The importance of thermoelastic damping as a fundamental dissipation mechanism for small-scale mechanical resonators is evaluated in light of recent efforts to design high-Q micrometer- and nanometer-scale electromechanical systems. The equations of linear thermoelasticity are used to give a simple derivation for thermoelastic damping of small flexural vibrations in thin beams. It is shown that Zener’s well-known approximation by a Lorentzian with a single thermal relaxation time slightly deviates from the exact expression.

Thermoelastic Damping in Micro- and Nano-Mechanical Systems.

From ultrasensitive detectors of fundamental forces to quantum networks and sensors, mechanical resonators are enabling next-generation technologies to operate in room-temperature environments. Currently, silicon nitride nanoresonators stand as a leading microchip platform in these advances by allowing for mechanical resonators whose motion is remarkably isolated from ambient thermal noise. However, to date, human intuition has remained the driving force behind design processes. Here, inspired by nature and guided by machine learning, a spiderweb nanomechanical resonator is developed that exhibits vibration modes, which are isolated from ambient thermal environments via a novel "torsional soft-clamping" mechanism discovered by the data-driven optimization algorithm. This bioinspired resonator is then fabricated, experimentally confirming a new paradigm in mechanics with quality factors above 1 billion in room-temperature environments. In contrast to other state-of-the-art resonators, this milestone is achieved with a compact design that does not require sub-micrometer lithographic features or complex phononic bandgaps, making it significantly easier and cheaper to manufacture at large scales. These results demonstrate the ability of machine learning to work in tandem with human intuition to augment creative possibilities and uncover new strategies in computing and nanotechnology.

Spiderweb Nanomechanical Resonators via Bayesian Optimization: Inspired by Nature and Guided by Machine Learning.

In strained mechanical resonators, the concurrence of tensile stress and geometric nonlinearity dramatically reduces dissipation. This phenomenon, called dissipation dilution, is employed in mirror suspensions of gravitational-wave interferometers and at the nanoscale, where soft clamping and strain engineering have allowed extremely high quality factors. However, these techniques have so far been applied only to amorphous materials, specifically Si3N4. Crystalline materials exhibit substantially lower intrinsic damping at cryogenic temperatures. Applying dissipation dilution engineering to strained crystalline materials could, therefore, enable extremely low loss nanomechanical resonators, as they combine low internal friction, high intrinsic strain and high yield strength. This potential has not yet been fully exploited. Here we demonstrate that single-crystal strained silicon—a material developed for high-mobility transistors—can be used to realize mechanical resonators with ultralow dissipation. We fabricate strained silicon nanostrings with high aspect ratios supporting megahertz mechanical modes with quality factors exceeding 1010 at 7 K, a tenfold improvement over values reported in Si3N4. We estimate a thermal-noise-limited force sensitivity of (5 ± 2) × 10–20 N Hz–1/2 at 7 K—approaching that of carbon nanotubes—and a heating rate of only 60 quanta per second. The low mass and high quality factors of our nanomechanical resonators make them particularly promising for quantum sensing and transduction. Soft clamping reduces the dissipation of nanomechanical resonators, but this method has been limited to amorphous materials. When applied in crystalline silicon, it enables resonators with quality factors beyond ten billion. 

/pdf/strained-crystalline-nanomechanical-resonators-with-quality-4421uynu.pdf

Strained crystalline nanomechanical resonators with quality factors above 10 billion

In recent years, several new applications of SiC (both 4H and 3C polytypes) have been proposed in different papers. In this review, several of these emerging applications have been reported to show the development status, the main problems to be solved and the outlooks for these new devices. The use of SiC for high temperature applications in space, high temperature CMOS, high radiation hard detectors, new optical devices, high frequency MEMS, new devices with integrated 2D materials and biosensors have been extensively reviewed in this paper. The development of these new applications, at least for the 4H-SiC ones, has been favored by the strong improvement in SiC technology and in the material quality and price, due to the increasing market for power devices. However, at the same time, these new applications need the development of new processes and the improvement of material properties (high temperature packages, channel mobility and threshold voltage instability improvement, thick epitaxial layers, low defects, long carrier lifetime, low epitaxial doping). Instead, in the case of 3C-SiC applications, several new projects have developed material processes to obtain more performing MEMS, photonics and biomedical devices. Despite the good performance of these devices and the potential market, the further development of the material and of the specific processes and the lack of several SiC foundries for these applications are limiting further development in these fields.

/pdf/emerging-sic-applications-beyond-power-electronic-devices-15eit286.pdf

Emerging SiC Applications beyond Power Electronic Devices

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.

Nanomechanical Dissipation and Strain Engineering

High-quality micro- and nanomechanical resonators are widely used in sensing, communications, and timing, and have future applications in quantum technologies and fundamental studies of quantum physics. Crystalline thin films are particularly attractive for such resonators due to their prospects for high quality, high intrinsic stress, high yield strength, and low dissipation. However, when such films are grown on a silicon substrate, interfacial defects arising from lattice mismatch with the substrate have been postulated to introduce additional dissipation. Here, we develop a back-side etching process for single-crystal silicon carbide microresonators that allows us to quantitatively verify this prediction. By engineering the geometry of the resonators and removing the defective interfacial layer, we achieve quality factors exceeding a million in silicon carbide trampoline resonators at room temperature, a factor of five higher than those achieved without removal of the interfacial defect layer. We predict that similar devices fabricated from ultrahigh-purity silicon carbide, leveraging its high yield strength, could enable room-temperature quality factors as high as 6 x 10(9).

/pdf/engineering-the-dissipation-of-crystalline-micromechanical-1i2nkjj3ca.pdf

Engineering the Dissipation of Crystalline Micromechanical Resonators

High quality micro- and nano-mechanical resonators are widely used in sensing, communications and timing, and have future applications in quantum technologies and fundamental studies of quantum physics. Crystalline thin-films are particularly attractive for such resonators due to their prospects for high quality, intrinsic stress and yield strength, and low dissipation. However, when grown on a silicon substrate, interfacial defects arising from lattice mismatch with the substrate have been postulated to introduce additional dissipation. Here, we develop a new backside etching process for single crystal silicon carbide microresonators that allows us to quantitatively verify this prediction. By engineering the geometry of the resonators and removing the defective interfacial layer, we achieve quality factors exceeding a million in silicon carbide trampoline resonators at room temperature, a factor of five higher than without the removal of the interfacial defect layer. We predict that similar devices fabricated from ultrahigh purity silicon carbide and leveraging its high yield strength, could enable room temperature quality factors as high as $6\times10^9$

/pdf/engineering-the-dissipation-of-crystalline-micromechanical-5c7ki5ooym.pdf

Engineering the dissipation of crystalline micromechanical resonators

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Engineering the Dissipation of Crystalline Micromechanical Resonators

Nanomechanical Dissipation and Strain Engineering

Engineering the dissipation of crystalline micromechanical resonators

Nanomechanical Dissipation and Strain Engineering