Incorporating photoemission into the theoretical unification of electron emission and space-charge limited current

Abstract

Photon emitters are becoming increasingly important due to their ability to generate high brightness, low emittance, and spatiotemporally coherent electron bunches for multiple applications; however, these emitters rarely produce electrons solely due to photoemission. Often, photon emitters are prone to undesired thermionic emission; alternatively, some devices intentionally leverage field and thermionic emission to increase output current. Regardless, attempting to extract higher currents from these devices raises concerns about space-charge buildup. While theories have examined the transitions between many of these mechanisms, none have used a common framework to unify photo-, thermionic, field, and space-charge limited emission simultaneously, typically represented individually by the Fowler–Dubridge (FD), Richardson–Laue–Dushman (RLD), Fowler–Nordheim (FN), and Child–Langmuir (CL) equations, respectively. This paper derives an exact solution unifying these mechanisms and reports conditions where emission bypasses RLD to directly transition from FD to FN based on asymptotically matching the three models at a nexus point. Furthermore, we provide a step-by-step approach for developing nexus phase space plots exhibiting the operating conditions for transitions among FD, RLD, FN, CL, Mott–Gurney for space-charge limited current with collisions, and Ohm's law for an external resistor. We demonstrate the utility of nexus plots for assessing the applicability of the simple well-known theories based on a single mechanism or the necessity to use more complicated solutions combining multiple mechanisms. As such, nexus theory provides a simple framework for guiding theorists in model development, simulation experts in algorithm development and selection, and experimentalists in device design.