Electron-electron interaction, band-tailing and activity coefficients in doped compensated semiconductors

Abstract

Self-consistent calculations of band-tailing in doped compensated semiconductors have been performed. The inter-particle interactions are approximated by screened Coulomb interactions and the carrier density is allowed to respond to the fluctuations in impurity density. This leads to fluctuations in the screening length and in the screened Hartree-Fock contribution to the electronic potential. the fluctuations in carrier concentration considerably reduce the magnitude of the band-tailing. In fully compensated material, large potential fluctuations are obtained and the theory suggests that metallic droplets of the type proposed by Shklovskii and Efros may form at very low temperatures or very high doping levels. It is found that electronic activity coefficient effects are very weak, until the Fermi level is strongly affected by Fermi statistics.