Lever arm of a metallic tip in scanning gate experiments

We present a scanning gate experiment on the electrostatic interaction between a semiconductor quantum dot and the metallic tip of a scanning force microscope. With the help of a feedback mechanism we can map the lever arm of the tip, using the quantum dot in a given quantum state as a sensitive electrometer. Besides the geometrically expected shape at length scales of hundreds of nanometers, we observe fine structure on much shorter length scales.