Modeling elastic and plastic relaxation in silicon-germanium heteroepitaxial nanostructures

My Ph. D. work led to the development of numerical methods devoted to the study of elastic and plastic relaxation in SiGe/Si (001) heteroepitaxial nanostructures. The meth- ods were successfully applied to the study of self-assembled nanostructures arising from the heteroepitaxial growth of Ge (or SiGe alloys) on Si substrate (three dimensional islands and thin films). First of all, I studied the mechanisms allowing for elastic relaxation. Tuning the initial condition, it was possible to calculate with Finite Element Method the elas- tic field in SiGe islands. Then the variation of compositional profile, observed during the three dimensional growth, were determined by an ad hoc Monte Carlo algorithm coupled with FEM. My main contributions, however, were in the field of plastic relaxation and the study of dislocations in nanostructures. First I developed a novel approach to handle misfit dislocation in nanostructures in the FEM framework. The developed method allows for determining the elastic field of dislocations in small size object, where the extended defects deeply interact with free surfaces and interfaces. It was shown how my novel computational strategy can be applied to the study of the plastic relaxation onset (introduction of the first dislocations) in Ge/Si islands, finding an excellent agreement with experimental data. Fur- thermore we depicted how by proper patterning of the Si (001) substrate it is possible to predict dislocation confinement, as confirmed experimentally by AFM and TEM analysis, in prescribed areas of the heteroepitaxial system, opening a viable path for dislocation en- gineering. Then, I adapted the microMegas dislocation dynamics (DD) code to dislocation propagation in nanostructures. The DD code was originally designed to study the time evolution of extended defects in bulk system. I therefore introduced suitable modifications for treating free surfaces and for handling the propagation of threading arms (dislocation touching free surfaces) in the system. Simulations performed in overgrown islands, predict a dislocation pattern at the SiGe island extremely similar to the experimentally observed dislocation microstructure.