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

Abstract

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.

Spin coating of an evaporating polymer solution

“…with a mass transfer coefficient k that is proportional to x 1=2 (to incorporate the effect of the gas flow above the disk, see also Bornside, Brown et al 36 ), where we also have assumed that the equilibrium solvent mass fraction is sufficiently small so that it can be set to zero. Finally, conservation of solvent at this surface gives…”

Extrusion Spin Coating: An Efficient and Deterministic Photoresist Coating Method in Microlithography

“…The shaded region at the center of the wafer denotes the overlapped region. The overlap at the center is unavoidable because an infinite rotational speed and an infinitely small extrusion head would be required at to maintain the constant coating speed as shown in (6). The amount of photoresist flow must be optimized to avoid nonuniformities by minimizing the overlap at the center.…”

“…2 [5], [6] later improved Meyerhofer's model using Raoult's law [7]. When convective outflow ceases and the thin film thins solely by evaporation, Bornside et al's model can be written as (5) where is the final coating thickness, is the initial solids content in photoresist, is the vapor pressure of the pure solvent, is the mole fraction of the solvent, is the molecular weight of the solvent, is the ideal gas constant, and is the temperature.…”

Effect of catch cup geometry on 3D boundary layer flow over the wafer surface in a spin coating

“…In early studies, Emslie et al [1] and Acrivos et al [2] studied the flow liquid layer on the rotating disk. Bornside et al [3] investigated the relation between the hydrodynamic instabilities of the gas flow over the wafer and the film uniformity of the spin coating. Zhu et al [4] calculated the flow in the spin coating device with catch cup by CFD.…”