Relaxation Kinetics of a Compressed Film on a Viscous Substrate

One mechanism for producing large single crystal films for which lattice-matched substrates are unavailable is to grow a very thin film on a substrate with a small mismatch, bond the free surface to a glass layer, remove the substrate and anneal the structure above the glass transition temperature in order to relieve the misfit strain. Due to in-plane expansion, the stresses relax and the relaxation process propagates from any free edge towards the center of the film. However, when the displacement of the expanding film reaches a critical value, the film can also separate from the substrate and a delamination crack can propagate. A simple model for the kinetics of stress relaxation and the rate of crack growth is derived for a misfitting film bonded to a non-Newtonian viscous substrate. A competing mechanism for stress relaxation of a compressively-stressed elastic films on a finite-thickness viscous substrate is a buckling instability which relieves stresses but destroys the planarity of the film. A linear-stability analysis determines the onset, rate of growth and wavelength of this instability. Unlike the free-standing film, the growth of the buckle instability occurs slowly with a characteristic time set by the viscosity of the glass. An approximate non-linear theory predicts the saturation of the buckling instability at intermediate times, followed by a long time coarsening of the buckling wavelength and a decrease of the stress within the film. Based on these results, the length and time scale over which one or the other relaxation mechanism dominates is estimated.