Surface evolution and self assembly of epitaxial thin films: nonlinear and anisotropic effects
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A strained epitaxial film can undergo surface instability and self assemble into discrete islands. The unique physical features of these islands make self-assembly an enabling technique for advanced device technology while control of the island size, shape, and alignment is critical. During the process of self-assembly, the stress field and the interface interaction have profound effects on the dynamics of surface evolution. In this dissertation, a continuum model is developed to study the nonlinear dynamics of surface pattern evolution and self assembly in epitaxial thin films. Within the framework of non-equilibrium thermodynamics, a nonlinear evolution equation is developed, and a spectral method is implemented for numerical simulations. The effects of stress and wetting are examined. It is found that, without wetting, the nonlinear stress field induces a “blow-up” instability. With wetting, the thin film self assembles into an array of discrete islands lying on a thin wetting layer. The dynamics of island formation and coarsening over a long time and a large area is well captured by the interplay of the nonlinear stress field and the wetting effect in the present model. For single-crystal epitaxy, the anisotropic material properties in the bulk and surface play important roles in the process of self assembly and pattern formation. In particular, this study investigates the effects of anisotropic mismatch stress and generally anisotropic elasticity. First, under an anisotropic mismatch stress, a bifurcation of surface pattern is predicted. The effect of anisotropic elasticity on pattern evolution is then investigated for two specific systems, one for SiGe films on Si substrates with different surface orientations, and the other for hexagonal silicides on Si substrates. It is shown that the consideration of elastic anisotropy reveals a much richer dynamics of surface pattern evolution as opposed to isotropic models. Based on the theoretical and numerical results from the present study, experimental approaches may be developed to control the size and organization of self assembled surface patterns in epitaxial systems.