_hh       1                                                (3.21a)
          hh <T><T-I>

                                      0
for optical phonon scattering, and Yhh0' the hole-hole reduction factor, is evaluated 'from equation (3.21).

     For acoustical phonon scattering it is assumed that Yhha decreases linearly with increasing dopant density from a value of one to a value Yhh = 97T/32  0.88 [17] in a certain range of impurity concentration. The exact relationship (Yhh = 1.0004 - 4.013378 x 109NA     1015   NA 3  10 17) is determined empirically with a best fit of the experimental data.

     Luong and Shaw [55] using a one-particle-like approximation from the Hartree-Fock theory, have shown that by inclusion of hole-hole scattering, the Brooks-Herring [48,49] formula is reduced by a factor which can be expressed in closed form as


       Yhh           1 [- - expP2]                                (3.22)
                             NA

where NA is the ionized acceptor density and p' is the screening hole density. In the case of neutral impurity scattering, hole-hole scattering has no significance because TN is independent of hole energy.

      Thus the overal scattering relaxation time in each hole band is calculated from equations (3.3), (3.5), and (3.6) with the terms of these equations properly corrected for the effects of hole-hole scattering. Because the individual energy surfaces are different from each other, the relaxation times also differ from each other and cannot be assumed equal except in restricted ranges of temperature and dopant density [43].