Growth of lattice-matched In0.53Ga0.47As/InP and In0.53Ga0.47As/In1-xGaxAsyP1-y quantum wells (QW's) by low-pressure metal-organic vapor-phase epitaxy with specific growth-interruption cycles leads to three simultaneous effects in the photoluminescence (PL) spectra: (I) energy shifts of all PL lines, (II) line broadenings, and (III) splitting of individual QW lines into multiplets associated with the formation of extended molecular-layer (ML) flat islands. Samples were grown with four or six single QW's exhibiting overlapping PL multiplets with up to twelve ''coherent'' lines in sequence and ML thickness differences of their parent islands. It is shown, by temperature-controlled PL and PL-decay-time measurements, that these flat islands behave as independent QW's at low temperatures, thus giving evidence of their large extensions. The unambiguous assignments of PL energies to island widths made possible by the coherence of the line sequence demonstrate significant and systematic deviations from pertinent theoretical calculations based on square-well potentials. It is argued that the potentials are not ideally squarelike but rather graded in the well due to an initial excess indium concentration caused by switching perturbations of the gas fluxes. For In0.53Ga0.47As/In1-xGaxAsyP1-y QW's this extra potential (i.e., the band-gap variation of In1-xGaxAs) is estimated to be 30 meV with a relaxation length of order 100 along the growth direction. The corresponding excess indium concentration is 6% over the lattice-match composition of 53%. Scanning cathodoluminescence (CL) was employed taking CL images and spot excitation spectra. ''Monochromatic'' images, recorded with light detection at different wavelengths of a particular luminescence line, reveal complementary, complex-shaped dark-bright lateral regions. The complementary regions fit perfectly together, even in details down to lateral extensions of below 1 μm. We conclude that such structure originates from lateral fluctuations of the nonsquare QW potentials associated with the composition gradient in the growth-interruption cycle. © 1992 The American Physical Society.