Phonon-tunnelling dissipation in mechanical resonators.

Microscale and nanoscale mechanical resonators have recently emerged as ubiquitous devices for use in advanced technological applications, for example, in mobile communications and inertial sensors, and as novel tools for fundamental scientific endeavours. Their performance is in many cases limited by the deleterious effects of mechanical damping. In this study, we report a significant advancement towards understanding and controlling support-induced losses in generic mechanical resonators. We begin by introducing an efficient numerical solver, based on the 'phonon-tunnelling' approach, capable of predicting the design-limited damping of high-quality mechanical resonators. Further, through careful device engineering, we isolate support-induced losses and perform a rigorous experimental test of the strong geometric dependence of this loss mechanism. Our results are in excellent agreement with the theory, demonstrating the predictive power of our approach. In combination with recent progress on complementary dissipation mechanisms, our phonon-tunnelling solver represents a major step towards accurate prediction of the mechanical quality factor.