Measurement of high-bandwidth nanonewton forces in a low-compliance configuration

Abstract

This paper presents a technique for precise and reproducible measurements of high bandwidth nanonewton forces in a low-compliance configuration. Precisely measuring high-bandwidth nanonewton forces is a critical enabler for many areas of nanotechnology. However, the prevailing nanonewton force measurement approaches can only measure low-frequency forces (<1 kHz) and/or of very high compliance, which causes large deflections at the force application location. As such, there is a need for low-compliance, high-bandwidth nanonewton force measurement techniques for a range of nanotechnology applications. To address this need, this paper introduces a microcantilever-based technique with a novel high-bandwidth calibration approach. To realize the low-compliance configuration without compromising measurement resolution, the force to be measured is applied close to the fixed-boundary of the microcantilever while measuring the displacement at the tip of the microcantilever using interferometry. The calibration function is obtained through modal testing of the microcantilever using an atomic force microscope (AFM) probe, resulting in a frequency dependent, complex-valued calibration function that maps the displacement measurements at the free-end of the cantilever into the forces at the application location. To present the technique, two different single-crystal silicon microcantilevers are fabricated, and are calibrated within 0.6 kHz to 20 kHz frequency range. A model-based approach is devised to expand the spatial range of calibration function, enabling calibration for multitude of force-application locations without requiring extensive experimentation. The sensitivity, compliance, resolution, and uncertainty of the force measurement technique are evaluated using the two sample microcantilevers. An experimental validation of the technique is completed by comparing the applied and measured nanonewton forces. The technique is then demonstrated by measuring forces during nano-scale material removal using nanomilling. The analyses results show that the proposed force measurement technique provides a resolution of 5 nN within 0.6 kHz to 1.5 kHz, and 1 nN within 1.5 kHz to 20 kHz ranges. The overall uncertainty and precision (repeatability) are determined to be 6.5% and 2.3%, respectively. It is concluded that the presented technique facilitates precise measurement of high-bandwidth and dynamic nanonewton forces in a low-compliance configuration.