Scaling properties of surface growth on rough substrates generated by standard models

In surface growth simulations, usually the substrate is initially considered smooth with no roughness. But as known in reality, many substrates in nature are initially rough. In this article, we study the sensitivity of dynamic scaling of different models on rough substrates generated by standard surface growth models. We implement the three growth procedures which are as follows; for the first two procedures two separate substrates are grown with the Random deposition (RD) and Restricted solid on solid (RSOS) for different time steps t1 before growing them both with the Ballistic deposition model (BD). But in the third growth procedure, as an inverse of the second procedure, particles deposit on the substrates by the BD model and become rough by the RSOS model. We conclude that the surfaces need a characteristic growth time (tx) to lose information about the substrate. We show that the characteristic time depends on both the time needed for roughening the substrate and the special surface growth models. In addition, we show that the dependence of the two parameters ‘tx’ and ‘t1’ is a power law dependence only for adequate short times of t1 which is also calculated.