Overview of Computer Simulation Techniques for Field Emission Study

In field emission study, computer simulations are used to basically acquire two types of information: field distribution around a field emitter and charged particles emission from the emitter, which includes tracing charged particle trajectories and evaluating space charge effect. These involve solving Maxwell equations, Lorenz force equations and calculating emission current from the Fowler-Nordheim equation. There are well established numerical methods to solve these equations, such as finite difference method (FDM), finite element method (FEM) and boundary element method (BEM). In term of simulating field distribution, there are many commercial or home-made software packages and programmes, ranging from much generalized software such as MATLAB to much specialised software such as SOURCE. The MATLAB and the SOURCE are all FEM-based software. FEM is flexible in field simulation because unstructured meshing technique can be used to fit to complicated shape of field emitters. However, it is more difficult to calculate electron trajectories in a FEM-based mesh domain than in a FDM-based mesh domain. Therefore the early simulation programmes were primarily FDM-based