Photodetector (PD) is considered as a key component in the applications of optical communications. With the technology development of germanium (Ge) epitaxy on silicon, the research on waveguide integrated germanium photodetector is becoming more popular for its good photo-response characteristics in the infrared wavelength band. However, to the best of our knowledge, the influence of Ge layer shape on the performance of photodetectors has not been paid attention yet. In this paper, the influence of different shapes of germanium layer on the performance of photodetectors was explored by using the simulation software of Lumerical FDTD and DEVICE. Moreover, responsivity and 3-dB bandwidth on mature silicon-on-insulator (SOI) platform were further studied, respectively. The morphology of epitaxial Ge layer in the lateral PIN-type waveguide integrated photodetector was fully optimized, and the photodetectors theoretically exhibit excellent output performance at the wavelength of 1550nm with a bias voltage of -1 V. Furthermore, the responsivity and 3-dB bandwidth of the trapezoidal Ge photodetectors are obviously higher than that of traditional rectangular germanium photodetectors with lower dark current. In detail, the responsivity in our proposed photodetector structure is 1.04 A/W, the 3-dB bandwidth is as high as 30.8 GHz, and the dark current is as low as 97 nA.