Simulations of denuded-zone formation during growth on surfaces with anisotropic diffusion

We have investigated the formation of denuded zones during epitaxial growth on surfaces exhibiting anisotropic diffusion of adparticles, such as Si(001)-231, using Monte Carlo simulations and a continuum model. In both the simulations, which were mainly for low-temperature cases ~small critical clusters!, and the continuum model, appropriate for high-temperature cases ~large critical clusters!, it was found that the ratio of denuded-zone widths W f and Ws in the fastand slow-diffusion directions scales with the ratio D f /Ds of the diffusion constants in the two directions with a power of 1/2, i.e., W f /Ws'(D f /Ds) , independent of various conditions including the degree of diffusion anisotropy. This supplies the foundation of a method for extracting the diffusion anisotropy from the denuded zone anisotropy which is experimentally measurable. Further, we find that unequal probabilities of a diffusing particle sticking to different types of step edges @e.g., SA and SB steps on Si~001!# does not affect the relation W f /Ws'(D f /Ds) 1/2 seriously unless the smaller of the two sticking probabilities is less than about 0.1. Finally, we examined the relation between the number of steps and the number of sites visited in anisotropic random walks, finding it is better described by a crossover from one-dimensional to two-dimensional behavior than by scaling behavior with a single exponent. This result has bearing on scaling arguments relating denuded-zone widths to diffusion constants for anisotropic diffusion.