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The scaling characteristics of both n- and p-channel Ge-on-insulator (GOI) as well as silicon-on-insulator (SOI) MOSFETs with channel length ranging from 20-130 nm are studied by a two-dimensional self-consistent fullband Monte Carlo device simulator. The transistors' intrinsic performance and subthreshold characteristics are investigated for various channel lengths and Ge layer thicknesses. Our results indicate that both n- and p-channel GOI MOSFETs can be scaled down to the nanoregion, due to the nonstationary transport, especially for the p-channel device. More than 10% performance improvement for nMOS and about 20% for pMOS can be achieved in GOI even when channel length is scaled down to 20 nm, as compared to SOI devices. However, the GOI devices suffer from more severe short channel effect and have larger p-n junction leakage current as compared to SOI counterpart. For high-performance CMOS applications, GOI devices are feasible if the junction leakage can be reduced by optimizing the device structure.