] which is based on the density functional theory (DFT), using plane wave pseudo potential formalism, in order to obtain response function calculations [11-13], computing are performed by the generalized gradient approximation (GGA) with the Fritz-Haber-Institute (FHI) pseudopotentials and Perdew-Burke-Ernzerh of exchange correlation [14], energy cutoff of the electronic wave functions was expanded in plane waves at 950 eV, which are well converged. The Monkhorst Pack Mesh scheme [15] k-points grid sampling was set at 4 x 4 x 4 to perform the irreducible Brillouin zone integrations. The initial crystal data of BaTiO3 in cubic structure with the space group Pm-3m reported in the literature [16], were used as a starting point. The optimized structure and minimum energy lattice constants of the relaxed cubic unit cell were initially computed. The electronic and optical properties were calculated for the equilibrium structures. Structural and electronic properties The calculated a-cell parameters are listed in Table1. It is apparent that the a-lattice parameter decreases with doped amount of the Sr and Ca elements, this result is due to the lower ionic radius value of Sr and Ca compared to Ba in the pure compound BaTiO3. The values obtained for the pure BaTiO3, SrTiO3 and CaTiO3 crystals are in perfect agreement with other theoretical and experimental values [17-19]. Table 1: Calculated a-cell parameter and band gap energy of Ca and Sr-substitued BaTiO3 BaTiO3 Cell parameter(a) (Å) Band gap Eg (eV) 4.123 4.008 [17] 4.011 [16] Exp 2.150 2.200 [23] Ahuja 3.270 [26] Exp Ba0.6Ca0.4TiO3 Ba0.4Ca0.6TiO3 CaTiO3 4.106 4.075 3.964 3.851[17] 3.895[18] Exp 2.201 2.263 2.433 2.780 [24] 3.500 [27] Exp Ba0.6Sr0.4TiO3 Ba0.4Sr0.6TiO3 SrTiO3 4.092 4.064 3.984 3.907 [17] 3.890 [18] Exp 2.222 2.266 2.380 2.200 [23] 3.250 [28] Exp The calculated band structures along the high symmetry directions in the first irreducible Brillouin Zone, in the same scale from -6 eV to 20 eV for all crystals are shown in figure1; these bands look very similar and agree with band structure published, previously in the literature [17-23]. The nature of the crystal components and the electrostatic interactions affect the dispersion of the band structure. The top of the valence band, for Ba0.6Ca0.4TiO3, Ba0.4Ca0.6TiO3, Ba0.6Sr0.4TiO3 and Ba0.4Sr0.6TiO3 compounds, is located at M-points. The highest valence states at M-points appear only about 0.1 eV after the highest states at Г points. The bottom of the conduction band is located at Г-points. The lowest valence states at Г- points appear only about 0.1 eV after the highest states at X-points. The analysis of all directions reveals medium energy dispersion along Г-M and M-X directions, while a lower dispersion is present along Г-X, equivalent to the revolution axis. Figure 1: Calculated band structure: a) Ba0.6Ca0.4TiO3, b) Ba0.6Sr0.4TiO3, c) Ba0.4Ca0.6TiO3, d) Ba0.4Sr0.6TiO3 The figures reveal also that all compounds exhibit an indirect band gap transition. From Table 1, we can see that the energy gap increases by increasing the Ca and Sr content. This effect of doping is in agreed with previous works [19,20]. The high band gap value is found to be 2.266 eV for Ba0.4Sr0.6TiO3. The calculated values for the pure BaTiO3, SrTiO3 and CaTiO3 (Figure 2) are found to be 2.15 eV, 2.380 eV and 2.433 eV respectively, which are in reasonable agreement with other theoretical data [21-24]. While they are slightly lower than available experimental results [26-28]. These results are well known by underestimate the band gap presented by DFT calculations [29-31]. Figure 3 shows plots of the total (TDOS) and partial (PDOS) densities of states for