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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]

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]

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 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]

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.

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]

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.

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.

In this paper, we present an experimental study of nonlinearities in degenerately doped flexural-mode silicon MEMS resonators. Two geometries (single and double-anchored) and two wafer orientations ( and ) are used to analyze the elastic effects of p-type (1.31 × 1016 to 1.61 × 1015 cm−3) and n-type (1.264 × 1015 to 2.64 × 1014 cm−3) degenerately doped double-ended tuning forks. We employ closed-loop frequency sweeps to characterize the amplitude-frequency response of each system. Experimental results show that geometric nonlinearities and electrostatic nonlinearities dominate material and crystalline orientation-dependent nonlinearities in the flexural mode. These results present an initial exploration into characterizing nonlinear mechanical behavior of resonators operating in lower frequency bending modes.

We present unexpected results showing that thinning the bottom substrate of a resonant MEMS tuning fork resonator decreases anchor damping. We also present findings that the tuning fork experiences more anchor damping when mounting the die with silver paste. This is important for wearable devices where minimizing the volumetric footprint of sensors is paramount.

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]

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]

This paper presents the implementation of a coupling mechanism on dynamically-balanced Dual Foucault Pendulum (DFP) gyroscopes, ordering the anti-phase and in-phase modes of vibration. A wide frequency separation is achieved between the desired anti-phase and the spurious in-phase resonance. Mode ordering of dual mass tuning fork gyroscopes provides isolation of the anti-phase resonance, resulting in the reduction of energy losses through mode conversion and improves common-mode rejection. A mode ordered Dual Foucault Pendulum (DFP) gyroscope at an operational frequency of 15 kHz was fabricated using the wafer-level epitaxial silicon encapsulation process. The quality factor higher than 700,000 was achieved after vacuum sealing with an activated getter. The coupling mechanism was explained and initial rate characterization of the device was reported.

This paper reports a simple, effective method to improve the bias stability of a resonant accelerometer over a large temperature range. By using the nonlinear amplitude-frequency effect, this technique further reduces residual temperature dependence of a passively temperature-compensated differential signal from two sensing resonators. Driving one resonator beam with a large excitation amplitude into the nonlinear regime moves its frequency-temperature characteristic closer to that of the other sensing beam. Preliminary results show a near fivefold improvement in 0g bias stability while maintaining high sensitivity and scale factor stability over the temperature range from −20°C to 80°C.

We present theoretical and experimental data on instability bands in a low-power resonant pull-in based MEMS vibration detector. The ohmic Silicon-to-Silicon switch was fabricated in a near-vacuum encapsulation epitaxially sealed process. The device requires a static bias (

This work demonstrates, for the first time, a wafer-scale encapsulation process for hermetic sealing of MEMS resonant structures incorporating fully differential electrodes, in and out of the device plane, and large lateral transduction gaps. The polysilicon electrode and device layers were deposited using an epitaxial silicon reactor with Tetra-Ethyl-Ortho-Silicate (TEOS) as a spacer material. Large transduction gaps were fabricated using vapor-phase xenon difluoride (XeF 2 ) and hydrofluoric acid (vHF) etches, with silicon and silicon dioxide as sacrificial materials, respectively. Transduction gaps of 0.7μm up to 50μm were fabricated and the polysilicon devices were driven into a strongly nonlinear regime using the bottom, top, and in-plane capacitive electrodes.

In this study, a novel method of measuring the Quality Factor (Q) of a MEMS tuning fork resonator at low temperature enabled us to accurately pinpoint the energy dissipation resulting from anchor damping [1]. We used this new method to perform the first direct examination of the impact of design of the anchors and the die mounting structures on the strength of anchor damping. Our results show that the elastic energy can escape the resonator through the anchor(s), and still be retained within the die, and that energy stored in the die can return to the resonator. Thus, the measured Q of the resonator is increased, depending on mounting structures far from the resonating element. Moreover, our data shows that the number of anchors does not change the total energy dissipation through the anchors.

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 aim of this study is to quantify the energy loss mechanisms for single anchored double-ended tuning forks (DETF) — particularly, gas damping, thermoelastic dissipation (TED) and anchor damping. We performed ring-down measurements of quality factor (Q) as a function of pressure to confirm the absence of air damping. We also measured Q over a wide temperature range including where the coefficient of thermal expansion (CTE) crosses zero, and consequently the effects from thermoelastic dissipation (TED) become negligible. This provides the first opportunity to directly quantify energy losses due to anchor damping and allows us to vary the mounting configuration to explore the impact of the mounting on the loss.

