The mechanics of spin coating of polymer films

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.

Surface-directed phase separation in nanometer polymer films: self-stratification and pattern replication

“…Such solvent quench [39,[54][55][56][57][58][59][60] accompanies the spin-casting process ( Fig. 5b-f) [38]. There are three consecutive phases of spin coating.…”

“…Then a drop of the solution was placed on a substrate, and the films were prepared through a rapid rotation of the substrate (spin casting) [38,39]. The combination of carefully adjusted total polymer concentration and spin speed resulted in films with average thickness of 400 -500 (s.-s.) and 50 -80 nm (p.r.…”

Flow of evaporating, gravity-driven thin liquid films over topography

“…That over a step-up topography, for example, is known to produce a free surface depression 1 just upstream of the topography, while flow over a step-down creates a Capillary ridge 2 before relaxation of the free surface further downstream. Of particular interest here is examining the validity of previous studies of evaporative flow during industrial spin coating 17,19,31 , which have assumed that the free surface profile can be predicted by dividing the process into two stages. In the first, flow-dominated stage, the film profile is considered to be controlled by a balance between a driving force and the capillary force within the lubrication approximation, under the assumption that neither the topography nor the free surface disturbance caused by it affect the distribution of solvent within the resin/solvent mixture.…”

Fabrication of highly ordered multilayer thin films and its applications

“…This observation suggests that it is possible to precisely control the adsorbed amount of polyelectrolytes in multilayer films by simply changing a wide range of solution concentration in spite of the strong repulsion among polyelectrolyte chains with the same charge. According to theoretical models and experimental results based on the spin coating of single thick layer films, the film thickness (H) is dependent on the spinning speed (Ω) and the initial solution concentration (C i ) as follows [Meyerhofer, 1978;Lawrence, 1988;Ohara, 1989;Flack, 1984]:…”