The Hall mobility of carriers hopping in an impurity band

Abstract

A simple new general formula for the Hall mobility μ_H is derived. It involves the contribution to the equilibrium hopping rates from Holstein's three-site process and the product of potential differences in the Miller–Abrahams network in zero magnetic field calculated with an electric field oriented in two orthogonal directions. We find that μ_H is proportional to site density in the r-percolation regime. The exponential behaviour found by previous authors is missing because the percolation exponentials cancel out of the current ratio which determines μ_H. For P-doped c-Si at 4 K, μ_H is in the order of 10⁻¹–10⁻² cm² V⁻¹ s⁻¹ and is considerably larger than the drift mobility.