In order to suppress dislocation generation, we develop a "three-step growth" method to heteroepitaxy low dislocation density germanium (Ge) layers on silicon with the MBE process. The method is composed of 3 growth steps: low temperature (LT) seed layer, LT-HT intermediate layer as well as high temperature (HT) epilayer, successively. Threading dislocation density (TDD) of epitaxial Ge layers is measured as low as 1.4 x 106 cm(-2) by optimizing the growth parameters. The results of Raman spectrum showed that the internal strain of heteroepitaxial Ge layers is tensile and homogeneous. During the growth of LT-HT intermediate layer, TDD reduction can be obtained by lowering the temperature ramping rate, and high rate deposition maintains smooth surface morphology in Ge epilayer. A mechanism based on thermodynamics is used to explain the TDD and surface morphological dependence on temperature ramping rate and deposition rate. Furthermore, we demonstrate that the Ge layer obtained can provide an excellent platform for III-V materials integrated on Si. (C) 2018 Elsevier B.V. All rights reserved.