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Open AccessArticle

A Modified Equation for Thickness of the Film Fabricated by Spin Coating

1
Department of Mathematics, Dankook University, Cheonan 31116, Korea
2
Department of Energy Engineering, Dankook University, Cheonan 31116, Korea
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(9), 1183; https://doi.org/10.3390/sym11091183
Received: 19 August 2019 / Revised: 30 August 2019 / Accepted: 10 September 2019 / Published: 18 September 2019
(This article belongs to the Special Issue Nonlinear, Convex, Nonsmooth, Functional Analysis in Symmetry)
According to the equation for Newtonian fluids, the film thickness after spin coating is determined by five parameters: angular velocity, spin coating time, viscosity, density of the coating material, and initial thickness of the material before spin coating. The spin coating process is commonly controlled by adjusting only the angular velocity parameter and the coating time in the Newtonian expression. However, the measured coating thickness obtained is then compared to the theoretical thickness calculated from the Newtonian fluid equation. The measured coating thickness usually varies somewhat from the theoretical thickness; further details are described in Section 1. Thus, the Newtonian fluid equation must be modified to better represent the actual film thickness. In this paper, we derive a new formula for the spin coating film thickness, which is based on the equation for Newtonian fluids, but modified to better represent film thicknesses obtained experimentally. The statistical analysis is performed to verify our modifications. View Full-Text
Keywords: spin coating process; modified Newton’s formula; statistical analysis; curve estimated function; polyhedron approximation spin coating process; modified Newton’s formula; statistical analysis; curve estimated function; polyhedron approximation
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MDPI and ACS Style

Lee, U.G.; Kim, W.-B.; Han, D.H.; Chung, H.S. A Modified Equation for Thickness of the Film Fabricated by Spin Coating. Symmetry 2019, 11, 1183.

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