Accurate ab initio determination of ballistic electron emission spectroscopy: Application to Au/Ge

Abstract

Ab initio nonequilibrium Keldysh formalism based on an $N$-order renormalization technique is used to compute $I(V)$ ballistic electron emission microscopy characteristics at the Au/Ge(001) interface. Such a formalism quantitatively reproduces precise experimental measurements under ultrahigh vacuum and low-temperature conditions. At $T=0$ K, the ballistic current follows the law ${(V\ensuremath{-}{V}_{\mathrm{SB}})}^{2.1}$, ${V}_{\mathrm{SB}}$ being the Schottky barrier. At $Tg0$ K, temperature effects become significant near the onset and must be taken into account to identify an accurate value for ${V}_{\mathrm{SB}}$ from a best-fit procedure. We find two values for ${V}_{\mathrm{SB}}$, 0.67 and 0.75 eV, which we associate with two different atomic registries at the interface.