Scaling and crossovers in nano-island decay: A kinetic Monte Carlo study

We have investigated the decay of nanopyramids on crystal surfaces. The decay time of each layer τ as a function of the layer size N is computed within a simple scaling argument. We find that the function is not, in general, a simple power law of the form τ ∼ N^β, but rather that a crossover between different power laws exists. We have then studied a model for pyramidal islands on a Si(1 0 0) surface by using kinetic Monte Carlo simulations. The model includes the effect of the surface reconstruction and symmetry. To probe different scaling regimes, different boundary conditions have been implemented. When periodic boundary conditions are chosen, we observe that the topmost layer extinction time apparently varies as a power of its initial area, with an exponent β = 1.27 ± 0.13. When absorbing boundary conditions are chosen, an apparent exponent β = 0.77 ± 0. 04 is observed. The crossover agrees with the analytical prediction. Experimental results for other systems are discussed.