The conductivity mobility in each of the three valence bands is calculated from
e
ci m (3.1)
where
f 3/2- dF = f (3.2)
1 I 3/2 {[;f° d
for the case of Fermi-Dirac statistics, and Ti represents the total scattering relaxation time in band i. Because each scattering mechanism has its own dependence on scattering energy, a simple closed form expression for total scattering relaxation time as a function of temperature cannot be obtained. The use of numerical techniques is necessary to solve for the relaxation time. In the case of p-type silicon, the peculiarities of a degenerate, warped, and nonparabolic valence band must be taken into account [1]. The possibility of interband as well as intraband transitions must also be taken into account in the analysis. With the inclusion of interband scattering as given by Bir et al. [43], the total relaxation time in the heavy- (i 1) and light-holes (i 2) bands is given by
T I + rDi Ti T i # j; i = 1,2; j = 1,2 (3.3)
lj
•D ij+,
where