A Model for Spin Coating with Topography

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Abstract
A theoretical model for spin coating on a substrate with topography is presented. The equations assume a thin film, with uniform properties in the direction normal to the substrate. By assuming a small amplitude for the substrate variations, two sets of coupled equations are derived, one for the mean value of the thickness and its composition, and another for the fluctuations. The viscosity and surface tension of the film, together with their variation with solvent content, play an important role in determining whether planar or conformal surfaces are achieved. Surface tension tends to planarize the film, whereas surface tension gradients tend to make the film more conformal. If viscosity rises very quickly as a result of solvent evaporation, the film topography becomes “frozen‐in,” and surface forces cannot planarize.

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