Partial-wave theory of the electrical resistivity of heavily-doped (degenerate) uncompensatedn-type Si at low temperatures

Abstract

We have calculated the electron mobility that results from ionized-impurity scattering in heavily-doped (degenerate) uncompensated $n$-type Si by using the donor-ion potentials suggested by Dingle and by Csavinszky. We have used Kohn's variational principle for the calculation of the zeroth-order partial-wave shift, and the Born-approximation expressions for the higher-order partial-wave shifts. Our calculations show that the resistivities calculated with Csavinszky's potential are in better agreement with the measured resistivities of Chapman et al. (P-doped Si, $T=4.2\mathrm{}$ K) than the resistivities calculated with Dingle's potential.