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We present a study on the quantification of energy dissipation of Micro-Electro-Mechanical System (MEMS) resonators. Toroidal Ring Gyroscope (TRG) was used as a platform to conduct the study. The main energy dissipation mechanisms in TRG include viscous air damping, Thermo-Elastic Damping (TED), anchor loss, and surface loss. During our experimental study, these energy dissipation mechanisms were minimized and controlled by venting the encapsulation and actively pumping down to high vacuum, cooling the temperature down to around 123 K, adjusting modal balance by electrostatic tuning, and pre-baking the device at high temperature (425 °C), respectively. At room temperature, the quality factor related to viscous air damping was measured to be 625,000, TED to be 170,000, and anchor loss to be 1,350,000. Finite Element Analysis (FEA) was conducted to support these findings. Relation between the anchor loss and electrostatic tuning was also explored. The effects of moisture-related surface loss have also been demonstrated by monitoring characteristics over a 2-year period of time. High temperature bake-out was proven to be effective in removing the moisture and reducing the surface loss. This paper combines topics that are scattered in literature on identification of energy dissipation mechanisms in kilohertz-range silicon MEMS resonators and presents the topic as a single methodology illustrating how the contribution of each energy dissipation mechanism can be quantified independently. To the best of our knowledge, this study is the first to experimentally quantify all major energy dissipation mechanisms in a kilohertz-range silicon MEMS resonator. [2020-0294]

Encapsulated bulk mode microresonators in the megahertz range are used in commercial timekeeping and sensing applications, but their performance is limited by the current state of the art of readout methods. We demonstrate a readout using dispersive coupling between a high-Q encapsulated bulk mode micromechanical resonator and a lumped element microwave resonator that is implemented with commercially available components and standard printed circuit board fabrication methods and operates at room temperature and pressure. A frequency domain measurement of the microwave readout system yields a displacement resolution of [Formula: see text], which demonstrates an improvement over the state of the art of displacement measurement in bulk-mode encapsulated microresonators. This approach can readily be implemented in cryogenic measurements, allowing for future work characterizing the thermomechanical noise of encapsulated bulk mode resonators at cryogenic temperatures.

Fatigue in thick ( $> 20~\mu \text{m}$ ), epitaxially deposited polysilicon MEMS is characterized from 25°C and up to 250°C in an environment free of oxygen and humidity. This work is the first to report fatigue initiated in the native epi-polysilicon, free from any contributions due to oxide or environmental conditions. Fatigue was most prominent above stresses of 1.5 GPa at all temperatures. Resonant frequency shift is used to measure crack growth, and elevated temperatures increased the total frequency drift and frequency drift rates. Since the epi-polysilicon surfaces roughen due to grain boundary migration during fabrication, we conclude that epi-polysilicon fatigue can be attributed to a subcritical cracking mechanism that arises from surface roughness. Furthermore, the measured increases in the critical crack length before failure suggest that the fracture toughness increases at the elevated temperatures. [2020-0068]

Numerical modelling of MicroElectroMechanical Systems (MEMS) resonators is still attracting increasing interest from the sensors community especially when the nonlinear regime is activated. Here, the dynamic response of two different types of double-ended tuning fork MEMS resonators is studied both in the linear and nonlinear regimes. A one Degree Of Freedom (1 dof) model able to predict the frequency response of the device is proposed. Geometric and electrostatic nonlinearities are simulated through Finite Elements and Integral Equations, respectively. The total dissipation of the resonator is computed by taking into account both the thermoelastic and the nonlinear fluid contributions. Experimental measurements performed on resonators fabricated in polysilicon and single crystal silicon validate the proposed model showing a very good agreement with theoretical predictions. [2020-0240]

