Electrostatic Calibration of MEMS Accelerometers

Capacitive MEMS accelerometers are widely used in various applications due to their small size, low cost, high sensitivity and low power consumption. These systems often comprise of a movable proof mass connected to a frame using mechanically compliant elements acting as springs, and sets of capacitive fingers for control and read-out. To achieve optimal performance, it is crucial to operate these devices in a zero-stiffness null state of the closed-loop system, where the restoring force of the springs is balanced by electrostatic forces. However, accurate determination of the critical voltage <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(V_{\text{CRIT }})$</tex> required to achieve this state remains a challenge. In this contribution we present a novel method for determining the critical voltage in capacitive accelerometers. Our method is based on measuring the rate at which the output bias changes with respect to nanometric displacement of the proof mass (i.e., force-displacement measurement) in a closed loop system. This approach enables precise control over the operating point of the accelerometer, leading to enhanced sensitivity, improved bias repeatability, and reduced noise. The proposed method can be readily integrated into the design and calibration processes of capacitive accelerometers, contributing to advancements in inertial sensing and other related fields such as nano-positioners and actuators, small force sensors, and microscope probes.