Theory of Many-Body Effects in Tunneling

A general expression for the current voltage relation in a metal-oxide-metal tunnel junction is derived on the assumption of many-body interactions in the metals as well as the oxide. In the absence of many-body effects in the barrier, the expression for the conductance we derive is similar to that obtained from the tunneling-Hamiltonian approach in that it depends on the convolution of the product of the two spectral functions of the metals with a quantity analogous to the tunneling coupling constant. The coupling or transfer matrix element here is frequency-dependent as well as momentum-dependent, and does not suffer from the high-energy divergences characteristic of the tunneling Hamiltonian. The effect of the local variation of the self-energy on the tunneling conductance is examined, and is shown to be capable of producing structure in the conductance proportional to both the real and imaginary parts of the frequency-dependent self-energy. Finally, the method is shown to be capable of describing the usual barrier-excitation-assisted tunneling current.