Nonlinear dynamics in aluminum nitride contour-mode resonators

In this work, we discuss the self-heating nonlinear dynamics of aluminum nitride contour mode resonators. The self-heating introduces a quadratic coupling between the resonator motion and its temperature. This coupling produces a nonlinear frequency response identical to the weakly nonlinear Duffing resonator in steady-state. However, since the thermal relaxation rate is much smaller than the mechanical relaxation rate, the dynamics of the resonator differ from the conventional Duffing resonator.