We investigate the photosensitivity spectra of photodiodes based on Si p - i - n structures with single-layered and multilayer self-assembled GeSi/Si(001) nanoisland arrays in the i region, which are grown using a technique combining Si molecular-beam epitaxy and Ge vapor-phase epitaxy, in dependence on the temperature, diode bias, and GeSi nanoisland parameters. We show that the temperature and field dependences of the diode photosensitivity in the spectral range of the interband optical absorption in GeSi nanoislands are determined by the ratio between the rate of emission of photoexcited holes from the nanoislands and the rate of the recombination of excess carriers in them. We demonstrate the possibility of determination of the hole recombination lifetime in GeSi nanoislands from the temperature and field dependences of the photosensitivity.