Influence of tip-induced band bending on tunnelling spectra of semiconductor surfaces

A theory based on the Bardeen formalism is developed for computing the tunnel current between a metal tip and a semiconductor surface. Tip-induced band bending in the semiconductor is included, with the electrostatic potential computed in a fully three-dimensional model whereas the tunnel current is computed in the limit of large tip radii. Localized states forming at the semiconductor surface as well as wavefunction tailing through the semiconductor depletion region are fully accounted for. Numerical results are provided and compared with data obtained from p-type GaAs surfaces, and generalization of the method to semiconductor heterojunctions is discussed.