Millimeter-Scale Piezoresistive Cantilevers for Accurate Force Measurements at the Nano-Newton Level

Abstract

This paper reports a development of millimeter-scale cantilevers equipped with piezoresistive deflection sensing metrology as a force sensor at the micro- and nano-Newton level. The cantilevers was designed and fabricated to minimize the error during the force transfer or calibration, so that they have full-bridge type piezoresistors, a large length and width and reference marks to facilitate the positioning of probes or tips onto the piezoresistive cantilevers. Their 6 mm-long and 0.4 mm-wide dimensions can reduce the error due to incomplete contact (or loading) position. The reference marks on the cantilever can give you a range of stiffness and force sensitivity with a single piezoresistive cantilever. The stiffness can vary from 25 N m⁻¹ at the first mark to 0.04 N m⁻¹ at the last. The full-bridge piezoresistors give an electrical signal proportional to the applied force with superior temperature independency. The fabricated piezoresistive cantilevers were calibrated with the KRISS nano force calibrator (NFC). The results showed that the stiffness and the force sensitivity at the last mark was determined to be 0.0502 N m⁻¹ and 0.357 (mV/V) μN⁻¹, respectively. The performances were tested by calibrating stiffness of commercial cantilevers using the cantilever-on-cantilever method with a fabricated cantilever and comparing calibration results with stiffness obtained from calibration using the NFC. Two results match to each other within approximately 10 % discrepancy.