Step-edge instability during epitaxial growth of graphene from SiC(0001)

A continuum equation for step motion is used to explain fingerlike structures observed when graphene is grown epitaxially by step flow decomposition of SiC(0001). A linear stability analysis predicts when a morphological perturbation of a straight moving step grows or decays as a function of growth temperature, the background pressure of Si maintained during growth, and the presence of an inert buffer gas used to retard the escape of Si atoms from the crystal surface. The theory gives semiquantitative agreement with experiment for the characteristic separation between fingers observed when graphene is grown in a low-pressure induction furnace or under ultrahigh vacuum conditions. A local heating mechanism is proposed as the driving force for instability.