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We have performed an extensive set of first-principles self-consistent-field (SCF) pseudopotential total-energy and force calculations for Si (001) - (22) and - (21) surfaces to arrive at an optimized model for the 21 surface. We started with the symmetric dimer model proposed by Abraham and Batra (AB) based on the Stillinger-Weber potential as well as the Yin-Cohen (YC) asymmetric dimer model to carry out the optimization procedure. We confirm the short dimer bond length obtained by YC, unlike in the AB model. However, a symmetric dimer model with a substantial (0. 45) inward relaxation of the top layer is found to be lower in energy than the AB model and is highly competitive with a slightly modified YC model. This supports the use of the symmetric model by Pandey in the construction of the extended defect model and also in the recent spin-unrestricted model calculations. From the 22 cell calculations we conclude that in the small-buckling limit, some energy gain is possible, provided that the dimers are tilted in opposite directions. We also establish that there is no barrier associated with the surface dimer formation but twisting of the dimers is energetically unfavorable. A detailed account of the Hellmann-Feynman forces is given for various structures.
Inder P. Batra (Thu,) studied this question.