T E-1 s 2 Oi'N i =1,2,3 (3.1)
Ni = 1m*. N'
~m~e Di
where NN is the density of'neutral impurities and m* is the geometric mean mass appropriate for evaluating the scaled Bohr radius term [48]. Sclar [51,52] has included the possibility of bound states in the evaluation of electron-hydrogen impurity scattering by using a threedimensional square well to estimate the influence of a weakly-bound state on the scattering. In this case the relaxation time is given by.
-l_ 232rfi (k T) 1/2m-* {2 / + k T £12 1 T,2;3 (3.18)
where 2
E l.136 x 10-1 - - (3.19)
M [O
0
is the binding energy of neutral acceptors.
For silicon doped with shallow impurities, this type of scattering is important at low temperatures where neutral impurities may outnumber ionized impurities. For the deeper levels, where neutral impurities can exist at highe r temperatures, the influence of neutral impurity scattering can extend over a wide range of temperatures.
3.7 Effect of Hole-Hole ScatteringThe expressions thus far presented for scattering relaxation time neglect the effect of hole-hole scattering. Although hole-hole scattering does not affect the current density directly since it cannot alter the total momentum, it tends to randomnize the way in which this total