Vacuum behavior and control of a MEMS stage with integrated thermal displacement sensor

We investigate the applicability of a MEMS stage in a vacuum environment. The stage is suspended by a flexure mechanism and is actuated by electrostatic comb-drives. The position of the stage is measured by an integrated sensor based on the conductance of heat through air. The vacuum behavior of the sensor and the stage is identified. A model for thermal conductivity and viscous damping as a function of the vacuum pressure is presented and validated by measuring the decreasing sensor response and the increasing Q-factor for decreasing pressure. We have identified the system in the frequency domain, which is used to compare the closed-loop behavior with three different controllers: an integral controller, an integral controller with low-pass filter, and an integral controller with notch filter. The integral controller can become unstable due to the high Q-factor in vacuum. Adding a low-pass or a notch filter improves the stability at low pressures. Since the integral controller with notch filter shows the lowest settling time, this is the preferred controller. Overall, we are able to control the position of the MEMS stage at a pressure of 1 mbar with a reduced resolution of approximately 1.1 μm, but with a good settling time of 2.2 ms.