Phonon Emission and Self-Energy Effects in Normal-Metal Tunneling

Abstract

We discuss the dependence of conductance on voltage for metal-insulator-metal junctions for the bias range from 0-1 V. The dependence is roughly parabolic but the minimum conductance need not occur at $V=0$. Small deviations from this parabolic conductance behavior are described. These are due to interactions of the tunneling electrons with impurities in the oxide, the oxide itself, or the surface layers of the metal electrodes. These emission processes are studied by calculating the even conductance and its derivative. This derivative, at low voltages, is a crude measure of the phonon density in the normal-metal electrode. We show that self-energy effects in the normal metal can be conveniently displayed by calculating the odd conductance. Such experimental effects are presented for normal Pb, and are in good agreement with the self-energy calculated from superconducting tunneling.