Noncontact Method for Calibration of Lateral Forces in Scanning Force Microscopy

Abstract

This paper describes a noncontact calibration procedure for lateral force microscopy in air and liquids. The procedure is based on the observation that the sensitivity of a force microscope may be calibrated using the raw thermal noise spectrum of the cantilever and its known spring constant, which can be found from the same uncalibrated thermal noise spectrum using Sader's method (Rev. Sci. Instrum.1999, 70, 3967-3969). In addition to the power spectrum of the cantilever thermal noise, this noncontact calibration method only requires knowledge of the plan view dimensions of the cantilever that could be measured using an optical microscope. This method is suitable for in situ force calibration even in viscous fluids through a two-step calibration procedure, where the cantilever thermal spectra are captured both in air and in the desired liquid. The lateral calibration performed with the thermal noise technique agrees well with sensitivity values obtained by the wedge calibration procedure. The approach examined in this paper allows for complete calibration of normal and lateral forces without contacting the surface, eliminating the possibility for any tip damage or contamination during calibration.

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

“…Under these assumptions correction for the difference in statically and dynamically deflected cantilevers is unnecessary. A similar conclusion was reached by Wagner et al, 11 and may also be reached by examining the mode shapes of cantilevers subjected to a static torque at their free end 29 and cantilevers free to oscillate torsionally. 30 In cases where the laser or tip is not at the end of the cantilever, a correction factor may be calculated from the tip setback, laser position, and respective mode-shapes.…”

“…Below we describe the measurements carried out to obtain γ tors by both the thermal noise method 11 and the shape independent method. 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).…”

“…12,13 Comparison of the thermal method with the well-established wedge method 14 showed qualitative agreement with significant deviations. 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.…”

“…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.…”

Solvent-induced immiscibility of polymer brushes eliminates dissipation channels

“…The stroke length is much larger than the swollen brush height of h brush E600 nm or the colloidal diameter. We calibrate the normal stiffness of our cantilevers using the thermal noise method as implemented in the Nanoscope 8 software (typically k n ¼ 0.4 N m À 1 ) and the torsional stiffness and sensitivity using the method of Wagner et al 30 (typical stiffness k l ¼ 65 N m À 1 ). After the experiments, the cantilevers are characterized with the high-resolution scanning electron microscope (HR-SEM Zeiss LEO 1550) to obtain the exact dimensions of the colloid and the cantilever (typical length l ¼ 470 mm, width w ¼ 60 mm and thickness t ¼ 3 mm).…”