  We introduce an off-lattice model with continuous particle distances and
pair-potential interactions which allows for the efficient simulation of
strained heteroepitaxial growth by means of kinetic Monte Carlo (KMC)
simulations. We discuss in detail the application of our model to the
simulation of three important strain relaxation mechanisms: First, the
formation of misfit dislocations in strained adsorbate films is investigated.
We find a power-law misfit dependence of the critical layer thickness, in
agreement with various experimental studies. Second, we study the
self-assembled island formation on a thin adsorbate wetting-layer
(Stranski-Krastanov growth). We show that an increased diffusion barrier on the
substrate is a possible kinetic reason for the formation of a stable
wetting-layer. The formation of islands can be ascribed to a partial relaxation
of adsorbate material which affects the diffusion barriers for adsorbate
particles. The dependence of island size and density on misfit, temperature and
particle flux is in good qualitative agreement with metal-organic vapor phase
epitaxy experiments. Finally, we consider surface alloying as strain relaxation
mechanism in multi-component systems. Equilibrium simulations show that the
competition between binding and strain energy yields regular stripe patterns.
Under non-equilibrium conditions we find pattern formation as well as the
experimentally observed island ramification. The comparison with a lattice gas
model shows that the stripe formation can solely be due to kinetic effects but
the misfit is essential for the ramification and stabilization of the surface
structures.
