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Precise calibration system for micro- and nano-force sensors

Over the past 15 years the atomic force microscopy has developed into a standard analytical method in micro- and nanosystems technology and contributes significantly to the rapid development in nanotechnology.  It allows microscopic images in an enlargement of several million times and thus the visualization of yet undiscovered details. The centerpiece of the atomic force microscope is the cantilever, consisting of a measuring tip which is located at a length of 100… 400 μm at the end of a flexible cantilever. When the spring stiffness of such a cantilever is calibrated, i.e. its force-deflection-characteristic, it can also be used for measuring the smallest forces on a microscopic scale.

The use of such exactly calibrated microforce sensors is now gaining increasing importance in the fields of medicine, biology, biophysics and material sciences. Calibrated microforce sensors are, for example, used in cancer research for examining nanomechanical properties of diseased cells. Measuring forces between DNA strands is a further example of use. In recent years an enormous demand for such cantilever calibration has developed worldwide.  In this respect, various metrological national institutes (PTB, NIST, KRISS) have developed calibration devices which are characterized by a partially unsatisfactory measuring accuracy.

Figure 1: Side view of the calibration assembly. The probing sphere and cantilever to be calibrated are presented in details.

Supported by the Federal Ministry of Education and Research, the Inno-Profile project “New fields of application for innovative force measuring and weighing techniques“ was under the scientific leadership and supervision of Dr. Falko Hilbrunner and Dr. Michael Kühnel from the Institute for Process Measurement and Sensor Technology of the TU Ilmenau. High-precision force calibrating devices were developed in the scope of the project with which it is possible to calibrate microscopically small force sensors as, for example, the mentioned cantilevers with a force resolution of one nanonewton, also observing their bend with a sensor resolution of greater than 0.1 nanometers.  Thus, measurement uncertainties occuring with their calibration are achieved of less than one percent, which is a significant improvement compared with the state of the art. The centerpiece of the force calibrating devices are commercial, monolithic-manufactured high-precision weighing systems according to the principle of electromagnetic force compensation (EMFC-weighing systems), adjusted to the specific application. Unlike the actual individual case of determining mass or force, they are also used as high-precision positioning systems when in conjunction with a digital servo control specifically developed for this application. Consequently, the cantelivers in this EMFC-weighing system can be serviced with nanometer resolution and deflected by the displacement Δz, while the acting force is simultaneously determined. Based on the two measurement values, the spring stiffness k of the cantilever is calculated.

In addition, the system covers a laser interferometer for precise displacement measurement. The system is characterized by a compact and cost-efficient assembly. A patent has already been granted for this innovative procedure.

Figure 2: Microscope image and schematic representation of a cantilever affected by the force F and deformed by the displacement Δz. This can be used to calculate the spring stiffness kc of the cantilever as a force-displacement-characteristic.

The very high measurement accuracy has already been confirmed by comparative measurements with PTB.  Measurement deviations are below 0.3 %, which means an improvement by the factor 10 in comparison with the previous state of technology.

Kühnel, M.; Schleichert, J.; Fröhlich, T.: System for traceable calibration of nanonewton forces and force vs. deformation curves. In: Proceedings of the 2016 NCSL International Workshop and Symposium. St. Paul, USA, 2016.

Kühnel, M.; et al: National comparison of spring constant measurements of atomic force microscope cantilevers. In: Measurement facing new challenges / IMEKO TC3 International Conference on Measurement of Force, Mass and Torque; 23 (Helsinki) : 2017.05.30-06.01. - Red Hook, NY : Curran Associates, Inc., ISBN 978-1-5108-4471-1, (2017), S. 222-227



Prof. Dr.-Ing. Thomas Fröhlich
Process Measurement Technology
Department of Mechanical Engineering