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 interi m results derived by modelling field electron emission from hemi-ellipsoida l emitters. The mathematical nature of the relationship between a new appro ach to emission-area extraction, recently proposed, and older approaches is demonstrated. The new approach is extended to cover field dependence in em ission area. Preliminary results are reported from an investigation into th e effects of making erroneous assumptions about the tunnelling barrier seen by the electron and the absence of field dependence in emission area. If w rong theoretical assumptions are made, then emission area can be overpredic ted by a factor of as much as 10 or 20. On the other hand, if correct theor etical assumptions are made, then the extracted emission area is close to a n emission area derived directly from the model calculations. The problemat ical nature of the concept of emission area, when emission area is a functi on of field, is pointed out. (C) 2001 Elsevier Science B.V. All rights rese rved.