Abstract
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.
Highlights
In contrast to silicon, it is still a challenge to grow germanium crystals without dislocations.In specific cases, it is even not wanted to grow dislocation free, but to keep the dislocation density in a certain range
It is even not wanted to grow dislocation free, but to keep the dislocation density in a certain range. This applies for Ge used in radiation detectors, where the Ge crystal is grown in hydrogen atmosphere and not in argon because of purity reasons
Dislocation multiplication is driven by thermal stresses, and tuning the thermal field in the crystal is of severe importance
Summary
It is still a challenge to grow germanium crystals without dislocations. In the case of inductive heating, which is required to grow Ge crystals for detectors, the tuning of the thermal field is much more challenging. Only the temperature field including the interface shape was computed for three distinctive growth stages. Later, they considered thermal stress, but for a configuration with a resistance heater [5]. In order to obtain information on dislocation density development, it is essential to simulate the entire growth process. This can be done in one run solving the time dependent heat transport equation. Any artificial shape can be given as an input for the computation
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