Surface structures of equilibrium restricted curvature model on two fractal substrates

With the aim to probe the effects of the microscopic details of fractal substrates on the scaling of discrete growth models, the surface structures of the equilibrium restricted curvature (ERC) model on Sierpinski arrowhead and crab substrates are analyzed by means of Monte Carlo simulations. These two fractal substrates have the same fractal dimension d_f, but possess different dynamic exponents of random walk z_rw. The results show that the surface structure of the ERC model on fractal substrates are related to not only the fractal dimension d_f, but also to the microscopic structures of the substrates expressed by the dynamic exponent of random walk z_rw. The ERC model growing on the two substrates follows the well-known Family–Vicsek scaling law and satisfies the scaling relations 2α+d_f ≈ z ≈ 2z_rw. In addition, the values of the scaling exponents are in good agreement with the analytical prediction of the fractional Mullins–Herring equation.