Impurity-Assisted Inelastic Tunneling: Many-Electron Theory

Abstract

The one-electron theory of impurity-assisted tunneling is extended to a many-electron system. A formal derivation of the wave function through second order in the interaction potential is given for an arbitrary barrier potential and an arbitrary interaction potential. Application to a one-dimensional square-barrier model with energy-loss mechanisms confined to the barrier region is made. The magnitude of the inelastic current resulting from the excitation of a molecular impurity is in agreement with the results of the transfer-Hamiltonian model if the appropriate current-carrying wave functions are used to calculate the transfer matrix elements. Additional second-order terms which give rise to logarithmic singularities and step-function decreases in the barrier-penetration factor are found for interaction potentials which are large near the boundaries of the tunnel barrier. Numerical calculations show that, for a molecular impurity at the boundary, the line shapes in $\frac{d^{2}I}{d{V}^2}$ versus $V$ are fundamentally different from those for an impurity inside the barrier by more than ∼ ½ K.