Numerical Modelling and Measurement of Spatial Coherence in a Lithographic System
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For the last five decades, optical lithography has been used universally for the manufacture of integrated circuits. The drive towards smaller circuit feature size, and the resulting increase in resolution of lithography systems, has been achieved by changing the source type. The original 300 - 400 nm discharge lamps have been replaced with more powerful and monochromatic excimer lasers, operating at user-selectable Ultra-Violet (UV) wavelengths from 157 - 351 nm. The success of UV lithography is due, in part, to the development of industrialized, line narrowed excimer lasers. However, the line narrowing process, along with the intrinsic coherence properties of the laser, results in a source with a considerable amount of spatial coherence. These partially coherent sources are complicated to model. Partially coherent image formation with two-dimensional intensity fields requires evaluating four-dimensional integrals. Thus calculations are complex, slow to process and place demands on system memory. The motivation behind this thesis is an improved understanding of the effects of spatial coherence in optical lithography, including beam homogenization in wafer-stepper systems. In this thesis, we expand the Elementary Function Method, a process similar to coherent mode decomposition, to develop a numerical model of a partially spatially coherent source. We design an experiment to measure the spatial coherence of a partially coherent laser source and present our results. The numerical model is tested on a theoretical Gaussian Schell-model source, and then applied to the excimer source. We examine the traditional method for beam conditioning, the imaging homogenizer, and develop a model of the physical process involved in beam homogenization. Our results show that the imaging homogenizer is designed for use with spatially incoherent sources, where it performs well. However, if the source incident on the homogenizer has any degree of spatial coherence, the intensity output is highly non-uniform.