A femtogram resolution mass sensor platform, based on SOI electrostatically driven resonant cantilever. Part I: electromechanical model and parameter extraction

A microcantilever based platform for mass detection in the femtogram range has been integrated in the doped top silicon layer of a SOI substrate. The on-plane fundamental resonance mode of the cantilever is excited electrostatically and detected capacitively by means of two parallel placed electrodes in a two port configuration. An electromechanical model of the cantilever-electrodes transducer and its implementation in a SPICE environment are presented. The model takes into account non-linearities from variable cantilever-electrode gap, fringing field contributions and real deflection shape of the cantilever for the calculation of the driving electrostatic force. A fitting of the model to the measured S(21) transmitted power frequency response is performed to extract the characteristic sensor parameters as Young modulus, Q factor, electrical parasitics and mass responsivity.