We report here on the optimization of the growth by atmospheric pressure MOVPE of double heterojunctions and superlattices of GaSb/InAs on both [111]A and [111]B GaAs substrates. The layers were not intentionally doped. Various indium precursors were used in this study to compare their effectiveness. Adduct purified TMIn, EDMIn, and a mixture of TMIn and TEIn were used. It was found that both the EDMIn and the mixture behaved essentially the same as TMIn in the growth of these structures. Various V/III ratios were tried for the InAs layer to establish whether different conditions were needed for the [111]A and [111]B cases in the double heterojunction structure. The superlattices were grown using a 2:1 ratio of GaSb to InAs on top of a thick (4 mum) buffer layer of GaSb. Various different switching and pause sequences were investigated at the interfaces to deliberately produce "InSb-like" interfaces which are expected from previous work on the double heterojunctions to give superior results. Both the semiconducting and semimetallic regions were studied. The superlattices were characterized by absorption methods when the band gap is positive in the semiconducting samples, and by magnetotransport studies in the semimetallic regime where the band gap is negative. The influence of the piezoelectric field on the optical properties in the infrared region of the thin layer superlattices (up to about 80 angstrom total thickness) is marked by a large increase in the measured absorption for the [111] samples compared to [100]. In the semimetallic regime, the structures showed close to intrinsic behaviour with electron: hole concentration ratios of 3:2. The [111]A structures showed large mobility enhancement over the equivalent [100] analogues.