A Coupled Approach to Compute the Dislocation Density Development during Czochralski Growth and Its Application to the Growth of High-Purity Germanium (HPGe)
Wolfram Miller,
Andrejs Sabanskis,
Alexander Gybin,
Kevin-P. Gradwohl,
Arved Wintzer,
Kaspars Dadzis,
Jānis Virbulis,
Radhakrishnan Sumathi
Affiliations
Wolfram Miller
Leibniz-Institut für Kristallzüchtung (IKZ), Max-Born-Str. 2, 12489 Berlin, Germany
Andrejs Sabanskis
Institute of Numerical Modelling, University of Latvia, Jelgavas Street 3, LV-1004 Riga, Latvia
Alexander Gybin
Leibniz-Institut für Kristallzüchtung (IKZ), Max-Born-Str. 2, 12489 Berlin, Germany
Kevin-P. Gradwohl
Leibniz-Institut für Kristallzüchtung (IKZ), Max-Born-Str. 2, 12489 Berlin, Germany
Arved Wintzer
Leibniz-Institut für Kristallzüchtung (IKZ), Max-Born-Str. 2, 12489 Berlin, Germany
Kaspars Dadzis
Leibniz-Institut für Kristallzüchtung (IKZ), Max-Born-Str. 2, 12489 Berlin, Germany
Jānis Virbulis
Institute of Numerical Modelling, University of Latvia, Jelgavas Street 3, LV-1004 Riga, Latvia
Radhakrishnan Sumathi
Leibniz-Institut für Kristallzüchtung (IKZ), Max-Born-Str. 2, 12489 Berlin, Germany
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.
