  We report the instrumentation and experimental results of a cryogenic
scanning microwave impedance microscope. The microwave probe and the scanning
stage are located inside the variable temperature insert of a helium cryostat.
Microwave signals in the distance modulation mode are used for monitoring the
tip-sample distance and adjusting the phase of the two output channels. The
ability to spatially resolve the metal-insulator transition in a doped silicon
sample is demonstrated. The data agree with a semi-quantitative finite-element
simulation. Effects of the thermal energy and electric fields on local charge
carriers can be seen in the images taken at different temperatures and DC
biases.
