  We present a scanning tunneling spectroscopy (STS) study of the local
electronic structure of single and bilayer graphene grown epitaxially on a
SiC(0001) surface. Low voltage topographic images reveal fine, atomic-scale
carbon networks, whereas higher bias images are dominated by emergent spatially
inhomogeneous large-scale structure similar to a carbon-rich reconstruction of
SiC(0001). STS spectroscopy shows a ~100meV gap-like feature around zero bias
for both monolayer and bilayer graphene/SiC, as well as significant spatial
inhomogeneity in electronic structure above the gap edge. Nanoscale structure
at the SiC/graphene interface is seen to correlate with observed electronic
spatial inhomogeneity. These results are important for potential devices
involving electronic transport or tunneling in graphene/SiC.
