Numerical Analysis of Germanium Crystal Growth by the Czochralski Method: Influence of Temperature‐Dependent versus Constant Electrical Conductivity

ABSTRACT

This study presents a numerical investigation of germanium crystal growth via the Czochralski (CZ) method. Two modelling approaches are compared: one that assumes constant electrical conductivity in the graphite crucible and molten germanium, and one that incorporates temperature‐dependent conductivity. The results show that the temperature‐dependent model provides predictions that better reflect the temperature‐dependent behavior of electromagnetic heating, heat transfer and melt convection. These factors lead to smoother thermal gradients, significantly reduced thermal stress and a lower dislocation density in the grown crystal. Specifically, the model predicts reductions of up to 98% in von Mises stress and of at least 15% in dislocation density compared to the constant‐property approach. These findings emphasize that simplified assumptions can obscure vital physical interactions and exaggerate defect formation. Therefore, incorporating realistic, temperature‐dependent material properties is essential for the reliable simulation and optimization of industrial CZ crystal growth processes.