This work demonstrates, for the first time, a wafer-scale encapsulation process incorporating fully circumferential electrodes (in-plane and out-of-plane) for applications towards multi-axis inertial sensing. Bottom and top electrodes were incorporated in the device package utilizing epitaxial silicon deposition. By this method, we present fully differential, vacuum-encapsulated, oxide-coated polysilicon resonators.

We present a tunable broadband shoaling mechanical amplifier and a method to extend its operation near the electrostatic pull-in instability. The model has been verified experimentally on a vacuum encapsulated silicon MEMS device. We show that by adding an appropriate mechanical compensation spring, the amplifier can be operated near the pull-in instability in a quasi-linear fashion. Furthermore, electrostatic band-pass region and amplification tuning is shown.

This paper reports, for the first time, on-chip ovenization of an epitaxially encapsulated resonant accelerometer to improve the stability of scale factor and bias. A double-ended tuning fork (DETF) resonator that shares the anchor with the sensing resonators is used to measure the device temperature. The measured temperature is maintained at a fixed set point using an on-chip silicon heater defined in the encapsulation layer. Preliminary results show significant improvement beyond the device's intrinsic passive temperature compensation. Over the temperature range from −20°C to 80°C, the 0g bias error is reduced by a factor of three, and the scale factor stability is improved by over an order of magnitude.

This paper presents a topology optimization approach for reducing thermo-elastic dissipation (TED) in MEMS resonators. This algorithm is applied to a clamped-clamped resonant beam to maximize the quality factor (Q). Optimal designs have a Q ten times higher than a solid beam and are 75% higher than previously optimized devices. Furthermore, new designs have intuitive topologies. Beams are fabricated in silicon wafers and experimental measurements of Q agree well with simulation.

We report a new Lorentz force magnetic sensor employing a matched pair of silicon micromechanical resonators on the same die. The two resonators are operated as closed-loop oscillators, where the change in oscillation amplitude is used as a measure of the magnetic field strength. The magnetometer, consisting of the two identical oscillators having opposing axes of field sensitivity, produces two similar oscillation amplitudes with nearly identical temperature sensitivities, providing continuous temperature compensation. Differential amplitude modulated (AM) output from the two oscillators reduces the sensor's offset by a factor of 12 to 26 μT, and suppresses the effect of the resonator's temperature coefficient of quality factor (TCQ) on the output, reducing the maximum drift error by a factor of 15 to ±0.49 μT, improving the sensor's bias instability from 86 nT to 26 nT, and increasing the averaging time to reach the bias instability from 1 s to 10 s. With 44-μW power dissipation, the sensor achieves a resolution of 50 nT/√Hz, limited by Brownian noise.

We measure the influence of ambient temperature (from −40 °C to 80 °C) on the threshold current for self-oscillations inathermal-piezoresistively pumped, capacitively sensed resonator. We demonstrate that for our flexural mode self-oscillator, the threshold current decreases with decreasing ambient temperature. We observe the generation of harmonics during self-oscillation with amplitudes that decrease and effective quality factors that increase with each successive mode. Following self-oscillations, we observe that the effective quality factor and amplitude is extremely sensitive to further DC current increases.

This paper presents a new dual-resonator MEMS magnetic sensor utilizing the Lorentz force. Sensor operation is demonstrated using quadrature frequency modulated (QFM) readout, where the magnetic field strength is measured by monitoring the change in oscillation frequency. The Lorentz force sensor, comprising of a matched pair of differentially operated closed-loop resonators on the same silicon die, produces two similar oscillation frequencies with nearly identical temperature sensitivities, providing a temperature-compensated FM output. The frequencies of the two oscillators are experimentally demonstrated to track each other over temperature, reducing the maximum drift error by a factor of 27 to ±2.2 µT, improving the sensor's bias instability from 170 nT to 63 nT, and increasing the averaging time to reach the bias instability from 0.3 s to 1.1 s. With 1 mA bias current, the device has a measured sensitivity of 2180 Hz/T and Brownian-noise-limited resolution of 60 nT/√Hz which is comparable to, or even better than, that of Hall-effect sensors available today.

