Four types of SGOI (SiGe on Insulator) wafers were fabricated by the combination of SiGe epitaxial growth, SIMOX (Separation by Implanted Oxygen) processes and oxidation. By the cross-sectional TEM (Transmission Electron Microscopy) and EDS (Energy Dispersive Spectroscopy), it is confirmed that each wafer has smooth interface between a top layer (Si or SiGe) and a BOX (buried oxide) layer and Ge atoms in SiGe layer distribute homogeneously for SGOI_A and SGOI_B. Using high-resolution X-ray diffractometry, the crystallographic properties of SiGe layer are characterized with in-plane and out of plane diffraction methods. The lattice constants are calculated for the planes of perpendicular and parallel to wafer surface and the degree of relaxation are estimated for the SiGe layer of each wafer. The rocking curve measurements reveal that the lattice turbulence of SiGe layer is influenced by SIMOX process conditions, Ge content and the layer thickness.