Geometric Tuning of Stress in Predisplaced Silicon Nitride Resonators.

We introduce a novel method to geometrically tune the tension in prestrained resonators by making SiN strings with a designed predisplacement. This enables us, for example, to study their dissipation mechanisms, which are strongly dependent on the stress. After release of the resonators from the substrate, their static displacement is extracted using scanning electron microscopy. The results match finite-element simulations, which allows a quantitative determination of the resulting stress. The in- and out-of-plane eigenmodes are sensed using on-chip Mach-Zehnder interferometers, and the resonance frequencies and quality factors are extracted. The geometrically controlled stress enables tuning not only of the frequencies but also of the damping rate. We develop a model that quantitatively captures the stress dependence of the dissipation in the same SiN film. We show that the predisplacement shape provides additional flexibility, including control over the frequency ratio and the quality factor for a targeted frequency.