Effect of Magnetic Field on the Energy of Surface Bound States

Abstract

We have performed a self-consistent calculation of the energy levels of electrons bound in the accumulation layer at the surface of a semiconductor in order to determine their dependence on magnetic field. The calculation was performed by solving Poisson's and Schrödinger's equations for the bound states and using a dielectric, i.e., linear-response, formalism to treat the mobile charge. Three different approaches to the dielectric response have been compared. The first treats the dielectric function in a bulk Thomas-Fermi approximation. The second introduces a local, but position-dependent, dielectric function to incorporate the vanishing of the mobile electron wave function at the surface. The third approach uses a nonlocal independent-particle response function for the mobile charge, again including the effect of the surface. We find that the modification of the dielectric function by the surface has a profound effect on the field dependence of the binding energies.