Computational methods for mesoscopic modelling of size-selection in nanoisland growth

In the growth of islands and dots on surfaces there are interesting cases, where size-selection of dots is associated with the kinetically determined metastable state affected by both the energetics and kinetics of the growth. The detailed studies of the growth in these cases have been hampered by computational difficulties due to slow convergence towards the metastable state. In this work, we examine the size selected growth of nanodots by using a mesoscopic reaction kinetic model (RKM) and present an efficient and accurate computational scheme known as the master equation discretization (MED). The computational reliability of the method is tested in a typical case of 2D-nanocluster growth and it is shown that this approach allows us to study in detail the evolution of the size distribution in all stages of the growth from the initial stage, with a high density of small dots, to the final long-lived stationary state.