Model for spin coating in microelectronic applications

A thorough investigation of the mass and momentum equations pertaining to the spin-coating process has been performed. A scaling analysis forms the foundation to determine the relevant characteristic quantities of the process and allows the assumptions and simplifications made by previous authors to be critically examined. Based on this analysis, the complete equations are reduced to a two-dimensional set of equations while retaining the essential physics of the problem. By further assuming a uniform film thickness over the disk, a one-dimensional model has been developed to assess the importance of the coupling between fluid flow and mass transfer during spin coating. The model predictions for the final film thickness can be presented in such a manner that the results superimpose onto one curve. In this way the film thickness and its relationships with process and material properties, initial solvent content, and spinning conditions can be succinctly expressed in terms of two characteristic parameters. The literature confusion over the exponent of the power-law dependence of the final film thickness on the rotational speed is also clarified. The model predicts an exponent of −1/2 which agrees with most experimental investigations. However, when the total spin time is too short, the exponent may deviate from −1/2. Finally, a split mechanism model that assumes that the spin-coating process could be divided into two stages, one where fluid flow is occurring exclusively and the other where only mass transfer occurs, has been shown to be quantitatively inaccurate.