Fermi energy and band-tail parameters in heavily doped semiconductors

The density of states in heavily doped semiconductors is investigated by using the Green function method and the Feynman-path integral formulation applied to n -type semiconductor. It is suggested that in the present theory it takes an approximate form $\text{exp √}\text{(3}\text{2)}\text{(E}\text{σ)}$ for negative energies, and a parabolic form for positive energies. The Fermi energy and the band-tail parameters at low temperatures are calculated in the Thomas-Fermi approximation. An application to n-type GaAs is given; the present results are also compared to the theoretical results of Hwang and Brews at 77°K.