The effects of gas phase convection on mass transfer in spin coating

The thickness uniformity of photoresist films deposited by spin coating critically influences the resolution of photolithography. This thickness uniformity depends on uniform evaporation from the film during drying. Simple scaling arguments demonstrate that, if the mass transfer coefficient at the surface of the wafer does not vary with radial position, then the dry coated resist film thickness will be independent of radial position. A model is presented for the compressible, laminar, steady-state, axisymmetric air flow in a spin coating apparatus for 6-in.-diam wafers. Flow fields computed by a finite-element–Newton method are used to evaluate the radial profile of the mass transfer coefficient at the surface of the rotating wafer, and to calculate the trajectories of particles that are generated as photoresist is flung from the edge of the spinning wafer. At a spin speed of 2000 revolutions/min and exhaust flow rate of 100 ℓ/min through the coater, the calculations predict that the mass transfer coefficient should be independent of radius. Comparison with film contours measured from experiments at these conditions indicates radial nonuniformities in the film thickness and suggests the importance of hydrodynamic instabilities in the gas on the uniformity of the coating.