Thin-Film AlN-on-Silicon Resonant Gyroscopes: Design, Fabrication, and Eigenmode Operation

Resonant MEMS gyroscopes have been rapidly adopted in various consumer, industrial, and automotive applications thanks to the significant improvements in their performance over the past decade. The current efforts in enhancing the performance of high-precision resonant gyroscopes are mainly focused on two seemingly contradictory metrics, larger bandwidth and lower noise level, to push the technology towards navigation applications. The key enabling factor for the realization of low-noise high-bandwidth resonant gyroscopes is the utilization of a strong electromechanical transducer at high frequencies. Thin-film piezoelectric-on-silicon technology provides a very efficient transduction mechanism suitable for implementation of bulk-mode resonant gyroscopes without the need for submicron capacitive gaps or large DC polarization voltages. More importantly, in-air operation of piezoelectric devices at moderate Q values allows for the cointegration of mode-matched gyroscopes and accelerometers on a common substrate for inertial measurement units. This work presents the design, fabrication, characterization, and method of mode matching of piezoelectric-on-silicon resonant gyroscopes. The degenerate in-plane flexural vibration mode shapes of the resonating structure are demonstrated to have a strong gyroscopic coupling as well as a large piezoelectric transduction coefficient. Eigenmode operation of resonant gyroscopes is introduced as the modal alignment technique for the piezoelectric devices independently of the transduction mechanism. Controlled displacement feedback is also employed as the frequency matching technique to accomplish complete mode matching of the piezoelectric gyroscopes.Ph.D

CMOS systems and circuits for sub-degree per hour MEMS gyroscopes

The objective of our research is to develop system architectures and CMOS circuits that interface with high-Q silicon microgyroscopes to implement navigation-grade angular rate sensors. The MEMS sensor used in this work is an in-plane bulk-micromachined mode-matched tuning fork gyroscope (M² – TFG ), fabricated on silicon-on-insulator substrate. The use of CMOS transimpedance amplifiers (TIA) as front-ends in high-Q MEMS resonant sensors is explored. A T-network TIA is proposed as the front-end for resonant capacitive detection. The T-TIA provides on-chip transimpedance gains of 25MΩ, has a measured capacitive resolution of 0.02aF /√Hz at 15kHz, a dynamic range of 104dB in a bandwidth of 10Hz and consumes 400μW of power. A second contribution is the development of an automated scheme to adaptively bias the mechanical structure, such that the sensor is operated in the mode-matched condition. Mode-matching leverages the inherently high quality factors of the microgyroscope, resulting in significant improvement in the Brownian noise floor, electronic noise, sensitivity and bias drift of the microsensor. We developed a novel architecture that utilizes the often ignored residual quadrature error in a gyroscope to achieve and maintain perfect mode-matching (i.e.0Hz split between the drive and sense mode frequencies), as well as electronically control the sensor bandwidth. A CMOS implementation is developed that allows mode-matching of the drive and sense frequencies of a gyroscope at a fraction of the time taken by current state of-the-art techniques. Further, this mode-matching technique allows for maintaining a controlled separation between the drive and sense resonant frequencies, providing a means of increasing sensor bandwidth and dynamic range. The mode-matching CMOS IC, implemented in a 0.5μm 2P3M process, and control algorithm have been interfaced with a 60μm thick M2−TFG to implement an angular rate sensor with bias drift as low as 0.1°/hr ℃ the lowest recorded to date for a silicon MEMS gyro.Ph.D.Committee Chair: Farrokh Ayazi; Committee Member: Jennifer Michaels; Committee Member: Levent Degertekin; Committee Member: Paul Hasler; Committee Member: W. Marshall Leac

Using electrostatic nonlinearities to enhance the performance of ring-based Coriolis vibratory gyroscopes

