Multiple image potential effects in a simple model of the Scanning Tunnelling Microscope (STM)

A classical electrostatic model is used to calculate the multiple image potential barrier reduction for an electron tunnelling between a metal surface and a spherical tip electrode. The tip electrode is modelled by a sphere or a hemisphere embedded in a plane and the metal surface is taken to be planar and grounded. The electrostatic potential in the region between the two electrodes is calculated for both the high symmetry (axial) case and the general (off-axis) case in terms of a multipolar expansion and a direct numerical method. The implications of the anisotropic barrier reduction by the multiple image potential for both magnitude of the tunnelling current and the lateral current distribution arising from the angular anisotropy on the Scanning Tunnelling Microscope are discussed. © 1987.