Abstract
Surface profiles of multilayer coatings of spin-on glass overtopography often display unexpected features, which have been attributed tothe effects of surface tension. Several nonlinear numerical models of thishave been developed and are compared here. The most comprehensive model,which is used as a yardstick, is based on a time-dependent two-dimensional(2D) model of two-phase fluid flow during spinning, which includes theeffects of convection, surface tension, concentration-dependent diffusionand viscosity and evaporation of a volatile liquid phase. The mathematicalmodel is a system of a time-dependent, 2D, convective-diffusion equationfor the volatile phase and the Navier-Stokes equations for thenon-volatile phase in a non-rectangular space domain with a movingboundary. A robust, efficient numerical method based on the transformationof the physical domain with a moving boundary into a rectangularcomputational domain that is invariant in time was developed. The problemin the transformed coordinates is solved by the implicit finite-differencemethod; an unconditionally monotone approximation is used for theconvective-diffusion terms. Two further simplified models requiringenormously reduced CPU time are also discussed and compared. Thecapabilities of the models are demonstrated with some practical examples ofspin-coat planarization.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
