Birefringence simulations for annealed ingots of the &lt;001&gt;-and &lt;111&gt;- growth calcium fluoride single crystals with consideration of creep deformation

Kitamura, Yoshiichiro; Ogino, Hirotaka; Miyazaki, Noriyuki; Mabuchi, Toshiro; Nawata, Teruhiko

doi:10.1088/1757-899x/10/1/012075

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“…Based on the papers published by the present authors (Ogino et al, 2008;Miyazaki et al, 2009;Kitamura et al, 2010aKitamura et al, , 2010b, the results of birefringence simulations of CaF 2 single crystal after annealing process are presented here. Such simulations comprise the heat transfer analysis that provides the temperature distribution in the single crystal during annealing process, the stress analysis to calculate the residual stress after annealing, and the analysis of birefringence in an annealed ingot induced by the residual stress.…”

Section: Stress Birefringence Simulations After Annealing Of Caf 2 Simentioning

confidence: 99%

“…For this purpose, let us derive the relation between Δe ij and ΔB ij respectively given by Kitamura and Miyazaki, Mechanical Engineering Reviews, Vol.4, No.1 (2017) (Ogino et al, 2008;Kitamura et al, 2009Kitamura et al, , 2010aKitamura et al, , 2010bKitamura et al, , 2010cKitamura et al, , 2012Miyazaki et al, 2009), the order of σ ij does not exceed 10 8 Pa. Therefore we assume that the order of residual stress in single crystal ingots is smaller than 10 8 Pa in the experiments performed by Levine et al (2003).…”

Section: Fig 36mentioning

confidence: 99%

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Birefringence simulations of single crystals

Kitamura

Miyazaki

2017

Mechanical Engineering Reviews

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Fluoride single crystals such as calcium fluoride (CaF 2 ) belonging to the cubic crystal system and magnesium fluoride (MgF 2 ) belonging to the tetragonal crystal system are utilized as optical elements in high power lithography systems. In such uses of the single crystals, birefringence is an important phenomenon that affects optical performance. Based on the papers published by the present authors, we review the birefringence of CaF 2 and MgF 2 single crystals. Intrinsic birefringence is dealt with in addition to stress birefringence. First of all calculation methods for stress birefringence are presented. They are the Jones calculus, an exact method, and the average stress method, an approximate method, and the relation between the two methods is given. In the stress birefringence simulations after annealing of CaF 2 single crystal, the importance of time-dependent nonlinear deformation behavior of a material called creep is pointed out in calculating residual stress that induces stress birefringence. When the wavelength of light becomes down to the vacuum ultraviolet region, CaF 2 single crystal shows intrinsic birefringence in addition to stress birefringence. Birefringence simulations of a CaF 2 single crystal chamber window of an ArF excimer laser light source are performed by considering both stress birefringence and intrinsic birefringence to evaluate the optical performance and to obtain the optimum condition of CaF 2 single crystal window. MgF 2 single crystal shows intrinsic birefringence even for visible light because of its strong crystal anisotropy. The results of birefringence analyses are shown for MgF 2 single crystal as an example of combining stress birefringence with intrinsic birefringence under a visible light condition.

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Section: Stress Birefringence Simulations After Annealing Of Caf 2 Simentioning

confidence: 99%