Energy exchange processes in field emission from atomically sharp metallic emitters

Abstract

Resistive heating, thermoelectric, and emission heating or cooling (e.g., the Nottingham effect) are examples of energy exchange processes which are fundamental in determining the thermal stability of electron emitters in high fields and temperatures. In this article, the studies of these energy exchange processes as a function of electrical and geometric properties of the emitter are reported. Specifically, Joule heating and associated thermoelectric effects have been calculated for an irradiated planar diode and a model point-contact diode with a conical tip. For a cone angle of 15°, significant temperature increases (T≥800 K) occur when the induced current densities are ≥108 A/cm2. The temperature rise is confined to the apex region and falls off rapidly beyond about 100 nm. The Nottingham energy exchange process was studied as a function of tip geometry. The inversion temperature, Ti, was calculated for a W tip modeled as a hyperboloid of revolution with a 10 nm radius of curvature. Ti was found to be significantly lower (≥100 K) for sharp emitters (for the same field at the apex) compared to a planar emitter. This can be explained by the relative increase in emission from higher energy states leading to cooling of the cathode emitter. Most significantly, the calculations show that for a given current density, the tip with the sharp geometry will operate at a lower inversion temperature relative to the planar emitter, a result which can be generalized to other pointed geometries.