Yuta Kitamura

Birefringence simulations of annealed ingot of calcium fluoride single crystal by considering creep behavior of ingot during annealing process

We developed an analysis system for simulating birefringence of an annealed ingot of CaF2 single crystal caused by the residual stress after annealing process. In the residual stress calculation, we can select either the elastic thermal stress analysis using a stress-free temperature or more exact stress analysis considering creep deformation. When we use the residual stress calculated from the creep deformation analysis of a CaF2 ingot, we can obtain reasonable results in comparison with the experimental results.

Birefringence simulations for annealed ingots of the -and - growth calcium fluoride single crystals with consideration of creep deformation

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. The finite element method was applied to the heat conduction analysis and the stress analysis. In these analyses, the temperature dependence of material properties and the crystal anisotropy were taken into account. In the residual stress calculation, we considered the time-dependent nonlinear deformation behavior of a material called creep. In the birefringence analysis, the distributions of optical path difference were calculated by using average stress method with consideration of the crystal anisotropy. We can perform the birefringence analysis of an ingot of CaF2 single crystal with any growth direction, using this analysis system, and we performed the analyses of the crystals with the and growth directions. From these analyses, we obtained reasonable results of optical path difference in comparison with the experimental results.

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

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.

Birefringence Simulation of Annealed Ingot of Magnesium Fluoride Single Crystal

We developed a method for simulating birefringence of an annealed ingot of MgF2 single crystal for lithography optics. This method provides the optical path difference caused by crystal symmetry and residual stress existing in the crystal. The method consists of the residual stress analysis and the birefringence analysis. The residual stres analysis comprises the heat conduction analysis and the elastic thermal stress analysis. The heat conduction analysis provides the temperature distribution during ingot annealing and the elastic thermal stress analysis provides the residual stress after annealing by using the result of the heat conduction analysis. Because there exists no experimental data on the inelastic behavior of MgF2 single crystal, the residual stress was estimated with the elastic thermal stress analysis by assuming a stress-free temperature, by which the inelastic behavior could be treated approximately. The finite element method was applied to both the heat conduction analysis and the elastic thermal stress analysis. In these analyses, the temperature dependence of material properties and the crystal anisotropy were taken into account. In the birefringence analysis, the distributions of optical path difference were calculated by an approximate method using the result of the residual stress analysis. This approximate method uses the average stress along the wave normal and is equivalent to the exact method in case of low stress dealt with the present study. In this analysis, it is possible to consider both the intrinsic birefringence and the stress birefringence in any crystal orientation.