Field emission microtriode theory and simulation

Summary form only given. Analytical techniques previously employed on diode geometries are extended to the problem of a field emission microtriode. Qualitative triode behavior may be determined using a simple analytical model. This model may be further enhanced by incorporating simulation results from a full boundary element solution to Laplace\´s Equation. The resulting quantitative seminumerical approach may be used to quickly determine triode dependence on unit cell geometry and material parameters. The simple, or "Saturn", model, replaces the field emission tip with a sphere and the gate with a charged ribbon. An analytic 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. This simple model, while giving quantitatively different current estimates, nevertheless makes qualitative predictions which are borne out in the full numerical simulation. Finally, the methodology used in the simple model motivates the approximations made in the semi-numerical approach. The boundary element method models the tip, gate and anode surfaces with charged ribbons. At present, we restrict our attention to electrodes with azimuthal symmetry.