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The electrical properties of mesoscopic devices have been investigated by passing current and measuring voltages through macroscopic current and voltage probes. Microscopic properties such as the probability
density distribution of electrons inside a quantum dot have, however, remained elusive. Here we use scanning gate microscopy (SGM) where the conducting tip of a scanning force microscope acts as a movable gate to study quantum dots realized in AlGaAs heterostructures. In general we find concentric rings in the scanning gate images indicating the equipotential lines of the tip induced potential at the location of the quantum dot. We have extended these experiments at temperatures down to 100 mK to a quantum dot which is electrostatically coupled to a quantum point contact read-out. In this case both the current through the dot as well as through the point contact are imaged as the tip scans across the sample. This way we identify the contributions of individual charging events of the dot as well as of neighboring impurity sites. We fabricated a special quantum dot covered with a homogeneous top gate except for the location of the dot, where the metallic top gate is opened by an oxide spot. This way we can minimize the influence of the impurity charging events.
We have used a quantum dot in the Coulomb blockade regime and a novel feedback mechanism to map the potential induced in the dot by the tip of a scanning force microscope with high resolution. We find that the tip-induced potential consists of a repulsive part that depends on tip bias and an attractive part that is independent of tip bias. We could also map the spatial variation of the tip’s lever arm under least invasive conditions. While results for the tip-induced potential were independent of the quantum state used, the lever arm showed fine structure that could be the “quantum fingerprint” of a given state. We discuss the necessary conditions for imaging of probability densities of individual quantum states in quantum dots.
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