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 coeffic...

[1]  K. Denbigh,et al.  The Principles of Chemical Equilibrium , 1956 .

[2]  F. Kreith,et al.  Heat and Mass Transfer From a Rotating Disk , 1959 .

[3]  W. Rheinboldt.  Numerical analysis of parametrized nonlinear equations , 1986 .

[4]  Y. Kohama,et al.  Spiral vortices in boundary layer transition regime on a rotating disk , 1980 .

[5]  R. Brown,et al.  Convection and mass-transport in laser-induced chemical vapor deposition , 1988 .

[6]  I. Cornet,et al.  Mass Transfer to a Rotating Disk , 1971 .

[7]  A. G. Emslie,et al.  Flow of a Viscous Liquid on a Rotating Disk , 1958 .

[8]  P. Holmes,et al.  New Approaches to Nonlinear Problems in Dynamics , 1981 .

[9]  P. Hood,et al.  Note on frontal solution program1 for unsymmetric matrices , 1977 .

[10]  Martin R. Maxey,et al.  The motion of small spherical particles in a cellular flow field , 1987 .

[11]  I. V. Prokhorov,et al.  Transitional flow conditions on a rotating disk , 1976 .

[12]  M. V. Dyke,et al.  An Album of Fluid Motion , 1982 .

[13]  Werner C. Rheinboldt,et al.  Solution Fields of Nonlinear Equations and Continuation Methods , 1980 .

[14]  A. Szeri,et al.  Stability of flow over a rotating disk , 1984 .

[15]  Y. Kohama.  Study on boundary layer transition of a rotating disk , 1984 .

[16]  C. Macosko,et al.  Spin Coating of a PMMA/Chlorobenzene Solution , 1991 .

[17]  D. Meyerhofer.  Characteristics of resist films produced by spinning , 1978 .

[18]  N. Gregory,et al.  On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk , 1955, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[19]  Ephraim M Sparrow,et al.  Mass Transfer, Flow, and Heat Transfer About a Rotating Disk , 1960 .

[20]  Mujeeb R. Malik,et al.  The neutral curve for stationary disturbances in rotating-disk flow , 1986, Journal of Fluid Mechanics.

[21]  T. Kármán.  Über laminare und turbulente Reibung , 1921 .