The influence of substrate temperature and InAs mole fraction on the incorporation of indium during molecular‐beam epitaxial growth of lattice mismatched InGaAs single quantum wells on GaAs have been investigated. For growth of In0.25Ga0.75As at temperatures ≪570 °C, a transition from two‐dimensional to three‐dimensional growth is observed at a certain thickness of InGaAs. This thickness appears to be related to the thickness at which misfit dislocations are generated since it depends upon the substrate temperature during growth. The thickness is largest for quantum wells grown at lower temperature and decreases as the substrate temperature increases. This transition from two‐dimensional to three‐dimensional growth is not observed at high temperatures (≫570 °C) where an indium‐induced (4×2) surface reconstruction exists. For growth at 590 °C, Auger electron spectroscopy measurements indicate that the indium atoms reside on the surface of the as‐grown layer. However, the growth front of InGaAs remains planar even though indium adatoms do not incorporate into an In0.25Ga0.75As square quantum well. This type of indium surface segregation during growth does eventually degrade the macroscopic morphology of the surface, but only after a capping layer is deposited on top of the InGaAs. Some surface degradation in capped structures is also observed for In0.15Ga0.85As and In0.07Ga0.93As single quantum wells when grown at high temperature (≫570 °C), although it is less severe for these lower indium concentrations.