This research investigates electrostatic nonlinearities in capacitively operated ring-based Coriolis vibrating gyroscopes (CVG’s). Large amplitude vibrations of the ring amplify the Coriolis force and are beneficial to achieving high-precision rate sensing. However, due to the miniature sizes of these devices and the narrow capacitive gaps, electrostatic nonlinearities manifest at relatively small ring displacements, thus resulting in the sensor output differing from what is expected of a standard linear device. As such, the current theory of operation commonly perceives electrostatic nonlinearities as an obstacle towards the development of high performance sensors. Electrostatic nonlinearities is the dominant source of nonlinearity in ring-based CVG’s. This work develops a mathematical model to analyse the influence of electrostatic nonlinearities on device performance. When the device operates using a basic electrostatic configuration incorporating only bias and drive voltages, it is found that the bias voltage induces single and mode-coupled cubic restoring forces, which are the main mechanisms through which electrostatic nonlinearities affect the ring dynamics and sensor output. These nonlinear restoring forces result in the amplitude-dependency of the drive and sense mode frequencies, and the presence of self-induced parametric excitation. These effects, in conjunction with the structural imperfections of the ring, degrade rate sensing performance by reducing the rate sensitivity and introducing bias rates and quadrature errors at larger drive amplitudes. A detailed theoretical analysis of the sense dynamics concludes that, depending on the interaction between the imperfections and the electrostatic nonlinearities, there are specific cases where the self-induced parametric excitation can enhance the rate sensitivity of the device. However, this enhancement cannot be achieved while retaining a trimmed sense response to keep the bias rate and quadrature error nullified. An analysis of the sense response and the modal forces shows that the imperfection-induced linear elastic coupling force and the nonlinear frequency imbalance are specifically responsible for the sensor output degradation. These nonlinear behaviours have also been validated against finite element results. The research also investigates the strategic use of electrostatic forces to counteract the effects of nonlinearity and enhance device performance. It is shown that through careful selection of the voltages applied to the electrodes, the form of the resulting electrostatic forces can be tailored to manipulate the sense mode dynamics for device performance enhancement. The presented work develops a general framework to achieve this direct electrostatic force manipulation by considering the variations of the capacitance, voltage and electrostatic potential energy from electrode to electrode, which then enables direct control of the form of the total electrostatic potential energy. Through the use of the framework, this research shows that the electrostatic nonlinearities can be manipulated to replicate the sensor outputs of a linear, trimmed device at larger drive amplitudes, or achieving parametric amplification of the sense response to enhance rate sensitivity without inducing bias rates and quadrature errors. The proposed general framework is used to determine the electrostatic configurations capable of negating self-induced parametric excitation by generating a separate parametric excitation in antiphase with the self-induced parametric excitation. The proposed implementation has potential to reduce sensor output nonlinearity and is most effective in devices where the drive amplitude dependencies of the drive and sense modes are equal, thus resulting in amplitude-insensitive frequency detuning in a manner similar to linear devices. This implementation can also be used in conjunction with a balancing voltage component to eliminate quadrature errors present in the sensor output caused by linear elastic coupling and nonlinear frequency imbalance. The combination of using parametric pumping and balancing voltage components trims the sensor output and have potential to suppress the sensor output nonlinearity further. The effectiveness of the chosen electrostatic configuration is validated against results from transient finite element studies. Rate measuring performance is enhanced further by parametrically exciting the sensor output to increase the quality factor of the device. To achieve enhanced performance the parametric excitation must be phase-tuneable and the proposed general framework is used to select electrostatic configurations capable of providing the required parametric excitation. Two approaches to develop the required parametric excitation are investigated. The first approach exploits linear electrostatic forces whilst the second approach uses quadratic electrostatic forces. Both approaches are shown to have potential to improve rate sensitivity through Q factor enhancing effects. However, the parametric excitation from the quadratic electrostatic forces is generally weaker unless compensated using larger parametric pumping voltages. On the other hand, it is found that the quadratic electrostatic forces promote nonlinear frequency balancing and so this approach is considered advantageous for achieving trimmed sensor output