This paper presents for the first time the design and characterization of an ultra-compact 3-axis roll-pitch-yaw gyroscope which employs a single vibrational element with a torsional drive mode and a multi-directional sense modes. Implemented in wafer-level Epitaxial Silicon Encapsulation (Epi-Seal) process, device occupies an area of 1.2 mm2. Initial characterization reported in this paper includes a scale factor, a noise level, and a cross-axis error measurement.

This paper presents a novel, versatile process for the fabrication of wide and deep cavities for silicon MEMS devices without the need for wafer bonding. Instead of filling large trenches with sacrificial materials before encapsulation or directly using wafer bonding, we present a method that utilizes isotropic etching with XeF 2 gas through a thin silicon dioxide film prior to the deposition of encapsulation materials to create and encapsulate large cavities. The process is demonstrated to be robust and can be easily incorporated into the fabrication of a variety of MEMS structures, including pressure sensors, ultrasonic devices, microfluidics chips, hermetically encapsulated silicon resonators, inertial sensors, and more.

We present an epitaxially-encapsulated 2×2mm2 quad-mass resonator (QMR) with shaped comb fingers for frequency tuning. While shaped electrodes have been used for frequency tuning of linear resonators, the device studied here has very high quality factor (g=100,000) resulting in a very narrowband resonance which, without the shaped electrodes, results in undesirable nonlinear behavior such as amplitude-frequency dependence and instability of the oscillator loop at large amplitudes. We demonstrate that through the shaped comb finger design, both frequency tuning (over 90Hz) and large amplitude oscillation (1.25 μm amplitude, a factor of 100 compared to performance without the shaped electrodes) are possible. Furthermore, we demonstrate how critical dimension loss in the fabrication process can change the shape of the designed shaped finger and introduce electrostatic stiffness hardening.

This paper reports a miniature Inertial Measurement Unit (IMU) implemented using a folded MEMS approach which allows for integration of high performance sensors, while providing a low cross-talk between the components. Foldable Si structures are manufactured on a wafer-level using MEMS techniques, co-fabricated or integrated with single-axis inertial sensors and then folded into a 3D configuration, forming the complete IMU. Electrical signals from the sensors on sidewalls of the IMU Cube are transferred through the dense network of metal traces on parylene, thus enabling the integration with signal processing electronics. For the first time, we characterized cross-talk between sensors on a folded 3D IMU. The experimental results provided an evidence that the folded IMU process is advantageous to a single-die approach, showing a lower Angle Random Walk (ARW) of the gyroscopes when operated simultaneously on different sidewalls of the IMU Cube.

In this work, we propose a novel temperature compensation method that utilizes a tri-mode operation scheme to generate a temperature-stable frequency reference over a large temperature range. Three resonant modes are excited simultaneously on a highly doped silicon MEMS resonator, and the unique TCf characteristic of each mode is fitted to a parabolic curve. A linear combination of the three frequencies is shown to eliminate the temperature dependence up to second order and produce a temperature-insensitive frequency output. Preliminary results verify the concept and show a ±14ppm temperature dependence of the output frequency across the temperature range of −40∼80°C.

We demonstrate how to identify regions of major thermo-elastic dissipation (TED) in MEMS resonators and reduce this energy loss by modifying the device geometry. To demonstrate this, various geometries of a disk resonating gyroscope (DRG) are used. Devices are fabricated and tested to show that the TED-limited quality factor (Q) can indeed be increased using geometric manipulation, as predicted by simulation.

This work demonstrates a unique temperature-compensated differential resonant accelerometer fabricated in a wafer-scale encapsulation process. By utilizing a pair of ultra-stable, high quality factor (>50,000) resonant beams as a strain gauge, we show differential operation with a scale factor of 427Hz/g and a bias instability of 0.16μg at 21s integration time. Furthermore, matched temperature coefficients of frequency (TCf) of the two beams provide a first order cancellation of temperature drift, resulting in a scale factor stability of 0.38% over the temperature range from −20°C to 80°C.

