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