Statistically screened impurity scattering in modulation-doped structures

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Abstract
The scattering of electrons by charged impurities in a semiconductor is conventionally seen as caused by relatively infrequent two-body collisions. In practice, electrical screening of the long-range Colomb interaction is usually invoked in order to eliminate the many distant interactions and this may often be a good approximation. In principle, however, the problem of the interaction with the many distant impurities should have a solution independent of screening strength. This problem is particularly acute in the case of scattering by remote impurities in modulation-doped structures. One approach which has been used in the past to reconcile Brooks-Herring and Conwell-Weisskopf formulations is to constrain scattering to be effected only by nearest neighbours. This implies weighting the scattering probability associated with a particular impurity with the possibility that there exists no nearer impurity. This procedure introduces a statistical cut-off to the interaction-an effect which is termed as statistical screening. This idea is applied to the case of impurity scattering in modulation-doped structures, and it is shown that the scattering potential of remote impurities in the barrier layer can be drastically reduced. Quantitative illustrations for the case of GaAs show that statistical screening can account for the very high mobilities that have been observed in modulation-doped structures.

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