Shape-Independent Lateral Force Calibration

Abstract

Current methods for lateral force calibration are often time-consuming, expensive, or cause significant wear of the tip. A quick and simple alternative is presented in which the linear relationship between force and voltage is exploited. The technique is independent of the shapes of the sample and cantilever and eliminates common problems, while maintaining better than 10% precision. This advance will facilitate quantitative comparisons between experiments.

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

“…18). By assuming Amontons' Law for friction and resolving the forces acting on the cantilever, it is possible to calculate the lateral force applied at the tip from the normal load, adhesion, angle of repose of the cantilever, and the surface topography.…”

“…The inputs to the shape independent method 18 are the angle of repose of the cantilever, the flexural force constant, the necessary displacement of the tip in Z to reach the imaging setpoint, the adhesion between the tip and the sample surface and the height and lateral deflection images in trace and retrace directions. The angle of repose is 10 • for the instrument used here, as specified by the manufacturer, in good agreement with our own measurements.…”

“…32 These images were "raw" with no levelling, scaling, resampling, or filtering applied. The calculated values and image text files were then input into the software package developed by Anderson et al 18 and the value of the coefficient of friction iteratively adjusted until the input and fitted values matched to the third significant figure. In some cases it was necessary to crop the images in the fast scan direction in order to remove turnaround effects.…”

“…18 These measurements were repeated for 8 different cantilevers, 4 made from single crystal silicon (All In One (AIO) probes, with aluminium back side coating, BudgetSensors, Bulgaria) and 4 made from silicon nitride with a gold back side coating (OMCL-RC800, Olympus, Japan also referred to as "ORC-8" by some suppliers). Cantilevers of each type are designated as A, B, C, and D, following the manufacturer's convention.…”

“…11 By contrast, other lateral calibration methods have shown strong quantitative agreement when compared with established techniques. [15][16][17] In the work presented here, we experimentally validate the thermal method developed by Wagner et al 11 by comparing it to the shape independent method developed by Anderson et al 18 for a selection of rectangular cantilevers commonly used for lateral force experiments including Lateral Force Microscopy 3 (LFM), Torsional Resonance 19 (TR) mode, and lateral force modulation 20 techniques. We find good quantitative agreement between the two methods, as long as the cantilever geometry is suitable for calibration by the torsional Sader method, that in-plane bending of the cantilever is accounted for and that it is ensured that there is no scaling of the lateral signal between the channel used for thermal noise calibration and the lateral deflection signal recorded in the AFM software.…”