GaAs/In.2Ga.8As/GaAs quantum well structures containing InGaAs layers of thickness over and under the critical thickness (hc) were studied, as grown by both conventional molecular beam epitaxy (C-MBE) and migration-enhanced epitaxy (MEE) techniques. A 6.0 monolayer per cycle (ML/cyc) growth rate, in contrast to a one or less-than-one ML/cyc growth rate used in a conventional MEE process, was used to grow In.2Ga.8As layers over hc. As-grown samples were characterized via photoluminescence, X-ray diffraction, and transmission electron microscopy (TEM). The 6.0 ML/cyc MEE-grown layers over hc show superior optical quality to MBE-grown layers with the same thickness. Both X-ray diffraction and TEM microstructure results indicate that the 6.0 ML/cyc MEE-grown In.2Ga.8As layers are still strained layers while those grown by conventional MBE method are not. The 6.0 ML/cyc MEE process seems to be advantageous for growing InGaAs layers over the critical thickness.