Modeling of NC-AFM experiments by the utilization of molecular dynamics and the harmonic oscillator model

Abstract

Atomic force microscopy is a widely-used instrument in nanotechnology and nanoscience. Imaging of single molecules, atoms or even bond structures and tip-sample interactions with pm and pN resolution are made possible with non-contact atomic force microscope (NC-AFM) techniques. Since very high resolution imaging is relatively recent and underlying effects are not yet fully understood, interpretation of images can be controversial and may differ. Therefore theoretical modeling is used alongside with experimental work in order to gain a better insight about underlying physical phenomena regarding NC-AFM images and related artifacts. In this thesis work, a simulator for NC-AFM experiments is suggested which utilizes the harmonic oscillator equations for AFM cantilever dynamics and molecular dynamics (MD) for the interaction between tip and sample. For this purpose, a model graphene surface with underlying platinum substrate and a platinum tip is created and their interaction is mapped at different distances with MD techniques. Calculated interaction forces are fitted to polynomials and imported to the harmonic oscillator model. With the harmonic oscillator model and imported interaction data, two different operating modes of NC-AFM are modeled: Constant Height and Topography Scan.When obtained force maps are investigated, tip asymmetry related artifacts are observed. Due to tip asymmetry, a shift in detected atom positions and overall spatial disturbance are observed. Furthermore, the mobility of atoms causes elongation of the tip and a bumpy formation of the sample surface near the tip. Elongation of the tip decreased the overall interaction due to increasing sharpness of the tip. Also an overall noise is detected due to individual, thermally-induced movements of atoms. Obtained NC-AFM scan results were able to map the surface as desired. In constant height mode, more attractive hollow-site regions of graphene are detected via high frequency shifts, as expected. Also due to increasing interaction, closer tip-surface distances resulted in higher frequency shifts. Increasing oscillation amplitudes caused a decrease in the ratio of short-range interactions over the whole oscillation cycle and hence decreased the frequency shift. In the topography scan mode, attractive hollow-site regions are tracked as expected; increasing the set frequency shift also increased the topography corrugation and decreased the mean tip-sample distance. Moreover, non-optimal (too slow or too fast) distance controllers resulted in tracking the surface in an unreliable way and controller-induced noise. With these results, a functional NC- AFM model is demonstrated which is able to satisfactorily simulate NC-AFM experiments.