Theoretical analysis of hall factor and hall mobility in p-type silicon

Abstract

Using a two-band (i.e. heavy-hole and light-hole band) model and the relaxation time approximation, the Hall factor was calculated for the case of silicon doped with boron. Contributions from scattering by acoustical and optical phonons and by ionized and neutral impurities were considered. In addition, the effects of hole-hole scattering, as well as valence band nonparabolicity and anistropy were also taken into account. The scattering and anistropy factors were separately evaluated to emphasize their individual contributions to the Hall factor. Theoretical values of the Hall factor at 300 K vary between 0.882 and 0.714 over the dopant density ranges 10 14 ≦ N A ≦ 3 × 10 18 cm −3. Hall mobilities for p-type silicon were calculated and compared with published data 100 ≤ T ≤ 400 K and 10 14 ≦ N A ≦ 3 × 10 18 cm −3. The present model is limited to the case of uncompensated material and for the weak field in which μ H B ⪡ 1.