Self-consistent results for energy levels, populations, and charge distributions are given for $n$-type inversion layers on $p$-type silicon. Quantum effects are taken into account in the effective-mass approximation, and the envelope wave function is assumed to vanish at the surface. Approximate analytic results are given for some special cases. Numerical results are given for representative surface orientations, bulk acceptor concentrations, inversion-layer electron concentrations, and temperatures.

• Received 13 January 1972

DOI:https://doi.org/10.1103/PhysRevB.5.4891