Crystal Growth Theory with considerations of strain

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Since it became possible to observe clean and flat surface in an atomic resolution, various growth modes are identified on the singular surface during heteroepitaxy, and morphological instabilities of steps are found an a vicinal surface. These self assembled nano structures are caused by the elastic strain in the crystal. So far the continuum elasticity (CE) approximation is used for the analysis, but for a crystal growth where a single atom processes as impingement or desorption are essential, an atomic-level model for elasticity is required. In the present project, I propose an elastic lattice model, and obtain interactions between surface defects as steps to detect the limit of CE theory. Furthermore, the effect of step interaction mediated by the strain is studied on the dynamical instabilities.Interaction induced by strain extends long-range, but for a thin substrate it is cut off at a separation about the thickness. On the other hand, thick substrate requires long CPU time for numerical simulation. The elastic lattice Green's function (GF) resolves this difficulty. By means of GF, steps across an island are found to interact differently from those across a pit when they are close to each other. After the finite size effect dies out, step interaction shows 1/r^2 behavior predicted by the CE, but its strength is weakened due to the atomic relaxation around the steps. On applying the model to two-dimensional heteroepitaxy, energy minimum configuration is traced systematically as a function of the coverage, and the possibility of a new growth mode is obtained.We also studied step instabilities on Si(001) vicinal surface, where surface reconstruction takes place, and the groove formation is concluded perpendicular to the steps. On a Si(111) surface where the surface phase transition occurs, the wandering instability of a step is explained close to the phase transition temperature, where two phases coexist.