DO TUNNELING ELECTRONS PROBE THE IMAGE INTERACTION ?

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Abstract
Some years ago Weinberg and Hartstein suggested that the discrepancy between their data on internal photoemission and photoassisted field emission was due to the inability of tunneling electrons to respond fully to the classical image potential. Since then much effort has been expended on explaining this as well as the more general problem of the effect of the full dynamical (i.e., velocity dependent quantum) image interaction on electron transport. However, neither problem has been definitively resolved. A major difficulty in the analyses using the classical image barrier has been the inability of over-simplified and inadequate models to explain observations in a manner consistent with the quantum mechanical limitations imposed on a tunneling electron. Specifically, the mean barrier approximations and the "image reduced" mean barrier are often imprecise approximations. Recently the logarithmic characteristics lnI (s;V = const) and lnV (s;I = const) have been determined using the STM. We have calculated lnI (s;V = const) for planar homo-junctions using two models with one-dimensional barriers, ϕ = ϕ (z) : (1) Simmons' mean barrier and hyperbolic approximations of the multiple image interaction, in the low bias limit, V ≪ ϕ0, the work function of the electrodes. (2) An exact integration of the Schrodinger equation to calculate the transmission across the full multiple image barrier. These calculations are discussed and compared with the experimental curves as well as some reported calculations by Binning et al

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