Power-law scaling for solid-state dewetting of thin films: an Onsager variational approach

We examine the kinetics of surface diffusion-controlled, solid-state dewetting by consideration of the retraction of the contact in a semi-infinite solid thin film on a flat rigid substrate. The analysis is performed within the framework of the Onsager variational principle applied to surface diffusion-controlled morphology evolution. Based on this approach, we derive a simple, reduced-order model to quantitatively analyse the power-law scaling of the dewetting process. Using asymptotic analysis and numerical simulations for the reduced-order model, we find that the retraction distance grows as the $2/5$ power of time and the height of the ridge, adjacent to the contact, grows as the $1/5$ power of time for late time. While the asymptotic analysis focuses on late time and a relatively simple geometric model, the Onsager approach is applicable to all times and descriptions of the morphology of arbitrary complexity.