Nanomechanical Dissipation and Strain Engineering

Abstract

Nanomechanical resonators have applications in a wide variety of technologies ranging from biochemical sensors to mobile communications, quantum computing, inertial sensing, and precision navigation. The quality factor of the mechanical resonance is critical for many applications. Until recently, mechanical quality factors rarely exceeded a million. In the past few years however, new methods have been developed to exceed this boundary. These methods involve careful engineering of the structure of the nanomechanical resonator, including the use of acoustic bandgaps and nested structures to suppress dissipation into the substrate, and the use of dissipation dilution and strain engineering to increase the mechanical frequency and suppress intrinsic dissipation. Together, they have allowed quality factors to reach values near a billion at room temperature, resulting in exceptionally low dissipation. This review aims to provide a pedagogical introduction to these new methods, primarily targeted to readers who are new to the field, together with an overview of the existing state‐of‐the‐art, what may be possible in the future, and a perspective on the future applications of these extreme‐high quality resonators.

Geometric Tuning of Stress in Predisplaced Silicon Nitride Resonators

“…A straight beam will remain straight after the release process, but since it is then free in the y direction, its width will shrink. Via the Poisson ratio ν ≈ 0.23 this relaxes the longitudinal stress by a factor of 1 – ν, which is consistent with the value σ­( D 0 ) = 811 MPa in the plot. Furthermore, the larger the initial displacement, the lower the stress after release.…”

“…have a high Q value, an effect known as dissipation dilution. 19,38 Dynamic bending is, however, lossy and thus gives rise to internal material damping. 15,19 Bending most notably occurs near the anti nodes and near the clamping points of the beam.…”

“…19,38 Dynamic bending is, however, lossy and thus gives rise to internal material damping. 15,19 Bending most notably occurs near the anti nodes and near the clamping points of the beam. We employ a model inspired by Schmid et al 18 but with the mode shape calculated from the Euler− Bernoulli equation with tension included 27 (also see the Supporting Information) to find Q z : 41…”

“…Finally, different deposition parameters may result in different amounts of defects, making a systematic study of the stress dependence of the dissipation challenging. To overcome these limitations, several techniques for stress engineering have been pursued, 19 including bending of the chip, 20 phononic crystal patterning, 21 loss dilution, 21 clamp widening, 22 hierarchical structuring, 23 clamp tapering, 24 or altering the resonator design. 25,26 Here, we present a novel method to geometrically tune the stress of nanomechanical structures, 27 adding a new degree of freedom for e.g.…”

Stress Analysis and Q‐Factor of Free‐Standing (La,Sr)MnO3 Oxide Resonators

“…The length dependence observed for the LSMO(110) sample, indicates that in this case an additional contribution to the mechanical dissipation may come from clamping losses, that generally scale as the inverse of the length of the resonator. [ 51 ] This could also explain why we measure lower Q‐factor for the LSMO(110), in particular for the shorter bridges.…”