Low temperature scanning probe microscopy is a powerful tool for the investigation and manipulation of electrons on the nanometer scale. A capacitively coupled scanning probe microscope tip can be used to study electron motion and charging effects in semiconductor nanostructures at liquid helium temperatures. This technique, known as scanning gate microscopy, provides detailed information on the spatial variation of the underlying electronic properties of these systems.;In this thesis, we present details of the design and construction of the third generation low temperature scanning probe microscope (LT-SPM) built in the Westervelt lab. In addition to standard tip-sample scanning, the implemented design draws on the experiences of the first two generations to incorporate what are assessed to be the most valuable features of each. This design incorporates an extended evacuated cold space for sample and microscope, the ability to apply a 7 T magnetic field to the sample during SPM operation, and a novel low temperature coarse positioning mechanism, all at liquid helium temperatures.;We demonstrate the ability of the LT-SPM to capacitively couple to a nanometer scale patterned gold electrode. Electrostatic force microscopy (EFM) is used to measure forces on the SPM cantilever on the order of 10 nN and rates of change in capacitive coupling per unit length of 0.1 aF/nm. EFM is used to locate the position of a 200 nm isolated electrode and a 30 nm gap between two electrodes at the same potential.;We propose a method to tune the charge state and polarization of a series double quantum dot in a semiconductor nanowire using the LT-SPM tip as a local, moveable, electrostatic gate. The tip-dot interaction is mediated via capacitive coupling, and can thus be controlled with tip position and voltage. Simulations indicate that the LT-SPM has sufficiently high spatial resolution to independently tune the charge of each dot in these systems.
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