We investigated InAs deep quantum well structures (InAs QWs) made from InAs/AlGaAsSb materials on GaAs substrates by molecular beam epitaxy. In the InAs QWs, AlGaAsSb layers were lattice matched to InAs. Using reflection high-energy electron diffraction (RHEED) linescan images analysis, we show that AlGaAsSb on GaAs surfaces quickly relaxes within 3–7 monolayers (MLs). The initial stages of AlGaAsSb growth on GaAs(100) substrates and InAs growth on AlGaAsSb layers have been investigated by atomic force microscopy (AFM) and RHEED image analysis. A new growth mode, exhibiting ridgeline shapes during the initial stages of GaAsSb and AlGaAsSb growth on GaAs surfaces, was observed. At the interface of the InAs/AlGaAsSb, the two-dimensional growth of InAs was observed. The roughness at the InAs/AlGaAsSb interface was 3–4 MLs from AFM, high-resolution transmission electron microscopy and grazing incidence x-ray reflectivity analyses. We achieved very high electron mobilities of 32 000 cm2/V s at room temperature using a thin buffer layer of 600 nm AlGaAsSb.