Irreversible island nucleation and growth with anomalous diffusion in d>2

Recently, there has been significant interest in the effects of anomalous diffusion on island nucleation and growth. Of particular interest are the exponents χ and χ1 which describe the dependence of the island and monomer density on deposition rate as well as the dependence of these exponents on the anomalous diffusion exponent μ and critical island size. While most simulations have been focused on growth on a 2D and/or quasi-1D substrate, here we present simulation results for the irreversible growth of ramified islands in three-dimensions (d=3) for both the case of subdiffusion (μ<1) and superdiffusion (1<μ≤2). Good agreement is found in both cases with a recently developed theory (Amar and Semaan, 2016) which takes into account the critical island-size i, island fractal dimension df, substrate dimension d, and diffusion exponent μ. In addition, we confirm that in this case the critical value of μ is given by the general prediction μc=2∕d=2∕3. We also present results for the irreversible growth of point-islands in d=3 and d=4 for both monomer subdiffusion and superdiffusion, and good agreement with RE predictions is also obtained. In addition, our results confirm that for point-islands with d≥3 one has μc=1 rather than 2∕d. Results for the scaling of the capture-number distribution (CND), island-size distribution (ISD), and average capture number for the case of irreversible growth with monomer superdiffusion in d=2 are also presented. Surprisingly, we find that both the scaled ISD and CND depend very weakly on the monomer diffusion exponent μ. These results indicate that – in contrast to the scaling of the average capture number which depends on the monomer diffusion exponent μ – both the scaled ISD and CND are primarily determined by the capture-zone distribution, which depends primarily on the “history” of the nucleation process rather than the detailed mechanisms for monomer diffusion.