Stochastic theories and scaling relations for early-stage surface growth

Recent theories for the surface growth are reviewed, which describe the nucleation kinetics of binary alloys in the first layer and the nucleation on top of islands in the second layer. In the first part, describing the submonolayer regime, scaling relations for the number density of stable islands in dependence of the growth parameters are derived from an extension of the classical rate equation approach to binary systems. In the second part a general stochastic theory is presented that allows one to predict whether thin films become smooth or rough under non-equilibrium growth conditions.