The authors investigate by simulation the Coulomb effects on brightness and energy spread for cold field emitters. At first, we show that brightness is ultimately limited by Coulomb interactions. The authors analyze the maximum attainable brightness for tip radii ranging from 1?nm to 1??m. Remarkably, the brightness of a tip of 1?nm is comparable to a tip of 1??m. Higher brightness can be achieved by adding a plate at the base of the field emitter, and therefore decreasing the shank length. However, the brightness enhancement due to the protrusion is ultimately limited by large extractor voltages and increased energy spread. In particular, the energy spread for larger tip radii grows faster with brightness. The authors conclude that performance enhancement due to the protrusion works best for smaller tip radii.
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