Island nucleation and growth with anomalous diffusion

While most studies of submonolayer island nucleation and growth have been based on the assumption of ordinary monomer diffusion corresponding to diffusion exponent μ=1, in some cases either subdiffusive (μ<1) or superdiffusive (μ>1) behavior may occur. Here we present general expressions for the exponents describing the flux dependence of the island and monomer densities as a function of the critical island size i, substrate dimension d, island fractal dimension d_{f}, and diffusion exponent μ, where 0≤μ≤2. Our results are compared with kinetic Monte Carlo simulations for the case of irreversible island growth (i=1) with 0≤μ≤2 and d=2 as well as simulation results for d=1, 3, and 4, and excellent agreement is found.