Complete Analytical Solutions of Film Planarization during Spin Coating

Abstract

To offer a simple set of equations to designers and researchers for describing the degree of planarization (DOP), a first complete analytical solution of film planarization during spin coating is presented. The analytical solutions are suitable for an isolated feature and periodic features in the whole range of ο2 . The governing dimensionless parameter ο2 represents the ratio of centrifugal force to surface tension force during spin coating. For ο2→0 , surface tension is infinite, and the film is planar. For ο2→∞ , surface tension is zero, and the film is always conformal, with an equal thickness everywhere. The analytical solutions agree with the existing experiment data and numerical solutions. A comparison shows that the degree of planarization for an isolated trench is higher than that for an isolated ridge in the range of 10−5<ο2<3×101 , but they gradually become identical and independent of d/hf for ο2>3×101 and ο2<10−5 . For periodic features, DOPp is independent of dimensionless film thickness, d/hf , dimensionless line spacing, α, and ο2 in the range of ο2>3×102 and ο2<10 −2 . © 1999 The Electrochemical Society. All rights reserved.

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“…As a consequence, spin coating resides at the heart of micro- and nanofabrication and is part of many of the standard processes, in particular those involving lithography, such as pattern transfer, metal lift-off, and local ion implantation. It has been shown that substrate topography leads to a disturbance of the surface of the spin-coated film. − The effect impairs the flatness or planarity of the final film and has long been of concern to the semiconductor industry. Previous work has shown that for large (≥ (10 μm)) features, this relationship strongly depends on the local direction and rate of fluid flow during spin coating , (see Figure ).…”