Modeling of field emission : protrusive surface at high current regime - Divya Prasad (2009)
This report presents a two dimensional model for field emission from a sharp cathode in high current regime. The trajectories of the electrons emitted from various points on the cathode are determined. The continuity equation is used to determine the charge density in the cathode-anode gap. The space charge field at the apex of the cathode is calculated from this charge distribution. At high current, the space charge strength is high. This leads to a reduction in the surface electric field at the cathode. The reduced surface electric field called the Poisson Electric Field, FP, determines the Poisson current density, JP. For the Fowler Nordheim plots, a "turn over" region in the high Field Emitted Vacuum Space Charge limit is predicted. The report also presents the effect of varying the cathode work function phi, the height to width ratio (h/w) on the Laplace (without space charge) and Poisson (with space charge) current densities. The sharper the emitter, higher is the field at which turn over occurs. This turn over region is not noted in past experiments – possible reasons are noted. Possible ways to extend the analysis to three dimensions are given.