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Two independent lateral-force calibration methods for the atomic force microscope (AFM)--the hammerhead (HH) technique and the diamagnetic lateral force calibrator (D-LFC)--are systematically compared and found to agree to within 5 % or less, but with precision limited to about 15 %, using four different tee-shaped HH reference probes. The limitations of each method, both of which offer independent yet feasible paths toward traceable accuracy, are discussed and investigated. We find that stiff cantilevers may produce inconsistent D-LFC values through the application of excessively high normal loads. In addition, D-LFC results vary when the method is implemented using different modes of AFM feedback control, constant height and constant force modes, where the latter is more consistent with the HH method and closer to typical experimental conditions. Specifically, for the D-LFC apparatus used here, calibration in constant height mode introduced errors up to 14 %. In constant force mode using a relatively stiff cantilever, we observed an ≈ 4 % systematic error per μN of applied load for loads ≤ 1 μN. The issue of excessive load typically emerges for cantilevers whose flexural spring constant is large compared with the normal spring constant of the D-LFC setup (such that relatively small cantilever flexural displacements produce relatively large loads). Overall, the HH method carries a larger uncertainty, which is dominated by uncertainty in measurement of the flexural spring constant of the HH cantilever as well as in the effective length dimension of the cantilever probe. The D-LFC method relies on fewer parameters and thus has fewer uncertainties associated with it. We thus show that it is the preferred method of the two, as long as care is taken to perform the calibration in constant force mode with low applied loads.

Prototype cantilevers are presented that enable quantitative surface force measurements using contact-mode atomic force microscopy (AFM). The "hammerhead" cantilevers facilitate precise optical lever system calibrations for cantilever flexure and torsion, enabling quantifiable adhesion measurements and friction measurements by lateral force microscopy (LFM). Critically, a single hammerhead cantilever of known flexural stiffness and probe length dimension can be used to perform both a system calibration as well as surface force measurements in situ, which greatly increases force measurement precision and accuracy. During LFM calibration mode, a hammerhead cantilever allows an optical lever "torque sensitivity" to be generated for the quantification of LFM friction forces. Precise calibrations were performed on two different AFM instruments, in which torque sensitivity values were specified with sub-percent relative uncertainty. To examine the potential for accurate lateral force measurements using the prototype cantilevers, finite element analysis predicted measurement errors of a few percent or less, which could be reduced via refinement of calibration methodology or cantilever design. The cantilevers are compatible with commercial AFM instrumentation and can be used for other AFM techniques such as contact imaging and dynamic mode measurements., (© 2011 American Institute of Physics)

The evolution of the atomic force microscope into a useful tool for measuring mechanical properties of surfaces at the nanoscale has spurred the need for more precise and accurate methods for calibrating the spring constants of test cantilevers. Groups within international standards organizations such as the International Organization for Standardization and the Versailles Project on Advanced Materials and Standards (VAMAS) are conducting studies to determine which methods are best suited for these calibrations and to try to improve the reproducibility and accuracy of these measurements among different laboratories. This paper expands on a recent mini round robin within VAMAS Technical Working Area 29 to measure the spring constant of a single batch of triangular silicon nitride cantilevers sent to three international collaborators. Calibration techniques included reference cantilever, added mass, and two forms of thermal methods. Results are compared to measurements traceable to the International System of Units provided by an electrostatic force balance. A series of guidelines are also discussed for procedures that can improve the running of round robins in atomic force microscopy.

This note outlines a calibration method for atomic force microscope friction measurement that uses the "pivot" method of [Bogdanovic et al., Colloids Surf. B 19, 397 (2000)] to generate optical lever sensitivities for known torque applied to rectangular cantilevers. We demonstrate the key calibration parameter to be a linear function of the position at which it is determined along the length of the cantilevers. In this way the optical lever system can be calibrated for cantilever torque by applying loads at locations along the length of a cantilever, away from the integrated tip, so that issues such as tip damage or interference can be avoided.

The colloidal probe technique for atomic force microscopy (AFM) has allowed the investigation of an extensive range of surface force phenomena, including the measurement of frictional (lateral) forces between numerous materials. The quantitative accuracy of such friction measurements is often debated, in part due to a lack of confidence in existing calibration strategies. Here we compare three in situ AFM lateral force calibration techniques using a single colloidal probe, seeking to establish a foundation for quantitative measurement by linking these techniques to accurate force references available at the National Institute of Standards and Technology. We introduce a procedure for calibrating the AFM lateral force response to known electrostatic forces applied directly to the conductive colloidal probe. In a second procedure, we apply known force directly to the colloidal probe using a precalibrated piezo-resistive reference cantilever. We found agreement between these direct methods on the order of 2% (within random uncertainty for both measurements). In a third procedure, we performed a displacement-based calibration using the piezo-resistive reference cantilever as a stiffness reference artifact. The method demonstrated agreement on the order of 7% with the direct force methods, with the difference attributed to an expected systematic uncertainty, caused by in-plane deflection in the cantilever during loading. The comparison establishes the existing limits of instrument accuracy and sets down a basis for selection criteria for materials and methods in colloidal probe friction (lateral) force measurements via atomic force microscopy.

A proof-of-concept study is presented for a prototype atomic force microscope (AFM) cantilever and associated calibration procedure that provide a path for quantitative friction measurement using a lateral force microscope (LFM). The calibration procedure is based on the method proposed by Feiler et al. [Rev. Sci. Instrum. 71, 2746 (2000)] but allows for calibration and friction measurements to be carried out in situ and with greater precision. The modified AFM cantilever is equipped with lateral lever arms that facilitate the application of normal and lateral forces, comparable to those acting in a typical LFM friction experiment. The technique allows the user to select acceptable precision via a potentially unlimited number of calibration measurements across the full working range of the LFM photodetector. A microfabricated version of the cantilever would be compatible with typical commercial AFM instrumentation and allow for common AFM techniques such as topography imaging and other surface force measurements to be performed.

A method for calibrating the stiffness of atomic force microscope (AFM) cantilevers is demonstrated using an array of uniform microfabricated reference cantilevers. A series of force-displacement curves was obtained using a commercial AFM test cantilever on the reference cantilever array, and the data were analyzed using an implied Euler-Bernoulli model to extract the test cantilever spring constant from linear regression fitting. The method offers a factor of 5 improvement over the precision of the usual reference cantilever calibration method and, when combined with the Systeme International traceability potential of the cantilever array, can provide very accurate spring constant calibrations.

A method is presented that allows direct measurement of a wide range of spring constants of cantilevers using an indentation instrument with an integrated optical microscope. An uncertainty of less than 10% can be achieved for spring constants from 0.1 to 10(2) Nm. The technique makes it possible to measure the spring constant at any desired location on a cantilever of any shape, particularly at the tip location of an atomic force microscopy cantilever. The article also demonstrates a technique to detect and correct apparent length anomalies of cantilevers by analyzing spring constants at multiple positions.