Simulation of growth process of thin film on non-planar substrate

In (2 + 1) dimension, growth process of thin film on non-planar substrate in Kuramoto–Sivashinsky model is studied with numerical simulation approach. 15 15 semi-ellipsoids arranged orderly on the surface of substrate are used to represent initial rough surface. The results show that at the initial stage of growth process, the surface morphology of thin film appears to be gridstructure, and the interface width constantly decreases with the growth time, then reaches minimum. However, the grid-structure becomes ambiguous, and granules of different sizes distribute evenly on the surface of thin film with the increase of growth time. Thereafter, the average size of granules and the interface width gradually increase, and the surface morphology of thin film presents fractal properties. The numerical results of height–height correlation functions of thin film verify the surface morphology of thin film to be fractal for a longer growth time. By fitting of the height–height correlation functions of thin film with different growth times, the growth process is described quantitatively