Dynamical Monte Carlo simulation on response of DAS domain in quenched Si(1 1 1) surface

The response time of the dimer–adatom–stacking-fault (DAS) domain on the Si(1 1 1) surface due to sudden change of the surface temperature is investigated by applying the dynamical Monte Carlo method to a cell model. Some simplifications for transition rates necessary in the dynamical Monte Carlo method are introduced in order to determine their values. Relative values of the transition rates are determined by taking into account atomic configurations at cells in the DAS structure as well as the principle of the detailed balance. In addition all transition rates are assumed to have a pre-factor f exp(−EB/kBT) where T is the surface temperature; f and EB are parameters designating attempt frequency and activation energy, respectively. The time evolution of the DAS domain obtained from the simulation for supercooling shows that the DAS domain grows up with almost constant velocity. When the value of EB is assumed equal to the activation energy of the surface migration of adatoms, the choice of f = 1.7 × 1010 s−1 gives reasonable agreement with the growth velocity observed at supercooling. It is also found in our simulation that the response time of the DAS domain due to the sudden change of the temperature depends scarcely on the initial temperature but mainly on the final temperature. In addition it increases rapidly when the final temperature becomes near the transition temperature. These aspects obtained from our simulation correspond to the characteristics of the response time observed by experiments.