Quantitative dynamic force microscopy with inclined tip oscillation

Abstract

In the mathematical description of dynamic atomic force microscopy (AFM), the relation between the tip–surface normal interaction force, the measurement observables, and the probe excitation parameters is defined by an average of the normal force along the sampling path over the oscillation cycle. Usually, it is tacitly assumed that tip oscillation and force data recording follows the same path perpendicular to the surface. Experimentally, however, the sampling path representing the tip oscillating trajectory is often inclined with respect to the surface normal and the data recording path. Here, we extend the mathematical description of dynamic AFM to include the case of an inclined sampling path. We find that the inclination of the tip movement can have critical consequences for data interpretation, especially for measurements on nanostructured surfaces exhibiting significant lateral force components. Inclination effects are illustrated by simulation results that resemble the representative experimental conditions of measuring a heterogeneous atomic surface. We propose to measure the AFM observables along a path parallel to the oscillation direction in order to reliably recover the force along this direction.

Signal generation in dynamic interferometric displacement detection

“…This two-step procedure allows to determine all signal parameters with high accuracy. As the interferometric method is perfectly suited for the calibration of the cantilever oscillation amplitude, we exemplify the fit procedure and accuracy limits for the fit parameter 𝐴. Amplitude calibration means to relate the cantilever oscillation amplitude 𝐴 to the voltage 𝑉 𝑒𝑥𝑐 to yield the calibration factor 𝑆 = 𝐴/𝑉 𝑒𝑥𝑐 [14]. An accurate calibration is essential for quantitative NC-AFM and, therefore, various methods have been suggested to determine the calibration factor [10,[18][19][20][21].…”