Model for reaction-assisted polymer dissolution in LIGA

摘要

A new chemically oriented mathematical model for the development step of the LIGA process is presented (LIGA is an acronym for the German words Lithographic, Galvanoformung, and Abformung). The key assumption is that the developer can react with the polymeric resist material to increase the solubility of the latter, thereby partially overcoming the need to reduce the polymer size. The ease with which this reaction takes place is assumed to be determined by the number of side-chain scissions that occur during, the X-ray exposure phase of the process. The dynamics of the dissolution process are simulated by the solution of the reaction diffusion equations for this three-component, two-phase system, the three species being the unreacted and reacted polymers and the solvent. The mass fluxes are described by multicomponent diffusion (Stefan-Maxwell) equations, and the chemical potentials are assumed to be given by the Flory-Huggins theory. Sample calculations are used to determine the dependence of the dissolution rate on key system parameters such as the reaction rate constant, polymer size, solid-phase diffusivity, and Flory-Huggins interaction parameters. A simple photo-chemistry model is used to relate the reaction rate constant and the polymer size to the absorbed X-ray dose. The resulting formula for the dissolution rate as a function of the dose and temperature is fit to an extensive experimental database to evaluate a set of unknown global parameters. The results suggest that reaction-assisted dissolution is very important at low doses and low temperatures, the solubility of the unreacted polymer being too small for it to be dissolved at an appreciable rate. However, at high doses or at higher temperatures, the solubility is such that the reaction is no longer needed, and dissolution can take place via the conventional route. These results provide an explanation for the observed dependences of both the rate of dissolution and its activation energy on the absorbed dose. © 2005 Wiley Periodicals, Inc.