One-Electron and Phonon-Assisted Tunneling inn-Ge Schottky Barriers

The experimental tunneling conductance of metal-Ge contacts is compared to the predictions of the one-electron Schottky-barrier model in which all parameters are determined from experiments other than tunneling. Agreement is found in the magnitude and the shape of conductance-versus-bias curves for vacuum-cleaved Sb-doped Ge units. The qualitative features of the As-doped units are also in agreement, but a discrepancy in magnitude exists. Substantially larger conductance is found in air-cleaved junctions than in vacuum-cleaved junctions. Capacitance measurements reveal that the barrier height for air-cleaved junctions is $V_b=0.51\mathrm{}$ V, whereas $V_b=0.63\mathrm{}$ V for vacuum-cleaved junctions. Pronounced step increases in the conductance due to phonon-assisted tunneling occur at $eV=\pm \hslash \omega$, where $\hslash \omega$ is the energy of a Ge phonon at the Brillouin-zone boundary along the [111] direction. Structure is clearly observed at all four phonon energies (TA,LA,LO,TO). The magnitude of the LA phonon-assisted tunneling is accounted for in a theoretical calculation based upon a mechanism suggested by Kleinman to explain similar phenomena in Ge $p-n$ junctions. The strengths of the TA and LO phonon-assisted tunneling also appear to be in reasonable agreement with qualitative considerations, but the observed TO phonon-assisted tunneling is stronger than expected.