  We have performed optical microscopy, micro-photoelectron spectroscopy, and
micro-Raman scattering measurements on Y$_{0.63}$Ca$_{0.37}$TiO$_3$ single
crystals in order to clarify the interplay between the microstructure and the
temperature dependent electronic transport mechanisms in this material. Optical
microscopy observations reveal dark and bright domain patterns on the surface
with length scales of the order of several to a hundred micrometers showing a
pronounced temperature dependent evolution. Spatially resolved photoelectron
spectroscopy measurements show the different electronic character of these
domains. Using micro-Raman spectroscopy, we observe a distinct temperature
dependence of the crystal structure of these domains. On the basis of these
findings the different domains are assigned to insulating and metallic volume
fractions, respectively. By decreasing the temperature, the volume fraction of
the conducting domains increases, hence allowing the electrons to percolate
through the sample at temperatures lower than $\sim$150 K.
