A Model for Effective Field Enhancement for Fowler-Nordheim Field Emission

Summary form only given. A field enhancement factor is often required at the macroscopic scale in order to explain field emission current densities due to geometric features. The local field enhancement factor beta is often introduced in the Fowler-Nordheim equation to represent the geometrical effects at the surface of cathode. Local variation of beta determines the local dependence of injection current by the Fowler-Nordheim law. In computational models, it is impractical to determine the time-dependent local surface field each time step on a microscopic space scale. Effective beta is introduced in this paper which allows us to study the emission properties at a macroscopic scale. Microscopic (subgrid) local effective beta is calculated only at the initial time step, and then the effective beta can be recomputed under different surface electrical field through this model. The model allows reduction of dimensionality as well as the ability to include subgrid effects. The model is demonstrated on fundamental cases and compared to a calculation with a mesh fine enough to resolve the geometric features