In this work we present measurements of drive-induced negative nonlinear dissipation present in doubly clamped microbeams fabricated in a hermetically sealed package. We characterize the amplitude-frequency nonlinearity and nonlinear dissipation present in this system under direct drive. The negative nature of the nonlinear dissipation is observed when measuring either the directly- or parametrically-actuated response. By comparing to the free ringdown response, we confirm that the nonlinear dissipation is induced by driving the resonator. Drive-induced nonlinear damping is an important consideration for resonant sensors and oscillators operated at large amplitudes. [2020-0140]

We present a Lame mode resonator whose limiting damping mechanism depends on its anchor geometry. The device is anchor-limited when the anchors are stiffer and is Akhiezer-limited with more compliant anchors. This result is determined by observing the temperature dependence of the quality factor (Q) for devices with different lateral dimensions and different anchor designs. The total measured Q increases by an order of magnitude with the more compliant anchors and reaches a room temperature fxQ product of $\boldsymbol {2.2\times 10^{13}}$ . We studied the relationship between the device design and the anchor design and the measured Q(T) results to identify the contributions from different dissipation mechanisms. This investigation provides insight into how anchor design affects anchor damping. [2020-0195]

We study thermal-piezoresistive cooling in silicon micromechanical resonators at large currents and high temperatures. Crossing a thermal transition region corresponds to a steep reduction in resonance frequency, an abrupt plateauing in the effective quality factor, and a large increase in thermomechanical fluctuations. Comparing measurements with simulations suggests that the second-order temperature coefficients of elasticity of doped silicon are not sufficient to capture the drop in resonance frequency at large currents. Overall, our results show that there are clear thermal limits to cooling a resonant mode using current-controlled thermal-piezoresistive feedback in silicon. [2020-0205]

We demonstrate two novel dual-mode ovenized MEMS resonators, each with an in-chip device layer micro-oven that utilizes less than 30mW for resonator temperature control over variations in external temperature from −40°C to +60°C. The device layer micro-oven enables correction for ambient temperature variations and achieves a 1-week frequency stability for the output mode over temperature near 1.5 ppb for the Lame-mode resonator. The devices were built in the Epi-Seal fabrication process and take advantage of the exceptional long-term stability of MEMS resonators built in that process. These results exceed all prior reports for frequency stability over time and temperature for MEMS resonators and have the potential to impact the development of miniature, low-power time references. [2019-0054]

The Kerr Parametric Oscillator (KPO) is a nonlinear resonator system that is often described as a synthetic two-level system. In the presence of noise, the system switches between two states via a fluctuating trajectory in phase space, instead of following a straight path. The presence of such fluctuating trajectories makes it hard to establish a precise count or even a useful definition, of the “lifetime” of the state. Addressing this issue, we compare several rate counting methods that allow to estimate a lifetime for the levels. In particular, we establish that a peak in the Allan variance of fluctuations can also be used to determine the levels’ lifetime. Our work provides a basis for characterizing KPO net- works for simulated annealing where an accurate determination of the state lifetime is of fundamental importance., Applied Physics Letters, 121 (16), ISSN:0003-6951, ISSN:1077-3118

Micromechanical oscillators provide periodic output signals for clocks and sensors by vibrating in a single mechanical mode. The mode is conventionally excited into self-sustained oscillations and stabilized with an external electronic feedback loop. A paradigm is emerging for sustaining vibrations by coupling the mechanical mode with internal degrees of freedom, such as photons, electrons, or auxiliary mechanical modes. An open question in these hybrid vibrational systems is the corresponding internal sources of nonlinearity that can stabilize the oscillations, and their impact on oscillator performance. Here, we delineate two kinds of amplitude-stabilization mechanisms in micromechanical oscillators, geometric nonlinear damping and repulsive contact, and show that these mechanisms can coexist in the same device and their interplay and resonance frequency stability can be tuned in situ by adjusting the feedback strength. An auxiliary source of viscous dissipation and nonlinear dissipation accompanies the repulsive contact, which stabilizes the amplitude during sidewall collisions. The onset of self-sustained oscillations yields distinct spectral-temporal signatures that can be used to identify the amplitude stabilization nonlinearities.

