Surface instability and cusp formation in heteroepitaxial thin films

We study thin films subjected to strongly coupled stress and diffusion at small length scales. The mechanisms by which surface morphology evolves are investigated by a series of theoretical and experimental studies. The methods we use include complex variable theory of elasticity, J-integral method, anisotropic elasticity, boundary integral method, surface diffusion equation, dislocation theory and molecular dynamics method. We show that the stress drives atomic diffusion along the film surface in such a way that an initially flat film evolves into an undulating profile with cusp-like surface valleys with singular stress concentration. Modeling at atomic resolution shows that the cusp formation leads to creation of various nanoscale defects in the form of dislocations and deformation twins. Controlled annealing experiments are performed to validate theoretical predictions. Future studies will involve combination of continuum and atomistic analysis to model the growth and evolution of structures at nanoscale.