Unlocking higher harmonics in atomic force microscopy with gentle interactions.

Sergio Santos,Albert Verdaguer,Josep Font,Victor Barcons

doi:10.3762/bjnano.5.29

Abstract

In dynamic atomic force microscopy, nanoscale properties are encoded in the higher harmonics. Nevertheless, when gentle interactions and minimal invasiveness are required, these harmonics are typically undetectable. Here, we propose to externally drive an arbitrary number of exact higher harmonics above the noise level. In this way, multiple contrast channels that are sensitive to compositional variations are made accessible. Numerical integration of the equation of motion shows that the external introduction of exact harmonic frequencies does not compromise the fundamental frequency. Thermal fluctuations are also considered within the detection bandwidth of interest and discussed in terms of higher-harmonic phase contrast in the presence and absence of an external excitation of higher harmonics. Higher harmonic phase shifts further provide the means to directly decouple the true topography from that induced by compositional heterogeneity.

Highlights

It has long been recognized in the community that higher harmonics encode detailed information about the non-linearities of the tip–sample interaction in dynamic atomic force microscopy (AFM) [1,2,3,4,5]
Multiple contrast channels that are sensitive to compositional variations are made accessible
Exact multiple harmonics of the fundamental drive frequency are externally excited above the noise level to open multiple contrast channels that are sensitive to compositional variations

Summary

Introduction

It has long been recognized in the community that higher harmonics encode detailed information about the non-linearities of the tip–sample interaction in dynamic atomic force microscopy (AFM) [1,2,3,4,5]. Exact multiple harmonics of the fundamental drive frequency are externally excited above the noise level to open multiple contrast channels that are sensitive to compositional variations. Once these amplitudes are sufficiently high, the phase shifts Δ have been employed to map the composition through variations in the tip–sample Hamaker constant, H, in Equation 10.

Results

Conclusion