First-principles analysis of nanoelectromechanical systems using Loewner equation

TL;DR

This paper introduces an analytical approach using the Loewner equation to accurately evaluate electrostatic properties, including field enhancement factors, in nanoelectromechanical systems with complex geometries, advancing beyond traditional numerical methods.

Contribution

It extends the application of the Loewner equation to curved nanoelectromechanical geometries, enabling exact analytical evaluation of field enhancement factors and current responses.

Findings

Exact evaluation of field enhancement factor near emitter apex.

Analytical method applicable to curved geometries.

Signature of emitted current response due to nanostructure oscillation.

Abstract

The Loewner equation (LE) is used to obtain conformal mappings that lead to exact and analytical expressions for several electrostatic properties of realistic quasi-unidimensional nanoelectromechanical systems (NEMS). The LE approach also embraces curved geometries, impossible to be addressed by traditional methods such as the Schwarz-Christoffel transformation, often used in this scenario. Among the possible applications of the formalism, we show that it allows for an exact evaluation of the field enhancement factor (FEF) close to the apex of different emitters. Despite its key role in the demodulation process for radio-receiver nano-devices, actual FEF values have been mostly obtained via numerical and/or phenomenological approaches. This work extends the already huge universe of applications of the LE and provides an analytical method to evaluate the FEF, even for curved emitters. Furthermore, our results provide a signature of the varying emitted current's response due to the nanostructure oscillation, justifying its role in the demodulation process of radio-frequency.