Buckling and post-buckling kinetics of compressed thin films on viscous substrates

Abstract Compressively stressed films and islands can buckle provided their substrates can flow or creep. A linear-stability theory, based upon plate theory, is developed which determines the onset, rate of growth and wavelength of the buckling instability for compressively-stressed elastic films on finite-thickness viscous substrates. Although the condition for the onset of the buckling instability of the film on a glass layer is the same as that for a compressively-stressed free-standing film, the instability of the film on the viscous substrate grows slowly, with a typically long characteristic time. The linear stability analysis is extended to include the effects of interfacial shear stresses and shear deformation of the film within a rigorous linear elasticity calculation. The corrections to the original critical unstable wavelength and maximally unstable mode are found to be minimal, especially for small to moderate values of the compressive stress. The role of substrate elasticity is shown to have a higher order effect in modifying the growth rate. An approximate non-linear theory is developed that 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. The present analysis provides the tools necessary for designing stress relaxation strategies.