Spin coating: One-dimensional model

The model of the spin-coating process presented here accounts for variations of concentration, viscosity, and diffusivity across the thickness of the spin-coated film. The flow of the liquid is governed by a balance between centrifugal driving force and viscous resisting force. Radial variations in film thickness and concentration are neglected. The Galerkin/finite-element method is employed to solve the equation set. Film thinning slows initially due to decreasing film thickness and ceases finally due to dramatically increasing viscosity of the coating liquid as solvents evaporate. The formation of a region of extremely low solvent concentration and correspondingly high viscosity and low binary diffusivity at the free surface, i.e., a solid ‘‘skin,’’ is predicted. Coating defects can occur if convective flow has not completely ceased when this skin forms. Skin formation can be eliminated or delayed by partially saturating the overlying gas with solvent or by using mixed solvents (having both high and low volatilities) in the coating liquid. The temperature variation in the film during coating varies negligibly from the ambient.