In this paper, we observe amplitude-dependent nonlinear dissipation in experimental measurements of the quality factor (Q). The ringdown response is used to quantify the magnitude of the amplitude-dependent effect in both polysilicon and single crystal silicon (SCS). The Q is reduced in both materials, up to 15.6%, and has a stronger influence on the measurements of Q in polysilicon than in SCS. Since the measured limiting dissipation mechanism in these resonators is thermoelastic dissipation (TED), we suggest these results align with models of amplitude-dependent TED. [2020-0160]

This work demonstrates that thin slots strategically placed in MEMS ring resonators are able to enhance the quality factor (Q) of the device operated in a wineglass mode in the isothermal region. The devices are optimized using COMSOL for an increased Q through increased slot size, using the Zener curve as a comparative baseline. These parts are fabricated and encapsulated in an ultra-clean environment, and tested in various temperature and pressure conditions to directly measure changes in anchor, gas, and thermoelastic dissipation across temperature. [2020-0156]

The thermomechanical motion imposes the fundamental noise limit in room-temperature resonant sensors and oscillators. Due to the inherently low sensitivity of capacitive transduction in microelectromechanical (MEM) resonators, its effects are often masked by noise in the subsequent amplifier and measurement stages. In this work, we demonstrate a capacitive transduction scheme for measuring kHz-MHz frequency MEM resonators across 1 $\mu \text{m}$ capacitive gaps with 99.8% thermomechanical-noise-limited resolution. We delineate the transimpedance gain and noise of our custom off-chip differential transimpedance amplifier setup. The thermomechanical noise spectrum can provide estimates of the resonant frequency, quality factor, and electromechanical transduction factor comparable to the commonly used driven response, without the downsides of capacitive feedthrough or nonlinearity. [2019-0115]

This paper demonstrates a post-fabrication technique for creating highly compliant structures inside a hermetic, wafer-scale encapsulation process. Single crystal silicon micro-tethers were fabricated alongside compliant structures to temporarily provide additional anchoring and increased device rigidity during the fabrication process. This technique mitigates in-process stiction for compliant devices by tethering the large, free-moving structures during fabrication. After successful fabrication, the micro-tethers can be selectively removed by two methods. The first method utilizes a potential voltage difference across the device. Joule heating can be concentrated in the micro-tether and the device separated after supplying requisite heat energy. The second method utilizes mechanical fracturing where a large external force is applied to separate the device from the tether. Micro-tethers in this paper were attached to differential resonant beam accelerometers, and were designed for detachment by each method: Joule heating and mechanical fracture. Our results show that the $40\mu \text{m}$ thick device can be successfully detached by both methods, indicated by the device sensitivity increase from ~100 Hz/g to ~400 Hz/g. [2018-0091]

Millions of micro electro mechanical system sensors are fabricated each year using an ultra-clean process that allows for a vacuum-encapsulated cavity. These devices have a multi-layer structure that contains hidden layers with highly doped silicon, which makes common imaging techniques ineffective. Thus, examining device features post-fabrication, and testing, is a significant challenge. Here, we use a combination of micro- and nano-scale x-ray computed tomography to study device features and assess failure mechanisms in such devices without destroying the ultra-clean cavity. This provides a unique opportunity to examine surfaces and trace failure mechanisms to specific steps in the fabrication process.

This paper presents a novel wafer-level thin-film encapsulation process that allows both narrow and wide trenches, which are necessary for traditional structures such as comb-drives. Fully functional devices with trench widths up to 50 $\mu \text{m}$ are fabricated by employing a vapor phase XeF2 isotropic silicon etch to create large cavities and an epitaxial deposition seal to encapsulate the devices in an ultra-clean, high vacuum environment with no native oxide and humidity. In this paper, we demonstrate the robustness of the proposed fabrication process, as well as the inherent benefits of the high-temperature epitaxial encapsulation process: high quality factor, extreme stability, exceptional aging, and fatigue performance. [2017-0098]

