Hole and electron mobilities in heavily doped silicon: comparison of theory and experiment

Abstract

Most device models for npn or pnp transistors assume that hole (electron) mobilities in n-type and p-type silicon are equal. Partial-wave phase shift calculations for the contributions of carrier-dopant ion scattering to the carrier mobilities lead to unequal minority hole (electron) and majority hole (electron) mobilities at the same doping density. These calculations are valid over the doping range of 2 x 10 19 to 8 x 10 19 cm −3 in n-type and p-type silicon and contain the assumptions that the holes and electrons move in isotropic parabolic energy bands and are scattered by the screened Coulomb potentials of the dopant ions. When the effects of carrier-acoustic phonon and carrier-carrier scatterings are included, these calculations agree to within the spread of experimental value for the majority mobilities reported in the literature. This agreement is a substantial improvement by factors of 2–4 over the results of earlier theories such as first order Born and nondegenerate theories. The results of this work, particularly the inequality of minority and majority carrier mobilities, have implications for the modeling of both bipolar and field effect transistors.