Valley-dependent two-dimensional transport in (100), (110), and (111) Si inversion layers at low temperatures and carrier densities

Motivated by interesting recent experimental results, we consider theoretically charged-impurity scattering-limited two-dimensional (2D) electronic transport in (100), (110), and (111)-Si inversion layers at low temperatures and carrier densities, where screening effects are important. We show conclusively that, given the same bare Coulomb disorder, the 2D mobility for a given system increases monotonically with increasing valley degeneracy. We also show that the temperature and the parallel magnetic field dependence of the 2D conductivity is strongly enhanced by increasing valley degeneracy. We analytically consider the low-temperature limit of 2D transport, particularly its theoretical dependence on valley degeneracy, comparing with our full numerical results and with the available experimental results. We make qualitative and quantitative predictions for the parallel magnetic field induced 2D magnetoresistance in recently fabricated high-mobility 6-valley Si(111)-on-vacuum inversion layers. We also provide a theory for 2D transport in ultrahigh mobility Si(111) structures recently fabricated in the laboratory, discussing the possibility of observing the fractional quantum Hall effect in such Si(111) structures. DOI: 10.1103/PhysRevB.87.075306