A multi-layered structure of a semiconducotr device includes a substrate, and a heteroepitaxial layer having a low dislocation defect density on the substrate. The heteroepitaxial layer consists of a main epitaxial layer and at least one intermediate epitaxial layer sandwished in the main epitaxial layer. At their interface, the heteroepitaxial layer, i.e., the bottom portion of the main epitaxial layer, and the substrate have different lattice constants. Also, the intermediate epitaxial layer has a different lattice constant from that of the portions of the main epitaxial layer contiguous to the intermediate epitaxial layer. The intermediate epitaxial layer also has a thickness smaller than the net thickness of the main epitaxial layer such that the intermediate epitaxial layer absorbs the strain in the heteroepitaxial layer. Thus, it is possible to obtain a multi-layered structure comprising an epitaxial layer that is relatively thin and has a low dislocation defect density.