Characterization of electrostatically coupled microcantilevers

The use of tightly packed arrays of probes can achieve the much desirable goal of increasing the throughput of scanning probe devices. However the proximity of the probes induces coupling in their dynamics, which increases the complexity of the overall device. In this paper we analyze and model the behavior of a pair of electrostatically and mechanically coupled microcantilevers. For the common case of periodic driving voltage, we show that the underlying linearized dynamics are governed by a pair of coupled Mathieu equations. We provide experimental evidence that confirms the validity of the mathematical model proposed, which is verified by finite element simulations as well. The coefficients of electrostatic and mechanical coupling are estimated respectively by frequency identification methods and noise analysis. Finally, we discuss parametric resonance for coupled oscillators and include a mapping of the first order coupled parametric resonance region.