The model of the spin-coating process presented here accounts for variations of concentration, viscosity, and diffusivity across the thickness of the spin-coated film. The flow of the liquid is governed by a balance between centrifugal driving force and viscous resisting force. Radial variations in film thickness and concentration are neglected. The Galerkin/finite-element method is employed to solve the equation set. Film thinning slows initially due to decreasing film thickness and ceases finally due to dramatically increasing viscosity of the coating liquid as solvents evaporate, The formation of a region of extremely low solvent concentration and correspondingly high viscosity and low binary diffusivity at the free surface, Le., a solid "skin," is predicted. Coating defects can occur if convective flow has not completely ceased when this skin forms. Skin formation can be eliminated or delayed by partially saturating the overlying gas with solvent or by using mixed solvents (having both high and low volatilities) in the coating liquid. The temperature variation in the film during coating varies negligibly from the ambient.

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Measurements of carbon incorporated into a 2 in. diam Czochralski silicon crystal are compared with predictions computed using a three-step simulation: (i) the temperature field is computed throughout the melt and all solid regions of the furnace without heat transfer by gas convection; (it) the temperature and flow fields for the argon purge gas are computed with the temperatures at all solid surfaces set from the first step in the simulation; (iii) the concentrations of dilute SiO and CO in the purge gas, as well as the concentration of carbon in the melt, are computed using the temperature and flow fields computed in step (it). The concentration of carbon in the crystal is readily computed from the concentration of carbon in the melt. The predicted carbon concentrations are approximately a factor of 2 lower than the measured concentrations, with the discrepancy likely due to inaccurate thermodynamic and kinetic data. Additional simulations show that the concentration of carbon in the crystal increases with increasing gas pressure and decreases with increasing mass flux of gas through the furnace at constant pressure. Finally, convective cooling by the flowing gas is shown to be unimportant relative to radiation thereby justifying the decoupling used in the first step of the simulation.