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

Abstract

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.

A non-contact, thermal noise based method for the calibration of lateral deflection sensitivity in atomic force microscopy

“…P white is the frequency independent background noise of the detection system and S(f) is the PSD of a damped harmonic oscillator driven by white noise, given by 6,21,23,24 …”

Nanomechanics of Amyloid Materials Studied by Atomic Force Microscopy

“…Therefore, it is necessary to calibrate the spring constant for each probe used. There are several methods to determine the spring constant of the cantilever with similar uncertainties (Cook, et al, 2006;Gibson et al, 2005;Ohler, 2007). The most commonly used calibration method is the thermal noise method, which has an uncertainty of 5% (Ohler, 2007).…”

A virtual instrument to standardise the calibration of atomic force microscope cantilevers

“…This is often performed in situ with the cantilever loaded into the AFM using a number of methods; see Ref. [1][2][3][4] for reviews. The requirement for calibration stems from well-known variability in the material and dimensional properties (particularly thickness) of commercially available cantilevers.…”

“…Based on early reports of these calibration methods and more recent research that include an inter-laboratory study [1][2][3][4][5][6][7], error estimates for their operation have been formulated. Such (averaged) estimates are typically used to quantify the accuracy of individual force measurements, but do not account for the variation of measurement uncertainty between different users and laboratories.…”

“…While applicable to any cantilever, spring constant measurements from this method are known to depend on several factors including the laser spot size and position, z-displacement piezo calibration, static-to-dynamic optical lever sensitivity and nonlinearity in the deflection curve on hard contact [1][2][3][4][5][6]9, 10]. Thus, variations in calibration accuracy can easily emerge between laboratories and even different users within a single laboratory.…”