Design of a tri-axial surface micromachined MEMS vibrating gyroscope

Gyroscopes are one of the next killer applications for the MEMS (Micro-Electro-Mechanical-Systems) sensors industry. Many mature applications have already been developed and produced in limited volumes for the automotive, consumer, industrial, medical, and military markets. Plenty of high-volume applications, over 100 million per year, have been calling for low-cost gyroscopes. Bulk silicon is a promising candidate for low-cost gyroscopes due to its large scale availability and maturity of its manufacturing industry. Nevertheless, it is not suitable for a real monolithic IC integration and requires a dedicated packaging. New designs are supposed to eliminate the need for magnets and metal case package, and allow for a real monolithic MEMS-IC (Integrated Circuit) electronic system. In addition, a drastic cost reduction could be achieved by utilizing off-the-shelf plastic packaging with lead frames for the final assembly. The present paper puts forward the design of a novel tri-axial gyroscope based on rotating comb-drives acting as both capacitive sensors and actuators. The comb-drives are comprised of a single monolithic moving component (rotor) and fixed parts (stators). The former is made out of different concentrated masses connected by curved silicon beams in order to decouple the motion signals. The sensor was devised to be fabricated through the PolyMUMPs® process and it is intended for working in air in order to semplify the MEMS-IC monolithic integration

Using electrostatic nonlinearities to enhance the performance of ring-based Coriolis vibratory gyroscopes

This research investigates electrostatic nonlinearities in capacitively operated ring-based Coriolis vibrating gyroscopes (CVG’s). Large amplitude vibrations of the ring amplify the Coriolis force and are beneficial to achieving high-precision rate sensing. However, due to the miniature sizes of these devices and the narrow capacitive gaps, electrostatic nonlinearities manifest at relatively small ring displacements, thus resulting in the sensor output differing from what is expected of a standard linear device. As such, the current theory of operation commonly perceives electrostatic nonlinearities as an obstacle towards the development of high performance sensors. Electrostatic nonlinearities is the dominant source of nonlinearity in ring-based CVG’s. This work develops a mathematical model to analyse the influence of electrostatic nonlinearities on device performance. When the device operates using a basic electrostatic configuration incorporating only bias and drive voltages, it is found that the bias voltage induces single and mode-coupled cubic restoring forces, which are the main mechanisms through which electrostatic nonlinearities affect the ring dynamics and sensor output. These nonlinear restoring forces result in the amplitude-dependency of the drive and sense mode frequencies, and the presence of self-induced parametric excitation. These effects, in conjunction with the structural imperfections of the ring, degrade rate sensing performance by reducing the rate sensitivity and introducing bias rates and quadrature errors at larger drive amplitudes. A detailed theoretical analysis of the sense dynamics concludes that, depending on the interaction between the imperfections and the electrostatic nonlinearities, there are specific cases where the self-induced parametric excitation can enhance the rate sensitivity of the device. However, this enhancement cannot be achieved while retaining a trimmed sense response to keep the bias rate and quadrature error nullified. An analysis of the sense response and the modal forces shows that the imperfection-induced linear elastic coupling force and the nonlinear frequency imbalance are specifically responsible for the sensor output degradation. These nonlinear behaviours have also been validated against finite element results. The research also investigates the strategic use of electrostatic forces to counteract the effects of nonlinearity and enhance device performance. It is shown that through careful selection of the voltages applied to the electrodes, the form of the resulting electrostatic forces can be tailored to manipulate the sense mode dynamics for device performance enhancement. The presented work develops a general framework to achieve this direct electrostatic force manipulation by considering the variations of the capacitance, voltage and electrostatic potential energy from electrode to electrode, which then enables direct control of the form of the total electrostatic potential energy. Through the use of the framework, this research shows that the electrostatic nonlinearities can be manipulated to replicate the sensor outputs of a linear, trimmed device at larger drive amplitudes, or achieving parametric amplification of the sense response to enhance rate sensitivity without inducing bias rates and quadrature errors. The proposed general framework is used to determine the electrostatic configurations capable of negating self-induced parametric excitation by generating a separate parametric excitation in antiphase with the self-induced parametric excitation. The proposed implementation has potential to reduce sensor output nonlinearity and is most effective in devices where the drive amplitude dependencies of the drive and sense modes are equal, thus resulting in amplitude-insensitive frequency detuning in a manner similar to linear devices. This implementation can also be used in conjunction with a balancing voltage component to eliminate quadrature errors present in the sensor output caused by linear elastic coupling and nonlinear frequency imbalance. The combination of using parametric pumping and balancing voltage components trims the sensor output and have potential to suppress the sensor output nonlinearity further. The effectiveness of the chosen electrostatic configuration is validated against results from transient finite element studies. Rate measuring performance is enhanced further by parametrically exciting the sensor output to increase the quality factor of the device. To achieve enhanced performance the parametric excitation must be phase-tuneable and the proposed general framework is used to select electrostatic configurations capable of providing the required parametric excitation. Two approaches to develop the required parametric excitation are investigated. The first approach exploits linear electrostatic forces whilst the second approach uses quadratic electrostatic forces. Both approaches are shown to have potential to improve rate sensitivity through Q factor enhancing effects. However, the parametric excitation from the quadratic electrostatic forces is generally weaker unless compensated using larger parametric pumping voltages. On the other hand, it is found that the quadratic electrostatic forces promote nonlinear frequency balancing and so this approach is considered advantageous for achieving trimmed sensor output

