Localization of Electrons in Impure Semiconductors by a Magnetic Field

Abstract

The magnetic-field-dependent activation energy required to explain the rapid increase in the Hall coefficient with decreasing temperature in $n$-type InSb from 2°-5°K and in fields of up to 15 kG, observed by Putley and other workers, is interpreted in terms of the energy gap between the two lowest donor levels. This gap appears to be rather insensitive to carrier screening. Further, the existence of a threshold magnetic field, below which no activation energy is found, is interpreted as evidence of a Wigner transition, in which the electrons in the lowest impurity band cease to conduct when the donor-wave-function overlap, or the effective mass for electron transport, reaches a critical value. Finally, the relation between the activation energy for conduction in the extreme high-field limit and the Yafet-Keyes-Adams ionization energy is briefly discussed. It is anticipated that this ionization energy will be more closely approached at high fields, but perhaps never quite attained in practice.