Cantilever Spring-Constant Calibration in Atomic Force Microscopy

Abstract

The measurement of small forces by atomic force microscopy (AFM) is of increasing importance in many applications. For example, in analytical applications where individual molecules are probed, or nanoindentation measurements as a source of information about materials properties on a nanometer scale. The fundamentals of AFM force measurement, and some of these applications, are briefly reviewed. In most cases absolute, not relative, measurements of forces are needed for valid comparisons with theory and other measurement techniques (such as optical tweezers). We review methods of AFM force calibration and the major uncertainties involved. The force range considered in this work is roughly from 10 pN to around 500 nN. We describe some issues of the repeatability of force measurements that can be important in common AFM instruments. In most cases the aspect that then limits the accuracy with which forces can be measured is the uncertainty in the stiffness (more specifically the normal force constant) of the atomic force microscope cantilever at the center of the instrument. It is known that commercially available microfabricated atomic force microscope cantilevers have a wide range of force constant, for cantilevers of nominally the same type and even the same production batch. Calibration is necessary, and many methods have been used over the years. We compare the accuracy that can be achieved and the ease of use of these different methods, including theoretical (dimensional), thermal, static and dynamic methods and their variants. A device developed at NPL should help overcome many of the problems of force constant calibration, at least for the most common AFM configurations. This is a microfabricated silicon device, which, because of its very small mass, is not susceptible to vibration as a larger device would be. A new calibration method based on electrical and Doppler measurements allows the calibration of the force constant of this device traceable to the SI newton. It can then be sent to AFM users for straightforward calibration of AFM force constants. We conclude with a brief discussion of the special problems of calibration of lateral forces, such as those obtained in frictional force measurements.