Hall Effect in Impurity Conduction

The existence of a nonvanishing Hall effect in the "impurity conduction" regime of a semiconductor is demonstrated. In this regime (prevalent at low temperatures and at low impurity concentrations) the dominant electron transport mechanism is the phonon-induced hopping of charge carriers from occupied to unoccupied majority sites. The basic element of the theory is the existence of a (magnetic) field-dependent contribution to the jump probability between two sites. This contribution is computed and is shown to arise from the interference between the amplitude for a direct transition between the initial and final sites and the amplitude for an indirect, second-order transition, involving intermediate occupancy of a third site. The theory is applied to the case of an ac applied electric field. For values of the physical parameters representative of those occurring, for example in the ac measurements of Pollak and Geballe, the maximum Hall angle, though small (10^-6), is found to exceed the "normal" value (Hc) ₃ₑ₈₅ₓ by a factor 10^2.