Implications of nonparabolicity, warping, and inelastic phonon scattering on hole transport in pure Si and Ge within the effective mass framework

摘要

Hole mobility over a wide range of temperatures in pure Si and Ge is studied within the framework of effective mass theory using the Monte Carlo method. With this aim, we have implemented a three-band model (heavy, light, and split-off holes) introducing nonparabolicity even for the latter, which is usually considered parabolic in the literature. The warping in the heavy and light bands was taken into account, maintaining a spherical model for the split-off band. We also developed scattering rate expressions to be used in a Monte Carlo procedure with the nonparabolicity and warping effects included explicitly in the scattering rate expressions, an aspect neglected in the literature. In so doing, we calculated exactly the nonparabolicity functions for the valence band from the expressions provided by Kane [J. Phys. Chem. Solids 1, 82 (1956)]. Further, we modeled the acoustic phonons on an inelastic mechanism, generalizing previous work, and applying a temperature-dependent average to obtain typical values of the energy of the acoustic phonons involved in the scattering processes. We show that our treatment of hole transport provides results close to those reported experimentally and comparable to those obtained with more complex methods, but requiring much less computing time.