Investigation of the Schottky Conjecture for compound structures modeled with line charges

Abstract

Schottky's Conjecture (SC) posits that when a compound conductive structure is formed by placing a protrusion on top of an underlying base, the total field enhancement factor is the product of the field enhancement factors that would be produced by the base and protrusion in isolation. This is a powerful concept, which, in principle, allows separate treatment of the electrostatic effects of geometric features occurring at differing length scales. Recent work suggests that the degree to which the SC holds depends on the shape of the protrusion and base, and, in particular, on their relative sizes and their degree of self-similarity. Here, we use a Line Charge Model (LCM) to study the applicability of the SC to compound, quasiellipsoidal structures. The general features of compound structures produced by the LCM are discussed. The SC consistently overpredicted the computed field enhancement factor but was seen to provide reasonable estimates, correct to within a factor of 2 or better, when the protrusion was sufficiently small compared to the base; a dependence of the threshold protrusion height on the base radius was identified. This range of applicability of the SC is more restrictive than that previously reported in the literature, and potential causes of this are discussed.