Diffusion driven morphological instabilities of crystalline solids
The morphological instability of solids is of importance to determine the performance and reliability of electronic devices. In this study, we, using both the theory of linear instability and first-order perturbation techniques, study the morphological stability of solid surfaces.
Firstly, we analyze the growth behavior of a non-stressed annular crystalline tube controlled by volume diffusion. The surface evolution of the annular tube is established on the basis of lattice diffusion and the linear stability analysis. The surface perturbation will grow when the perturbation frequency is less than the critical frequency, which is equal to the inverse of the inner surface radius.
Secondly, we discuss the surface evolution of a stressed annular crystalline tube controlled by surface diffusion with two interfacial contact conditions between an elastic layer and the substrate, (a) the frictionless contact and (b) the coherent contact. The driving force controlling the surface evolution is the gradient of chemical potential associated with surface energy and the stored strain energy in the elastic layer. The dispersion relations are developed.
Thirdly, we consider stress-driven interfacial instability of a bilayer structure---the interaction between the free surface and the interface. We analyze the morphological instability of a bilayer system consisting of a dislocation-free film and an elastic substrate. We reveal the propagation of surface perturbations from the free surface to the interface and identify the characteristic frequencies for the initiation of morphological instability of the system.
Finally, we investigate the surface evolution of planar solid in an electrical field and consider the effect of electromechanical coupling on two systems, (a) conducting thin films and (b) conducting half-space. We find that the electromechanical interaction can either enhance or suppress the surface instability introduced by surface perturbations, depending on the competition among surface energy, elastic energy and electrical energy.
Keywords. Morphology, Instability, Diffusion, Perturbation, Solid.