A new multiscale approach to rapidly determine the local emission current density of nanoscale metallic field emitters

We advocate the use of lookup tables in the development of extremely fast and accurate multiscale models based on the coupling of a quantum-mechanical wave impedance approach and finite-element simulations to determine the local emission current density (LECD) from a metallic emitter of arbitrary shape. The lookup tables are prepopulated with numerical solutions of LECD that can be adjusted to accommodate any form of higher order physics, which is critical for current state-of-the-art emitters. Results show that the use of lookup tables can speed up numerical simulations of the field emission current from metallic cathodes by a factor of about 1000 x while retaining high precision, with a maximum error of less than 1% when compared to direct numerical solutions. Implementation of nanoscale emitter physics into lookup tables is discussed and used to assess the validity of the Kemble approximation for nanoscale metallic cathodes. The use of lookup tables is illustrated through a calculation of the LECDs of a metallic field emitter with a rugged surface and from an array of ellipsoid-on-a-post emitters. Section V contains our conclusions and suggestions for future work.