A mathematical model for spin coating of polymer resists

The success of lithographic processes in microelectronics fabrication depends on the reproducible generation of desired polymer resist film thickness and profile uniformity. Numerous process variables affect the outcome of spin coating of resists on wafers. A thorough understanding of the intricate interdependence of process parameters is essential to guide future process design and improvement. A mathematical model is derived to elucidate the dominant mechanisms governing film formation. The non-Newtonian character of the resist solution is taken into account, as well as the changes in resist viscosity and solvent diffusivity with changing polymer concentration. Results obtained from this model show that polymer film thickness is controlled by convective radial flow of the resist solution and solvent evaporation. The former process governs film thickness during the early stages of the process, while the latter becomes significant in later stages. The model accurately describes the experimentally observed dependence of film thickness on the variables affecting the spin-coating process.