Master of Science

thesisMicroelectromechanical gyroscopes are readily used in cars and cell phones. Tactical gyroscopes are available inexpensively and they offer 0.01 to 0.1 % scale factor inaccuracy. On the other hand, strategic gyroscopes with much better performance levels are 100,000 times more expensive. The main objective of this work is to explore the possibility of developing inexpensive strategic grade gyroscopes using microelectromechanical systems technology. Most of the available gyroscopes are surface micromachined due to fabrication issues and misalignment problems involved in multistep fabrication processes necessary to use the bulk of the wafer as the proofmass in MEMS gyroscopes. It can be shown that the sensitivity of the gyroscope is inversely proportional to the natural frequency; so if bulk micromachining technique is used it is possible to decrease the natural frequency further than current limits of surface micromachining in order to increase sensitivity. This thesis is focused on proposing a way to use bulk of the silicon wafer in the gyroscope to decrease the natural frequency to very low levels, such as sub-KHz regime, that cannot be achieved by single mask surface micromachining processes. It then proposes a solution for solving the misalignment problems caused by using multiple fabrication steps and masks instead of using only one mask in surface micromachined gyroscopes. In our design discrete proofmasses are linked together around a circle by compliant structures to ensure the highest effective mass and lowest effective spring constant. By using a proposed double sided fabrication technology the effect of misalignments on frequency mismatch can be reduced. ANSYS software simulations show that 20 µm misalignment between the masks causes a frequency shift equal to 0.3% of the natural frequency that can be compensated using electrostatic frequency tuning. Acceleration parasitic effects can also be a major problem in a low natural frequency gyroscope. In our design a multiple sensing electrode configuration is used that cancels the acceleration effects completely. The sensitivity of the gyroscope with 3126 Hz natural frequency is simulated to be 574 mV/(deg/sec) , or about four times higher than 132 mV/(deg/sec) , which was used as a benchmark for a sensitive gyroscope

Development of a low damping MEMS resonator

MEMS based low damping inertial resonators are the key element in the development of precision vibratory gyroscopes. High quality factor (Q factor) is a crucial parameter for the development of high precision inertial resonators. Q factor indicates how efficient a resonator is at retaining its energy during oscillations. Q factor can be limited by different types of energy losses, such as anchor damping, squeeze-film damping, and thermoelastic damping (TED). Understanding the energy loss-mechanism can show a path for designing high Q resonator. This thesis explores the effects of different design parameters on Q factor of 3D inertial resonators. TED loss mechanisms in a 3D non-inverted wineglass (hemispherical) shell resonator and a disk resonator were investigated. Both the disk and shell share the same vibration modes, and they are widely used as a vibratory resonator shape. Investigation with loss-mechanism shows that robust mechanical materials such as fused silica can offer ultra-low damping during oscillation. TED loss resulting from the effects of geometric parameters (such as thickness, height, and radius), mass imbalance, thickness non-uniformity, and edge defects were investigated. Glassblowing was used to fabricate hemispherical 3D shell resonators and conventional silicon based dry etching was used to fabricate micro disk resonators. The results presented in this thesis can facilitate selecting efficient geometric and material properties for achieving a higher Q-factor in 3D inertial resonators. Enhancing the Q-factor in MEMS based 3D resonators can further enable the development of high precision resonators and gyroscopes

