We present a theoretical analysis of a packagable method for calibrating the force and displacement of a micro electro mechanical system (MEMS) that is subject to geometric and material property variations. Property variations are usually due to variations in the fabrication processes, packaging, and environmental exposure. Force and displacement are among the most important fundamental mechanical quantities for investigating, discovering, and exploiting micro and nanoscale phenomena. However, finding a practical and traceable method to accurately and precisely measure the minute forces and displacements in MEMS has been elusive. One reason is because the force generated by MEMS is quite often smaller than the force that can be measured by conventional force sensors. Similarly, displacements in MEMS can be as small as a fraction of the diameter of an atom, which is beyond the capabilities of standard displacement sensors. Our present analysis addresses the calibration of force and displacement for MEMS comprising comb drive sensors and actuators. Our approach for calibrating force and displacement is based on the strong and sensitive coupling between mechanical performance and electronic measurands at the microscale. That is, variations in geometry and material properties affect performance, which can be capacitively measured using on-chip or off-the-shelf capacitance meters. A novelty in our analysis is the elimination of unknown properties, which allows us to express mechanical quantities and their uncertainties solely in terms of electrical measurands. We derive analytical expressions for extracting measurements of force, displacement, stiffness, and their uncertainties by electrical probing. And we show how our method is expected to a few orders more precise than convention.
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- Calibrating Force and Displacement in the Face of Property Variation
Jason V. Clark
- Springer New York
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