Boundary element simulation of electron trajectories for a field emitter

Abstract

Summary form only given. The details of the electron emission from field emitter array structures and trajectories into the acceleration region of the gun structure are required for the design of proposed next generation inductive output amplifiers (IOAs). A model that corresponds well to the actual geometry of the gated field emitter is expected to provide a more accurate comparison with the experimentally measured quantities. The axially symmetric unit cell model selected consists of an anode, a gate with hole, and a base plane with a vertical emitter tip protruding. The small sizes characteristic of the apex of the emitter tips in comparison to the size and distances of the other electrodes suggest the use of a nonuniform discretization of the computational domain. The use of typical finite-difference formulations with uniform mesh is therefore contraindicated. A variable-mesh finite-difference or finite element technique could be used. However, because of the sensitivity of the emission upon the local geometry in the small region near the emitter tip, a boundary-element model was chosen. The boundary element technique discretizes the boundary into sections (in our model, annular ribbons). These sections are taken to be quite small in the vicinity of edges and corners and increase in size in the smooth boundary areas. The list of boundary elements and their physical attributes is developed from a parameterization suggested by experimentally pertinent quantities. These quantities include work function, potential, tip radius, tip height, gate hole radius, base-gate distance, gate-anode distance, gate thickness, and type of tip, i.e., sphere on cone, ellipsoid, tip on post, post height.