  Graphene and other 2D materials give a platform for electromechanical sensing
of biomolecules in aqueous, room temperature environments. The electronic
current changes in response to mechanical deflection, indicating the presence
of forces due to interactions with, e.g., molecular species. We develop
illustrative models of these sensors in order to give explicit, compact
expressions for the current and signal-to-noise ratio. Electromechanical
structures have an electron transmission function that follows a generalized
Voigt profile, with thermal fluctuations giving a Gaussian smearing analogous
to thermal Doppler broadening in solution/gas-phase spectroscopic applications.
The Lorentzian component of the profile comes from the contact to the
electrodes. After providing an accurate approximate form of this profile, we
calculate the mechanical susceptibility for a representative two-level bridge
and the current fluctuations for electromechanical detection. These results
give the underlying mechanics of electromechanical sensing in more complex
scenarios, such as graphene deflectometry.