Vers des centrales inertielles compactes basées sur des nanojauges piezorésistives : problématique de co-intégration

This thesis was carried out in an industrial context of strong competition in connection with miniature silicon sensors for the huge so-called “consumer” market, where the “Smartphone” is the killer application; its increasing functionality creates a need for the so-called ‘10-axis' inertial multi-sensors (3-axis accelerometer, 3-axis magnetometer, 3-axis gyro sensor and pressure). Similarly to integrated circuits, cost constraints on such sensors translate into a requirement in terms of integration density. The M & NEMS (Micro- & Nano- Electro-Mechanical-Systems) technology has been developed to meet this expectation. It is based on the integration of nanoscale (~ 250 nm) strain gauges together with micrometric electromechanical structures, which ensure unrivaled compactness, paving the way for the co-integration of multiple inertial sensors on the same silicon chip. However, the different nature of the physical quantities to be measured imposes additional constraints, sometimes conflicting, which leads to a difficult co-integration. Based on this observation, we have explored and developed solutions to allow operation under the same ambient pressure, of accelerometers together with Coriolis force based gyroscopes. This issue of co-integration extends beyond the accelerometer-gyroscope couple. Issues inherent to the pressure sensor and to the 3-axis accelerometer measurements, are also addressed in this thesisCette thèse a été effectuée dans un contexte industriel de forte concurrence en lien avec les capteurs miniatures en silicium, destinés au gigantesque marché dit "consumer", dont l'application phare est le "Smartphone", pour laquelle les fonctionnalités accrues engendrent un besoin en matière de multi-capteurs inertiels dits 10-axes (accéléromètre 3-axes, magnétomètre 3-axes, gyromètre 3-axes et capteur de pression). Tout comme les circuits intégrés, les contraintes de coût de tels capteurs se traduisent par une exigence en termes de densité d'intégration. La technologie M&NEMS (Micro- & Nano- Electro Mechanical Systems) a été développée pour répondre à cette attente. Elle repose sur l'intégration de jauges de contraintes de dimensions nanométriques (~250 nm) avec des structures électromécaniques micrométriques, ce qui prodigue une compacité hors-pair des capteurs, ouvrant la voie à la co-intégration de multi-capteurs sur la même puce de silicium. Toutefois, la nature différente des grandeurs physiques à mesurer impose des contraintes supplémentaires, parfois opposées, ce qui rend leur co-intégration difficile. Partant de ce constat, nous avons exploré et développé, des solutions devant permettre le fonctionnement sous une même pression environnante, d'accéléromètres et de gyromètres à force de Coriolis. Cette problématique de co-intégration, s'étend au-delà du couple accéléromètre-gyromètre. Des questions inhérentes au capteur de pression ainsi qu'aux 3 axes de mesure d'un accéléromètre, sont également traitées dans cette thès

Design and implementation of a control scheme for a MEMS rate integrating gyroscope

