Dynamics of an electrostatically controlled bulk micromachined silicon torsion mirror in air

Static and dynamic characterizations of micromirrors are important to understand the mirror's responses for different inputs under various conditions. The characterizations are important not only to choose and operate a mirror for a particular end application but also to continuously provide feedback to the design and processing teams in a new mirror development. This feedback should include device behavior, system parameters, and material properties. The dynamic behavior of the mirrors is significant to implement adaptive control algorithms to precisely position the mirror. In this thesis, instrumentation techniques to measure the static and dynamic responses of a bulk micromachined Silicon torsion mirror have been developed. These measurements include tilt angle versus driving voltage curves and frequency response curves. Several important parameters, like the torsion spring constant, damping ratio, natural frequency, moment of inertia, and mass were estimated for the mirror. These parameters were incorporated in the mirror model to simulate the mirror responses. Agreement of the simulated and experimental results confirmed the validity of the measurement techniques. Effects of nonlinearity in the torsion springs resulted in deviations between the actual and the simulated mirror responses at higher voltages and at larger angles. The measured parameters were further used to simulate the dynamic responses, response to a step voltage, capacitance variations, and the dynamic deformations of the mirror. The various parameters estimated will be central to implementing feedback control algorithms to accurately position the mirror throughout the entire gap.