Scanning single-electron transistor array microscope to probe a two-dimensional electron system under quantum Hall conditions below 40 milli-Kelvin

Abstract

In this thesis a newly built scanning single-electron transistor microscope in a highly vibration damped laboratory environment is presented. The main purpose of this setup is to obtain electrostatic potential distributions of surface near electron systems. Additionally, the microscope is sensitive to changes in capacitance, charge, contact potential, and temperature. One unique feature of this setup is the one-dimensional array of up to eight probing tips with a fixed spacing of 4 µm between them. Furthermore, the combination of its almost negligible influence on the sample while scanning over the surface, as well as its working temperature of less than 40 milli-Kelvin distinguishes it from the few other microscopes of its kind. At the beginning of the thesis the description of the microscope setup and functionality with an extensive characterization can be found. Moreover, electrostatic simulations based on the finite element method are presented to explain and understand measurement data obtained for the tip-sample approach and compensation. In the last sections the calibration technique used to measure Hall potential distributions is explained and the necessary set of measurements for the case of the integer filling factor four is shown. As a prospect for future measurements this microscope allows to obtain Hall potential distributions of samples under fractional quantum Hall conditions. In addition, the microscope is capable of intentionally disturbing the investigated electron system locally and simultaneously determining its response with the neighboring probing tips.