Semiconductor-Metal Transition in Many-Valley Semiconductors

Abstract

The common conclusion that the Thomas-Fermi approximation for screening leading to a poor estimate of the critical donor concentration for a metal-insulator transition in many-valley semiconductors is critically examined. The many-body effects are introduced in a simple way, partly in the kinetic energy term as a mass renormalization in the spirit of the Fermi liquid theory and partly in the potential energy term when random distribution of impurities leading to Anderson localization is considered. In the absence of localization we obtain a*N c 1/3 = 0.36v -1/3 for the value of Mott constant, where v refers to the number of equivalent conduction band minima and a * is the orbit size of the donor electron in the semiconductor. When an impurity distribution is included we lose a simple expression as given above; instead we get an expression for the energy containing two parameters, the mass in the kinetic energy and the distribution parameter a in the potential energy. The mass is fixed choosing the ionization energy of an isocoric impurity in the low doping regime, and the value of a is fixed demanding the vanishing of the donor binding energy. Thus we are able to account for the variation of the binding energy with the donor concentration for several donors in Si and Ge. Our results are compared with the existing data, and the agreement is good.