We have investigated InAs deep quantum well structures (InAs DQWs) made from InAs/A1GaAsSb materials on GaAs substrates by molecular beam epitaxy (MBE). In the InAs DQWs, AlGaAsSb layers are lattice-matched to InAs. Using reflection high-energy electron diffraction (RHEED) linescan image analysis, we show that AlGaAsSb on GaAs surfaces quickly relaxes within 3 to 7 monolayers (MLs). The initial stages of AlxGa1-xAsSb (0≤x≤0.5) growth on GaAs (100) substrates and InAs growth on AlGaAsSb layers have been investigated by atomic force microscopy. The ridgeline shapes of AlGaAsSb are observed at the initial stage on GaAs surfaces. In the interface of the InAs/AIGaAsSb, two-dimensional (2D) growth of InAs has been observed. With a thin buffer layer of 600 nm AlGaAsSb, we have achieved very high electron mobilities of more than 32000 cm2/V-s at room temperature.