Phase-space ab-initio direct and reverse ballistic-electron emission spectroscopy: Schottky barriers determination for Au/Ge(100)

We develop a phase space abinitio formalism to compute Ballistic Electron Emission Spectroscopy current voltage I(V)'s in a metal semiconductor interface. We consider injection of electrons into the conduction band for direct bias and injection of holes into the valence band or injection of secondary Auger electrons into the conduction band for reverse bias. Here, an abinitio description of the semiconductor inversion layer (spanning hundreds of Angstroms) is needed. Such formalism is helpful to get parameter free best fit values for the Schottky barrier, a key technological characteristic for metal semiconductor rectifying interfaces. We have applied the theory to characterize the Au/Ge(001) interface; a double barrier is found for electrons injected into the conduction band either directly or created by the Auger process while only a single barrier has been identified for holes injected into the valence band.