Analytical Solutions of Film Planarization during Spin Coating

Abstract

Analytical solutions of film planarization for both trench and ridge during spin coating are presented in order to offer a simple equation to designers and researchers for describing the degree of planarization (DOP). We found that in the case of high Ω2 (Ω2>100), DOP is independent of d/hf for the isolated trench and ridge. The governing dimensionless parameter Ω2 = ρω2w3r0/(γhf) represents the ratio of centrifugal forces to surface tension forces in the coating where ρ and γ are density and surface tension of the fluid, respectively, ω is rotation speed, r0 is radius of position of the feature on the wafer, d and w are height and width of the feature, respectively, and hf is liquid film thickness. We also found that for high Ω2 (Ω2>100), there is an identical DOP value for trench and ridge. However, for low Ω2 (Ω2<1), the values of DOP for trench and ridge are different even under a fixed set of Ω2 and d/hf. Under low Ω2 conditions, the trends of DOP variation for trench and ridge are almost contradictory. Experimental data proposed by Peurrung and Graves in J. Electrochem. Soc. are shown for comparison, and results from the present analytical solutions agree with their data.