INELASTIC PROCESSES IN TIME-DEPENDENT TUNNELING IN A SCANNING TUNNELING MICROSCOPE JUNCTION

Experiments on frequency mixing and tunneling time measurements have stirred renewed interest in the problem of tunneling through time dependent barriers in a vacuum diode configuration such as the scanning tunneling microscope (STM) junction. In the present work we have formulated a theory of photoassisted emission for a planar bimetallic junction with both a static dc voltage and a time dependent bias of angular frequency omega. An expression for the current is derived using kinetic theory and the transfer Hamiltonian method. The wave functions are determined from time dependent perturbation theory and are calculated recursively to infinite order. Although the current is initially calculated within the free-electron model, this kinetic formalism allows for the inclusion of band-structure effects through the density of states factors. The photoassisted inelastic tunneling current was calculated as a function of frequency, fields, barrier parameters, and material asymmetry. The results are applied to an analysis of the tunneling time experiments of Nguyen et al. [H. Q. Nguyen et al., IEEE Trans. Electron Devices 36, 2671 (1989)]. The conclusions impose some constraints but do not limit the experimental procedure used for extracting tunneling times in an irradiated STM junction.