Strain engineering of nonlinear nanoresonators from hardening to softening

Although strain engineering and soft-clamping techniques for attaining high Q -factors in nanoresonators have received much attention, their impact on nonlinear dynamics is not fully understood. In this study, we show that nonlinearity of high- Q Si 3 N 4 nanomechanical string resonators can be substantially tuned by support design. Through careful engineering of support geometries, we control both stress and mechanical nonlinearities, effectively tuning nonlinear stiffness of two orders of magnitude. Our approach also allows control over the sign of the Duffing constant resulting in nonlinear softening of the mechanical mode that conventionally exhibits hardening behavior. We elucidate the influence of support design on the magnitude and trend of the nonlinearity using both analytical and finite element-based reduced-order models that validate our experimental findings. Our work provides evidence of the role of soft-clamping on the nonlinear dynamic response of nanoresonators, offering an alternative pathway for nullifying or enhancing nonlinearity in a reproducible and passive manner. In the design optimization of resonance frequencies and Q-factor of nanomechanical resonators, the influence of geometric design on the nonlinear dynamics has been rarely investigated. Here, the authors tune the stress field via soft-clamping, simultaneously increasing both the Q-factor and the onset of nonlinearity of a Si3N4 string resonator.