Experimental Study of the Origin of Nonlinear Damping in Very High Frequency Contour Mode Resonators

This article investigates the sources of nonlinearities in aluminum nitride (AlN) contour mode resonators (CMRs) operating at very high frequencies (VHF) and having Q primarily limited by anchor losses. In this work, we demonstrate that the damped Duffing response observed in moderately-driven VHF CMRs is due to self-heating and geometric nonlinearities. 224-MHz CMRs of different anchor’s length (L a ) and width (W a ) are fabricated, tested, and modeled via a modified Butterworth-Van Dyke (mBVD) circuit that includes variable motional capacitance and resistance. The nonlinear elastic (α) and damping (β/α) coefficients resultant from fitting correlate with L a /W a (or thermal resistance), and L a (or nonlinear deformation), respectively. The latter is also proved via finite element analysis (FEA).