Approximate universality in the tunneling potential for curved field emitters—A line charge model approach

Field emission tips with an apex radius of curvature below 100 nm are not adequately described by the standard theoretical models based on Fowler–Nordheim and Murphy–Good formalisms. This is due to breakdown “constant electric field” assumption within tunneling region leading substantial errors in current predictions. A uniformly applicable curvature-corrected field theory requires that potential approximately universal irrespective emitter shape. Using line charge model, it established analytically smooth generic follow this trend when anode far away. verified using COMSOL for various shapes including locally non-parabolic “hemisphere a cylindrical post.” It also found numerically provides adequate approximation close proximity as well presence other emitters.