White-beam X-ray topography has been performed to provide direct evidence of micro-voids in dislocation-free high-purity germanium single crystals. The voids are visible because of a dynamical diffraction contrast. It is shown that voids occur only in dislocation-free parts of the crystal and do not show up in regions with homogeneous and moderate dislocation density. It is further suggested that the voids originate from clustering of vacancies during the growth process. A general method is proposed to verify the presence of voids for any crystalline material of high structural perfection.

A numerical scheme was developed to compute the thermal and stress fields of the Czochralski process in a quasi-time dependent mode. The growth velocity was computed from the geometrical changes in melt and crystal due to pulling for every stage, for which the thermal and stress fields were computed by using the open source software Elmer. The method was applied to the Czochralski growth of Ge crystals by inductive heating. From a series of growth experiments, we chose one as a reference to check the validity of the scheme with respect to this Czochralski process. A good agreement both for the shapes of the melt/crystal interface at various time steps and the change in power consumption with process time was observed.

The evolution of the dislocation density during Czochralski growth is computed by the combination of global thermal calculations and local computation of the stress and dislocation density in the crystal. The global simulation was performed using the open-source software Elmer (version 8.4) and the local simulation with the open-source software MACPLAS (version of 23.1.2023). Interpolation both in space and time was used to transfer the boundary conditions from the global simulations to the local model, which uses a different mesh discretization and a considerably smaller time step. We applied this approach to the Czochralski growth of a high-purity Ge crystal. The heater power change predicted by the global model as well as the final dislocation density distribution in the crystal simulated by the local model are correlated to the experimental results.