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A method to obtain high-quality strain–relaxed SiGe buffer layers on Si(001) substrates is presented. In this method, the strain relaxation of the SiGe layer is performed using a two-step procedure. Firstly, a low-temperature-grown SiGe layer, whose surface is covered by a thin Si cap layer, is thermally annealed. At this stage, the strain is incompletely relaxed and an atomically flat surface can be realized. Then, a second SiGe layer is grown on the first layer to achieve further strain relaxation. Transmission electron microscopy has clearly revealed that dislocations are dispersively introduced into the first SiGe/Si substrate interface and thus no pile up of dislocations occurs. The formation of a periodic undulation on the growth surface of the second SiGe layer is the key to inducing a drastic reduction in the threading dislocation density. © 2001 American Institute of Physics.