Stability of ordered missing-dimer structures and the ordering dynamics on Si(001)

The stability of (2 x n)-ordered missing-dimer structures on Si(001) and the ordering dynamics of missing dimers are investigated. The surface free energy of (2 x n)-ordered missing-dimer structure was calculated under strains parallel or perpendicular to the dimer row using the Stillinger-Weber potential among Si atoms. The (2 x n)-ordered missing-dimer structure becomes more stable than the (2 x 1)-ordered surface without missing-dimers only if a compressive strain larger than 0.5% is applied parallel to the dimer row. The relaxation process towards the equilibrium configuration of excess missing dimers formed initially at random on the (001) surface was studied by a time-dependent Monte Carlo simulation based on the lattice gas model. The ordering of missing dimers towards the (2 x n) structure evolves via a three-stage relaxation process at 300 K, while it evolves via a one-stage, fast relaxation process at 600 and 900 K. The degree of ordering at equilibrium is significantly improved as the annealing temperature decreases and the missing-dimer concentration increases. The effect of the missing-dimer hopping across the dimer row is also studied. (C) 1998 Elsevier Science B.V.