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 poly͑methyl methacrylate͒ ͑PMMA͒/anisole and poly͑pyromellitic dianhydride-co-4,4Ј-oxydianiline͒ ͑PMDA-ODA͒ amic acid/n-methyl pyrrolidone ͑NMP͒ 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 ͑D͒, mass-transfer coefficient (k c ), and Sherwood number ͑Sh͒ 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.Baking is very important for preparing photoresists and spin-on dielectrics in microelectronics. 1,2 For example, the lithographic process in the manufacturing of integrated circuits ͑ICs͒ includes the following major steps: priming, spin-coating of photoresist ͑PR͒, soft-baking, exposure, postexposure baking, developing, and hard baking, etc. Soft-baking is used to control the free volume ͑or solvent content͒ of the spin-coated PR film by selection of baking parameters, i.e., baking temperature and time. The photochemical reaction in the lithographic process largely depends on the diffusion ability of a photoactive compound in the PR film. 3,4 Hence, control of the free volume inside the PR film by soft-baking before exposure significantly affects the quality of the lithography, including photospeed, 3 contamination, 5 contrast, 6 and critical dimension variation. 6 Furthermore, soft-baking also controls mechanical properties since the adhesion of a PR film to a substrate is affected by the solvent content inside the PR film. 3 For spin-on dielectrics, multistep baking is required to control the possible voids in the film or film uniformity. Hence, understanding of the baking mechanism is ve...

Three-points approach to three-parameters diffusivity of mobile phase in polymer film

“…Consequently, diffusivity of mobile phase in polymer film is strongly dependent on its concentration. Concentration-dependence of diffusivity for a mobile phase in polymer film often plays the leading role in many diffusion-controlled polymer solution processes, for example solvent diffusion in polymer film in photoresist engineering processes (Byers et al, 2003;Flack et al, 1984;Lin and Chen, 2001;Mack et al, 1994Mack et al, , 1998Petersen et al, 1995), in gradientindex plastic optical fiber fabrication (Hsu and Lin, 2003). Usually in mathematical modeling, empirical or theory-based mobile phase diffusivity is introduced, for example, the classical, threeparameters free volume model, Fujita-Doolittle equation (Fujita et al, 1960), is used frequently in polymer solution processing Three-parameters diffusivity Three-points approach T 75 /T 50 and T 50 /T 25 database First guess of optimization A B S T R A C T In this work, a three-points approach for estimating three-parameters diffusivity of mobile phase via desorption process from polymer film is proposed.…”

Fabricação e caracterização de Guia de Onda Polimerica a base de PMMA modificado por plasma de CHF3

“…É uma etapa importante, de acordo com Moreau (apud Nemer), uma vez que afeta significativamente a velocidade de revelação, resolução, adesão e também erosão do fotoresiste não exposto durante a revelação [97]. Nesta etapa, estão envolvidas: difusão do solvente para a superfície do filme, evaporação e o transporte do vapor de solvente [98].…”