Strain-free GaAs epitaxial layers on Si can be achieved by introducing a CaF2 buffer layer. Here, molecular beam epitaxial growth of GaAs on CaF2/Si(111) substrates has been thoroughly investigated. Three growth regimes have been distinguished. In the low temperature regime, growth was always in a three-dimensional mode, while, in the high temperature regime, two-dimensional nucleation was achieved. However, continued growth in the high temperature regime resulted in the formation of twins after epitaxial initiation. Between those two regimes, there is a narrow temperature window in which high quality GaAs can be grown on the top of CaF2/Si(111). Under optimal growth conditions in this window, 1 mum thick GaAs layers were grown wich exhibited good crystal quality (a minimum ion channeling yield of 3.5% was achieved at the GaAs surface) along with specular surface morphology. Such high quality GaAs on the top of CaF2/Si(111) substrates was achieved previously only by using electron-beam modification of the CaF2 surface.