Electric Potential and Field Near Pointed Shaped Surfaces

Abstract

The trajectories of charged particles, emitted from within or from the close vicinity of pointed shaped surfaces, requires the knowledge of the electric field resulting from the potential bias between surface and detector, or screen. Frequently it is necessary the use of numerical methods for solving Laplace's equation as a result of difficulties in obtaining an analytical expression. Recently we have shown that, when any two coordinate surfaces of an orthogonal system are kept at two different but constant potentials, it is possible to obtain an analytical solution for the potential in a relatively simple manner. Using this general property of orthogonal coordinate systems, we present the solution for the electric potential and field in the vicinity of pointed surfaces for several cases of practical interest in field emission, field ionisation, atomprobe field ion spectroscopy and related phenomena.