Analytical and seminumerical models for gated field emitter arrays. I. Theory

Abstract

A simple analytic approach for gated field emission array unit cell modeling, the ‘‘Saturn’’ model, has been developed and serves to show how those parameters which most affect inductive output amplifier performance are dependent on the material and geometry of the unit cell. The Saturn model replaces the field emission tip with a sphere and the gate with a charged ring. A relation then exists between the gate radius, the gate voltage, the sphere radius, the field, and its angular variation on the sphere, from which the total emitted current may be given analytically, and from which the geometric and material dependence of those quantities which most affect amplifier performance (Fowler Nordheim A and B parameters, tip field, capacitance, and field enhancement factor) can be qualitatively determined. The qualitative predictions of this model may be made quantitative (the ‘‘seminumerical model’’) by the inclusion of a subset of parameters normally provided in a full boundary element numerical simulation which accounts for how the field varies along the surface of the emitter. The manner in which a statistical distribution of tip radii affects the least-squares estimate of the A and B parameters is shown.