Si diffusion path for pit-free graphene growth on SiC(0001)

Abstract

Density functional theory calculations reveal that the interfacial 6$\sqrt{3}$ \ifmmode\times\else\texttimes\fi{} 6$\sqrt{3}$ structure [a warped graphene layer with periodic inclusions of pentagon-hexagon-heptagon (H${}_{5,6,7}$) defects] facilitates a Si diffusion path vertically through the interface layer during epitaxial growth of graphene on SiC(0001). The calculated diffusion barrier is 4.7 eV, competitive with Si interstitial diffusion of \ensuremath{\sim}3.5 eV in SiC [M. Bockstedte et al., Phys. Rev. B 68, 205201 (2003)]. Scanning tunneling microscopy study shows that, for growth in an Ar background, where Si desorption is suppressed and all diffusion channels contribute, graphene films with reduced pit density can be grown on nominally flat SiC substrates. On the other hand, for Si diffusion-limited growth in ultrahigh vacuum, the Si interstitial diffusion is the energetically favorable path where the step edges serve as the necessary outlet toward Si desorption. The much higher density of step edges on vicinal substrates also facilitates the growth of pit-free graphene.