TC f Manipulation in AlScN Nanomechanical Resonators Using Dual-Mode Parametric Excitation

In this work, we present resonator temperature coefficient of frequency (TCf) manipulation method by using the Duffing nonlinearities and non-dispersive coupling in two resonance modes within the same acoustic cavity. This temperature sensing technique leverages parametric pumping with a lock-in frequency, concurrently inducing signal and idler tones with opposite TCf signs. To demonstrate temperature sensing, aluminum scandium nitride (Al $_{\mathrm {1-x}}$ ScxN) (x =0.2) drumhead nanomechanical resonators with two resonance modes of vibration (0,1) and (1,1) are fabricated, and the TCf trends of the driven resonance modes and parametrically induced modes are carefully studied. A signal TC $f_{1}$ of −178 ppm/K and an idler TC $f_{2}$ of +88 ppm/K with a linear trend is experimentally measured, marking the first positive TCf measured on resonators with a negative driven-mode TCf. A one-dimensional lumped parameter model is presented to elucidate the underlying mechanisms of generating opposite TCf signs, showing an excellent match with the measured data. Furthermore, we demonstrate direct TCf manipulations through beat frequency ( $f_{b}$ ) modulation, using internal mixing of the induced signals and their harmonics, which can improve the temperature tunability of the resonant system. The presented work drastically simplifies the system-level integration of the resonant sensing systems by eliminating the need for interface electronics and dual feedback loops. [2024-0080]