Thermal Nonlinearities in Contour Mode AlN Resonators

In this paper, we analyze the origin of elastic nonlinearities in aluminium nitride contour mode resonators (CMRs). Our study highlights that the nonlinear behavior is due to thermal effects when the resonators are electrically excited and the input is slowly (slow with respect to the device thermal time constant) swept through the excitation frequencies close to the main resonance. An analytical expression that relates the nonlinear behavior of the device to its geometry and material properties is derived. Amplitude-frequency (A-f) and third-order intermodulation (IMD3) measurements on 1-GHz AlN CMRs are employed to demonstrate the theoretical reasoning. The two experiments confirm the validity of the analytical derivation when the system is dominated by thermally induced nonlinearities. In the case of large frequency difference between the modulation frequencies, purely elastic nonlinearity can also be extracted from the IMD3 measurements.