PhD ThesisMEMS gyroscopes are found across a large range of applications, from low precision low cost applications through to high budget projects that require almost perfect accuracy. MEMS gyroscopes fall into two categories – ‘rate’ and ‘rate integrating’, with the latter offering superior performance. The key advantage that the rate integrating type possesses is that it directly measures angle, eliminating the need for any integration step. This reduces the potential for errors, particularly at high rates. However, the manufacturing precision required is far tighter than that of the rate gyroscope, and this has thus far limited the development of rate integrating gyroscopes. This thesis proposes a method for reducing the effect of structural imperfections on the performance of a rate integrating gyroscope. By taking a conventional rate gyroscope and adjusting its control scheme to operate in rate integrating mode, the thesis shows that it is possible to artificially eliminate the effect of some structural imperfections on the accuracy of angular measurement through the combined use of electrostatic tuning and capacitive forcing. Further, it demonstrates that it is viable to base the designs for rate integrating gyroscopes on existing rate gyroscope architectures, albeit with some modifications. Initially, the control scheme is derived through the method of multiple scales and its potential efficacy demonstrated through computational modelling using Simulink. The control scheme is then implemented onto an existing rate gyroscope architecture, with a series of tests conducted that benchmark the gyroscope performance in comparison to standard performance measures. Experimental work demonstrates the angle measurement capability of the rate integrating control scheme, with the gyroscope shown to be able to measure angle, although not to the precision necessary for commercial implementation. However, the scheme is shown to be viable with some modifications to the gyroscope architecture, and initial tests on an alternative architecture based on these results are presented.United Technologies and System

Development and experimental analysis of a micromachined Resonant Gyrocope

This thesis is concerned with the development and experimental analysis of a resonant gyroscope. Initially, this involved the development of a fabrication process suitable for the construction of metallic microstructures, employing a combination of nickel electroforming and sacrificial layer techniques to realise free-standing and self-supporting mechanical elements. This was undertaken and achieved. Simple beam elements of typically 2.7mm x 1mm x 40µm dimensions have been constructed and subject to analysis using laser doppler interferometry. This analysis tool was used to implement a fill modal analysis in order to experimentally derive dynamic parameters. The characteristic resonance frequencies of these cantilevers have been measured, with 3.14kHz, 23.79kHz, 37.94kHz and 71.22kHz being the typical frequencies of the first four resonant modes. Q-factors of 912, 532, 1490 and 752 have been measured for these modes respectively at 0.01mbar ambient pressure. Additionally the mode shapes of each resonance was derived experimentally and found to be in excellent agreement with finite element predictions. A 4mm nickel ring gyroscope structure has been constructed and analysed using both optical analysis tools and electrical techniques. Using laser doppler interferometry the first four out-of-plane modes of the ring structure were found to be typically 9.893 kHz, 11.349 kHz, 11.418 kHz and 13.904 kHz with respective Q-factors of 1151, 1659, 1573 and 1407 at 0.01 mbar ambient pressure. Although electrical measurements were found to be obscured through cross coupling between drive and detection circuitry, the in-plane operational modes of the gyroscope were sucessfully determined. The Cos2Ө and Sin2Ө operational modes were measured at 36.141 kHz and 36.346 kHz, highlighting a frequency split of 205kHz. Again all experimentally derived modal parameters were in good agreement with finite element predictions. Furthermore, using the analysis model, the angular resolution of the gyroscope has been predicted to be approximately 4.75º/s

