The formation of graphene on the (0001) surface of SiC (the Si-face) is studied by atomic force microscopy, low-energy electron microscopy, and scanning tunneling microscopy/spectroscopy. The graphene forms due to preferential sublimation of Si from the surface at high temperature, and the formation has been studied in both high-vacuum and 1 atm argon environments. In vacuum, a few monolayers of graphene forms at temperatures around 1400 degrees C, whereas in argon a temperature of about 1600 degrees C is required in order to obtain a single graphene monolayer. In both cases considerable step motion on the surface is observed, with the resulting formation of step bunches separated laterally by greater than or similar to 10 mu m. Between the step bunches, a layer-by-layer growth of the graphene is found. The presence of a disordered, secondary graphitic phase on the surface of the graphene is also identified. (C) 2010 American Vacuum Society. [DOI: 10.1116/1.3420393]