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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.

Mesoporous metals are used in applications requiring high specific surface area and fast mass transport in an electrically conductive network and are primarily produced via dealloying. However, dea...

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]

This paper presents a novel spring disk resonator gyroscope (SRG). The SRG consists of coupled concentric serpentine spring-like rings to reduce mode stiffness while maintaining a device footprint the same as that of existing standard DRGs: 600um in diameter. The $Q$ is increased by a factor of 2.5, and the ring down-time of 934ms is 4 times longer than that of a standard DRG.

MEMS Thermal accelerometers are typically driven and sensed entirely at DC, an approach that contributes to their relatively high drift and noise. This work presents several novel operation modes based on independent modulation of the heater and the detectors: DC heating and AC sensing, AC heating and DC sensing, and full AC. The improvement in noise density offered by modulating the detectors is measured, showing a 23% reduction as compared to pure DC operation. Both AC heating modes exhibited an order of magnitude less drift at 100 seconds than DC heating. These results demonstrate the substantial improvements modulated operating schemes can offer for both noise and ultra-low frequency stability in thermal accelerometers.

In this work, we compared the survivability of epitaxially encapsulated (EPI) MEMS disc resonating gyroscopes (DRGs) with ten different designs up to shocks near 50,000g. Though most DRGs survived, there are clear differences in the performance of devices post shock. Devices are clustered into their respective shock groups, but some devices maintain their superior performance even in the face of extreme shock. This work expands on the previous work of understanding shock resistance in gyroscopes and which devices may maintain performance under various conditions.

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.

Electrothermal measurement techniques often require thin dielectric barriers to isolate active electrical test structures from samples of interest. The combined need for electrical passivation but thermal proximity necessitates the use of an electrically thick but thermally thin barrier layer. Here, we demonstrate a hybrid approach toward constructing sub-300 nm SiO2 multilayer barriers based upon low-temperature plasma-enhanced atomic layer deposition and high density plasma chemical vapor deposition. Using pairs of buried metal test structures, we quantify changes in device resistance and cross-talk after covering the dielectric barrier with thin evaporated gold films and thick electroplated copper films. We show that a hybrid approach to passivating electrothermal measurement devices outperforms individual homogenous barriers formed by either deposition technique.

This paper reports on the implementation of a vacuum-encapsulated bi-axial resonant accelerometer utilizing the electrostatic frequency modulation (eFM) technique. A novel flexure structure is designed to enable fully-decoupled in-plane displacement of the proof-mass to minimize cross-axis sensitivity. A differential readout scheme leveraging pairs of high quality factor (>12k) free-free beam resonators mitigates the first-order nonlinearities due to temperature effects and unwanted response to proof-mass spurious modes. The fabricated device measures a scale factor of 45.8 Hz/g with negligible cross-axis sensitivity (

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]

For the first time ever, we demonstrate an Epi-Seal encapsulated, self-excited Franklin oscillator. This electromechanical switch oscillator, is driven by a constant input of 3.8 [V], sustains self-oscillations at a frequency of 88.6 [kHz], and requires a power of only $1.5 [\mu \mathrm{W}_{\mathrm{RMS}}]$ . We demonstrate over 200 million switching cycles, with two events of contact/charge transfer in each cycle. We demonstrate that a high mechanical restoring force is crucial for long-term reliability of switch oscillators. Furthermore, we implement a new driving scheme that further increases the long-term reliability. The relevance of this device is its potential as a new concept for a low cost, low power, wafer level MEMS oscillator.

The design, fabrication and experimental validation of two MicroElectroMechanical Systems (MEMS) Double-Ended Tuning-Fork (DETF) resonators that exhibit an intrinsic sub-350 ppm thermal stability in the temperature range [5°C–85°C] are reported. A strategy for the optimization of the design of MEMS resonators that exhibit high thermal stability and high quality factor is also provided and a good agreement with experimental data is achieved. The main advantage of the proposed strategy is that it does not require any experimental calibration of the model parameters and can be in principle applied to different kind of resonators, thus representing a powerful tool for the apriori design of thermally stable MEMS resonators with high quality factors.

The frequency stability is a key parameter to determine the performance of a micro-electro-mechanical (MEM) resonator. In this study, we utilized the mechanism of 1:2 internal resonance (IR) in a hermetically encapsulated beam resonator with a high Q-factor (>4000) to improve the frequency stability. When a MEM resonator is driven by a single-frequency actuation and conditions for IR are satisfied, two engaged modes are simultaneously resonated with their phases locked together through a strong and effective intermodal energy transfer. The increased inertia of these two active resonant modes leads to the frequency stabilization in both frequency outputs. In an open-loop experimental setting, we demonstrated that the IR achieved a six-fold improvement in the frequency stability. This paper reports the first implementation of IR in an encapsulated high-Q beam resonator.

We observe significant temperature hysteresis in the resonant frequency and quality factor of silicon piezoresistive microcantilevers from room temperature down to 40 K. The hysteresis becomes increasingly pronounced as the support beam length is reduced from $100\ \mu \mathrm{m}$ to $30\ \mu \mathrm{m}$ , leading to over a twenty-fold difference in $Q$ values between the temperature sweep downwards and upwards for the $30\ \mu \mathrm{m}$ support beam device. Our work suggests that temperature hysteresis is an important consideration for thermal-piezoresistive oscillators and other microelectromechanical resonators that require multiple anchor points.

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.

We report on the implementation of a novel vacuum-encapsulated dual-axis resonant accelerometer utilizing electrostatic stiffness modulation. Novel flexure designs are used to enable fully-decoupled in-plane dual-axis translational motions of the proof-mass to achieve low cross-axis sensitivity with the translational mode frequencies above 20 kHz for high bandwidth applications. Differential frequency readout scheme mitigates the temperature effects on frequency stability of resonators and reduces off-axis sensitivity. The fabricated device measures a scale factor of 22Hz/g (119ppm/g) with low cross-axis sensitivity. The accelerometer demonstrates high performance with 18μg/√Hz VRW and 27μg BI in ambient environment. Optimization of the oscillator circuits and implementation of chip-level ovenization can further improve the performance of the design, with potentials to reach sub-μg performance for emerging high-bandwidth application.

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.

We use parametric suppression for signal amplifi-cation in a phase-modulated microelectromechanical (MEM) charge detector. Simultaneously driving and parametrically pumping a MEM resonator with the appropriate relative phase increases the phase slope near the resonant frequency. We use this to increase the sensitivity of a MEM electrometer more than tenfold.

This paper presents an investigation into the origin of nonlinear dissipation in MEMS flexural mode resonators driven in a highly nonlinear regime. By comparing devices with different combinations of thermoelastic and gas damping, and utilizing the ringdown response at different pressures, we observe a larger presence of nonlinear dissipation in pressure damped resonators, but also continue to observe some nonlinear dissipation at high vacuum suggesting additional nonlinear contributions from thermoelastic dissipation.