Quantitative description of phenolic polymer dissolution using the concept of gel layer

New model(1,2) using the concept of gel layer was recently presented that aimed to provide a theoretical interpretation for experimental data of dissolution behavior to control the lithographic performance of the photoresist. The dependence of the dissolution rate of phenolic polymer on the aqueous base concentration and molecular weight of resin can be analytically described by mathematical modeling considering the formation of gel layer, which is formed by the entry of aqueous base and deprotonation of some of the phenol group. The new polymer dissolution model is based on the suggested mechanism that the diffusion of base and deprotonation reaction of the phenolic group of polymer take place simultaneously through a gel layer. The fundamental equation, which is derived from the concept of gel layer, correctly fits experimental data(11) for aqueous base concentration and molecular weight dependence of dissolution rate of phenolic polymer. In addition, the model can predict the experimentally critical minimum base concentration below which dissolution is no longer observed. As a result, the mathematical expression by this approach offers a fully quantitative and analytical understanding of the dissolution rate.