Simulation of the Postexposure Bake Process of Chemically Amplified Resists by Reaction–Diffusion Equations

In this work, a time-dependent postexposure bake (PEB) simulator is presented by solving a set of reaction–diffusion equations modeling the deprotection reaction of polymers and the diffusion of acids in chemically amplified resists. The simulator is time-dependent in the sense that model parameters including both reaction parameters and diffusion coefficients are treated as time-dependent functions in the entire course of the PEB process. The alternating direction implicit method is utilized to iteratively solve the set of reaction–diffusion equations. An error-control scheme is devised for automatic time-stepping. This PEB simulator is, hence, capable of simulating the effects of the temperature–time history of a wafer. It is then applied to simulate the resist profiles of line/space patterns and contact holes.