Appl. Phys. A 66, S597–S605 (1998) Applied Physics A Materials Science & Processing  Springer-Verlag 1998 Inﬂuence of the topography on adhesion measured by SFM Th. Stifter ∗ , E. Weilandt, O. Marti, S. Hild Abteilung Experimentelle Physik, Universität Ulm, D-89069 Ulm, Germany (Fax: +49-731/502-3036, E-mail: thomas.stifter@physik.uni-ulm.de) Received: 25 July 1997/Accepted: 1 October 1997 Abstract. Surface properties such as adhesion are inﬂuenced by the surface topography. This dependency complicates any quantitative investigation of the material constants. A simple and efﬁcient model is used to calculate the inﬂuence of the to- pography on the pull of force determined by a scanning force microscope (SFM). In the model the SFM tip is represented by a sphere. The sample surface is modeled by two geome- tries: a step on a plane and a blister (spherical cap) on a plane. The atomic interaction between the tip and the surface is of the Lennard–Jones type. The theoretical results are compared with SFM-measurements on highly oriented pyrolytic graph- ite (HOPG) in electrolytic environment. The calculations are in good agreement with the measured images. The SFM has become an indispensable tool for surface in- vestigations on the nanometer scale. With the SFM it is pos- sible to image the sample topography and properties such as friction [1–3], local stiffness [4], the adhesive force [5–8], and magnetic [9] and electrical forces [9]. In order to inves- tigate these properties, specialized measurement modes are used. One main interest in SFM investigations is to determine macroscopic material constants, such as the friction coefﬁ- cient, on a microscopic scale. It has been shown that this is very difﬁcult. To determine the inﬂuence of material param- eters on the measured signals the interaction between the tip and the sample has to be examined. Because material proper- ties are often not directly accessible and the measured signal depends nonlinearly on various parameters, it is necessary to compare simulations and measurements. When formulating a theory, one can have two sometimes contradicting aims: either one focuses on the behavior of the interaction between the tip and the sample or one is interested in explaining the results of a speciﬁc experimental setup. The ﬁrst concept is represented by the theories of Hertz [10], Johnson et al. [11], Derjaguin et al. [12], and Maugis [13]. ∗ Corresponding author These theories describe the interactions necessary to the un- derstanding of the tip–sample system. The second concept is exempliﬁed by the works of Burnham [14] and Rabe [15]. Their goal is to compare computer simulations with a real experiment. The model for the SFM typically consists of a sphere or point mass representing the tip and a plane rep- resenting the sample. However, these simpliﬁcations often make a comparison between the theoretical and the measured results impossible. For example, the representation of the sur- face by a plane is not sufﬁcient if the calculations should describe the dependence on topographical changes. Investi- gating surface properties, e.g. the adhesive force, on a corru- gated sample, one notices that SFM images show a change in the properties correlated with topographical features. The adhesive force often decreases strongly at slopes even if the height differences at the surface are rather small (see SFM images in Fig. 1). It is interesting to explore whether these variations in the adhesive force are mainly inﬂuenced by the curvature of the surface or by a localized variation of chemical bonds, the ar- rangement of the atoms, or molecules at the same place. To investigate these questions, a simple theoretical model of the system SFM tip and sample surface is used in the ﬁrst part of this paper to calculate the topography observed by the tip and the force needed to retract the tip from the sample surface. The theoretical results are compared with SFM measure- ments on highly oriented pyrolytic graphite (HOPG) in the second part of this paper. HOPG is used because of its well- deﬁned surface structure and its easy preparation. 1 The model The model takes into consideration only interactions due to the shape of the tip and surface topography. So only in- teractions describing the topographic inﬂuence are retained. The contribution of the chemical binding or other speciﬁc or steric interactions are not considered. The microscopic inter- action potential between the tip and the surface is the sum of the interactions between the atoms. In our model, atoms are