Modelling effects of surface tension on surface topology in spin coatings for integrated optics and micromechanics

Surface profiles of multilayer coatings of spin-on glass over topography of ten display unexpected features, which have been attributed to the effects of surface tension. Several nonlinear numerical models of this have been de veloped 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 Row during spinning, which includes the effects of convecti on, surface tension, concentration-dependent diffusion and viscosity and ev aporation of a volatile liquid phase. The mathematical model is a system of a time-dependent, 2D, convective-diffusion equation for the volatile phase and the Navier-Stokes equations for the non-volatile phase in a non-rectan gular space domain with a moving boundary. A robust, efficient numerical me thod based on the transformation of the physical domain with a moving bound ary into a rectangular computational domain that is invariant in time was d eveloped. The problem in the transformed coordinates is solved by the impli cit finite-difference method; an unconditionally monotone approximation is used for the convective-diffusion terms. Two further simplified models requ iring enormously reduced CPU time are also discussed and compared. The capa bilities of the models are demonstrated with some practical examples of spi n-coat planarization.