Parallel Plate Capacitive Detection of Large Amplitude Motion in MEMS

Detection of motion with parallel plate capacitors is commonly used in MEMS; small amplitude of motion is typically assumed. In this paper, we derive precise and constructive equations for the case of parallel plate capacitive detection of large amplitude of motion. These equations are solved in closed form without using a small displacement assumption. A precise relationship between the amplitude of the mechanical motion and the amplitude of the electrical sensing signals is obtained which allows the elimination of the nonlinearity error. To illustrate the theoretical findings, MEMS test structures were designed and fabricated. Experiments confirm the developed theory. The proposed algorithms of detection are especially valuable for capacitive detection of arbitrary amplitudes of motion in resonant structures such as gyroscopes, resonant microbalances, and chemical sensors.