Vertical pin structures of Ge photodiodes (PDs) integrated with Si optical waveguides are fabricated by depositing Ge epitaxial layers on Si-on-insulator (SOI) layers, and the performances of n+-Ge/i-Ge/p+-SOI PDs are compared with those of p+-Ge/i-Ge/n+-SOI PDs. Both types of PDs show responsivities as high as 1.0 A/W at 1.55 µm, while the dark leakage current is different, which is consistent with previous reports on free-space PDs formed on bulk Si wafers. The dark current of the p+-Ge/i-Ge/n+-SOI PDs is higher by more than one order of magnitude. Taking into account the activation energies for dark current as well as the dependence on PD area, the dark current of the n+-Ge/i-Ge/p+-SOI PDs is dominated by the thermal generation of carriers via mid-gap defect levels in Ge, while for the p+-Ge/i-Ge/n+-SOI PDs, the dark current is ascribed to not only thermal generation but also other mechanisms such as locally formed conduction paths.