Low-temperature and high magnetic field dynamic scanning capacitance   microscope
  We demonstrate a dynamic scanning capacitance microscope (DSCM) that operates at large bandwidths, cryogenic temperatures and high magnetic fields. The setup is based on a non-contact atomic force microscope (AFM) with a quartz tuning fork sensor with non-optical excitation and read-out for topography, force and dissipation measurements. The metallic AFM tip forms part of an rf resonator with a transmission characteristics modulated by the sample properties and the tip-sample capacitance. The tip motion gives rise to a modulation of the capacitance at the frequency of the AFM sensor and its harmonics, which can be recorded simultaneously with the AFM data. We use an intuitive model to describe and analyze the resonator transmission and show that for most experimental conditions it is proportional to the complex tip-sample conductance, which depends on both the tip-sample capacitance and the sample resistivity. We demonstrate the performance of the DSCM on metal disks buried under a polymer layer and we discuss images recorded on a two-dimensional electron gas in the quantum Hall effect regime, i.e. at cryogenic temperatures and high magnetic fields, where we directly image the formation of compressible stripes at the physical edge of the sample. 
A. Baumgartner, M.E. Suddards and C.J. Mellor