The molecular-beam epitaxy of CaF2 layers on Si(Ill) substrates was studied in the temperature range between 370 and 700 degreesC. A strong temperature dependence of the CaF2 surface morphology was found. Layer-by-layer growth modes were found in two temperature ranges: (i) between 430 and 490 degreesC, where growth of atomically flat CaF2 epilayers occurred, and (ii) at similar to700 degreesC, where a step flow mode resulted in a relatively smooth CaF2 surface containing some rough regions, possibly due to the thermal decomposition of the interface layer. At similar to540 degreesC, the triangular island shape observed at lower growth temperatures changed to a more hexagonal shape expected for thermodynamic equilibrium, but the top monolayer islands still exhibited a triangular shape, which can be attributed to a relatively higher lateral adatom impingement rate per unit length of island perimeter. The mechanisms of the complex temperature-dependent growth behavior are discussed in detail. (C) 2004 American Vacuum Society.