High-Q Fused Silica Micro-Shell Resonators for Navigation-Grade MEMS Gyroscopes

This research aims to develop the resonator for a navigation-grade microelectromechanical system (MEMS) Coriolis vibratory gyroscope (CVG) that will bring inertial navigation capabilities to a wider range of applications by reducing gyroscope size and cost. To achieve the desired gyroscope performance, the gyroscope resonator must have low energy dissipation and a highly symmetric structure. Several challenges arise at the micro-scale due to the increased sensitivity to imperfections and increased susceptibility to energy loss mechanisms. This work investigates the lower limit on energy dissipation in a micro-shell resonator known as the birdbath (BB) resonator. The BB resonator is designed to mitigate the energy loss mechanisms that commonly limit MEMS resonators, including anchor loss and thermoelastic dissipation, through a unique shape and fabrication process and through the use of fused silica as the structural material. A blowtorch molding process is used to form high aspect ratio fused silica shells with a range of wall profiles, providing a high level of control in three dimensions that is not possible with conventional micromachining techniques. Prototype BB resonators were developed prior to this dissertation work but they achieved low quality factors (Q) and low ring-down time constants (T) on the order of 100 thousand and 1 s, respectively. The goal of this work is to drastically increase performance above these initial results. Each relevant energy loss mechanism is considered in order to identify the dominant loss mechanism for a given device. Process improvements are implemented to mitigate each loss mechanism, including improved thermal management during blowtorch molding, cleaner lapping and polishing, reduced upfront surface contamination, and methods to remove contaminants after fabrication. Following optimization, Qs up to 10 million and Ts up to 500 s are measured, representing a marked improvement over the prototype resonators. It is found that BB resonators are now limited by surface loss, as indicated by the observed inverse relationship between Q and surface-to-volume ratio. The surface-loss-limited regime results in a high sensitivity to added surface layers. The addition of a conductive layer to enable electrostatic transduction is found to have a large impact, decreasing Q by 50% with the addition of only 30 angstroms of metal. It is suggested that the origin of this loss may be interfacial slippage due to a large increase in stress that occurs at the interface during oscillation. Experimental investigation into the dependence of Q on conductive layer composition, thickness, deposition conditions, and post-deposition treatments is carried out. Following treatments to removed adsorbed contaminants from the surface, resonators with a 15/50 angstrom Ti/Pt layer are found to maintain 60% of their initial Qs. Indium tin oxide (ITO) is identified as a promising conductive layer candidate, with initial experiments producing shells that maintain 70% of their initial Q. The values of Q and T produced in this work are unprecedented for MEMS resonators. Even accounting for the losses that accompany conductive layer deposition, birdbath resonator gyroscopes are expected to achieve navigation-grade performance.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/146096/1/taln_1.pd

Micro-Resonators: The Quest for Superior Performance

Microelectromechanical resonators are no longer solely a subject of research in university and government labs; they have found a variety of applications at industrial scale, where their market is predicted to grow steadily. Nevertheless, many barriers to enhance their performance and further spread their application remain to be overcome. In this Special Issue, we will focus our attention to some of the persistent challenges of micro-/nano-resonators such as nonlinearity, temperature stability, acceleration sensitivity, limits of quality factor, and failure modes that require a more in-depth understanding of the physics of vibration at small scale. The goal is to seek innovative solutions that take advantage of unique material properties and original designs to push the performance of micro-resonators beyond what is conventionally achievable. Contributions from academia discussing less-known characteristics of micro-resonators and from industry depicting the challenges of large-scale implementation of resonators are encouraged with the hopes of further stimulating the growth of this field, which is rich with fascinating physics and challenging problems

High-Performance Micromachined Vibratory Rate- and Rate-Integrating Gyroscopes.

We aim to reduce vibration sensitivity by developing gyros that operate in the balanced mode. The balanced mode creates zero net momentum and reduces energy loss through an anchor. The gyro can differentially cancel measurement errors from external vibration along both sensor axes. The vibration sensitivity of the balanced-mode gyroscope including structural imbalance from microfabrication reduces as the absolute difference between in-phase parasitic mode and operating mode frequencies increases. The parasitic sensing mode frequency is designed larger than the operating mode frequency to achieve both improved vibration insensitivity and shock resistivity. A single anchor is used to minimize thermoresidual stress change. We developed two gyroscope based on these design principles. The Balanced Oscillating Gyro (BOG) is a quad-mass tuning-fork rate gyroscope. The relationship between gyro design and modal characteristics is studied extensively using finite element method (FEM). The gyro is fabricated using the planar Si-on-glass (SOG) process with a device thickness of 100 micrometers. The BOG is evaluated using the first-generation analog interface circuitry. Under a frequency mismatch of 5Hz between driving and sense modes, the angle random walk (ARW) is measured to be 0.44deg/sec/sqrt(Hz). The Cylindrical Rate-Integrating Gyroscope (CING) operates in whole-angle mode. The gyro is completely axisymmetric and self-aligned to maximize mechanical isotropy. The gyro offers a large frequency ratio of ~1.7 between parasitic and the wineglass modes. The CING is fabricated using the 3D Si-on-glass (SOG) process with a device thickness of 300 micrometers. The 1st and 2nd generation CINGs operate at 18kHz and 3kHz, respectively and demonstrate a frequency mismatch of <1% and a large Q (~20,000 at 18kHz and ~100,000 at 3kHz under exact mode matching). In the rate-sensing mode, the first-generation CING (18kHz) demonstrates an Ag of 0.05, an angle random walk (ARW) of 7deg/sqrt(hr), and a bias stability of 72deg/hr without temperature compensation. In the rate-sensing mode, the second-generation CING measures an Ag of 0.0065, an ARW of 0.09deg/sqrt(hr), and a bias stability of 129deg/hr without temperature compensation. In the rate-integration mode, the second-generation CING demonstrates precession with an Ag of 0.011±0.001 under a frequency mismatch of 20~80mHz during several hours of operation.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91440/1/jycho_1.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/91440/2/jycho_2.pd

