Abstract:Thermoelastic dissipation (TED) is a fundamental energy loss process, which bears concern in all microelectromechanical resonators. High aspect ratio (R/h) 3-D microhemispherical shell resonators (µHSRs) have exceptionally low stiffness and are sensitive to dissipation forces both internally and at their surfaces. TED in µHSRs originating in the bulk of the shell and near its surfaces due to asperities (roughness) is investigated. Rayleigh's inextensional solutions for the lowest frequency vibration modes of µ… Show more
“…As such, we do not expect strong surface losses in the devices used in this study. The elimination of roughness in these devices should also suppress any additional “surface TED” that can arise from surface stresses localized near small-scale features or asperities on device surfaces 14 .Figure 1SEM image of an encapsulated Lamé-mode resonator after partial breakage of the die; this image shows the top encapsulation layer, the electrode and device layer, and the thick substrate underneath.…”
Silicon Microelectromechanical Systems (MEMS) resonators have broad commercial applications for timing and inertial sensing. However, the performance of MEMS resonators is constrained by dissipation mechanisms, some of which are easily detected and well-understood, but some of which have never been directly observed. In this work, we present measurements of the quality factor, Q, for a family of single crystal silicon Lamé-mode resonators as a function of temperature, from 80–300 K. By comparing these Q measurements on resonators with variations in design, dimensions, and anchors, we have been able to show that gas damping, thermoelastic dissipation, and anchor damping are not significant dissipation mechanisms for these resonators. The measured f · Q product for these devices approaches 2 × 1013, which is consistent with the expected range for Akhiezer damping, and the dependence of Q on temperature and geometry is consistent with expectations for Akhiezer damping. These results thus provide the first clear, direct detection of Akhiezer dissipation in a MEMS resonator, which is widely considered to be the ultimate limit to Q in silicon MEMS devices.
“…As such, we do not expect strong surface losses in the devices used in this study. The elimination of roughness in these devices should also suppress any additional “surface TED” that can arise from surface stresses localized near small-scale features or asperities on device surfaces 14 .Figure 1SEM image of an encapsulated Lamé-mode resonator after partial breakage of the die; this image shows the top encapsulation layer, the electrode and device layer, and the thick substrate underneath.…”
Silicon Microelectromechanical Systems (MEMS) resonators have broad commercial applications for timing and inertial sensing. However, the performance of MEMS resonators is constrained by dissipation mechanisms, some of which are easily detected and well-understood, but some of which have never been directly observed. In this work, we present measurements of the quality factor, Q, for a family of single crystal silicon Lamé-mode resonators as a function of temperature, from 80–300 K. By comparing these Q measurements on resonators with variations in design, dimensions, and anchors, we have been able to show that gas damping, thermoelastic dissipation, and anchor damping are not significant dissipation mechanisms for these resonators. The measured f · Q product for these devices approaches 2 × 1013, which is consistent with the expected range for Akhiezer damping, and the dependence of Q on temperature and geometry is consistent with expectations for Akhiezer damping. These results thus provide the first clear, direct detection of Akhiezer dissipation in a MEMS resonator, which is widely considered to be the ultimate limit to Q in silicon MEMS devices.
“…For example, Fig. 1c shows that microscale sidewall roughness along the sidewall of completely-solid millimeter-wide SiC disks substantially drops Q TED from 36 M to 3 M, making surface TED 20 the main damping mechanism in this work. Figure 1d shows dissipation in solid SiC disk resonators operating in the secondary elliptical mode (m = 3) is bound by Akhiezer ( f · Q = 6 · 10 14 Hz) and bulk TED ( f · Q = 1.2 · 10 14 Hz), with a combined theoretical f · Q limit of 1 · 10 14 Hz.…”
Micromechanical resonators with ultra-low energy dissipation are essential for a wide range of applications, such as navigation in GPS-denied environments. Routinely implemented in silicon (Si), their energy dissipation often reaches the quantum limits of Si, which can be surpassed by using materials with lower intrinsic loss. This paper explores dissipation limits in 4H monocrystalline silicon carbide-on-insulator (4H-SiCOI) mechanical resonators fabricated at wafer-level, and reports on ultra-high quality-factors (Q) in gyroscopic-mode disk resonators. The SiC disk resonators are anchored upon an acoustically-engineered Si substrate containing a phononic crystal which suppresses anchor loss and promises QANCHOR near 1 Billion by design. Operating deep in the adiabatic regime, the bulk acoustic wave (BAW) modes of solid SiC disks are mostly free of bulk thermoelastic damping. Capacitively-transduced SiC BAW disk resonators consistently display gyroscopic m = 3 modes with Q-factors above 2 Million (M) at 6.29 MHz, limited by surface TED due to microscale roughness along the disk sidewalls. The surface TED limit is revealed by optical measurements on a SiC disk, with nanoscale smooth sidewalls, exhibiting Q = 18 M at 5.3 MHz, corresponding to f · Q = 9 · 1013 Hz, a 5-fold improvement over the Akhiezer limit of Si. Our results pave the path for integrated SiC resonators and resonant gyroscopes with Q-factors beyond the reach of Si.
“…Upon examination, the disk showed fabrication nonidealities such as horizontal and vertical striation. Previous work has shown defects and asperities in shell resonators significantly contribute to TED [12]. While shells with surface roughness show Qs below 100,000 [13], attributable to a high surface area to volume ratio, the effect of surface defects on disks is less explored.…”
This work introduces a 3D design incorporating a phononic crystal to decouple a centrally-supported silicon carbide bulk acoustic wave disk resonator from its Si handle layer. By overcoming thermoelastic and anchor losses in bulk acoustic wave resonators, this scheme allows for probing the phonon-phonon dissipation limits i.e. Akhiezer loss. Using a custom silicon carbide on insulator platform, SiC disk resonators anchored upon phononic crystal were fabricated and optically measured. SiC disk resonators exhibit Q-factors near 4M with a record f•Q product of 1.85x10 13 Hz for the radial breathing mode operating at 5 MHz, limited by thermoelastic losses. This is the highest f•Q measured in monocrystalline silicon carbide resonators, an important step toward the batch fabrication of inertial-grade SiC BAW gyroscopes.
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