The temperature dependences of crystalline quality, epitaxial relations, and interface properties of CaF2 on Si(111) are studied by x-ray diffraction and electrical measurements. While the CaF2 films grown at temperatures above 400-degrees-C exhibit B-type epitaxy, the films grown at temperatures below 400-degrees-C show A-type epitaxy. Using low substrate temperatures, we also obtained A-type CaF2 on SiGe(111) and off-orientated Si(111). In addition to the change in epitaxial relations, the interface state density is significantly reduced when the growth temperature of the CaF2 films decreases. Although flat capacitance-voltage (C-V) curves are observed from capacitors made of CaF2 films grown at 600-800-degrees-C, suggesting a pinned interface, unpinned C-V characteristics are observed from capacitors made of either A- or B-type epitaxial CaF2/Si(111) grown at 200-500-degrees-C, and polycrystalline-CaF2/Si(111) grown at 25-100-degrees-C. The C-V characteristics are also dependent on the post-annealing temperature. Our results indicate that the interface state density of CaF2/Si(111) is dominated by thermal history, rather than crystalline quality or orientation, of the CaF2 film.