Ballistic electron emission microscope by real space multiple scattering theory

Ballistic Electron Emission Microscope (BEEM) is a microscope to investigate Schottky barrier based on Scanning Tunneling Microscope (STM) setup. The theoretical scheme widely used for STM is mostly focusing on an electric current from the tip tunneling through the vacuum to the sample surface. However, this model is not applicable for BEEM, since in the BEEM case, electrons tunneling through the vacuum are transported in the material over a very long range. We propose a theoretical model based on the real space full potential multiple scattering theory in order to describe this transport phenomena within the one electron picture. It is analogous to the theoretical model of angle resolved photoemission, except that the electron is emitted from the tip. This framework describes the tunneling effect and the multiple scattering in the tip and the sample and between them. Moreover this theory can be applied for non-Hermitian Hamiltonian, so that the loss of electrons at the Schottky barrier can be mimicked by introducing an imaginary part in the optical potential.