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It is well known that sufficiently strong electrostatic fields are able tochange the morphology of Large Area Field Emitters (LAFEs). This phenomenonaffects the electrostatic interactions between adjacent sites on a LAFE duringfield emission and may lead to several consequences, such as: the emitter'sdegradation, diffusion of absorbed particles on the emitter's surface,deflection due to electrostatic forces and mechanical stress. Theseconsequences are undesirable for technological applications, since they maysignificantly affect the macroscopic current density on the LAFE. Despite thetechnological importance, these processes are not completely understood yet.Moreover, the electrostatic effects due to the proximity between emitters on aLAFE may compete with the morphological ones. The balance between these effectsmay lead to a non trivial behavior in the apex-Field Enhancement Factor (FEF).The present work intends to study the interplay between proximity andmorphological effects by studying a model amenable for an analytical treatment.In order to do that, a conducting system under an external electrostatic field,with a profile limited by two mirror-reflected triangular protrusions on aninfinite line, is considered. The FEF near the apex of each emitter is obtainedas a function of their shape and the distance between them via aSchwarz-Christoffel transformation. Our results suggest that a tradeoff betweenmorphological and proximity effects on a LAFE may provide an explanation forthe observed reduction of the local FEF and its variation at small distancesbetween the emitter sites.

Interplay between morphological and shielding effects in field emission via Schwarz-Christoffel transformation