InGaAs/InP heterostructures having atomically controlled interfaces are grown by gas source migration-enhanced epitaxy (GS MEE) on (001)InP substrates at 350-degrees-C. RHEED intensity oscillations persisted for over 1 b with the same amplitude and phase during the growth of InGaAs and InP for appropriate supply times of Group III and Group V atoms and proper supply interruption times. The RHEED intensity traces during the growth of InGaAs/InP superlattices as well as Raman spectra from InGaAs/InP quantum well structures suggest the formation of tailored InGaAs/InP heterointerfaces.