In this paper, we demonstrate a dual frequency oven-controlled MEMS resonator that can be designed to have an output frequency of 1.27 Mhz or 13 Mhz depending on the crystal orientation of the device. Both modes operate based on closed-loop thermal compensation that can offer PPB (parts-per-billion) level temperature stability over a wide temperature range using low power and exhibit strong shock robustness. As the device is rotated 45- degrees with respect to the $ $ plane of the wafer, the two modes used in oven control exhibit a unique temperature coefficient of frequency (tcF) reversal that allows selection of the output frequency for timing reference applications. The stiffer inplane mode has better temperature stability and shock resistance whereas the plate-bending mode offers ease of drive. Both devices retain stability performance after multiple 12,000g level shocks. [2020-0143]

Parametric resonators have wide utility as bits, sensors, and frequency references. Controlling the phase states of a parametric resonator enables signal generation and computation, but so far the states' rich dynamics in the presence of nonlinearities have received little attention. The authors delineate the regimes of nonlinearities for which parametric phase control is possible, and use this to experimentally operate on now-accessible solutions of the parametric response. In the context of micro- and nanoelectromechanical resonators, this work can foster numerous applications for parametric pumping in $e.g.$ scanning probe microscopes, signal amplifiers, and inertial sensors.

Understanding and controlling modal coupling in micro/nanomechanical devices is integral to the design of high-accuracy timing references and inertial sensors. However, insight into specific physical mechanisms underlying modal coupling, and the ability to tune such interactions is limited. Here, we demonstrate that tuneable mode coupling can be achieved in capacitive microelectromechanical devices with dynamic electrostatic fields enabling strong coupling between otherwise uncoupled modes. A vacuum-sealed microelectromechanical silicon ring resonator is employed in this work, with relevance to the gyroscopic lateral modes of vibration. It is shown that a parametric pumping scheme can be implemented through capacitive electrodes surrounding the device that allows for the mode coupling strength to be dynamically tuned, as well as allowing greater flexibility in the control of the coupling stiffness. Electrostatic pump based sideband coupling is demonstrated, and compared to conventional strain-mediated sideband operations. Electrostatic coupling is shown to be very efficient, enabling strong, tunable dynamical coupling., Micro- and nanomechanical resonators play a crucial role in sensing applications. Here, the authors demonstrate electrically tunable modal coupling in capacitive microelectromechanical gyroscopic ring resonators that allows for improving the performance micro/nano-sensors relying on precise control of the degree of modal coupling.

Ultra-high-speed video microscopy and numerical modeling were used to assess the dynamics of microbubbles at the surface of urinary stones. Lipid-shell microbubbles designed to accumulate on stone surfaces were driven by bursts of ultrasound in the sub-MHz range with pressure amplitudes on the order of 1 MPa. Microbubbles were observed to undergo repeated cycles of expansion and violent collapse. At maximum expansion, the microbubbles' cross-section resembled an ellipse truncated by the stone. Approximating the bubble shape as an oblate spheroid, this study modeled the collapse by solving the multicomponent Euler equations with a two-dimensional-axisymmetric code with adaptive mesh refinement for fine resolution of the gas-liquid interface. Modeled bubble collapse and high-speed video microscopy showed a distinctive circumferential pinching during the collapse. In the numerical model, this pinching was associated with bidirectional microjetting normal to the rigid surface and toroidal collapse of the bubble. Modeled pressure spikes had amplitudes two-to-three orders of magnitude greater than that of the driving wave. Micro-computed tomography was used to study surface erosion and formation of microcracks from the action of microbubbles. This study suggests that engineered microbubbles enable stone-treatment modalities with driving pressures significantly lower than those required without the microbubbles.

