Analytic model of a compound thermal-field emitter and its performance

Abstract

A methodology for implementing the recently developed reformulated general thermal-field equation describing simultaneous thermal and field emission contributions to electron emission is developed, with modifications directed to enhancing speed and accuracy of computation as demanded by emitter characterization and electron beam simulations. An accurate factor to correct both thermal-field (TF) and high field (Fowler-Nordheim or FN) predictions based on a rapid Lorentzian fit model is given. The analytic protrusion model is constructed from modifications to a point dipole model that allow surface elements and field enhancement factors to be rapidly evaluated. The model is applied to an analytical model of a protrusion on a bump in a diode configuration to characterize how current-voltage I(V) relations are affected by TF emission conditions. In addition, it is also shown (i) how aggressively Schottky’s conjecture is undermined as the protrusion dimensions become larger; (ii) how the total current in the TF regime can be substantially larger than predicted by canonical [FN and Richardson-Laue-Dushman (RLD)] formulations; (iii) how an optimal protrusion size may exist; and (iv) how the inference of field enhancement, notional emission area, and work function are poorly predicted using conventional methods relying on the canonical FN and RLD equations even outside the thermal-field regime, even though data can be linear on FN and RLD plots.