Quality factor (Q) is an important property of micro- and nano-electromechanical (MEM/NEM) resonators that underlie timing references, frequency sources, atomic force microscopes, gyroscopes, and mass sensors. Various methods have been utilized to tune the effective quality factor of MEM/NEM resonators, including external proportional feedback control, optical pumping, mechanical pumping, thermal-piezoresistive pumping, and parametric pumping. This work reviews these mechanisms and compares the effective Q tuning using a position-proportional and a velocity-proportional force expression. We further clarify the relationship between the mechanical Q, the effective Q, and the thermomechanical noise of a resonator. We finally show that parametric pumping and thermal-piezoresistive pumping enhance the effective Q of a micromechanical resonator by experimentally studying the thermomechanical noise spectrum of a device subjected to both techniques. (C) 2018 Author(s).

This work describes a new method for autonomous mode-matching and quadrature nulling of a Microelectromechanical system (MEMS) wineglass mode gyroscope, utilizing particle swarm optimization. Use of this derivative-free optimization scheme allows for multi-objective optimization of gyroscopic performance parameters. Modal frequency split and both mode shapes' quadrature and amplitude were optimized through this method. Optimal parameters for frequency split, quadratures, and principle axis amplitudes were found to be 0.71 Hz, 13.9 and 10.5 mV, and 284.6 and 299.6 mV, respectively. Autonomous calibration greatly increased the scale factor of the sensor and enhanced the noise performance to levels typically achieved by diligent hand tuning.

This work demonstrates, for the first time, ovenization of a fully-encapsulated dual-mode silicon MEMS resonator operational over a large ambient temperature range. We maintain a localized, elevated operating temperature by utilizing the temperature coefficient of frequency (TCf) difference between two excitation modes of the same resonant body as a thermometer, and by integrating a micro-oven in the encapsulation layer. Preliminary results of real-time compensation demonstrate a stability of ±250ppb of the in-plane Lame-mode frequency over −20°C to 80°C.

We present an epitaxially-encapsulated 2×2 mm2 quad-mass gyroscope (QMG). Relative to the earlier QMG which measured 8×8 mm2 and required an external vacuum package and getter [1], this device is 16x smaller in area and is vacuum-sealed at the wafer-level. Due to the device's small size, high quality factor (Q) and large oscillation amplitude are required to achieve low noise. However, the device's high Q (85,000) makes it highly sensitive to mechanical nonlinearity, resulting in amplitude-frequency dependence and instability of the oscillator loop at large amplitudes. To overcome these problems, we demonstrate electrostatic compensation of the mechanical nonlinearity, enabling 10x greater amplitude and therefore scale factor (SF). Together with closed-loop amplitude control and quadrature compensation, this enables angle-random walk of 0.42 mdeg/s/VHz, comparable to the best QMG published to date. Closed-loop amplitude control and quadrature null are used to achieve a bias instability of 1.6 deg/hr.

In this study we demonstrate for the first time integration of differential internal electrodes into a Disk Resonator Gyroscope (DRG) design within a wafer-scale encapsulation process. The differential internal electrodes design enables the mode-matching operation of the device with low DC power supplies (±5 V) thanks to the enhanced transduction area, while maintaining similar performance to the previously reported baseline DRG. The mode-matching operation yields a scale-factor of 1.37 mV/(7s) and an ARW of 0.29 °/√hr.

This work describes a new method for mode-matching and quadrature nulling of a MEMS wineglass mode gyroscope utilizing particle swarm optimization. Use of the derivative-free optimization scheme allowed for multiobjective optimization of gyroscopic performance parameters. Modal frequency split, quadrature and amplitude of both mode shapes were optimized through this method. Optimization greatly increased the scale factor of the sensor as well as enhanced the noise performance for all device geometries and materials studied. The stochastic nature of our method allowed robust calibration for devices of varying geometry and resonator material.

This paper introduces a ‘high-frequency’ resonant tri-axial tuning fork gyroscope (TFG) with a single-drive mode of operation. The quad-mass device is implemented on a 2×2 mm2 vacuum-packaged die fabricated using the epi-seal process, making this one of the smallest wafer-level packaged 3-axis gyros. In contrast to conventional resonant TFGs, the resonant frequencies are designed to be relatively high (∼138 kHz) permitting high bandwidth for mode-matched operation and enhancing resistance to shock and vibration. The results show sensitivity to all three axes with mode-matched operation for the Z-axis and mode-split for the X- and Y-axes.