In the above article [1] , two authors, Christopher P. Cameron and Gabrielle D. Vukasin, were mistakenly omitted from the byline. The correct byline should read

We present an experimental study of conservative nonlinearities in bulk acoustic mode (bulk-mode) silicon MEMS resonators with degenerate doping. Three types of bulk acoustic mode resonators oriented in $\langle 110\rangle $ and $\langle 100\rangle $ silicon crystalline directions are used to analyze both linear and nonlinear elastic behavior of silicon with p- ( $N \cong 4.19e+18$ to $1.63e+20$ cm $^{-3}$ ) and n-type ( $N \cong 1.58e+18$ to $5.91e+19$ cm $^{-3}$ ) doping. For accurate characterization of the amplitude-dependent nonlinear stiffness constant, we employ two methods: amplitude-frequency response and ringdown measurement. Experimental results show that the nonlinear behavior of these resonators is dominated by material-dependent mechanical nonlinearities and strongly depends on the doping type and crystal orientation. These results are useful for understanding the material-induced nonlinear properties of doped silicon and design of MEMS resonators with desired dynamic behavior, and may provide a new avenue for tailoring resonator response characteristics. [2015-0301]

We investigate the phase dynamics of a closed-loop MEMS-based oscillator and demonstrate how one can exploit nonlinear behavior to improve oscillator phase noise characteristics by synchronizing the oscillator with a weak harmonic drive. Analytical predictions are based on an oscillator model that incorporates a resonator element with a weak cubic (i.e., Duffing type) nonlinearity, weak coupling to a clean external harmonic drive, and both thermal and frequency noise terms. The method of stochastic averaging is used to derive an expression for the rate of phase diffusion induced by the noises, and the results predict a remarkable phase noise reduction of three order of magnitude when the oscillator is synchronized to the weak external field. The predictions are experimentally demonstrated using a closed-loop oscillator with a double-anchored double-ended-tuning-fork MEMS resonator with coupling to a small external sinusoidal signal from a signal generator, demonstrating a 30 dB/Hz drop in phase noise. The results show how one can generate a clean high-power signal from a relative noisy oscillator by synchronizing it with a low-power external signal. The results also confirm recent studies showing that the parameter range of synchronization is significantly expanded when the resonator operates in its nonlinear regime. [2016-0067]

Specimen preparation remains a practical challenge in transmission electron microscopy and frequently limits the quality of structural and chemical characterization data obtained. Prevailing methods for thinning of specimens to electron transparency are serial in nature, time consuming, and prone to producing artifacts and specimen failure. This work presents an alternative method for the preparation of plan-view specimens using isotropic vapor-phase etching with integrated etch stops. An ultrathin amorphous etch-stop layer simultaneously serves as an electron transparent support membrane whose thickness is defined by a controlled growth process such as atomic layer deposition with sub-nanometer precision. This approach eliminates the need for mechanical polishing or ion milling to achieve electron transparency, and reduces the occurrence of preparation induced artifacts. Furthermore, multiple specimens from a plurality of samples can be thinned in parallel due to high selectivity of the vapor-phase etching process. These features enable dramatic reductions in preparation time and cost without sacrificing specimen quality and provide advantages over wet etching techniques. Finally, we demonstrate a platform for high-throughput transmission electron microscopy of plan-view specimens by combining the parallel preparation capabilities of vapor-phase etching with wafer-scale micro- and nanofabrication.

A systematic experimental and theoretical evaluation of stiction between intermittently contacting silicon surfaces in an ultra-clean encapsulation process is presented, evaluating magnitude of stiction forces, the reversible nature of sidewall contact, and repeatability of results. The uniquely stable environment and the lack of native oxide are leveraged to enable reliable collision and contact models, which confirm the nature of the asperity contact. In addition, we demonstrate a series of dynamic mechanical anti-stiction solutions and the mechanisms by which they mitigate stiction. These devices are shown to reduce susceptibility to stiction-related failure by 50%. [2015-0291]

