Calibration methods of force sensors in the micro-Newton range

Abstract

A micromachined capacitive force sensor operating in the micro-Newton range has been calibrated using both dynamic and static methods. Both calibrations are non-destructive, accurate and traceable to Systeme International (SI) fundamental units. The dynamic calibration is a differential mass loading resonant method where the resonance frequency with and without an added mass is measured. This gives enough information to compute the spring constant. In this paper, we evaluate the resonant mass loading method for more complex MEMS devices. Analytical calculations and finite element analysis have been performed to investigate the dynamic properties of the sensor, e.g. modal interference. The frequency response was measured with the third harmonic method where the third harmonic of the current through the sensor was measured. To detect and analyse the resonance mode of the structure during excitation, a scanning laser Doppler vibrometer was used. Two designs of a capacitive nanoindenter force sensor with flexure-type springs have been evaluated using these methods. The quality of the resonant calibration method has been tested using static mass loading in combination with transmission electron microscopy imaging of the sensor displacement. This shows that the resonant method can be extended to calibrate more complex structures than plain cantilevers. Both calibration methods used are traceable to SI fundamental units as they are based on masses weighed on a calibrated scale. The masses used do not need to be fixed or glued in any way, making the calibration non-destructive. (10 refs.)