  Previous experimental observations for H intercalation under graphene on SiC
surfaces motivate clarification of configuration stabilities and kinetic
processes related to intercalation. From first-principles
density-functional-theory (DFT) calculations, we analyze H adsorption and
intercalation for graphene on a 6H-SiC(0001) surface, where the system includes
two single-atom-thick graphene layers: the top-layer graphene (TLG) and the
underling buffer-layer graphene (BLG) above the terminal Si layer. Our chemical
potential analysis shows that, in the low-H coverage regime (described by a
single H atom within a sufficiently large supercell), intercalation into the
gallery between TLG and BLG, or into the gallery underneath BLG, is more
favorable thermodynamically than adsorption on top of TLG. However,
intercalation into the gallery between TLG and BLG is most favorable. We obtain
energy barriers of about 1.3 eV and 2.3 eV for a H atom diffusing on and under
TLG, respectively. From an additional analysis of the energy landscape in the
vicinity of a step on the TLG, we assess how readily one guest H atom on the
TLG terrace can directly penetrate the TLG into the gallery between TLG and BLG
versus crossing a TLG step to access the gallery. We also perform DFT
calculations for higher H coverages revealing a shift in favorability to
intercalation of H underneath BLG, as well as characterizing the variation with
H coverage in interlayer spacings.
