Strain engineering for ultra-coherent nanomechanical oscillators

Elastic strain engineering utilizes stress to realize unusual material properties. For instance, strain is used to enhance the electron mobility in semiconductor thin films. In the context of nanomechanics, the pursuit of ultra-coherent resonators has led to intense study of “dissipation dilution”, a technique where the stiffness of a material is effectively increased without added loss. Dissipation dilution causes the anomalously high quality factor of thin-film Si₃N₄ nanomechanical resonators; however, the paradigm has so far relied only on the strain produced during material deposition. Geometric strain engineering techniques—capable of producing local stresses near the material yield strength—remain largely unexplored. Here, we will present a spatially non-uniform phononic crystal pattern, used to co-localize the strain and flexural motion of a Si₃N₄ nanobeam, while increasing the former to near the yield strength. This combined approach produces string-like modes with Qf products approaching 10¹⁵ Hz, exceeding previous values for a room-temperature mechanical oscillator of any size. The devices we have realized can have force sensitivities of aN/rtHz perform hundreds of quantum coherent cycles at room temperature, and attain Q>400 million at megahertz frequencies.