where f is the Fermi-Dirac distribution function and cpq is the permutation tensor. Since equations (2.11) through (2.13) do not assume an effective mass, they are valid both for parabolic and nonparabolic band structures. These equations are then evaluated for the model described in Section 2.2.
This procedure yields single mi, mti, and mi for an equivalent
model which is isotropic and parabolic. These values, in general, will be temperature and carrier-concentration dependent. Although equations (2.6) and (2.11) through (2.13) are expressed in terms of Fermi-Dirac statistics to stress their generality, conductivity and Hall effective masses were derived using Boltzmann statistics to simplify the form of the equation. To obtain values of mi and mi we also require a procedure for evaluating and <2 > in equations (2.9) and (2.10). This will be discussed in Chapter III. The following sections present the expressions for the effective masses in the individual bands.
2.3.1 The Heavy-Hole Band
In this band, the effective masses are given by
M1 m° [f(-y)]2/3 (2.14)
mo0 f(-Y) (2.15)
mCl = - P fland
mwher 0 fi(_„eie (2.16)
where y is defined 1n equation (2.5). In these equations
f(y) = (1 + 0.05y + 0.01635y 2 + 0.000908Y 3 +