A Model for Drying Control Cosolvent Selection for Spin-Coating Uniformity: The Thin Film Limit

Striation defects in spin-coated thin films are a result of unfavorable capillary forces that develop due to the physical processes commonly involved in the spin-coating technique. Solvent evaporation during spinning causes slight compositional changes in the coating during drying, and these changes lead to instability in the surface tension, which causes lateral motions of the drying fluid up to the point where it gels and freezes in the thickness variations. In an earlier publication, we looked at the case where evaporation happens fast enough that the compositional depletion is mostly a surface effect. In terms of the mass transport rate competition within the coating solution, that work covered the thick film limit of this instability problem. However, in many cases, the coatings are thin enough or diffusion of solvent within the coating is fast enough to require a different solvent mixing strategy, which is developed here. A simple perturbation analysis of surface roughness is developed, and evaporation is allowed in the thin film limit. The perturbation analysis allows for a simple rubric to be laid out for cosolvent additions that can reduce the Marangoni effect during the later stages of coating deposition and drying when the thin film limit applies.