momentum is distributed among holes of different energies. When the scattering mechanism is such as to lead to a nonuniform distribution, hole-hole scattering gives rise to a net transfer of momentum from, .holes which dissipate momentum less efficiently to those which dissipate momentum more efficiently, resulting in an overall greater rate of momentum transfer, and lower mobility [53]. Thus the size of the effect
of hole-hole scattering on the scattering relaxation time is a function of'the energy dependence of the relaxation time. The hole-hole reduction factor, Y hh' can be derived by means of a classical formulation introduced by Keyes [54]. When hole-hole collisions are much more frequent than hole-acceptor collisions, the average relaxation time for a parabolic band in the Keyes [54] approximation approaches the limiting form
<'T hh > = f(3.20)
f £"/2T_ f0d
where f0 is the Fermi-Dirac distribution function. On the other hand, if hole-hole collisions are neglected, the average relaxation time is given by equation (3.2).
Thus the hole-hole reduction factor (i.e., the ratio of to ) can be expressed as
hho £/{~.dc x f C 32T_ [ dc.
{F 3/2a ojd]