The Effects of Sample Tilt on Atomic Force Microscopy Deflections

The atomic force microscope (AFM) is used to measure the forces between a probe particle mounted at the end of the flexible AFM cantilever and a given substrate or sample. Most existing models that describe the cantilever deflections in AFM experiments assume the sample is perfectly leveled. However, the samples are rarely, if ever, placed exactly perpendicular to the approach direction of the cantilever. Moreover, AFM cantilevers are typically mounted at a downward angle, resulting in a difference between the vertical deflections registered by the AFM and the deflections of the cantilever. The effects of both sample and cantilever tilt on the deflections obtained for the approach-to-contact (AtC) portion of an AFM deflection-distance curve have not been previously considered. Prior work only considered the impact of cantilever tilt on the deflections obtained for the pull-off (PO) portion of the AFM deflection-distance curve. Using a recently developed model of the AtC and PO, which accounts for both the attractive and repulsive interactions between the probe and sample, as well as the surface roughness of the substrate, we present a computational study of the effects of both sample and cantilever tilt on the AtC and PO deflections. We also perform AFM experiments with probes of two different sizes and a sapphire substrate held at various sample tilt angles. Overall, the experimental results are in good agreement with the predictions of the model. The PO deflections exhibit the expected decrease as sample tilt angle is increased, while the AtC deflections are weakly dependent on sample tilt angle, except at large angles. Both the experiments and model predictions indicate that as long as the sample is leveled as best as possible, sample tilt has no significant effect on the AtC deflections and essentially no impact on the PO deflections.