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Abstract

This thesis discusses the development of a novel scanning capacitance microscope (SCM) that enables the investigation of the local capacitance and conductivity of surfaces and near-surface nanostructures at cryogenic temperatures and high magnetic fields.

Simultaneous atomic force microscopy (AFM) and SCM measurements can be made at a temperature of 1.5K and a magnetic field of 12T. The AFM/SCM sensor is based on a quartz-tuning fork with an etched metal tip. SCM measurements are made using an RF tuned filter design which allows changes in capacitance to be measured with sub-attofarad resolution and a bandwidth of 200Hz.

Test measurements were made over an evaporated gold film. The capacitance distance curve was recovered from the measured quantities using a deconvolution scheme normally used for force-distance curves.

Measurements have been made of a two-dimensional electron gas in the quantum Hall effect (QHE) regime. Highly conductive stripes form near the edge of the sample at integer Landau level filling factors in agreement with theoretical predictions. These measurements are the first direct imaging of the compressible stripes at the physical edge of a Hall bar device. Measurements were also made by point spectroscopy in a region that was locally depleted. Around this region a ring-shaped stripe of considerably larger width than at the sample edge is observed. The increased width was explained in terms of a shallower potential gradient compared to the physical edge of the sample.

Preliminary measurements have demonstrated that the microscope is capable of imaging edge states whilst passing current through the device.