Semiconductor devices such as vertical-cavity surface-emitting lasers (VCSELs) or semiconductor-saturable absorber mirrors (SESAMs) require high-reflection mirrors. Moreover, in VCSELs, it is beneficial to have a crystalline mirror, which is as thin as possible in order to ensure a high thermal conductivity for efficient heat-sinking of the laser. On the other hand, the wavelength tuning range of a SESAM is limited by the reflection bandwidth of its distributed Bragg reflector (DBR). Thus, broadband mirrors are preferable here. This paper reports a three-pair DBR grown by molecular beam epitaxy (MBE) using BaCaF2 and GaAs on a GaAs (100) substrate. Due to the high ratio in refractive indices of GaAs and the group-IIa-fluorides, high-reflectivity mirrors and wide bandwidths can be obtained with low total thicknesses. We also investigated growth and stability of the material BaCaF2, as well as its thermal conductivity both as single layer and Bragg reflector. Observed peeling of the layers could be avoided by implementing a fluorine treatment previous to the BaCaF2 growth.