Generation of surface plasmons in a supported metal particles with an external electron beam:II Classical energy loss theory

Abstract

The theoretical predictions of the relative excitation probabilities of surface plasmons, using the coherent-state theory, are in good agreement with the experimentally observed relative heights of the surface plasmon peaks, This is partially because the field created by the induced charges on the support surface is not properly taken into account in the quantum theory.The Classical energy loss theory is based on Ritchie's work. Consider the total potential distribution in the space created by an incident electron under the non-retardation approximation (as shown in fig. 1), is the field created by the induced charges. Matching the solution of ψ on the boundaries, as a function of the incident electron position rt, the excitation probability of the surface plasmon as a function of ω is: