The morphology of graphene formed on the (000 1̄) surface (the C-face) and the (0001) surface (the Si-face) of SiC, by annealing in ultrahigh vacuum or in an argon environment, is studied by atomic force microscopy and low-energy electron microscopy. The graphene forms due to preferential sublimation of Si from the surface. In vacuum, this sublimation occurs much more rapidly for the C face than the Si face so that 150°C lower annealing temperatures are required for the C face to obtain films of comparable thickness. The evolution of the morphology as a function of graphene thickness is examined, revealing significant differences between the C face and the Si face. For annealing near 1320°C, graphene films of about 2 monolayers (MLs) thickness are formed on the Si face but 16 ML is found for the C face. In both cases, step bunches are formed on the surface and the films grow continuously (carpetlike) over the step bunches. For the Si face, in particular, layer-by-layer growth of the graphene is observed in areas between the step bunches. At 1170°C, for the C face, a more three-dimensional type of growth is found. The average thickness is then about 4 ML but with a wide variation in local thickness (2-7 ML) over the surface. The spatial arrangement of constant-thickness domains are found to be correlated with step bunches on the surface, which form in a more restricted manner than at 1320°C. It is argued that these domains are somewhat disconnected so that no strong driving force for planarization of the film exists. In a 1 atm argon environment, permitting higher growth temperatures, the graphene morphology for the Si face is found to become more layer by layerlike even for graphene thickness as low as 1 ML. However, for the C face the morphology becomes much worse, with the surface displaying markedly inhomogeneous nucleation of the graphene. It is demonstrated that these surface are unintentionally oxidized, which accounts for the inhomogeneous growth. © 2010 The American Physical Society.