Mound morphology of the 2+1 -dimensional Wolf–Villain model caused by the step-edge diffusion effect

Abstract

The mound morphology of the 2+1-dimensional Wolf–Villain model is studied by numerical simulation. The diffusion rule of this model has an intrinsic mechanism, i.e., the step-edge diffusion, to create a local uphill particle current, which leads to the formation of the mound. In the simulation, a noise reduction technique is employed to enhance the local uphill particle current. Our results for the dynamic exponent 1 / z and the roughness exponent α obtained from the surface width show a dependence on the strength of the step-edge diffusion. On the other hand, λ ( t ) , which describes the separation of the mounds, grows as a function of time in a power-law form in the regime where the coalescence of mounds occurs, λ ( t ) ∼ t n , with n ≈ 0.23 – 0.25 for a wide range of the deposition conditions under the step-edge diffusion effect. For m = 1 , a noise reduction factor of unity, the behavior of λ ( t ) in the saturated regime is also simulated. We find that the evolution behavior of λ ( t ) in the whole process can be described by the standard Family–Vicsek scaling.