We present a detailed experimental study on the electrostatic interaction between a quantum dot and the metallic tip of a scanning force microscope. Our method allowed us to quantitatively map the tip-induced potential and to determine the spatial dependence of the tips lever arm with high resolution. We find that two parts of the tip-induced potential can be distinguished, one that depends on the voltage applied to the tip and one that is independent of this voltage. The first part is due to the metallic tip while we interpret the second part as the effect of a charged dielectric particle on the tip. In the measurements of the lever arm we find fine structure that depends on which quantum state we study. The results are discussed in view of scanning gate experiments where the tip is used as a movable gate to study nanostructures.
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