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 32000 cm(2)/Vs at room temperature using a thin buffer layer of 600 nm AlGaAsSb.