We report on the integration of Ge p-i-n heterojunction photodiodes on Si substrates. The crucial role of interface defects at the Ge/Si interface on the performance of photodetectors is analyzed and taken into account in the design of the devices. We have designed and fabricated high performance p-i-n Ge photodiodes for the near infrared. Pure Ge is grown by ultra-high-vacuum CVD followed by a cyclic thermal annealing and ion implantation. Devices are fabricated using standard photolithography. The photodiodes exhibit maximum responsivity of 0.8 A/W at 1.3 micrometers and 0.7 A/W at 1.55 micrometers , reverse dark currents in the 20 mA/cm2 range at 1V and response times as short as 520 ps. Our devices are the first p-i-n Ge on Si photodetectors fabricated by CVD and exhibit high performances for a wide range of applications.