High-performance　Ge-on-SOI　p-i-n　waveguide　photodetectors　with　different　sizes　were　fabricated.　The　performances,　in　terms　of　dark-current,　photo　current　responsivity　and　3-dB　bandwidth,　were　well　studied.　A　responsivity　of　0.842　A/W　at　1550　nm　and　dark　current　of　70　nA　was　measured　from　this　detector　at　-1　V.　The　detector　with　a　size　of　4　mu　m　x　10　mu　m　demonstrated　an　optical　band　width　of　19　GHz　at　-5　V　for　1550　nm.　Both　the　experimental　results　and　the　finite-difference　time　domain　simulation　show　that,　when　the　device　size　is　above　a　certain　threshold,　the　absorption　is　not　sensitively　dependent　on　such　designing　parameters　as　the　width　and　length　of　the　photodetector.