Abstract
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.
Highlights
In Ref. [1], Emslie, Bonner and Peck proposed differential equations in cylindrical polar coordinates to calculate the thickness of Newtonian liquid on a rotating disk
This paper introduces a modified equation for thickness of the film fabricated by spin coating like Equation (7) that is based on curve estimation and polyhedron approximation
Importance of Results and Formulas in This Paper which was introduced in the 1950s, to determine spin coating film thickness
Summary
In Ref. [1], Emslie, Bonner and Peck proposed differential equations in cylindrical polar coordinates to calculate the thickness of Newtonian liquid on a rotating disk. We focus on a coating thickness range of 4 to 20 μm using experimental limits of ω = 1000, 2000 and and t = 300, 450 and 600 s In these experimental conditions, the equation for thickness of the film fabricated by spin coating is given by the formula: h(ω ) = √. The existing equation for Newtonian fluids has five parameters: viscosity and density of material, spin coating speed and time, and initial height of the material before spin starting Due to these various parameters, there is a difference in thickness to apply the existing equation to actual experiments. We establish the modified equation for thickness of the film fabricated by spin coating in the spin coating process as a curve estimated function, and begin by referring to Table 1 above. The theoretical equation must be modified with a curve estimated function to provide a more accurate calculated film thickness
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