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

First-principles analysis of nanoelectromechanical systems using Loewner equation