About the robustness of Schottky conjecture when quasi-one-dimensional stages are present

Abstract

The Schwarz–Christoffel transformation is used to analytically evaluate the field enhancement factor close to the apex of two-stage conducting structures consisting of a vertical line centered on the top of an isosceles trapezoidal protrusion on an infinite line. This way the validity of the Schottky conjecture (SC) is assessed for different ratios involving the dimensions of the system, which is expected to model quasi-one-dimensional structures, such as nanotubes, on the top of multistage structures used in different scientific and technological applications. The results obtained in this work suggest that the SC remains a good approximation beyond the region in which it is usually expected to be valid.