Simple model for swelling-induced stresses in a supported polymer thin film

Solvent transport in multilayer thin film structures can induce damaging stresses. It is important to understand these quantitatively for the design of processing methods for microelectronics manufacture. As a model for such systems, this article focuses on the connection between solvent transport in a thin, supported film and the induced bending curvature of the film/substrate combination. We develop a simple mechanical model to calculate the bending curvature based on the transport-induced stresses. A phenomenological moving boundary description of non-Fickian solvent transport often found in glassy polymers has been used. The evaluation of dimensionless bending curvature for a number of generic cases is presented. As an application of the model, experimental data for a polymide (PI)/quartz-n-methyl-2-pyrrolidinone (NMP) system involving significant swelling (15–20%) of the PI film is analyzed. The analysis shows that the measured bending during the transport of NMP in the PI film compares well with that predicted based on an “intermediate,” non-Fickian diffusion mechanism of NMP, consistent with the finding obtained from a laser interferometric study. Estimation of the swelling-induced stress shows that it is large and as significant as that due to thermal “curing.”