MEMS gyroscopes have become an essential component in consumer, industrial and automotive applications, owing to their small form factor and low production cost. However, their poor stability, also known as drift, has hindered their penetration into high-end tactical and navigation applications, where highly stable bias and scale factor are required over long period of time to avoid significant positioning error. Improving the long-term stability of MEMS gyroscopes has created new challenges in both the physical sensor design and fabrication, as well as the system architecture used for interfacing with the physical sensor. The objective of this research is to develop interface circuits and systems for in-situ control and self-calibration of MEMS resonators and resonant gyroscopes to enhance the stability of bias and scale factor without the need for any mechanical rotary stage, or expensive bulky lab characterization equipment. The self-calibration techniques developed in this work provide 1-2 orders of magnitude improvement in the drift of bias and scale factor of a resonant gyroscope over temperature and time.

Design and analysis of polysilicon and single crystal silicon gyroscopes have been carried out. Variations in suspension design have been explored. Designs that utilize in-plane and out-of-plane sensing are studied. Damping plays an important role in determining the sense response. Reduction in damping directly affects sensor performance. The various damping mechanisms that are prevalent in gyroscopes are studied. Perforations on the proof mass are observed to significantly reduce the damping in the device when operated in air. The effects of perforation geometry and density have been analyzed. The analysis results show that there is a two orders of magnitude reduction in damping of thick gyroscope structures with optimized perforation design. Equivalent circuit lumped parameter models have been developed to analyze gyroscope performance. The simulation results of these models have been compared with results obtained from SABER, a MEMS specific system level design tool from Coventorware. The lumped parameter models are observed to produce faster simulation results with an accuracy comparable to that of Coventorware Three gyroscopes specific to the PolyMUMPS fabrication process have been designed and their performance analyzed. Two of the designs sense motion out-of-plane and the other senses motion in-plane. Results of the simulation show that for a given damping, the gyro design with in-plane modes gives a resolution of 4º/s. The out-of-plane gyroscopes have two variations in suspension. The hammock suspension resolves a rate of 25º/s in a 200 Hz bandwidth while the design with folded beam suspension resolves a rate of 2º/s in a 12 Hz bandwidth. A single crystal silicon in-plane gyroscope has been designed with vertical electrodes to sense Coriolis motion. This design gives an order of magnitude higher Capacitance change for a given rotation in comparison to conventional comb-finger design. The effects of process induced residual stress on the characteristic frequencies of the polysilicon gyroscopes are also studied. The in-plane gyroscope is found to be robust to stress variations. Analysis results indicate that the tuning fork gyroscope with the hammock suspension is the most susceptible to compressive residual stress, with a significant drop in sensitivity at high stress values.

This thesis, for the first time in literature, introduces a comprehensive study about analog controller designs for MEMS vibratory gyroscopes. A controller of a MEMS gyroscope is mandatory for robust operation, which is insensitive to sensor parameters and ambient con- ditions. Errors in the controller design not only deteriorate transient performance, such as settling time and overshoot, but also cause performance degradation due to stability problems. Accordingly, true controller design for a gyroscope is critical work in terms of functionality and system performance. This thesis gives details for modeling, analysis of closed-loop sys- tems, and design procedure for drive and sense modes. Controller loops are implemented both with discrete components and in a CMOS technology as an integrated circuit. Simulation and test results verify the modeling, analysis, and design procedure discussed in this thesis. Drive mode system developed previously at METU is optimized by taking circuit imperfec- tions into account, which results in an improved transient performance of 50 msec settling time with no overshoot for a 4&mu / m drive mode oscillation amplitude. This system has a 60 phase margin with the help of the pole-zero cancellation technique. In addition, a new gener- iv ation and simple drive mode controller for tactical grade applications is designed and verified with a moderate transient performance. Two different sense mode controller design procedures are also developed according to a new base-band equivalent model derived for mismatch operation, as a new contribution to the literature. Firstly, a PID controller is designed for low frequency separation between the drive and sense modes of the gyroscope. Secondly, an integral controller is used for moderate and high mismatch amount. The controller system designed with the new base-band equivalent model improves the linearity, angle random walk, and bias instability by factors of 4, 9, and 3, respectively. Proposed drive and sense mode controllers are also designed and implemented using a 0.6&mu / m standard CMOS process. These chips are the first functional chips developed at METU de- signed for MEMS gyroscopes. Functionality of the proposed three systems, i.e., conventional drive mode controller, new generation drive mode controller, and sense mode controller, are verified with tests. The first prototypes result in 0.033 degree/sqrt/(hr) angle random walk and 3 degree/hr bias instability for open-loop operation, which is very promising and can be improved even further in future designs.

This thesis presents the development of wafer level vacuum packaging processes using Au-Si eutectic and glass frit bonding contributing to the improvement of packaging concepts for a variety of MEMS devices. In the first phase of this research, micromachined resonators and pirani vacuum gauges are designed for the evaluation of the vacuum package performance. These designs are verified using MATLAB and Coventorware finite element modeling tool. Designed resonators and pirani vacuum gauges and previously developed gyroscopes with lateral feedthroughs are fabricated with a newly developed Silicon-On-Glass (SOG) process. In addition to these, a process for the fabrication of similar devices with vertical feedthroughs is initiated for achieving simplified packaging process and lower parasitic capacitances. Cap wafers for both types of devices with lateral and vertical feedthroughs are designed and fabricated. The optimization of Au-Si eutectic bonding is carried out on both planar and non-planar surfaces. The bonding quality is evaluated using the deflection test, which is based on the deflection of a thinned diaphragm due to the pressure difference between inside and outside the package. A 100% yield bonding on planar surfaces is achieved at 390&ordm / C with a v holding time and bond force of 60 min and 1500 N, respectively. On the other hand, bonding on surfaces where 0.15&mu / m feedthrough lines exist can be done at 420&ordm / C with a 100% yield using same holding time and bond force. Furthermore, glass frit bonding on glass wafers with lateral feedthroughs is performed at temperatures between 435-450&ordm / C using different holding periods and bond forces. The yield is varied from %33 to %99.4 depending on the process parameters. The fabricated devices are wafer level vacuum packaged using the optimized glass frit and Au-Si eutectic bonding recipes. The performances of wafer level packages are evaluated using the integrated gyroscopes, resonators, and pirani vacuum gauges. Pressures ranging from 10 mTorr to 60 mTorr and 0.1 Torr to 0.7 Torr are observed in the glass frit packages, satisfying the requirements of various MEMS devices in the literature. It is also optically verified that Au-Si eutectic packages result in vacuum cavities, and further study is needed to quantify the vacuum level with vacuum sensors based on the resonating structures and pirani vacuum gauges.