Image charge method for electrostatic calculations in field emission diodes

We present a 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 method, we describe the field characteristics of a field-emission diode as a function of the gap between the electrodes for different tip shapes. The three-dimensional potential barrier (including image corrections) for electron field emission is also calculated.