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Post-Packaged Measurement of MEMS Stiffness, Mass, Damping, and Actuation Force
Keywords: MEMS Stiffness, Mass, Damping, Actuation Force
What is presented: We present a practical MEMS metrology technology that can be used to extract system stiffness, mass, damping, and excitation force after a MEMS is packaged. Presently the technology applies to planar MEMS with comb drives. Our method is quick, accurate, and precise. Why important: Our technology will likely be important for manufacture, accuracy, and controllability. During manufacture, MEMS metrology can be 30% to 40% of the cost. This high cost is due to factory testing tools that are impractical and not optimized for batch fabrication. The tools often apply an external disturbance that the MEMS are electronically tuned to. Accuracy is a critical problem area in MEMS. Often MEMS are more sensitive and precise than the tools used to calibrate them. And there are no ASTM standards in MEMS for measuring stiffness, mass, damping, and force. Since there is a lack of standards, high cost in metrology, and low return on measurement due to large uncertainties, it has been difficult for manufacturers and their customers to agree on calibration technologies. Moreover, calibration in controlled laboratory conditions may not be consistent with conduction due to harsh environmental changes or long-term dormancy. Conventional calibration methods often treat MEMS as a black box, where numerous parameters remain uncharacterized. Without complete characterization, a complete understanding of what is being sensed is unlikely. However, by measuring the stiffness, mass, damping, and excitation forces on-chip, MEMS can become self-calibrating and offer more complete analysis of what is being sensed. What is different: Our method consists of using on-chip or off-the-shelf electronics to measure changes in capacitance to measure geometry, displacement, stiffness, and comb drive force. Upon measuring stiffness, mass is determined by velocity resonant frequency. The benefit of using changes in capacitance is that our technology is independent of meter accuracy; that is, it is the precision of the meter that matters. E.g. Zeptofarad precision has been realized by a few groups. Such an independence from absolute measurements allows our technology to be repeatable between different laboratories, where parasitics will likely differ. Results: We validate our electro-metrology technology for geometry, displacement, stiffness, and force. Our results of geometry compares favorably against geometry measured by a scanning electron microscope by 2 orders of magnitude. We validate displacement by measuring the distance traveled between a pair fabricated displacement stops. Stiffness and force are simi-validated by applying an identical (but unknown) AFM-cantilever force to two different MEMS which are each calibrated using our method. Although such a method does not directly provide a traceable measurement of force, it does imply the possibility of developing a standard of measure because the same value of force is obtained across different devices.
Jason Vaughn Clark, Assistant Professor
Purdue University
West Lafayette, IN

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