Birefringence simulations of annealed ingot of calcium fluoride single crystal: consideration of creep behavior of ingot during annealing process

Noriyuki Miyazaki; Hirotaka Ogino; Yuta Kitamura; Toshiro Mabuchi; Teruhiko Nawata

doi:10.1117/12.812457

16 March 2009 Birefringence simulations of annealed ingot of calcium fluoride single crystal: consideration of creep behavior of ingot during annealing process

Noriyuki Miyazaki, Hirotaka Ogino, Yuta Kitamura, Toshiro Mabuchi, Teruhiko Nawata

Author Affiliations +

Proceedings Volume 7274, Optical Microlithography XXII; 72743H (2009) https://doi.org/10.1117/12.812457
Event: SPIE Advanced Lithography, 2009, San Jose, California, United States

Abstract

We developed an analysis system for simulating birefringence of an annealed ingot of CaF₂ single crystal caused by the residual stress after annealing process. The analysis system comprises the heat conduction analysis that provides the temperature distribution during the ingot annealing, the stress analysis to calculate the residual stress after ingot annealing, and the birefringence analysis of an annealed ingot induced by the residual stress. In the residual stress calculation, we can select either the elastic thermal stress analysis using the assumption of a stress-free temperature or more exact stress analysis considering the time-dependent nonlinear behavior of a material called creep. When we use the residual stress calculated from the creep deformation analysis of a CaF₂ ingot, we can obtain reasonable results both for the optical path difference values and for its distributions in comparison with the experimental results.

Citation Download Citation

Noriyuki Miyazaki, Hirotaka Ogino, Yuta Kitamura, Toshiro Mabuchi, and Teruhiko Nawata "Birefringence simulations of annealed ingot of calcium fluoride single crystal: consideration of creep behavior of ingot during annealing process", Proc. SPIE 7274, Optical Microlithography XXII, 72743H (16 March 2009); https://doi.org/10.1117/12.812457

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