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Electronic and optical properties of the spinel oxides GeB2O4 (B = Mg, Zn and Cd): an ab initio study 
Allali D.1,2, Bouhemadou A.3, Zerarga F.4, Sahnoune F.1
1 Physics and Chemistry of Materials Lab, Department of Physics, University Mohamed Boudiaf of M’sila, 28000, M’sila, Algeria.
2 Faculte´ de technologie, Universite´ Mohamed Boudiaf-M’sila, B.P 166 Ichbilia, 28000 M’sila, Algeria.
E-mail: allalidjamel@yahoo.fr
3 Laboratory for Developing New Materials and their Characterization, University of Setif 1, 19000 Setif, Algeria.
4 University Abderrahmane Mira,  Department of Physics, 06000 Bejaia, Algeria.

Abstract
We report ab initio density functional theory calculations of the structural, electronic and optical properties of the spinel oxides GeMg2O4, GeZng2O4 and GeCd2O4 using the full-potential linearized augmented plane-wave method [1]. The structural parameters calculated using both the local density [2] and generalized gradient approximations [3] to the exchange-correlation potential are consistent with the literature data. To calculate the electronic properties, the exchange-correlation potential is treated with various functionals, and we ﬁnd that the newly developed Tran–Blaha-modiﬁed Becke–Johnson functional [4-6] signiﬁcantly improves the band gap. We predict a direct band gap in all of the considered GeB2O4 compounds, and the band gaps continuously decrease as the atomic size of the B element increases. The decrease in the fundamental direct band gap (Γ–Γ) from GeMg2O4 to GeZn2O4 to GeCd2O4 can be attributed to p–d mixing in the upper valence bands of GeZn2O4 and GeCd2O4. The lowest conduction band is well dispersive, similar to that found for transparent conducting oxides such as ZnO. This band is mainly deﬁned by the s and p electrons of the Ge and B (B = Mg, Zn, Cd) atoms. The topmost valence band is considerably less dispersive and is deﬁned by O-2p and B–d electrons. The charge-carrier effective masses are evaluated at the topmost valence band and at the bottommost conduction band that were calculated. The frequency-dependent complex dielectric function, absorption coefﬁcient, refractive index, extinction coefﬁcient, reﬂectivity and electron energy loss function were estimated. We ﬁnd that the value of the zero-frequency limit of the dielectric function ε(0) increases as the band gap decreases. The origins of the peaks and structures in the optical spectra are determined in terms of the calculated energy band structures.

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