Design and Analysis of Extremely Low-Noise MEMS Gyroscopes for Navigation

Inertial measurement sensors that include three gyroscopes and three accelerometers are key elements of inertial navigation systems. Miniaturization of these sensors is desirable to achieve low manufacturing cost, high durability, low weight, small size, and low energy consumption. However, there is a tradeoff between miniaturization of inertial sensors and their performance. Developing all the necessary components for navigation using inertial sensors in a small volume requires major redesign and innovation in these sensors. The main goal of this research is to identify, analyze and optimize parameters that limit the performance of miniaturized inertial gyroscopes and provide comprehensive design guidelines for achieving multi-axis navigation-grade MEMS gyroscopes. It is shown that the fundamental performance limit of inertial gyroscopes is angle random walk (ARW) due to thermo-mechanical and electronic noises. Theoretical models show that resonant frequency, frequency mismatch between sensing and driving modes, effective mass, quality factor (Q), driving amplitude, sensing gap, sensing area and angular gain are the most important parameters that need to be optimized for best noise and most practical device design. In this research, two different structures are considered for low-noise MEMS gyroscopes: 1) shell gyroscopes in yaw direction, and 2) a novel super sensitive stacked (S3) gyroscope for pitch/roll directions. Extensive analytical and FEM numerical modeling was conducted throughout this research to investigate the mechanisms that affect Q and noise in shell resonators used in yaw-rate gyroscopes. These models provided insight into ways to significantly improve resonator design, structure, fabrication, and assembly and helped fabricate fused silica shells with Qs as high as 10 million (at least an order of magnitude larger than other similar shells). Noise performance of these fused silica shell gyroscopes with 5 mm dimeter improved by about two orders of magnitude (< 5×10-3 °/√hr), representing one of the best noise performances reported for a MEMS gyroscope. To build a high-performance MEMS-based planar vibratory pitch/roll gyroscope, it is critical to have a resonator with high Q in the out-of-plane resonant mode. Existing out-of-plane resonators suffer from low Q due to anchor loss or/and thermoelastic dissipation (TED). Increasing the thickness of the out-of-plane resonator reduces TED, but this increases the anchor loss. To reduce anchor loss significantly, a novel structure called S3 is designed. In this structure, two similar resonators are stacked on top of each other and move in opposite directions, thus providing a balanced stacked resonator with reduced anchor loss. The reduction of anchor loss allows larger thickness of silicon S3 gyroscopes, leading to a very low TED. A large-scale model of a stacked balanced resonator is fabricated and tested. The initial results show more than 50 times improvement in Q (measured in air) when resonators are stacked. It is expected that by testing this device in vacuum, Q would improve by more than three orders of magnitude. The S3 design also has an extremely large effective mass, a very large angular gain, a large driving amplitude, a very small sensing gap, and a large sensing area. It is estimated that a 500 µm thick silicon S3 gyroscope provides ARW of about 1.5×10-5 °/√hr (more than two orders of magnitude better performance than a navigation-grade gyroscope). This extraordinary small value can be improved for 1mm thick fused silica to 7.6×10-7 °/√hr if the technology for etching fused silica could be developed in the future.PHDElectrical and Computer EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147701/1/darvishi_1.pd

Inertial MEMS: readout, test and application

This thesis moves towards the investigation of Micro Electro-Mechanical Systems (MEMS) intertial sensors from different perspectives and points of view: readout, test and application. Chapter 1 deals with the state-of-the-art for the interfaces usually employed for 3- axes micromachined gyroscopes. Several architecture based on multiplexing schemes in order to extremely simplify the analog front-end which can be based on a single charge amplifier are analysed and compared. A novel solution that experiments an innovative readout technique based on a special analog-Code Division Multiplexing Access (CDMA) is presented; this architecture can reach a considerable reduction of the Analog Front-End (AFE) with reference to other multiplexing schemes. Many family codes have been considered in order to find the best trade-off between performance and complexity. System-level simulations prove the effectiveness of this technique in processing all the required signals. A case study is also analysed: a comparison with the SD740 micro-machined integrated inertial module with tri-axial gyroscope by SensorDynamics AG is provided. MEMS accelerometers are widely used in the automotive and aeronautics fields and are becoming extremely popular in a wide range of consumer electronics products. The cost of testing is a major one within the manufacturing process, because MEMS accelerometer characterization requires a series of tests that include physical stimuli. The calibration and the functional testing are the most challenging and a wide selection of Automatic Test Equipments (ATEs) is available on the market for this purpose; those equipments provide a full characterization of the Device Under Test (DUT), from low-g to high-g levels, even over temperature. Chapter 2 presents a novel solution that experiments an innovative procedure to perform a characterization at medium-g levels. The presented approach can be applied to low-cost ATEs obtaining challenging results. The procedure is deeply investigated and an experimental setup is described. A case study is also analysed: some already trimmed Three Degrees of Freedom (3DoF)-Inertial Measurement Unit (IMU) modules (three-axes accelerometer integrated with a mixed signal ASIC), from SensorDynamics AG are tested with the experimental setup and analysed, for the first time, at medium-g levels. Standard preprocessing techniques for removing the ground response from vehicle- mounted Ground Penetrating Radar (GPR) data may fail when used on rough terrain. In Chapter 3, a Laser Imaging Detection and Ranging (LIDAR) system and a Global Positioning System (GPS)/IMU is integrated into a prototype system with the GPR and provided high-resolution measurements of the ground surface. Two modifications to preprocessing were proposed for mitigating the ground bounce based on the available LIDAR data. An experiment is carried out on a set of GPR/LIDAR data collected with the integrated prototype vehicle over lanes with artificially rough terrain, consisting of targets buried under or near mounds, ruts and potholes. A stabilization technique for multi-element vehicle-mounted GPR is also presented