density [21,22]. Below 50 K, hole effective mass remains constant as indicated in high frequency magnetoconductivity experiments [23]. However, at higher temperatures and for higher acceptor impurity densities, two mechanisms are responsible for the temperature dependence of the effective mass: the thermal expansion of the lattice, and the explicit effect of temperature. The effect of the thermal expansion can be estimated from the stress dependence of the effective mass [24], and has been shown to be negligible [21,25]. The explicit temperature effect however is of great importance. It consists of three parts:
(a) the temperature variation of the Fermi distribution function in a nonparabolic band, (b) the temperature dependent distribution function of the split-off band, and (c) the temperature variation of the curvature at the band extremum due to the interaction between holes and lattice phonons.
Following the work of Lax and Mavroides [20], but using Fermi-Dirac statistics.and a simplified model of the valence band structure for silicon, Barber [25] obtained an expression for the density-of-states effective mass, m*, which is temperature and hole-density dependent. Barber, however, did not apply the nonparabolic model of the valence band to the study of conductivity or Hall effective mass in p-type silicon. Costato and Reggiani [26] also developed expressions for mD and m*, the band conductivity effective mass, which show a variation with temperature, but they neglected the effects of the split-off band and the temperature variation of the band curvature.
In this study, the expressions for density-of-states effective mass, conductivity effective mass, and Hall effective mass of holes are derived based on the following definitions. The density-of-states effective