Electromechanical model of a resonating nano-cantilever-based sensor for high-resolution and high-sensitivity mass detection

A simple linear electromechanical model for an electrostatically driven resonating cantilever is derived. The model has been developed in order to determine dynamic quantities such as the capacitive current flowing through the cantilever-driver system at the resonance frequency, and it allows us to calculate static magnitudes such as position and voltage of collapse or the voltage versus deflection characteristic. The model is used to demonstrate the theoretical sensitivity on the attogram scale of a mass sensor based on a nanometre-scale cantilever, and to analyse the effect of an extra feedback loop in the control circuit to increase the Q factor.