Heteroepitaxial films on CdTe have been grown by molecular beam epitaxy (MBE) on InSb (001) orientation substrates at growth temperatures ≲220 °C. The structural perfection of these films has been explored by double crystal x‐ray diffraction techniques, which reveal that films of ∼1 &mgr;m thick grown at 150 and 220 °C are free of low‐angle grain boundaries and are exactly lattice matched to the InSb substrate. The lattice parameter mismatch is accommodated by misfit elastic strain.