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

We develop a phase-space ab-initio 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 (V>0) and injection of holes into the valence band or injection of secondary Auger electrons into the conduction band for reverse bias (V<0). Here, an ab-initio 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.