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.Engineering MechanicsAerospace Engineering and Engineering Mechanic