This paper presents a thin-film wafer-level encapsulation process based on an epitaxial deposition seal that incorporates both narrow and wide lateral transduction gaps (0.7–50 $\mu \text{m}$ ), both in-plane and out-of-plane electrodes, and does not require release etch-holes in the device layer. Resonant structures fabricated in this process demonstrate high-quality factors ( $f\times Q$ products of up to $2.27e+13$ Hz) and exceptional stability (±18 ppb over one month) with no obvious aging trends. Studies on cavity pressure indicate that vacuum levels better than 0.1 Pa can be achieved after final encapsulation, thus reducing gas damping for high surface-to-volume devices. The vast diversity of functioning devices built in this process demonstrates the potential for combinations of high-performance MEMS devices in a single process and/or single chip. [2015-0278]

We present a technique for estimation of the model parameters for a single-mode vibration of symmetric micromechanical resonators, including the coefficients of conservative and dissipative nonlinearities. The nonlinearities result in an amplitude-dependent frequency and a nonexponential decay, which are characterized from the ringdown response. An analysis of the amplitude of the ringdown response allows one to estimate the linear damping constant and the dissipative nonlinearity, and the zero-crossing points in the ringdown measurement can be used for characterization of the linear natural frequency and the Duffing and quintic nonlinearities of the vibrational mode, which arise from a combination of mechanical and electrostatic effects. [2015-0263]

We derive the displacement noise spectrum of a parametrically pumped resonator below the onset for self-excited oscillations. We extend the fluctuation-dissipation response of a thermomechanical-noise-driven resonator to the case of degenerate parametric pumping as a function of pump magnitude and frequency while properly accounting for the quadrature-dependence of the parametric thermal noise squeezing. We use measurements with a microelectromechanical cantilever to corroborate our model.

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.

In this paper, we present the fabrication and test results of an oxide-coated polysilicon disk resonator gyroscope in a wafer-scale encapsulation process. We demonstrate the effects of an oxide coating on the device structure and the key performance parameters of resonant-based sensors, such as the temperature coefficient of frequency and quality factor ( $Q$ ). Results from the as-fabricated device show that a thin oxide coating reduces the surface roughness of a fully encapsulated device by $10\times $ , compared with a polysilicon device without the oxide coating. This increases the uniformity across the wafer, providing higher process yield. The open-loop rate measurement mode reveals an angle random walk of 0.18°/ $\surd $ hr and a bias instability of 1.43°/hr. [2015-0124]

We report on characterization of Si-to-Si contact microswitches fabricated in an ultraclean encapsulation process. This three-terminal microswitch relies on a curved beam (source) that actuates toward the contact terminal (drain) by charging the control terminal (gate). The operation range of this switch from −60 °C to 300 °C is investigated, which approximately yields a resistance drift of $- 200~\Omega $ /K. Our experiments include tests of the high-temperature lifetime during continuous ON–OFF cycles. By reducing Joule heating at the contact, preliminary results demonstrate at least $10^{\mathrm {\mathbf {6}}}$ cycles longer lifetime at 400 °C. Subsequently, the failure mode is investigated and reported. The study of ultraclean Si-to-Si contact-based microswitches provides a crucial guideline to the field of mechanical and electrical failure mechanisms for harsh environment applications. [2014–0373]

We present multifunctional integrated sensors (MFISES) that combine temperature, humidity, pressure, air speed, chemical gas, magnetic, and acceleration sensing on a single 2-mm $\times 2$ -mm die. We fabricate the MFISES in a wafer scale encapsulation process to hermetically seal the sensor functions with moving parts at low vacuum, and then surface micromachine the environmental sensors on top of the sealed layer. The encapsulation process provides very stable conditions for the pressure, magnetic, and acceleration sensors, and enables the deployment of the MFISES in dynamic environmental conditions without special postprocess packaging. We quantify the performance requirements for sensor applications in weather stations, indoor climate control, road activity monitoring, chemical sensing, and parking monitoring. We compare the performance of the MFISES to the application requirements to demon- strate the utility of an integrated sensor in a wide range of applications. [2014-0117]

