The transverse structure of cold field electron emission

Solutions of Schrödinger’s equation have been obtained for electron emission from a small area in a system of planar electrodes. In a uniform field, wave components with non-zero transverse phase constant see a greater height and width of the potential barrier than the normal component does, the extra energy being that corresponding to the transverse momentum. Also the total intensity shows a Gaussian decrease as beam radius increases, even for a point source. The characteristic Gaussian radius increases as the square root of the distance from the starting plane. In contrast, flow from a point source into a region of uniform potential does not show these effects, but spreads much more broadly.