Cryogenic microwave imaging of metal-insulator transition in doped silicon

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 semiquantitative 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.