Theoretical study of hydrogen-covered diamond (100) surfaces: A chemical potential analysis

The bare and hydrogen-covered diamond (100) surfaces were investigated through pseudopotential density-functional calculations within the local-density approximation. Different coverages, ranging from one to two, were considered. These corresponded to different structures including 1x1, 2x1, and 3x1, and different hydrogen-carbon arrangements including monohydride, dihydride, and configurations in between. The formation energy of each phase was expressed as a function of hydrogen chemical potential. As the chemical potential increased, the stable phase successively changed from bare 2x1 to (2x1):H, to (3x1):1.33H, and finally to the canted (1x1):2H. Setting the chemical potential at the energy per hydrogen in H$_2$ and in a free atom gave the (3x1):1.33H and the canted (1x1):2H phase as the most stable one, respectively. However, after comparing with the formation energy of CH$_4$, only the (2x1):H and (3x1):1.33H phases were stable against spontaneous formation of CH$_4$. The former existed over a chemical potential range ten times larger than the latter, which may explain why the latter, despite of having a low energy, has not been observed so far. Finally, the vibrational energies of the C-H stretch mode were calculated for the (2x1):H phase.