Eur. Phys. J. B (2012) 85: 153
https://doi.org/10.1140/epjb/e2012-21064-9

Regular Article

Theory of band gap bowing of disordered substitutional II-VI and III-V semiconductor alloys

Institute for Theoretical Physics, University of Bremen, Gebäude NW1, Otto-Hahn-Allee, 28359 Bremen, Germany

^a e-mail: dmourad@itp.uni-bremen.de

Received: 22 December 2011
Received in final form: 20 February 2012
Published online: 16 May 2012

Abstract

For a wide class of technologically relevant compound III-V and II-VI semiconductor materials AC and BC mixed crystals (alloys) of the type A_xB_1−xC can be realized. As the electronic properties like the bulk band gap vary continuously with x, any band gap in between that of the pure AC and BC systems can be obtained by choosing the appropriate concentration x, granted that the respective ratio is miscible and thermodynamically stable. In most cases the band gap does not vary linearly with x, but a pronounced bowing behavior as a function of the concentration is observed. In this paper we show that the electronic properties of such A_xB_1−xC semiconductors and, in particular, the band gap bowing can well be described and understood starting from empirical tight-binding models for the pure AC and BC systems. The electronic properties of the A_xB_1−xC system can be described by choosing the tight-binding parameters of the AC or BC system with probabilities x and 1 − x, respectively. We demonstrate this by exact diagonalization of finite but large supercells and by means of calculations within the established coherent potential approximation (CPA) We apply this treatment to the II-VI system Cd_xZn_1−xSe, to the III-V system In_xGa_1−xAs and to the III-nitride system Ga_xAl_1−xN.