Localization of a Conduction Electron Near a Semiconductor-Insulator Interface by a Charged Centre Situated in the Insulator

Abstract

A conduction electron bound to a charged shallow impurity located near a semiconductor-insulator interface outside as well as inside the semiconductor is considered within the model of a hydrogen-like atom in a semi-infinite space. The problem is solved exactly including the impurity electrostatic image at the interface. The electron electrostatic image is next allowed for by the variational method. Rapidly convergent expansions of the wavefunctions are found. The discrete energy spectrum is calculated against the distance of the impurity from the interface. For the impurity located inside the semiconductor at a distance from the interface, the energy levels are lower than in the semiconductor bulk due to the impurity image, and have long-range asymptotics. Near the surface, the levels have a minimum and then rise quickly because of the spatial confining of the electron wave-function. As the impurity leaves the semiconductor and recedes from it into the insulator, the discrete levels crowd together approaching the continuum as the inverse of the distance from the surface, but they all persist for an arbitrarily remote impurity. For the impurity located in the insulator far from the semiconductor, semiclassical asymptotics of the solutions are obtained, and an approximation of the solutions in cylindrical coordinates is derived.