This thesis describes a general system simulation of microelectromechanical systems (MEMS) based on lumped-parameter modeling. First-order analytic models are derived for mechanical equations of motion of a suspended plate, squeeze-film damping, fixed-fixed, crab-leg, folded-flexure, and serpentine spring constants, parallel-plate and comb-finger electrostatic actuators, and capacitive position sensors. The models are implemented in a circuit simulation program (SPICE) and in a numerical simulation program (MATLAB).
Verification of the models and simulations motivated creation of an integrated testbed for research in multi-mode digital control of MEMS: a suspended polysilicon plate having four capacitive-bridge vertical position sensors, each with an integrated CMOS buffer amplifier, four differential electrostatic feedback actuators on the plate's corners, and an interdigitated comb for lateral force input. Sigma-delta (C-A) force-balance control is implemented for each corner of the plate. The testbed is configured with a 0.25 N/m spring constant, 0.47 ug mass, and a vertical resonance of 3.7 kHz. In air, vertical displacement and tilt of the plate in two axes are controlled within +/- 25 nm and +/- 0.03 degrees, respectively. Measured noise acceleration is 19 milli-G with -69 dB dynamic range in a 50 Hz bandwidth. When operating in a low-pressure ambient, the mechanically underdamped system experiences limit-cycle oscillations, which are bounded through the use of digital lead compensation. An analytic model of the sigma-deltaloop, as well as simulation, successfully predicts the limit-cycle behavior.
In a separate part of this thesis, thermal microassembly techniques are demonstrated which extend the capabilities of surface micromachining technology. Polysilicon fuses act as temporary anchors that can be cleanly severed by application of a single 300 mA, 1 us pulse. Fuse applications include configurable springs and frequency trimming of microresonators. Welding technology is used to pre-stress springs and actively align structures. An aluminum microbridge is used to form a robust weld, connecting two polysilicon structures. The surface tension of the molten aluminum produces a force of approximately 15 uN, which is about 100 times larger than electrostatic comb-drive forces. A series of current pulses is used to melt the aluminum without destroying the weld joint.
September 30, 1994
Fedder, G. K. (1994). Simulation of Microelectromechanical Systems. United States: University of California, Berkeley.