The theory of dipole scattering in semiconductors

The theory of dipole scattering in non-degenerate semiconductors has been formulated without making the Brooks-Herring approximation, namely that the potential distribution is slowly varying. The applicability of the Brooks-Herring theory is shown to depend on a parameter γ 2 = 5.8 × 10 -15 n/T 2 , where n is the free-carrier density and T is the absolute temperature. For moderate doping strengths, for example N D similar N A similar 10 17 cm -3 , where N D and N A are the density of donor and acceptor ions respectively, the Brooks-Herring result is accurate when 0.001 ⩽ γ 2 ⩽ 0.07. For heavily doped samples, for example N D similar N A similar 10 20 cm -3 , the present treatment shows significant departures from the Brooks-Herring theory.