Ba0.4Ca0.6TiO3, Ba0.4Sr0.6TiO3, Ba0.6Ca0.4TiO3 and Ba0.6Ca0.4TiO3. A low displacement of the density is observed in conduction band to high energy as function of Ca and Sr concentration. The analysis of TDOS and PDOS variation versus photon energy reveals that the maximum of the valence band is occupied by the orbital O-2p, and the minimum of the conduction band is occupied by the orbital Ti-3d. From -4 eV to -1 eV, appears the mixed contribution of O-2p, Ti-3d and a low contribution of Ba-6s, Ca-4s and Sr-5s orbitals. Beyond 6 eV, a low contribution of O-2s, O-2p, Ti-3s, Ti-3d, Ba-5p, Ba-6s, Ca-3p, Ca-4s, Sr-5s and Sr-4p orbitals appears too. Optical properties The real and imaginary components of the dielectric function are used to calculate the optical properties of Ba1-xCaxTiO3 and Ba1-xSrxTiO3 solid solutions, such as the reflectivity R (ω), energy loss L(ω), refractive index n (ω )and extinction coefficient k (ω) from the following relationships [22]: Where ε1(ω) and ε2(ω) are the real and imaginary parts of the frequency         1/2 22 1 2 1     ωε+ωε+ωε=ωn 12         1/2 1 22 1 2 1      ωεωε+ωε=ωk 2       1 1 2 +ωε ωε =ωR       22 2 1 2)( ωεωε ωε ωL   O. Tahiri et al. Electronic and optical properties of Ba(1-x)Ca(x)TiO3 and Ba(1-x)Sr(x)TiO3 (x=0.4, 0.6) OAJ Materials and Devices, Vol 3 #1, 2004 (2018) – DOI: 10.23647/ca.md20182004 Figure 2: Total and partial densities of states of the pure BaTiO3, CaTiO3 and SrTiO3 Figure 3: Total and partial densities of states: a) Ba0.6Ca0.4TiO3, b) Ba0.6Sr0.4TiO3,c) Ba0.4Ca0.6TiO3, d) Ba0.4Sr0.6TiO3 O. Tahiri et al. Electronic and optical properties of Ba(1-x)Ca(x)TiO3 and Ba(1-x)Sr(x)TiO3 (x=0.4, 0.6) OAJ Materials and Devices, Vol 3 #1, 2004 (2018) – DOI: 10.23647/ca.md20182004 complex dielectric function ε(ω)= ε1(ω)+iε2(ω), which are calculated from the Kramers-Kronig relationship and the momentum matrix elements between the occupied and unoccupied wave functions[32-33]. The calculated reflectivity R(ω) of the studied compounds, in the energy range from 0 to 30 eV, are shown in figure 4 For the energy values less than 1 eV and above 22 eV, the reflectivity is lower than 17% for all compounds, which indicates that these compounds are transparent, and expected to be poor electrical conductors at this range. Figure 4: Variation of reflectivity R(ω) versus photon energy: a) Ba0.6Ca0.4TiO3 and Ba0.6Sr0.4TiO3- b) Ba0.4Ca0.6TiO3 and Ba0.4Sr0.6TiO3 The curves show that the first optical critical point (A1) of the reflectivity occurs at 3.271 eV and 3.790 eV for Ba0.6Ca0.4TiO3 and Ba0.4Ca0.6TiO3, and at 3.907 eV and 3.790 eV for Ba0.6Sr0.4TiO3 and Ba0.4Sr0.6TiO3. These points give the threshold for indirect optical transitions between the valence band (VB) and the conduction band (CB), which are known as the fundamental absorption edge due to the interaction between the O-2p and Ti-3d states [34-35]. After this threshold energy (first critical point), the curves decrease towards another critical point A2, this peak is caused by the interaction between the O-2p and higher-energy conduction bands, whereas the peak A3 is due to the interactions between Ti-3d and O-2s. We can observe that the first peaks resulting from transition between O-2p and Ti-3d are dominant. Figure 5: Variation of energy loss L(ω) versus photon energy: a) Ba0.6Ca0.4TiO3 and Ba0.6Sr0.4TiO3- b) Ba0.4Ca0.6TiO3 and Ba0.4Sr0.6TiO3 As shown in figure 5, the energy loss gives a sharp peak at 21 eV, which is related with the reduction of reflectivity R(ω), and gives the plasma frequency ωp, according to Drude theory [36]. Figure 6: Variation of refractive index n(ω) versus photon energy: a) Ba0.4Ca0.6TiO3 and Ba0.4Sr0.6TiO3 