A domain decompositon algorithm for thermal analysis in x-ray lithography with cylindrical geometry

摘要

X-ray lithogrpahy is na important technique in micro fabrication used to obtain structures and devices with a high aspect ratio. The process is composed of a mask and a photoresist deposited on a substrate (with a gap between mask and resist). Predictions of the temperature distribution in the different layers (mask, gap, photoresist and substrate) and of the potential temperature rise are esential for determining the effect of high flux x-ray exposure on distortions in the photoresist due to thermal expansion. In this tudy, we develop a three-dimensional numerical method for obtaining the temperature profile in an x-ray irradiation process by using a hybrid finite element-finite difference scheme for solving three-dimensional parabolic equations on thin layers with a cylindrical geometry. A domain decomposition algorithm is then obtained based on a parallel Gaussian elimination for solving block tridiagonal linear systems. Numerical results show the method to be efficient.