Simplified Analysis of Point-Cathode Electron Sources

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Abstract
The accelerating field of a point‐cathode electron source is divided into two regions, a diverging spherical‐field region located in the immediate vicinity of the point cathode, and a converging‐field region which occupies most of the cathode‐anode space. Analysis of this model gives the Gaussian source size, axial position of the source, and spherical‐ and chromatic‐aberration constants of the pointed‐cathode electron gun. After including diffraction effects, the electron‐optical parameters are optimized for minimum possible source size. The current density which appears to be emitted by the apparent source is introduced as a figure of merit for this type of electron gun, and the performance of field‐emission and Schottky‐emission pointed cathodes are compared. Source diameters below 100 Å are predicted for oriented‐tungsten field‐emission pointed cathodes, with apparent current densities exceeding 104 A/cm2; source diameter below 1000 Å are predicted for oriented‐tungsten Schottky‐emission pointed cathodes, with apparent current densities of approximately 100 A/cm2.