b) Ba0.6Ca0.4TiO3 and Ba0.6Sr0.4TiO3 The variation of refractive index n(ω), with photon energy, for the titled compounds are shown in figure 6. At 0 frequency, the value of the refractive index is found to be about 2.25 for Ba0.6Ca0.4TiO3 and Ba0.6Sr0.4TiO3, and 2.30 for Ba0.4Ca0.6TiO3 and Ba0.4Sr0.6TiO3. Their variations enhanced beyond the zero frequency, increase with energy in transparency region and limit reaching their maximum values in the UV region at A1 point. The obtained values are 3.204 for Ba0.6Ca0.4TiO3, 3.201 for Ba0.4Ca0.6TiO3, 3.040 for Ba0.6Sr0.4TiO3 and 3.258 for Ba0.4Sr0.6TiO3. Beyond the maximum point (A1), the refractive index decreases with few oscillations to A2 and A3 points. Then, it tend to the unity after plasma frequency which exhibit an insulators-like behaviour. In general, the spectra are shifted towards low energies by changing the cations from Ba to Ca and Sr. The calculated extinction coefficient k(ω) for Ba0.6Ca0.4TiO3 and Ba0.4Sr0.4TiO3 and for Ba0.6Ca0.6TiO3 and Ba0.4Sr0.6TiO3 is displayed in figure 7a and figure 7b respectively.The analysis of the curves depicts a constant value between 0 eV and the optical edge value, and then, the extinction coefficient increases with Ca and Sr content, accompanied by some swings which are due to the extinction of the plasmons. The absorption edge starts from about 2 eV, corresponding to the energy gap. This originates from the transition between O-2p states located at the top of the valence bands to the Ti-3d states dominating in the bottom of the conduction bands. Table II gathers the values of the critical points (A1). The higher value was observed for Ba0.4Ca0.6TiO3 (1.970 at 4.485 eV). Figure 7: Variation of extinction coefficient k(ω) versus photon energy: a) Ba0.6Ca0.4TiO3 and Ba0.6Sr0.4TiO3 b) Ba0.4Ca0.6TiO3 and Ba0.4Sr0.6TiO3 O. Tahiri et al. Electronic and optical properties of Ba(1-x)Ca(x)TiO3 and Ba(1-x)Sr(x)TiO3 (x=0.4, 0.6) OAJ Materials and Devices, Vol 3 #1, 2004 (2018) – DOI: 10.23647/ca.md20182004 Table 2. Maximum values of the first peaks for optical constants. Conclusion We have investigated the structural, electronic and optical properties of Ba1- xCaxTiO3 and Ba1-xSrxTiO3 (x=0.4, 0.6) using DFT calculations with GGA approximation as implemented in the ABINIT package. The results show that the fundamental gap of all compounds exhibits an indirect transition at M-points, with low energy dispersion along height symmetry directions wich is large compared to BaTiO3 situated at - point. The calculated energy band gaps are 2.201 eV, 2.222 eV, 2.263 eV and 2.266 eV for Ba0.6Ca0.4TiO3, Ba0.6Sr0.4TiO3, Ba0.4Ca0.6TiO3 and Ba0.4Sr0.6TiO3 respectively. 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Souza Filho, Drude Theory–Free Carrier Contribution to the Optical Properties. In Solid State Properties, Springer-Verlag Berlin Heidelberg, pp. 329-344. (2018) O. Tahiri et al. Electronic and optical properties of Ba(1-x)Ca(x)TiO3 and Ba(1-x)Sr(x)TiO3 (x=0.4, 0.6) OAJ Materials and Devices, Vol 3 #1, 2004 (2018) – DOI: 10.23647/ca.md20182004 Important: Articles are published under the responsability of authors, in particular concerning the respect of copyrights. Readers are aware that the contents of published articles may involve hazardous experiments if reproduced; the reproduction of experimental procedures described in articles is under the responsability of readers and their own analysis of potential danger. Reprint freely distributable – Open access article Materials and Devices is an Open Access journal which publishes original, and peer-reviewed papers accessible only via internet, freely for all. 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