  It is important for modern scanning microwave microscopes to overcome the
effect of the surface roughness. Here, we report microwave conductivity imaging
of the phase-separated iron chalcogenide K$_x$Fe$_y$Se$_2$ ($x=0.8$,
$y=1.6$-$2$), in which electric conductivity-induced contrast is distinguished
from topography-induced contrast using a combination of a scanning tunneling
microscope and a scanning microwave microscope (STM-SMM). We observed the
characteristic modulation of the local electric property that originates from
the mesoscopic phase separation of the metallic and semiconducting phases in
two different scanning modes: constant current (CC) mode and constant $Q$ (CQ)
mode. In particular, CQ scanning is useful because we obtain a qualitative
image in which the topographic contrast is largely eliminated without
degradation of the spatial resolution.
