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

Nic Mullin,Jamie K Hobbs

doi:10.1063/1.4901221

Abstract

Calibration of lateral forces and displacements has been a long standing problem in lateral force microscopies. Recently, it was shown by Wagner et al. that the thermal noise spectrum of the first torsional mode may be used to calibrate the deflection sensitivity of the detector. This method is quick, non-destructive and may be performed in situ in air or liquid. Here we make a full quantitative comparison of the lateral inverse optical lever sensitivity obtained by the lateral thermal noise method and the shape independent method developed by Anderson et al. We find that the thermal method provides accurate results for a wide variety of rectangular cantilevers, provided that the geometry of the cantilever is suitable for torsional stiffness calibration by the torsional Sader method, in-plane bending of the cantilever may be eliminated or accounted for and that any scaling of the lateral deflection signal between the measurement of the lateral thermal noise and the measurement of the lateral deflection is eliminated or corrected for. We also demonstrate that the thermal method may be used to characterize the linearity of the detector signal as a function of position, and find a deviation of less than 8% for the instrument used.

Highlights

Atomic Force Microscopy (AFM)1 is a widely used surface characterization technique that allows both imaging and measurement of tip-surface forces by monitoring the deflection of a flexible cantilever
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
Cantilevers of each type are designated as A, B, C, and D, following the manufacturer’s convention. These cantilevers cover a range of resonant frequencies and force constants, including the typical values used for Lateral Force Microscopy3 (LFM),3 lateral force modulation,20 and Torsional Resonance19 (TR)-mode19 AFM

Summary

Introduction

Atomic Force Microscopy (AFM) is a widely used surface characterization technique that allows both imaging and measurement of tip-surface forces by monitoring the deflection of a flexible cantilever. In the vast majority of instruments, cantilever deflection is measured by the optical lever technique.. In the vast majority of instruments, cantilever deflection is measured by the optical lever technique.4 This gives an output in volts; it is necessary to calibrate the measured cantilever deflection signal into units of force if quantitative data are required. The deflection signal is calibrated into spatial units by performing an approach curve onto a non-compliant surface. The inverse gradient of the contact region of this curve gives the Inverse Optical Lever Sensitivity (InvOLS) in nanometres of tip displacement per volt of detector signal. The deflection voltage may be multiplied by the InvOLS and the force constant to calculate the force

Methods

Results

Conclusion