Numerical Simulations Of Growth Surface Roughness And Extremal Height Of The Restricted Solid-on-solid Model On Several Typical Fractal Substrates

In recent years, The extensive research to the kinetic growth phenomenon in experimtal and theoretical have been studied and obtained valuable results. The structure of substrate has an important influence on behaviors of the growth surface.Particularly, the affect of the structure of fractal substrate on the properties of growing surface attracted great interest. By analyzing the dynamic behavior of the discrete growth model on different substrates, we investigated the influence of structures of fractal substrates on the dynamical properties of a discrete growth model.In order to investigate the influence of structures of substrates on the dynamic properties of the restricted solid-on-solid model, the surface roughness and extremel height distribution of the restricted solid-on-solid model for Sierpinski arrow and Crab with the same fractal dimension and Koch curve and Koch lattice with the similar random walk dimension, are studied by means of Monte Carlo numerical simulations in this article.The results show that the restricted solid-on-solid model on Sierpinski arrow and Crab fractal substrates exhibit excellent dynamic scaling behavior, and the well-estabilished Family-Vicsek is still satisfied. It is shown that the scaling exponents calculated on fractal substrates are different. The scaling behavior of discrete growth models on fractal substrates is affected by fractal structure and different spectrum dimensions result in different surface properties of the surface width. Furthermore, the saturated surface growth height can not satisfy the three kinds of usual extreme statistical distribution, which are Weibull, Gumbel and Frechet extreme value statistical distribution, but fitted the Asym2 Sig distribution. While both the Koch curve and Koch lattice substrates have different fractal dimension and spectral dimension. we calculated the date and got the same roughness index within the error on two fractal substrates. The saturated surface height maximum(height minimum) on two fractal substrates with similar statistical distribution can well collapse together and are also fitted by the Asym2 Sig distribution. It means that the random walk dimension mainly affects the saturation properties of the discrete model.