A simple and efficient quasi 3-dimensional viscoelastic model and software for simulation of tapping-mode atomic force microscopy.

Santiago D Solares

doi:10.3762/bjnano.6.229

Abstract

This paper introduces a quasi-3-dimensional (Q3D) viscoelastic model and software tool for use in atomic force microscopy (AFM) simulations. The model is based on a 2-dimensional array of standard linear solid (SLS) model elements. The well-known 1-dimensional SLS model is a textbook example in viscoelastic theory but is relatively new in AFM simulation. It is the simplest model that offers a qualitatively correct description of the most fundamental viscoelastic behaviors, namely stress relaxation and creep. However, this simple model does not reflect the correct curvature in the repulsive portion of the force curve, so its application in the quantitative interpretation of AFM experiments is relatively limited. In the proposed Q3D model the use of an array of SLS elements leads to force curves that have the typical upward curvature in the repulsive region, while still offering a very low computational cost. Furthermore, the use of a multidimensional model allows for the study of AFM tips having non-ideal geometries, which can be extremely useful in practice. Examples of typical force curves are provided for single- and multifrequency tapping-mode imaging, for both of which the force curves exhibit the expected features. Finally, a software tool to simulate amplitude and phase spectroscopy curves is provided, which can be easily modified to implement other controls schemes in order to aid in the interpretation of AFM experiments.

Highlights

The quantification of tip–sample dissipation in atomic force microscopy (AFM) has been an ongoing subject of interest since the early days of the technique [1,2]
Given the spherical symmetry of the ideal AFM tip, it is convenient to use polar coordinates, whereby the surface is modeled as a set symmetric AFM tips and surfaces, including a defective tip that has a cluster protruding from its apex
A quasi-3D viscoelastic model, consisting of a 2D array of standard linear solid elements has been proposed for the simulation of AFM imaging of viscoelatic surfaces

Summary

Introduction

The quantification of tip–sample dissipation in atomic force microscopy (AFM) has been an ongoing subject of interest since the early days of the technique [1,2]. The incorrect curvature of the force curve is a serious shortcoming of the 1D SLS model within AFM, because it precludes the quantitative interpretation of the results of an experiment in terms of a real 3D tip interacting with a flat surface, and makes it impossible to extract approximate parameters such as the Young’s modulus [12].

Results

Conclusion