The growth of CaF2 films with a thickness of approximately 3-4 nm on well-oriented Si(1 1 1) substrates by molecular beam epitaxy at temperatures between 410 and 560 degreesC were investigated by ex vacuo atomic force microscopy. Layer-by-layer growth producing atomically flat CaF2 surfaces has been observed in a very narrow growth temperature window between approximately 430 and 470 degreesC. Perfect triangular shaped islands of one CaF2 layer height are found on the surface with all corners aligned with the Si( I I!) directions. indicating a pure B-stacking of the CaF2 film. Surprisingly, also the substrate steps have been overgrown without visible defects. Below 410 degreesC, two different island orientations revealed a mixture of A- and B-stacking areas in the films. Above similar to520 degreesC non-wetting of the CaF interface layer leads to epitaxial films with a rough surface morphology.