  An off-lattice, continuous space Kinetic Monte Carlo (KMC) algorithm is
discussed and applied in the investigation of strained heteroepitaxial crystal
growth. As a starting point, we study a simplifying (1+1)-dimensional situation
with inter-atomic interactions given by simple pair-potentials. The model
exhibits the appearance of strain-induced misfit dislocations at a
characteristic film thickness. In our simulations we observe a power law
dependence of this critical thickness on the lattice misfit, which is in
agreement with experimental results for semiconductor compounds. We furthermore
investigate the emergence of strain induced multilayer islands or "Dots" upon
an adsorbate wetting layer in the so-called Stranski-Krastanov (SK) growth
mode. At a characteristic kinetic film thickness, a transition from monolayer
to multilayer islands occurs. We discuss the microscopic causes of the
SK-transition and its dependence on the model parameters, i.e. lattice misfit,
growth rate, and substrate temperature.
