Nonlinear Behavior of Multiple Cluster Growth Simulated by Monte Carlo Method

Monte Carlo simulations have been carried out to investigate the kinetic growth process of ultrathinfilm. It is found that the area of cluster S(t) grows with time t as t^k , where growth exponent k is less than 1 when averaged from all clusters. The further results indicate that the cluster growth is nonlinear, i.e., the bigger the cluster area S is, the faster it grows (the larger the k). Similar results also show the fractal dimension D increases with the increasing S. Both the slope a of lgk-lgS and the slope δ of 1gD-lgS are positive and related to the nucleation and growth kinetics.