A theory of density-of-states effective masses in heavily doped silicon at high temperatures and its applications

A theory of density-of-states effective masses in the n(p)-type heavily doped silicon at high temperatures, T, was developed, taking into account the effects of nonparabolicity in the band and Fermi–Dirac statistics. It was applied to determine the intrinsic carrier density at 200⩽T (K)⩽500 accurate to within 4.8%, and at 300 K semi-empirical forms for band gap narrowing (BGN) and apparent BGN with an accuracy of 17% and for optical gap with a precision of 1%, giving rise to a satisfactory description of both electrical and optical data. Furthermore, at 280⩽T (K)⩽400, the BGN can be assumed to be T-independent, with a precision of 8.8%.