Thermal-field emission from cones and wires

Electron sources exploiting field emission generally have sharp geometries in the form of cones and wires. Often, they operate under elevated temperatures. A sharply curved emitter affects the emission barrier past which the electrons must be emitted via thermal-field processes, as does a space charge in metal-insulator-metal and metal-oxide-semiconductor devices: all can be examined using the Gamow factor θ(E) on which the general thermal-field equation is based. A methodology to evaluate θ(E) based on shape factor methods is given that emphasizes analytical methods, speed, and accuracy of execution and is applied to curvature and space-charge modified barriers characterized by the addition of a quadratic barrier term. The implications for thermal, field, and thermal-field emission are assessed. In addition to the known temperature rise that attends current through a wire, tapering of the emitter apex is a source of additional temperature increases, which are assessed using a simple model that provides an upper temperature limit appropriate for tip-on-post or poor thermally conductive materials.