  With expanding interest in graphene-based electronics, it is crucial that
high quality graphene films be grown. Sublimation of Si from the 4H-SiC(0001)
Si-terminated) surface in ultrahigh vacuum is a demonstrated method to produce
epitaxial graphene sheets on a semiconductor. In this paper we show that
graphene grown from the SiC$(000\bar{1})$ (C-terminated) surface are of higher
quality than those previously grown on SiC(0001). Graphene grown on the C-face
can have structural domain sizes more than three times larger than those grown
on the Si-face while at the same time reducing SiC substrate disorder from
sublimation by an order of magnitude.
