Tip and surface properties from the distance dependence of tip–surface interactions

Macroscopic “background” interactions, such as van der Waals and electrostatic forces, determine the frequency change in non-contact atomic force microscopy (NCAFM). We demonstrate that by analysing the distance dependence of these interactions one can extract more information about the tip radius, charge and chemical composition, as well as about the surface charging and conductivity. For this purpose we calculate the interaction of different NC-AFM tips with a charged and neutral CaF2 (111) surface and with an ideal metal surface. Force versus distance curves demonstrate a remarkably different behaviour, especially at long distances, dependent on whether the tip is conductive, oxidised or charged. Comparison with experimental curves proves that this analysis can predict tip properties. PACS: 68.37.Ps; 68.35.Dv; 61.50.Ah; 61.72Bb Many interpretation problems in non-contact atomic force microscopy (NC-AFM) experiments are due to the lack of physical information about the tip, surface and tip–surface interaction. In general, experiments cannot identify resolved features and theory cannot help without more information about the tip and surface structures [1, 2]. Atomic-scale contrast in NC-AFM images is determined by relatively small spatial variations (of the order of 1 Hz) in the cantilever frequency change. The overall frequency change itself is determined mainly by “background” van der Waals and electrostatic forces, as reviewed in [3]. We will demonstrate that by analysing the distance dependence of these forces one can extract more information about the tip radius, charge and chemical composition, as well as the surface properties. There has been a number of previous studies of force versus distance curves. Recent theoretical and experimental studies on semiconductors [4–7] and insulators [8] have used short-range force versus distance curves to analyse the mechanism of contrast and the changes in interactions over ∗Corresponding author. (E-mail: [email protected]) NC-AFM 2000 – Third International Conference on Non-Contact Atomic Force Microscopy, July 16–19, 2000 in Hamburg, Germany different surface sites. Analysis of the tip–surface interaction at longer-range has also been performed [9, 10], but the possible components of the long-range interaction were not studied in detail. Recent experimental studies [11, 12] have tried to separate out the tip–surface interaction components. These studies assume that any electrostatic interaction has been compensated for by applied bias and the tip–surface interaction is van der Waals alone. However, they were unable to explain the unphysically long-range chemical forces needed to fit the strength of interaction at medium range. It has been shown previously [3, 13, 14] that many other interactions can be significant in AFM, and van der Waals is rarely the sole component of the long-range tip–surface interaction. In fact, it is the other components of the tip–surface interaction which often hold the most information about the tip and surface structure. The image force, for example, depends crucially on the conduction and oxidation of the tip, whereas the van der Waals interaction is dominated by the tip radius. The aim of this theoretical study is to find better ways of characterising tips and surfaces by systematically using frequency change versus distance curves. We consider two generic cases prompted by our attempts to understand the experimental NC-AFM data on insulating and metallic surfaces. Firstly, the tip interaction with the surface of bulk insulator calcium difluoride (111) has been studied. We demonstrate that, by analysing frequency change versus distance curves after scanning, one should be able to distinguish between the interaction due to a very blunt tip or an electrostatic interaction of a charged tip and surface. Secondly, we suggest that one can use the tip interaction with a well-characterised metal surface in order to find out more about the tip structure, conductivity and charge. By comparing tip–surface interactions for different tip types, characteristic tip “fingerprints” can be established. These fingerprints can be then compared to experimental results on metal surfaces and used to predict the chemical and physical properties of the tip.