Traceable Lateral Force Calibration (TLFC) for Atomic Force Microscopy
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METHODS
Traceable Lateral Force Calibration (TLFC) for Atomic Force Microscopy Arnab Bhattacharjee1 · Nikolay T. Garabedian2 · Christopher L. Evans1 · David L. Burris1 Received: 5 October 2020 / Accepted: 8 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Efforts to reliably measure AFM lateral forces have been impeded by the difficulties in obtaining appropriate calibration standards, applying those force standards to the apex of the tip, and quantifying calibration uncertainty. Here we propose a new method, Traceable Lateral Force Calibration (TLFC), which combines the reliability of direct methods with the convenience of indirect/semi-direct methods. Like other direct methods, ours comprise three essential steps: (1) fabrication of a spring (the Traceable Reference Lever or TRL); (2) calibration of the TRL spring constant; (3) conversion of measurable TRL deflections into absolute lateral force measurements based on its pre-calibrated spring constant (TLFC method). The TRL device, a simple two-axis cantilever, is easy to design, fabricate, and directly pre-calibrate with a standard laboratory microbalance. Following pre-calibration, the TRL device becomes a convenient absolute standard for AFM lateral force measurements. This paper describes the complete method and demonstrates its primary merits, which include (1) traceability to measurement standards; (2) ease of use by outside user groups; (3) absolute measurement errors 1 N/m normal stiffness); (4) robustness over a wide range of common loads, instruments, probes, and environments. While the method and proof-of-concept devices described in this paper were designed primarily for moderate to high load cantilevers (> 1 N/m), we discuss how a next generation of compliant TRL devices can be used with the TLFC method to reliably calibrate arbitrary AFM cantilevers ( 100,000 N/m). N = 3 repeat measurements are shown for the lateral orientation using a representative TRL device in Fig. 2c. This particular cantilever was a hardened 17-4H steel shaft with a diameter of 0.791 ± 0.002 mm and length of 163.5 ± 0.3 mm. In both directions, the response of the cantilever was linear (R2 = 0.999997), predictable (kTRL = 2.70 ± 0.01 N/m measured versus 2.64 ± 0.18 N/m predicted based on nominal material and geometric properties), and repeatable (N = 3 repeats with independent contact probe repositioning on the target).
Before moving to AFM calibration, it is worth reiterating two important advantages of TLFC from the perspective of device calibration. First, as opposed to DLFC spring calibration, which is based on a fit to its free vibration response, TRL spring calibration uses direct and traceable force and displacement measurements of easily quantifiable uncertainties. Second, while DLFC spring constants increase with load due to a reduced levitation gap [14, 15], the lateral spring constant of the TRL is independent of normal and frictional forces when the deformations are within the elastic limits of the device.
2.2 AFM La
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