Numerical transmission probabilities and the oscillatory photo-induced field emission current: Static and dynamic image charge effects

Numerical calculations are reported for the transmission probability of electrons incident upon a model potential barrier typically used in discussing electron emission from metal surfaces. These calculations are utilized in an attempt to explain the unexpected oscillatory photocurrent which was observed in a previous study of the electric field dependence of the photoinduced field emission current. Transmission resonances are observed in these calculations and a simple theory is described which adequately accounts for the electric field strengths at which these resonances occur. An important result of these calculations is that the model potential barrier given by $\text{V(x) = ?eFx ? (}\text{1}\text{4π?}{}_0\text{)(}\text{e}{}^2\text{4x}\text{)}$ cannot explain the oscillatory behavior of the photo-field current. Arguments are presented which question the static nature of the image charge potential employed in this simple model and a modification is introduced which incorporates in a very approximate fashion the time dependence involved in the formation of the image charge potential. Calculations based on this model correctly predict the periodicity of the observed oscillations and give a frequency which is in reasonable agreement with the measured value.