Monte Carlo simulation of the hall effect in degenerate GaAs

Abstract

This paper describes a simulation of the Hall effect in GaAs using a single particle Monte Carlo method. The Pauli exclusion principle and Fermi-Dirac statistics are included in the simulation so that the calculations are extended to the case of transport in degenerate materials with electron concentrations up to 10 19 cm −3. Hall mobility and drift mobility for electrons in the low-field ohmic transport regime are calculated from the Monte Carlo results and compared with available typical experimental data. These results demonstrate the importance of including electron-electron interactions in Monte Carlo simulations for GaAs with carrier concentrations above 10 17 cm −3. They also suggest the need for an evaluation of current models for ionized impurity scattering applied to degenerate materials and an examination of the role of energy band structure details in Monte Carlos simulations in degenerate materials.