Brian J. Spencer
State University of New York, Buffalo
We present mathematical and experimental aspects of stress-driven morphological transitions occuring in strained solid films. Using a relatively simple continuum model including the effects of surface diffusion, elasticity and surface energy, the morphology of the film can be modeled by a surface evolution equation coupled to elasticity equations in the bulk. From this framework the speaker will discuss the stress-driven instability of planar films, the nonlinear evolution of the instability, and the formation of strained solid drops (“islands” or “quantum dots”). Finally, recent results on the equilibrium shapes of strained solid drops will be highlighted: an asymptotic small-slope theory that gives multiple drop shapes as eigensolutions to a linear integro-differential equation; and numerical work on the influence of anisotropic surface energy that explains the discontinuous droplet shape transitions seen in experiment as a manifestations of a bistable bifurcation diagram for the shape of strained islands.