The high strength, radiation hardness and cost-effectiveness make Germanium the substrate of choice for high-efficiency multi-junction solar cells for space applications. Numerical modeling and large-scale simulation are important and indispensable tools in the analysis and development of crystal growth process. In this study, germanium single crystals with low dislocation density were produced by Czochralski method by applying the necking technique. Chemical etching pits method was used to measure the dislocation density, and a professional modeling software CrysVUn was used to obtain the thermal-stress distribution. The results show that the thermal-stress of the sample with diameter of 15 mm is nearly equal to that of other samples, so the thermal-stress does not influence the dislocation multiplication. Based on the result, the dislocation density must be strangely increased caused by gravity. The high strength, radiation hardness and cost-effectiveness make Germanium the substrate of choice for high-efficiency multi-junction solar cells for space applications. Numerical modeling and large-scale simulation are important and indispensable tools in the analysis and development of crystal growth process . In this study, germanium single crystals with low dislocation density were produced by Czochralski method by applying the necking technique. Chemical etching pits method was used to measure the dislocation density, and a professional modeling software CrysVUn was used to obtain the thermal-stress distribution . The results show that the thermal-stress of the sample with diameter of 15 mm is nearly equal to that of other samples, so the thermal-stress does not influence the dislocation multiplication. Based on the result, the dislocation density must be strangely increased caused by gravity.