Phase-shift calculation of ionized impurity scattering in semiconductors

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Abstract
Partial-wave phase shifts for the scattering of electrons and holes of arbitrary degeneracy by a screened Coulomb potential have been calculated assuming isotropic, parabolic energy bands. For free particles in the effective-mass approximation, all such interactions can be characterized by two parameters. At each point in this two-dimensional space, two final results have been obtained from which the transport integrals can be evaluated. One is a sum of the phase shifts which must be employed in satisfying the Friedel sum rule, while the other corresponds to the total momentum-transfer cross section due to all partial waves. For a parametric space which includes nearly all experimental conditions of interest, these results are presented in approximate analytic form. Over a broad range of electron and hole concentrations and temperatures in Ge, Si, and GaAs, comparison is made between ionized-impurity mobilities calculated from the phase shifts and those obtained in the Born approximation.