Direct calculation of the tunneling current

A simple model Hamiltonian is proposed for a metal-insulator- metal tunneling junction, which permits the direct calculation of the tunneling current without introducing any effective Hamiltonian. The model rests on the use of localized functions; this procedure avoids the difficult matching problem at the boundary between the barrier and the electrodes. Moreover the use of Kjeldysh's perturbation theory for nonequilibrium system allows an explicit calculation of the current to all orders in the applied bias. It is found that the transfer coefficient appearing in the expression for the current is energy dependent. This model can be systematically extended to include many body effects.