Stochastic approach to modeling photoresist development

Abstract

In this paper a continuous approximation to the critical ionization (CI) model has been derived and shown to match the CI model extremely closely. Further, both of these models were shown to match the widely used Mack model of dissolution over the lithographically significant ranges of development rates. The variance of the dissolution rate is shown to arise from the variation in the development path required to bypass randomly insoluble polymer molecules rather than just the variance in the polymer solubility itself. Percolation theory, where the percolation probability is equal to the probability that a polymer molecule will become soluble, has the potential for providing the theoretical framework required to determine this variance in dissolution path.