Semiclassical theory of cold field electron emission from nanoscale emitter tips

This work presents a semianalytical theory of cold field emission, based on a multidimensional, semiclassical approximation to the time-independent Schrödinger equation. The theory enables the derivation of the total emitted current and total energy distribution equations for emitters of arbitrary material, geometry, and dimensionality and also serves to unify the existing regimes of cold field emission theory. Furthermore, the close connection between the semiclassical approximation and classical mechanics provides a method for the interpretation and analysis of nanoscale emitter properties in terms of the more familiar concepts and quantities of classical physics. The application of the theory to emission from the surface of a cylindrical, metallic nanowire yields results that are in good agreement with the exact solutions and demonstrates that the multidimensional semiclassical approach obviates the need for the Langer correction in cylindrical coordinates and produces normalizable wave functions without turning point singularities inside the emitter.