Compositionally undulating step-graded InAsyP1-y buffer layers were grown by metal-organic chemical vapor deposition (MOCVD) to relax the strain of In0.68Ga0.32As with InP substrate. The strain relaxation and surface morphology are strongly dependent on the thickness of each step-graded buffer layer. With an optimized buffer thickness design, a 3-ttm-thick In0.68Ga0.32As epilayer shows a high crystal quality with no measurable tetragonal distortion and a very low surface roughness of 2.74 nm was obtained. Transmission Electron Microscopy (TEM) measurement revealed a threading dislocation density on the order of or below similar to 10(6) cm(-2). Our results indicate that the compositionally undulating step-graded InAsyP1-y buffers grown on InP are very promising to be virtual substrates of infrared and high speed metamorphic devices. (C) 2012 Elsevier B.V. All rights reserved.