Quantum mechanical analysis of the elastic propagation of electrons in the Au/Si system: application to Ballistic Electron Emission Microscopy

We present a Green's function approach based on a LCAO scheme to compute the elastic propagation of electrons injected from a STM tip into a metallic film. The obtained 2D current distribution in real and reciprocal space furnish a good representation of the elastic component of Ballistic Electron Emission Microscopy (BEEM) currents. Since this component accurately approximates the total current in the near threshold region, this procedure allows --in contrast to prior analyses-- to take into account effects of the metal band structure in the modeling of these experiments. The Au band structure, and in particular its gaps appearing in the [111] and [100] directions provides a good explanation for the previously irreconcilable results of nanometric resolution and similarity of BEEM spectra on both Au/Si(111) and Au/Si(100).