distance between charged impurities. This is equivalent to assuming that a-charge carrier sees only one charged impurity at a time, the effect of the other charged impurities being sufficiently screened as to be negligible. This approach was improved by Brooks [48] and Herring [49] who associated the cut-off of the Coulomb potential with a screening distance, the free carriers being assumed to provide screening against the charge of the impurities. In the low dopant density limit, the scattering relaxation time due to ionized impurities is given by [48,49]
4
-e 4NAG(bi)
-l A2m i)I/2 s2koT) 3/2 i 1,2,3 (3.14)
where
G(bi) =n(bi+l) (b+lT (3.15)
and,
247T m*iFs(koT)2
b1 e2h2p,
where p' is the screening carrier density, p' = p + NA( NA/NA), for
ND = 0.
3.6 Neutral Impurity Scattering
Scattering by neutral impurities in semiconductors has been considered by Erginsoy [50] as a variation of the problem of the scattering of electrons by neutral hydogen atoms. The result is a temperature independent relaxation time given by