Calculation of surface energy and simulation of reconstruction for diamond cubic crystals (0 0 1) surface

The energies of the ideal (1 × 1), dimer (2 × 1) and trimer (3 × 1) structures on (0 0 1) surfaces have been calculated by using MEAM for three diamond cubic crystals C, Si and Ge. From energy minimization, the dimer (2 × 1) and trimer (3 × 1) reconstructions can be formed naturally and without any barrier. The dimer corresponding to the lowest energy implies it is the easiest to be formed and the most stable as well. This is consistent with the experimental result and other theoretical prediction. Determined dimer bond length of 2.43 Å for Si drops in the experimental range of 2.20-2.47 Å, and of 2.5 Å for Ge is close to the 2.55 Å measured by X-ray diffraction. The trimer, constructed here firstly, has not been observed in the experimental due to its slightly higher energy than dimer. Its bond lengths have been determined to be 1.96, 2.64 and 2.75 Å for C, Si and Ge, respectively. Further experimental testing is needed.