  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.
