mass, m*, enters in the normalization of the distribution function; the conductivity effective mass, m*, is the mass of a mobile charge carrier under the influence of an external electric field; and the Hall effective mass, m*, is the mass of a mobile charge carrier under the application of external electric and magnetic fields. The reason for these particular definitions of effective masses is that the primary application of this work is to generate improved theoretical calculations of Hall mobility, resistivity, and conductivity mobility [17]. The derived expressions were used to calculate hole effective masses in p-type silicon over a wide range of temperature and dopant density. Since the crystal structure of silicon has cubic symmetry, the ohmic mobility and the low-field Hall coefficient are isotropic. An angular average of the effective masses may be performed taking into account separately the warping of the individual bands so that expressions for m*, m*, and m* of isotropic form can be derived. Values calculated from these expressions-differ from one another because of the warping and nonparabolicity, and consequently effective mass in each band depends on temperature and dopant density in its own way. The valence band structure of silicon is pr esented in Section 2.2, and in Section 2.3 expressions for m*, m*, and m* are derived.
2.2 The Valence Band Structure of Silicon
Theoretical calculations by Kane [27] have established some basic features of the valence band of silicon. It consists of heavy-hole and light-hole bands, degenerate at k = 0, and a third band displaced down in energy at T = 0 by spin orbit coupling.
The heavy-hole band is characterized by holes with an energy independent, but direction-dependent effective mass. The light-hole band