An Improved Ionized Impurity Scattering Model for Monte Carlo Calculations

Abstract

The well known Brooks-Herring (BH) formula for charged-impurity (CI) scattering overestimates the mobility of electrons in highly doped semiconductors. The BH approach relies on a static, single-site description of the carrier-impurity interactions neglecting many-particle effects. We propose a physically based charged-impurity scattering model including Fermi- Dirac statistics, dispersive screening, and two-ion scattering. An approximation for the dielectric function is made to avoid numerical integrations. The resulting scattering rate formulas are analytical. Monte Carlo calculations were performed for majority electrons in bulk silicon at 300 K with impurity concentrations from 10¹⁵ cm^–3 to 10²¹ cm^–3.