Solution of Master and Fokker-Planck equations by propagator methods, applied to Au/NaCl thin film nucleation

Novel numerical solutions of Master and Fokker-Planck equations are described and compared for equivalent discrete and continuous problems. The two methods involve the calculation of long-time-step propagator matrices, whose single application is equivalent to many iterations of a finite difference scheme. For the discrete method we present two analytic propagators which are exact for growth-only (no decay) processes, and two approximate propagators for growth and decay processes. The continuous method couples a discrete boundary condition for small clusters with an efficient continuous description for large clusters. These two methods are applied to the nucleation and growth of vapor-deposited thin films whose atoms cluster together to form islands (Volmer-Weber growth). Mobility coalescence of islands is included to show how "slow" nonlinear processes may be included in the model.