  We study a minimal model to understand the formation of clusters on surfaces
in the presence of surface defects. We consider reaction diffusion model in
which atoms undergoes reactions at the defect centers to form clusters. Volume
exclusion between particles is introduced through a drift term in the reaction
diffusion equation that arises due the repulsive force field produced by the
clustering atoms. The volume exclusion terms can be derived from master
equation with a concentration dependent hopping rate. Perturbative analysis is
performed for both cross-exclusion and self-exclusion one dimensional system.
For two dimension numerical analysis is performed. We have found that the
clusterization process slows down due to exclusion. As a result the size of the
clusters reduces. In this model reaction scheme has algebraic nonlinearity and
plausible mechanism is also given.