Design and Implementation of Silicon-Based MEMS Resonators for Application in Ultra Stable High Frequency Oscillators

The focus of this work is to design and implement resonators for ultra-stable high-frequency ( \u3e 100MHz) silicon-based MEMS oscillators. Specifically, two novel types of resonators are introduced that push the performance of silicon-based MEMS resonators to new limits. Thin film Piezoelectric-on-Silicon (TPoS) resonators have been shown to be suitable for oscillator applications due to their combined high quality factor, coupling efficiency, power handling and doping-dependent temperature-frequency behavior. This thesis is an attempt to utilize the TPoS platform and optimize it for extremely stable high-frequency oscillator applications. To achieve the said objective, two main research venues are explored. Firstly, quality factor is systematically studied and anisotropy of single crystalline silicon (SCS) is exploited to enable high-quality factor side-supported radial-mode (aka breathing mode) TPoS disc resonators through minimization of anchor-loss. It is then experimentally demonstrated that in TPoS disc resonators with tethers aligned to [100], unloaded quality factor improves from ~450 for the second harmonic mode at 43 MHz to ~11,500 for the eighth harmonic mode at 196 MHz. Secondly, thickness quasi-Lamé modes are studied and demonstrated in TPoS resonators for the first time. It is shown that thickness quasi-Lamé modes (TQLM) could be efficiently excited in silicon with very high quality factor (Q). A quality factor of 23.2 k is measured in vacuum at 185 MHz for a fundamental TQLM-TPoS resonators designed within a circular acoustic isolation frame. Quality factor of 12.6 k and 6 k are also measured for the second- and third- harmonic TQLM TPoS resonators at 366 MHz and 555 MHz respectively. Turn-over temperatures between 40 °C to 125 °C are also designed and measured for TQLM TPoS resonators fabricated on degenerately N-doped silicon substrates. The reported extremely high quality factor, very low motional resistance, and tunable turn-over temperatures \u3e 80 °C make these resonators a great candidate for ultra-stable oven-controlled high-frequency MEMS oscillators

Integrated Ultra-High Q Bulk Acoustic Wave Resonators in Thick Monocrystalline Silicon Carbide

Monocrystalline 4H-silicon carbide has emerged as an intriguiging substrate for wafer level fabrication of ultra-high Q electrostatic acoustic resonators. As a wide band-gap semiconductor, it's already under heavy investigation in the field of power electronics for its exemplary electrical and thermal robustness; further, its stoichiometric properties find it germane to a diverse array of applications from biomedical sensors to quantum photonics. Acoustically, it possesses sublime structural properties and mechanical dissipation characteristics, with theoretical mechanical quality factors prescribed by phonon scattering limits surpassing silicon by an order of magnitude. High Q is almost universally desirable: improved motional resistance and insertion loss, greater displacements, longer decay times, along with reduced phase and Brownian noise translate to more sensitive, stable, efficient and precise instruments. This thesis expounds upon a platform for thick, single crystal silicon carbide resonant MEMS, explores the roots of dissipation and the structural properties most pertinent to thick single crystal silicon carbide bulk acoustic wave resonators and their applications in inertial sensors. Record-high measured mechanical quality factors demonstrate proof of concept resonators ready to make the leap toward high performance sensors and instruments. Strong emphasis is placed on developments in fabrication techniques and processes to enable the implementation of silicon carbide in sensors across the gamut of environments and applications.Ph.D

Disc resonator gyroscope fabrication process requiring no bonding alignment

A method of fabricating a resonant vibratory sensor, such as a disc resonator gyro. A silicon baseplate wafer for a disc resonator gyro is provided with one or more locating marks. The disc resonator gyro is fabricated by bonding a blank resonator wafer, such as an SOI wafer, to the fabricated baseplate, and fabricating the resonator structure according to a pattern based at least in part upon the location of the at least one locating mark of the fabricated baseplate. MEMS-based processing is used for the fabrication processing. In some embodiments, the locating mark is visualized using optical and/or infrared viewing methods. A disc resonator gyroscope manufactured according to these methods is described

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

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