A new approach to ionized-impurity scattering

The Brooks-Herring (BH) approach to ionized impurity scattering overestimates the low-field mobility of electrons in doped semiconductors. We present a consistent ionised-impurity scattering model which, in addition to the BH model, accounts for degenerate statistics, dispersive screening, two-ion scattering and the atomic form factor of the impurity atom. The dielectric function is accurately approximated by a rational function. From the Schwinger scattering amplitude a correction to the first Born amplitude is derived. The charge distribution of the impurities is described by the Thomas-Fermi theory in the energy functional formulation. Despite the various physical effects added an analytical expression for the scattering rate is retained which allows for efficient usage in Monte Carlo transport calculations. Results of such calculations are presented for majority and minority electron mobility in silicon. The results not only confirm the experimental data of the mobility enhancement of minority electrons in degenerate silicon but also the lower electron mobility in As-doped silicon in comparison to P-doped silicon.