This paper reports the frequency-dependent electrothermal behaviors of a freestanding doped-silicon heated microcantilever probe operating under periodic (ac) Joule heating. We conducted a frequency-domain finite-element analysis (FEA) and compared the steady periodic solution with 3ω experiment results. The computed thermal transfer function of the cantilever accurately predicts the ac electrothermal behaviors over a full spectrum of operational frequencies, which could not be accomplished with the 1D approximation. In addition, the thermal transfer functions of the cantilever in vacuum and in air were compared, through which the frequency-dependent heat transfer coefficient of the air was quantified. With the developed FEA model, design parameters of the cantilever (i.e., the size and the constriction width of the cantilever heater) and their effects on the ac electrothermal behaviors were carefully investigated. Although this work focused on doped-Si heated microcantilever probes, the developed FEA model can be applied for the ac electrothermal analysis of general microelectromechanical systems.

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