CaF2 single crystals are required for the most suitable lens materials for the ArF laser lithography stepper because of its excellent transparency and laser durability in the DUV region. We have succeeded in growing the large size and high quality CaF2 single crystals with both <111> and <100> orientation, and the diameter of 300mm by means of the Czochralski (CZ) method. The refractive index homogeneity is one of the most important optical properties required for the lithography lens material. Particularly, the residual homogeneity which is a high-order refractive index distribution after subtraction of Zernike 36 coefficient is very important. The vein-like striations were observed in the residual homogeneity pattern of the CaF2 single crystals. The structure of CaF2 single crystal correlating with the residual homogeneity is characterized by using the reflection X-ray topography. It is observed that the structure of CaF2 single crystal composed with sub-grains parted by the small-angle tilt boundaries. The sub-grains are grown along the growth direction. It is understood that the large angle tilt type sub-boundaries among the domains composed of small sub-grains correspond to the vein-like striations. In the growth of CaF2 single crystal, the sub-grain structure of seed is introduced into grown crystal. While the bending of crystal lattice plane from the neck toward the shoulder lead to the large angle tilt type sub-boundaries. Use of high crystalline seed and control of crystal lattice plane in the shoulder are effective in the growth of high crystalline CaF2 single crystal getting good residual homogeneity.