Strain engineering of nonlinear nanoresonators from hardening to softening

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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 Si3N4 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.

Original languageEnglish
Article number53
Number of pages7
JournalCommunications Physics
Issue number1
Publication statusPublished - 2024


The research leading to these results received funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement 802093 (ERC starting grant ENIGMA). Z.L. acknowledges financial support from the China Scholarship Council and the early assistance on the FE reduced-order modeling from Vincent Bos. This work is also part of the project, Probing the physics of exotic superconductors with microchip Casimir experiments (740.018.020) of the research program NWO Start-up, which is partly financed by the Dutch Research Council (NWO). M.X. and R.A.N. acknowledge valuable support from the Kavli Nanolab Delft.


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