A High Dynamic Range Hourglass-Beam Accelerometer Array with Temperature-and-Stress-Induced Drift Compensation using Deep Neural Networks

An emerging application in "Navigation through High Shock" is driving a need for small-size, low-weight, and low-power accelerometers that can detect 10 kg amplitudes over 10 kHz bandwidth with a resolution of 10 mg (an effective dynamic range of 120 dB, where 1 g = 9.8m/s²). Simultaneously, the accelerometer should achieve bias instability within 100 μg and eliminate long-term drift to extend bias instability levels to integration times of 100 s and beyond. This thesis describes three transducer design variants of CMOS-MEMS capacitive accelerometer array systems fabricated in a standard 0.18 μm CMOS process. The highest transducer sensitivity accelerometer has a measured full-scale range of +-5 kg, a bandwidth larger than 10 kHz, with a minimum resolution of 5mg and a minimum bias instability of 700 μg. The resolution and full-scale range of the accelerometers correspond to a dynamic range of 120 dB that is on par with state-of-the-art accelerometers. 

This thesis demonstrates several key enablers to capacitive accelerometer technology that allow meeting the unprecedented high-g and high-dynamic-range requirements of the Navigation through High Shock specifications. First, an interdigitated tapered comb-finger electrode design allows a maximum 10 μm stroke in response to kg shock events while providing a more than five times higher sense capacitance and sense-to-parasitic-capacitance ratio as compared with a conventional parallel-plate design under the same electrode displacement. Second, an hourglass spring beam design that uniformly distributes distortion strain energy across the spring beam provides an optimal mechanical transfer function of an accelerometer transducer given fabrication critical dimensions and the full-scale input target. The interdigitated tapered comb-finger electrode design and hourglass spring beam design lend the accelerometers a maximum of 40 dB boost in transducer sensitivity and a 20 dB enhancement in dynamic range from a legacy design. Third, a MEMS-array offset compensation technique that is area-efficient and low power permits a wideoffset tuning range with high resolution of the arrayed accelerometer system. Fourth,the input range and fast ring-down time of a legacy resonant-frequency-staggered accelerometer array are experimentally validated, which presents significantly less ring-down than state-of-the-art high-shock accelerometers. And fifth, a convex optimization approach further improves an order of magnitude of the figure of merit that delineates the trade-off between transducer sensitivity and ring-down time of the legacy resonant-frequency-staggered accelerometer array.

This thesis work has met most of the Navigation through High Shock specifications except achieving bias instability within 100 μg and extended 100 μg bias instability up to integration times of 100 s and beyond. The bias instability is limited by the DC supply flicker noise of the modulation voltage. Nevertheless, there is a path toward the 100 μg bias instability with further improvement on the accelerometer systems and testbeds. Extending 100 μg bias instability of an accelerometer over integration times of 100 s and beyond entails a low-level acceleration random walk. A thorough understanding of the source of acceleration random walk and method to alleviate this major bias error terms for MEMS accelerometers becomes crucial. The duality relation between acceleration random walk and 1/ f² noise of the accelerometer system is well-studied. However, the physical source of acceleration random walk and 1/ f² noise of the accelerometer system is an uncharted field in the literature. This thesis proposed a hypothesis that sets out to overthrow the widely-accepted stochastic model for acceleration random walk in the inertial and navigation areas. The hypothesis states — the dominant source of 1/f² noise of the accelerometer system (or acceleration random walk) arises from temperature-and-stress states variation of the system and acceleration random walk at the integration times up to several hours can be treated as a deterministic error. To validate the thesis hypothesis, this work broadens the commonly-used temperature compensation technique for accelerometers with stress compensation by allocating a large array of temperature sensors and small footprint FET-based stress sensors across the accelerometer chip. A temperature-and-stress-induced drift compensation technique under a deep neural net framework not only demonstrates extendedlow bias instability levels of the accelerometer to integration times beyond 100 s, but shows elimination of acceleration random walk up to 4 h. The drift compensation demonstrates complementary effects of stress versus temperature and shows potential for creating highly stable sensors that measure their on-chip environment and locally process the data for compensation. In addition, the result bolsters the hypothesis that the 1/ f² noise of the accelerometer system and acceleration random walk at the integration times up to several hours can be treated as a deterministic error.