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 ${\mathrm{sp}}^2$ and ${\mathrm{sp}}^3$ hybrids coexist: e.g., it provides a qualitative account of the step energy order without detailed calculation. Our findings agree with experimental observations.

• Received 26 March 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.026101