Bond-counting rule for carbon and its application to the roughness of diamond (001).

Despite that carbon is tetravalent identical to silicon, first-principles calculations reveal that stable step structures on diamond (001) are entirely different from those on silicon. Moreover, pristine Si(001) is flat; pristine diamond (001) could be rough due to negative step formation energies. A generic bond-counting rule is established, which should apply to most carbon structures where sp2 and sp3 hybrids coexist: e.g., it provides a qualitative account of the step energy order without detailed calculation. Our findings agree with experimental observations.