This dissertation discusses the design, simulation and characterization of process-compatible accelerometers and gyroscopes for the implementation of multi-degree-of-freedom (multi-DOF) systems. All components presented herein were designed to operate under the same vacuum-sealed environment to facilitate batch fabrication and wafer-level packaging (WLP), enabling the development of small form-factor single-die inertial measurement units (IMUs). The high-aspect-ratio poly and single-crystal silicon (HARPSS) process flow was used to co-fabricate the devices that compose the system, enabling the implementation ultra-narrow capacitive gaps (< 300 nm) in thick device-layer substrates (40 um). The presented gyroscopes were implemented as high-frequency BAW disk resonators operating in a mode-matched condition. A new technique to reduced dependencies on environmental stimuli such as temperature, vibration and shock was introduced. Novel decoupling springs were utilized to effectively isolate the gyros from their substrate, minimizing the effect that external sources of error have on offset and scale-factor. The substrate-decoupled (SD) BAW gyros were interfaced with a customized IC to achieve supreme random-vibration immunity (0.012 (deg/s)/g) and excellent rejection to shock (0.075 (deg/s)/g). With a scale factor of 800 uV/(deg/s), the complete SD-BAW gyro system attains a large full-scale range (2500 deg/s) with excellent linearity. The measured angle-random walk (ARW) of 0.36 deg/rthr and bias-instability of 10.5 deg/hr are dominated by the thermal and flicker noise of the IC, respectively. Additional measurements using external electronics show bias-instability values as low as 3.5 deg/hr. To implement the final monolithic multi-DOF IMU, accelerometers were carefully designed to operate in the same vacuum environment required for the gyroscopes. Narrow capacitive gaps were used to adjust the accelerometer squeeze-film damping (SFD) levels, preventing an under-damped response. Robust simulation techniques were developed using finite-element analysis (FEA) tools to extract accurate values of SFD, which were then match with measured results. Ultra-small single proof-mass tri-axial accelerometers with Brownian-noise as low as 30 ug/rtHz were interfaced with front-end electronics exhibiting scale-factor values in the order of 5 to 10 mV/g and cross-axis sensitivities of less than 3% before any electronic compensation.

Im Fokus dieser Arbeit stehen Dämpfungseffekte schwingfähiger Mikroelektromechanischer Systeme (MEMS), die nach dem kapazitiven Wirkprinzip arbeiten. Die verschiedenen Dissipationsprozesse und die zugehörigen analytischen Modelle sowie numerischen Berechnungsmöglichkeiten auf physikalischer Ebene werden vorgestellt und mit eigenen experimentellen Ergebnissen verglichen. Der Schwerpunkt liegt dabei auf der fluidischen Dämpfung im Kontinuum und bei leichter Verdünnung, was bei den meisten kapazitiven MEMS den dominierenden Verlusteffekt darstellt.:1 Überblick 2 Grundlagen zur Beschreibung von Mikrosystemen 3 Herstellung und Charakterisierung 4 Fluidische Dämpfung 5 Weitere dissipative Effekte mikromechanischer Systeme 6 Zusammenfassung und Ausblick / This thesis focuses on damping effects of vibrational micro-electromechanical systems (MEMS) with capacitive working principle. The different dissipation processes and the associated analytical models as well as numerical calculation possibilities on a physical level are presented and compared to own experimental results. The main emphasis is on fluidic damping in the continuum regime and with slight rarefaction, which is the dominant loss effect in most capacitive MEMS.:1 Überblick 2 Grundlagen zur Beschreibung von Mikrosystemen 3 Herstellung und Charakterisierung 4 Fluidische Dämpfung 5 Weitere dissipative Effekte mikromechanischer Systeme 6 Zusammenfassung und Ausblick