Theoretical Analysis of the Baking Process in Two Polymer/Solvent Systems: PMMA/Anisole and PMDA-ODA/NMP

Abstract

Baking of polymer solutions is very important for preparing uniform thin films in microelectronics. In this study, a general theoretical analysis for baking was developed to predict the variation of polymer film thickness with baking temperature and time. The theoretical analysis result was justified by experimental results from poly(methyl methacrylate) (PMMA)/anisole and poly(pyromellitic dianhydride-co-4,4′-oxydianiline) (PMDA-ODA) amic acid/n-methyl pyrrolidone (NMP) systems. The theoretical analysis included a fixed boundary problem with a temperature-dependent-only diffusion coefficient, and moving boundary problems based on the diffusion coefficient from the Fujita-Doolittle equation and the Vrentas-Duda equation, respectively. The simulated results showed that the modeling equations based on the moving boundary problem with the Vrentas-Duda equation successfully predicted the variation of film thickness in comparison with the other two models. The diffusion coefficient (D), mass-transfer coefficient and Sherwood number (Sh) were used to explain the trend of the baking curves. In the cases of the PMMA/anisole system, the values of Sh increase significantly with increased baking time while the values of D show the opposite trend. This suggests that the baking mechanism has shifted from the evaporation-control mechanism to the diffusion-control mechanism. However, the values of Sh in the polyimide/NMP system are all larger than 15 because of the low diffusion coefficient of the solvent NMP. Hence, the transition of the evaporation-control to the diffusion-control no longer exists in the polymer/solvent system with a high-boiling-point solvent. The model based on the moving boundary problem with the Vrentas-Duda equation simulates a wide range of Sh values and results in higher accuracy than the other two models. © 2001 The Electrochemical Society. All rights reserved.