An analytical expression for quantum-well tunneling lifetimes

Abstract

An analytical expression is presented for the tunneling-escape lifetime of an electron occupying a quantum state localized in a quantum well in a heterostructure, using the perturbation approach. In the present derivation, an orthogonal basis set of wave functions is used, and all the terms in the perturbation expansion are included. The present formulation is exact and free from the inconsistencies in the transfer Hamiltonian method found recently by Fransson et al. [Phys. Rev. B 64, 153403 (2001)]. The tunneling lifetimes obtained by the present formulation agree with those obtained by the complex energy method. The analytical expression is useful in modeling tunneling devices in the sequential tunneling picture. We find that coupling of quantum states outside the quantum well to excited states localized in the quantum well is very important, and including these terms changes the tunneling lifetime by about six orders of magnitude.