Numerical study on performance of pyramidal and conical isotropic etched single emitters

A full three-dimensional model was implemented in order to investigate the electrical characteristics of conical and pyramidal isotropic etched emitters. The analysis was performed using the finite element method (FEM). The simulations of both emitters were modeled using a combination of tetrahedral and hexahedral elements that are capable of creating a mapped and regular mesh in the vacuum region and an irregular mesh near the surfaces of the emitter. The electric field strengths and electric potentials are computed and can be used to estimate the field enhancement factor as well as the current density using the Fowler–Nordheim (FN) theory. The FEM provides results at nodes located at discrete coordinates in space; therefore, the surface of the emitter can be generated through a function interpolating a set of scattered data points. The emission current is calculated through integration of the current density over the emitter tip surface. The influences of the device geometrical structure on its potential distribution, electric field and emission characteristics are discussed.