Resonators fabricated in heavily doped silicon have been noted to have a reduced frequency-temperature dependence compared with lightly doped silicon. The resonant frequency of silicon microelectromechanical systems (MEMS) resonators is largely governed by the material’s elastic properties, which are known to depend on doping. In this paper, a suite of different types and orientations of resonators were used to extract the first- and second-order temperature dependences of the elastic constants of p-doped silicon up to 1.7e20 $\mathrm{cm}^{\mathrm {\mathbf {-3}}}$ , and n-doped up to 6.6e19 $\mathrm{cm}^{\mathrm {\mathbf {-3}}}$ . It is shown that these temperature-dependent elastic constants may be used in finite element analysis to predict the frequency-temperature dependence of similarly doped silicon resonators. [2013-0331]

The quality factor of a resonator represents the decay of vibrational energy over time, and is directly related to the frequency response and other key parameters that determine performance of inertial sensors and oscillators. Accurate prediction of the quality factor is essential for designing high-performance microelectromechanical (MEMS) devices. Several energy dissipation mechanisms contribute to the quality factor. Due to computational complexity, highly simplified models for the dominant dissipation mechanism, such as Zener’s model for thermoelastic dissipation (TED), are often employed. However, the intuition provided by these models is inadequate to predict the quality factor of more complex designs and can be highly misleading. In this paper, we construct complete, quantitative, and predictive models with finite-element methods for the intrinsic energy dissipation mechanisms in MEMS resonators using full anisotropic representation of crystalline silicon and the temperature dependence of all parameters. We find that TED is often a more significant source of damping than has been assumed, because of the previously neglected role of crystalline anisotropy and small geometric features, such as etch release holes—all of which can now be included in practical models. We show that these models, along with simpler scaling models for extrinsic dissipation mechanisms, explain measurements of quality factor in diverse sets of MEMS resonators with unprecedented accuracy. [2014-0106]

In this paper, we present four design methods to overcome (100) silicon crystalline anisotropy and achieve mode-matching in wineglass-mode disk resonator gyroscope (DRG). These methods were validated through experimental characterization of more than 145 different devices that arose from simulations. With the proposed methods, the frequency split of the 250-kHz DRG wineglass modes in (100) silicon was reduced from >10 kHz to as low as 96 Hz (

The fatigue lifetime of single crystal silicon (SCS) was characterized in an environment free of oxygen, humidity, and organics. Long-term ( $> 10^{10}$ Hz) fatigue experiments performed with smooth-walled SCS devices showed no signs of fatigue damage up to 7.5 GPa. In contrast, experiments using SCS devices with a silicon dioxide (SiO2) coating and rough sidewalls due to scalloping from deep reactive ion etching exhibited fatigue drift at 2.7 GPa and suffered from short-term ( $10^{10}$ Hz) fatigue failure at stress levels >3 GPa. In these SCS-SiO2 experiments, the initiation of fracture occurs in the SiO2 layer. It is concluded that fatigue in this case is likely attributed to a subcritical cracking mechanism; not reaction-layer nor dislocation related. A cross-comparison with other works from literature is developed to show that packaging a pristine device in an inert environment is necessary in order to operate devices at high-stress levels. [2013-0267]

Sensitive capacitive transduction of micromechanical resonators can contribute significant electrical dissipation, which degrades the quality factor of the eigenmodes. We theoretically and experimentally demonstrate a scheme for isolating the electrical damping of a mechanical resonator due to Ohmic dissipation in the readout amplifier. The quality factor suppression arising from the amplifier is strongly dependent on the amplifier feedback resistance and parasitic capacitance. By studying the thermomechanical displacement noise spectrum of a doubly clamped micromechanical beam, we confirm that electrical dissipation tunes the actual, not effective, quality factor. Electrical dissipation is an important consideration in the design of sensitive capacitive displacement transducers, which are a key component in resonant sensors and oscillators.