The results of detailed optical, electrical, and structural studies performed on a series of (211)B oriented HgTe–CdTe superlattices grown by photon assisted molecular‐beam epitaxy are reported. Higher order optical transitions in infrared (IR) photoluminescence (PL) spectra were observed for the first time in HgTe–CdTe superlattices. Low residual carrier concentrations were measured in undoped superlattices. Acceptor‐bound excitonic transitions were observed in IR PL spectra of an arsenic doped superlattice for the first time. Excess carrier lifetimes of several hundred nanoseconds were measured, approaching that observed in the corresponding alloy. These results represent significant improvement in the electrical quality of HgTe–CdTe superlattices, and is another step towards the realization of a superlattice‐based IR device technology.