Pure Ge/Si heterostructures were epitaxially grown on Si in order to obtain Si-integrated photodetectors in the near-infrared region. Samples grown with different procedures are compared. Graded buffer layers of Si1-xGex with x variable as a function of depth were grown in order to relax the stress. On top of these, pure Ge layers were grown. The mechanism of strain relaxation has been investigated by transmission electron microscopy and the surface morphology by scanning electron microscopy. The results on different samples are discussed and compared in terms of structural properties and photoresponse, in an attempt to correlate structural defects to photodetector efficiency.