  We report molecular beam epitaxial growth of a SnTe (111) layer on a CdTe
template, fabricated by depositing it on a GaAs (111)A substrate, instead of
BaF$_2$ which has been conventionally used as a substrate. By optimizing
temperatures for the growth of both SnTe and CdTe layers, we could obtain SnTe
layers of the single phase grown only in the (111) orientation and of much
improved surface morphology from the viewpoint of the extension and the
flatness of flat regions, compared to the layers grown on BaF$_2$. In this
optimal growth condition, we have also achieved a low hole density of the order
of 10$^{17}$cm$^{-3}$ at 4K, the lowest value ever reported for SnTe thin films
without additional doping. In the magnetoresistance measurement on this
optimized SnTe layer, we observe characteristic negative magneto-conductance
which is attributed to the weak antilocalization effect of the two-dimensional
transport in the topological surface state.
