Novel postexposure bake simulator: First results

Abstract

We have designed and implemented a simulator that models the physics of the chemically amplified photoresist process postexposure bake (PEB) step, based on a general mathematical formulation. The photoacid loss due to kinetic reaction and the photoacid diffusion are simulated using experimentally determined model parameters. The PEB simulator, which can be used in conjunction with any lithographic image modeling software, has been integrated into the CXrL ToolSet, a comprehensive modeling system for x-ray lithography. The PEB simulator converts the deposited dose into an initial concentration of photoacid, and then computes its evolution and the corresponding evolution of the protected sites, for a given bake time and temperature. System dynamics are defined by coupled partial differential equations containing acid loss and diffusion terms. As the two phenomena take place at the same time during PEB, the numerical algorithm does not separate the terms in the calculation. An alternating direction implicit and explicit numerical differentiation technique for solving a multidimensional partial differential equation in x and z has been employed, resulting in a system which reduces computational complexity without loss of accuracy or speed. Linewidth can be extracted from the final profile of the protected sites, or, alternatively, the concentration of the protected sites can be converted into a dissolution rate and fed to other dissolution modeling tools to generate a developed resist profile. Process latitude simulations can be performed to study linewidth variation with respect to dose, gap or focus, bake temperature, and time. An initial evaluation has been performed by comparing simulation results with data from an x-ray lithography experimental study.