Three-dimensional image interaction for nonsmooth emitters

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Abstract
We present a generalized image–charge method to calculate the interaction energies of a charge placed between a metallic tip of arbitrary shape and a sample surface. The basic idea is to replace the electrodes by a set of image charges. These charges are adjusted in order to fit the boundary conditions on the surfaces. As an application of the technique, we have calculated the three-dimensional potential barrier (including image interaction) for electron field emission from sharp tips having different geometries. The influence of the presence of a little hemispherical bump on the apex is also discussed.

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