Crossover from Anisotropic-to-Isotropic Diffusion-Mediated Island Growth on Surfaces

We consider processes involving irreversible nucleation and growth of two-dimensional islands during submonolayer deposition, mediated by anisotropic diffusion. If h|| and h⊥ are hop rates in orthogonal directions, we set e = h⊥/h|| 1 and examine the decrease of the island density with increasing h||. We find a crossover from scaling characteristic of anisotropic diffusion to that characteristic of isotropic diffusion at h|| ~ r2te-2, where r is the deposition rate and t is time. For Si-on-Si(001) deposition with r = 1/600 MLs-1, this crossover should occur around 450 K.