A general computational method for electron emission and thermal effects in field emitting nanotips

Electron emission from nanometric size emitters becomes of increasing interest due to its involvement to sharp electron sources, vacuum breakdown phenomena and various other vacuum nanoelectronics applications. The most commonly used theoretical tools for the calculation of electron emission are still nowadays the Fowler-Nordheim and the Richardson-Laue-Dushman equations although it has been shown since the 1990s that they are inadequate for nanometrically sharp emitters or in the intermediate thermal-field regime. In this paper we develop a computational method for the calculation of emission currents and Nottingham heat, which automatically distinguishes among different emission regimes, and implements the appropriate calculation method for each. Our method covers all electron emission regimes (thermal, field and intermediate), aiming to maximize the calculation accuracy while minimizing the computational time. As an example, we implemented it in atomistic simulations of the thermal evolution of Cu nanotips under strong electric fields and found that the predicted behavior of such nanotips by the developed technique differs significantly from estimations obtained based on the Fowler-Nordheim equation. Finally, we show that our tool can be also successfully applied in the analysis of experimental I-V data.