The mechanics of spin coating of polymer films

TLDR

Spin coating, widely used in microelectronics, produces a solid film whose thickness depends on a diffusion boundary layer near the free surface, a dependence on diffusivity that has not been theoretically described before. The study aims to model spin coating by focusing on solvent evaporation, solute diffusion, and concentration‑dependent viscosity and diffusivity. The model treats solvent evaporation, solute diffusion, and concentration‑dependent viscosity and diffusivity, noting that evaporation increases viscosity and reduces flow. The model predicts dry film thickness as a function of spin speed and initial polymer concentration, yielding a simple approximate relation hf ∼ K C₀(ν₀D₀)¹⁄⁴ Ω⁻¹⁄² that matches limited experimental data; it also shows total spin time ∝ Ω⁻¹ and solvent evaporation rate ∝ Ω, contradicting prior assumptions.

Abstract

The process of spin coating is described, with particular attention to applications in microelectronics. The physical mechanisms involved in the process are discussed and those mechanisms that affect the final state are identified, viz., centrifugal and viscous forces, solute diffusion, and solvent evaporation: A model is proposed that incorporates only the latter mechanisms, with viscosity and diffusivity depending on solute concentration. The evaporation of solvent during spinning causes the solution viscosity to increase and the flow is reduced. The thickness of the final solid film is related to the thickness of a diffusion boundary layer near the free surface. The model predicts the final dry film thickness in terms of the primary process variables, spin speed, and initial polymer concentration. A similarity boundary-layer analysis leads to a simple approximate result for the final film thickness that is consistent with limited experimental data, hf ∼KC0(ν0D0)1/4/Ω1/2, where K is a number of order unity and the other quantities are, respectively, the initial polymer concentration, the kinematic viscosity, the solute diffusivity, and the spin speed. The dependence on diffusivity has not previously been described theoretically. The total spin time is shown to be proportional to Ω−1, in agreement with experiment. The rate of solvent evaporation is shown to be proportional to Ω, which contradicts previous assumptions.