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In this paper, we will demonstrate a novel approach to incorporate Si and/or Ge nanostructures into crystalline rare earth oxides using molecular beam epitaxy (MBE) for nanoelectronic devices application. By efficiently exploiting the growth kinetics during MBE we succeeded in creating semiconductor nanostructures exhibiting various dimensions, ranging from three dimensionally confined quantum dots (QDs) to the quantum wells, where the particles are confined in one dimension. The crystalline rare earth oxide that has been used in this study is the epitaxial gadolinium oxide (Gd2O3). The monolithic heterostructures comprised of Gd2O3-Ge/Si-Gd2O3 grown on Si substrate exhibit excellent crystalline quality with atomically sharp interface.