An Improved Model for Analyzing Hole Mobility and Resistivity in p‐Type Silicon Doped with Boron, Gallium, and Indium

Abstract

Using the relaxation time approximation, and a three‐band model (i.e., nonparabolic light‐hole band, parabolic heavy‐hole, and split‐off bands), theoretical calculations of hole mobility and resistivity were carried out for p‐type silicon doped with boron, gallium, and indium for dopant densities from 1014 to 1018 cm−3 and temperatures between 100 and 400 K. The theoretical analysis did not consider the effects of compensation, but scattering contributions from acoustical and optical phonons, and ionized and neutral impurities were considered. In addition, interband scattering, the effect of hole‐hole scattering, and the nonparabolic nature of the valence bands were also taken into account in the mobility formulations. To verify our theoretical calculations, resistivity measurements were performed on silicon samples (relatively free of compensating inpurities) doped with boron, gallium, and indium with dopant densities ranging from , for. Agreement between the calculated and measured resistivity values and the published mobilities (4) was within 10% over the range of temperature and dopant density studied.