Theory of screening and electron mobility: Application to n-type silicon.

Abstract

The dielectric function for semidegenerate [ital n]-type silicon is calculated in both the random-phase approximation (RPA) and the Singwi-Tosi-Land-Sjoelander (STLS) approximation in a study of linear screening theory and electron mobility. Using a spherical effective-mass model for the six conduction-band valleys, the Boltzmann equation is solved exactly for phonon plus impurity scattering and the resulting mobility is compared with experiment. Significant differences are found in doped silicon at nonzero temperatures between Boltzmann equation solutions in the RPA Born approximation and the less accurate force-force correlation function formula for the electrical resistivity due to electron-impurity scattering. Phonon scattering has only secondary importance and is treated by standard deformation-potential models. The problem of scattering by linearly screened ionized impurities is treated with exact phase-shift scattering theory. RPA phase-shift calculated electron mobilities in [ital n]-type silicon at 300 and 77 K agree more closely with experiment than the Born approximation or Thomas-Fermi calculations. The local field correction to RPA screening of impurity potentials is not significant in scattering cross sections when the electron-electron vertex function is included. However, assuming full ionization, the STLS dielectric function yields negative electronic compressibilities at 77 K in a concentration region centered approximately where the metal-insulator transition takesmore » place at [ital T]=0, and coinciding with strong violations of the Friedel sum rule by linearly screened potentials. Strong Coulomb interactions are indicated and imply an inadequacy of linear screening theory, the Born approximation, and the Boltzmann equation for electron-impurity scattering applied to the electron-gas model for doped silicon at low temperature, despite apparently good agreement with experiment.« less