  We report a new technique of scanning capacitance microscopy at microwave
frequencies. A near field scanning microwave microscope probe is kept at a
constant height of about 1nm above the samplewith the help of Scanning
Tunneling Microscope (STM) feedback. The microwaves are incident onto the
sample through a coaxial resonator that is terminated at one end with a sharp
tip (the same tip is used to conduct STM), and capacitively coupled to a
feedback circuit and microwave source at the other end. The feedback circuit
keeps the source locked onto the resonance frequency of the resonator and
outputs the frequency shift and quality factor change due to property
variations of the sample. The spatial resolution due to capacitance variations
is $\leq $ 2.5 nm. The microscope is broadband and experiments were performed
from 7 GHz to 11 GHz. We develop a quantitative transmission line model that
treats the tip to sample interaction as a series combination of capacitance and
effective sheet resistance in the sample.
