Nonlinear response of very high frequency contour mode resonators

•Red-shift of the resonance frequency in VHF CMRs is due to self-heating and variable damping.•Temperature-dependent stiffness, geometric nonlinearity captures nonlinearity in simulation.•Fabricated devices validate the theoretical, circuit, and numerical models.•A frequency-comb like response at microwave frequencies as an example real-life application. We explore the source of nonlinearities in Aluminum Nitride (AlN) Contour Mode Resonators (CMRs) operating in the Very High Frequency (VHF) range. We demonstrate that the red-shift of the resonance frequency found in VHF CMRs when the input RF power increases is due to nonlinear stiffness appearing from self-heating, and variable damping due to geometric nonlinearities. Moreover, we find a linear relationship between the variable damping coefficient and the resonator quality factor (Q). Such nonlinear mechanisms are modeled using a spring-mass-damper physical system and, in the electrical domain, a modified Butterworth-Van Dyke (MBVD) circuit where the nonlinear stiffness and variable damping are captured by a charge-dependent motional capacitor and a charge-dependent motional resistor, respectively. Detailed guidelines are provided to accurately analyze nonlinear CMRs using full-wave numerical simulations based on a finite-element method. Such simulations allow us to isolate the influence of each independent nonlinear mechanism and establish a relation between variable damping and geometric nonlinearities. Circuit and full-wave numerical simulations are in good agreement with measured data from fabricated 225 MHz CMRs exhibiting different Q. Finally, we exploit nonlinearities in high-Q CMRs to generate frequency combs at the MHz range opening the door to new exciting applications in telecommunication and sensing.