  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.
Moreover, the electrostatic effects due to the proximity between emitters on a
LAFE may compete with the morphological ones. The balance between these effects
may lead to a non trivial behavior in the apex-Field Enhancement Factor (FEF).
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,
with a profile limited by two mirror-reflected triangular protrusions on an
infinite line, is considered. The 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 a tradeoff between
morphological and proximity effects on a LAFE may provide an explanation for
the observed reduction of the local FEF and its variation at small distances
between the emitter sites.
