Digital computer studies of electron guns for electron microscopes†

A method of computing the electrostatic potential and electron trajectories in electron guns of the electron microscope type is described. Potentials are computed digitally using the successive over-relaxation technique, using two different mesh sizes. Electron trajectories are computed by a predictor-corrector method, using a bivariate interpolation formula for the electrostatic fields. Gun parameters of interest are readily obtained from the slope and displacement of trajectories as they leave the gun. Two electron guns with different grid shapes are investigated, and the grid shape is shown to influence the gun performance considerably. A re-entrant cone on the grid is shown to be deleterious in all respects, giving a source position of —12.1 mm compared with —5.1 mm, a source size of 20 µm compared with 8 µm, and a spherical aberration of 2.5 mm compared with 0.7 mm.