In this work, we characterized defects in SiGe-On-Insulator (SGOI) and Ge-On-Insulator (GOI) by optical and electrical methods. All the SGOI and GOI substrates in this work were fabricated using Ge condensation by dry oxidation method. Defect generation and transformation during the temperature ramp-up process of Ge condensation were clarified by photoluminescence. The location of main defect levels were determined to be above mid-gap by back-gate metal-oxide-semiconductor field-effect-transistor (MOSFET) current deep-level-transient-spectroscopy and dual-metal-oxide-semiconductor thermally stimulated capacitance. The defects in fabricated SGOI and GOI were directly observed by transmission-electron-microscopy. These defects unintentionally induced high hole concentration in SGOI and GOI. The dependence of energy level position on Ge fraction was investigated in detail for the defect-related acceptor levels by Hall effect and back-gate MOSFET drain current vs. gate bias voltage. The suppressions of defects by post-Al-deposition-annealing and forming gas annealing were also discussed.