Practical implementation of dynamic methods for measuring atomic force microscope cantilever spring constants

Measurement of atomic force microscope cantilever spring constants (k) is essential for many of the applications of this versatile instrument. Numerous techniques to measure k have been proposed. Among these, we found the thermal noise and Sader methods to be commonly applicable and relatively user-friendly, providing an in situ, non-destructive, fast measurement of k for a cantilever independent of its material or coating. Such advantages recommend these methods for widespread use. An impediment thereto is the significant complication involved in the initial implementation of the methods. Some details of the implementation are discussed in publications, while others are left unsaid. Here we present a complete, cohesive, and practically oriented discussion of the implementation of both the thermal noise and Sader methods of measuring cantilever spring constants. We review the relevant theory and discuss practical experimental means for determining the required quantities. We then present results that compare measurements of k by these two methods over nearly two orders of magnitude, and we discuss the likely origins of both statistical and systematic errors for both methods. In conclusion, we find that the two methods agree to within an average of 4% over the wide range of cantilevers measured. Given that the methods derive from distinct physics we find the agreement a compelling argument in favour of the accuracy of both, suggesting them as practical standards for the field.