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Automatic layout generation of electrostatic comb drive folded-flexure microresonators from user-supplied specifications is demonstrated. The microresonator is parameterized in terms of the physical dimensions of the device (e.g, length of the beams in the folded-flexure). With these dimensions and the applied voltage as the design variables, the design problem is formulated as a formal non-linearly constrained numerical optimization problem. Analytical models are derived for microresonator performance characteristics in terms of these design variables. These models are employed in the constraints which ensure proper functioning of the microresonator as well as meeting user specifications. A good resonator design requires that the other vibration modes of the structure do not interfere with the preferred mode of oscillation. Hence, there are constraints which require that the resonance frequency in the preferred direction is sufficiently lower than the frequencies of other vibration modes of the structure. The synthesis module includes models for three translational modes, three rotational modes, and vibration modes of the comb drive and the folded flexure beams. Microresonator layouts are generated for 5 frequencies using 4 different objective functions - each objective function driving the optimization to a different part of the design space. The objective functions used are minimize area, minimize voltage, minimize a normalized sum of area and voltage, and maximize displacement at resonance. When the out-of-plane mode separation constraints are also introduced, the structural thickness is also made a design variable, since, otherwise, these constraints cannot be met. These synthesis results are evaluated in three ways. First, the trends in the variations of the dimensions of the device with changes in preferred-mode resonance frequency for the same objective function are qualitatively reasoned. Further, changes in the relative dimensions with different objective functions for the same preferred-mode resonance frequency are also explained. Then, the accuracy of the physical models in the synthesis module is evaluated by comparison with FEM simulation results. Lastly, measurements are made on fabricated microresonators.
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