Band-edge density-of-states and carrier concentrations in intrinsic and p-type CuIn1−xGaxSe2

Abstract

The electronic structures of chalcopyrite CuIn1−xGaxSe2 have recently been reported to have strongly anisotropic and non-parabolic valence bands (VBs) even close to the Γ-point VB maximum. Also, the lowest conduction band (CB) is non-parabolic for energies 50–100 meV above the CB minimum. The details in the band-edge dispersion govern the material's electrical properties. In this study, we, therefore, analyze the electronic structure of the three uppermost VBs and the lowest CB in CuIn1−xGaxSe2 (x = 0, 0.5, and 1). The parameterized band dispersions are explored, and the density-of-states (DOS) as well as the constant energy surfaces are calculated and analyzed. The carrier concentration and the Fermi energy EF in the intrinsic alloys as functions of the temperature is determined from the DOS. The carrier concentration in p-type materials is modeled by assuming the presence of Cu vacancies as the acceptor type defect. We demonstrate that the non-parabolicity of the energy bands strongly affects the total DOS. Therefore, it is important to take into account full band dispersion of the VBs and CB when analyzing the free carrier concentration, like for instance, in studies of electronic transport and/or measurements that involve strong excitation conditions.