Numerical study of the electrostatic field gradients present in various planar emitter field emission configurations relevant to experimental research

Abstract

The generally assumed validity of the V∕dCA approximation for the cathode surface electric field under commonly employed electron field emission configurations was studied. Using appropriate typical dimensions for each configuration, the magnitude of the electric field over the cathode area under the probe was obtained, and especially near critical (i.e., sharp) regions that could lead to residual gas ionization, dielectric breakdown and emission of electrons from unintended areas. The results indicate that the V∕dCA approximation is far from being universally applicable to all the field emission measuring configurations. In particular, the cylindrical probe anode with flat tip gives the most uniform ES, which nearly equals V∕dCA over most of the cathode area under the probe. Spherical and hemispherical probes, on the other hand, result in ES close to V∕dCA only locally near the center, and much lower anywhere around the center. Moreover, the parallel-plate configurations lead to significantly detrimental field enhancement effects near the edges that discourage their use. These results have important implications in the correct evaluation of cold cathode materials for applications requiring large emitting areas or large current densities.