Nonlinear evolution of a morphological instability in a strained epitaxial film
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
A strained thin solid film deposited on a deformable substrate undergoes a morphological instability relaxing the elastic energy by surface transport. We study the time evolution of such a film wetting its substrate and derive dynamical equations that we solve numerically in 2D and 3D.
Indeed, the dynamics of semiconductor films is under active scrutiny due to its importance for both fundamental science and technological applications. Thin film elastic instabilities lead to the self-organization of nanostructures potentially useful e.g. for quantum dots, wires or electronic devices. A notorious experimental example is Silicon/Germanium films on a Silicon substrate which exhibit a variety of structures such as pre-pyramids, pyramids, domes and huts. It is well-known that a strained film is prone to the Asaro-Tiller-Grinfeld (ATG) instability driven by the interplay between the elastic stress relaxation by surface transport and the stabilizing surface energy. This instability was clearly demonstrated in experiments on the solid-liquid phase transition in helium at low temperature and more generally, for solid-liquid, solid-vapor or solid-vacuum interfaces with an intrinsic or external mechanical stress.
Hence, we study a dislocation free film coherently deposited on a substrate with a slightly different lattice parameter, which evolves through surface diffusion. When the film is infinitely thick or when the substrate is infinitely rigid, different approaches revealed finite-time blow-up solutions of the ATG instability which account well for experiments in thick enough films. However, these crack solutions do not describe experiments of thin films in the Stranski-Krastanov type of growth where instead, coarsening was measured.
We derive nonlinear and nonlocal equations which describe the dynamics of a thin film on a deformable substrate with a priori different elastic properties and account for wetting effects. When both nonlinear and wetting interactions are present, numerical simulations reveal a steady evolution. When the film initial height is higher than some critical value given by wetting effects, the surface evolves towards an array of islands separated by a wetting layer. The final stage is then an isolated island with a chemical potential monotonously decreasing with its volume. Consistently, the system undergoes a non-interrupted coarsening characterized by a power-law decrease of the island number with time which strongly depends on the system dimensionality.