Interplay between morphological and shielding effects in field emission via Schwarz-Christoffel transformation.
It is well known that sufficiently strong electrostatic fields are able to change the morphology of Large Area Field Emitters (LAFEs). This phenomenon affects the electrostatic interactions between adjacent sites on a LAFE during field emission and may lead to several consequences, such as: the emitter's degradation, diffusion of absorbed particles on the emitter's surface, deflection due to electrostatic forces and mechanical stress. These consequences are undesirable for technological applications, since they may significantly affect the macroscopic current density on the LAFE. Despite the technological importance, these processes are not completely understood yet. On the other hand, the proximity between emitters on a LAFE may lead to shielding effects that may compete with the morphological ones. The present work intends to study the interplay between proximity and morphological effects by studying a model amenable for an analytical treatment. In order to do that, a conducting system under an external electrostatic field, consisting of two mirror-reflected triangular protrusions on an infinite line, is considered. The Field Enhancement Factor (FEF) near the apex of each emitter is obtained as a function of their shape and the distance between them via a Schwarz-Christoffel transformation. Our results suggest that the tradeoff between shape and proximity effects on a LAFE may require a mechanism of saturation in the corresponding Fowler-Nordheim (FN) plot. Also, the results presented here may lead to a better understanding on the physics of multi-tip resonators for integrated emitter devices, in which the aforementioned effects are expected to compete during self-oscillations.
Publisher URL: http://arxiv.org/abs/1711.00202