One-dimensional combined field and thermionic emission model and comparison with experimental results

An integrated theoretical model has been developed to predict the entire range of emission from thermionic to field emission, including the mixed emission regime. The model assumes a Sommerfeld free electron model supply function, for which the Fermi-Dirac distribution applies with a nonzero temperature. The electron transmission coefficient is calculated in one dimension using a transfer matrix method TMM to solve the steady-state Schrödinger equation. Emission current densities have been measured for a periodic copper knife-edge cathode to compare with the TMM model result. It is shown that the computational result utilizing this model provides good agreement with the experimental data. Unambiguous and reliable estimates of the effective field enhancement factor eff eff=Es /Eg, where Es is the cathode surface electric field and Eg is the gap electric field between the cathode and anode and the effective work function eff are obtained from experimental measurements using this model by simultaneously fitting thermionic and field emission data for the cathode. Comparing the experimental and theoretical results reveals that finite temperature thermal contributions to the current emission can be significant in the operation of many field emission cathodes. © 2008 American Vacuum Society. DOI: 10.1116/1.2884755