Multifractal and percolation study on thin film growth with a cell-automata model

A new cell-automata model describing the growth process of cluster by an infection probability is introduced and investigated with Monte Carlo method. The multifractal property and the percolation property are included in this model. Analysis on the surface morphology shows interesting multifractal behavior in great agreement with the experiment AFM images, indicating that this model can simulate a series of film dynamic growth. A novel form of percolation-related phase transition other than power law in traditional scaling theory is also showed by introducing a simple grand canonical ensemble partition function Z(P)Z(P).