New results in the theory of Fowler-Nordheim plots and the modelling of hemi-ellipsoidal emitters.

This paper reports further progress in understanding the theory of emission-area extraction from Fowler-Nordheim plots, and reports some useful interim results derived by modelling field electron emission from hemi-ellipsoidal emitters. The mathematical nature of the relationship between a new approach to emission-area extraction, recently proposed, and older approaches is demonstrated. The new approach is extended to cover field dependence in emission area. Preliminary results are reported from an investigation into the effects of making erroneous assumptions about the tunnelling barrier seen by the electron and the absence of field dependence in emission area. If wrong theoretical assumptions are made, then emission area can be overpredicted by a factor of as much as 10 or 20. On the other hand, if correct theoretical assumptions are made, then the extracted emission area is close to an emission area derived directly from the model calculations. The problematical nature of the concept of emission area, when emission area is a function of field, is pointed out.