Dynamic scaling behaviors of the Etching model on fractal substrates

The dynamic scaling behaviors of the Etching model on fractal substrates are studied by means of Kinetic Monte Carlo simulations. Surface width and distributions of relative extremal height in the saturated surfaces are calculated respectively. Our results indicate that the structure of the substrates can affect the dynamic scaling properties of the surfaces and interfaces. Specially, the saturated properties of the surface, i.e. the roughness exponents α, are mainly determined by the dynamic exponents of random walk zRW on fractal lattices. In addition, it is shown that the relative extremal height of the saturated surfaces can be fitted by Asym2Sig (asymmetric double sigmoidal) distribution.