*Article* **Numerical Simulation of Species Segregation and 2D Distribution in the Floating Zone Silicon Crystals**

**Kirils Surovovs 1,\*, Maksims Surovovs 1, Andrejs Sabanskis 1, Janis Virbulis ¯ 1, Kaspars Dadzis 2, Robert Menzel <sup>2</sup> and Nikolay Abrosimov <sup>2</sup>**


**Abstract:** The distribution of dopants and impurities in silicon grown with the floating zone method determines the electrical resistivity and other important properties of the crystals. A crucial process that defines the transport of these species is the segregation at the crystallization interface. To investigate the influence of the melt flow on the effective segregation coefficient as well as on the global species transport and the resulting distribution in the grown crystal, we developed a new coupled numerical model. Our simulation results include the shape of phase boundaries, melt flow velocity and temperature, species distribution in the melt and, finally, the radial and axial distributions in the grown crystal. We concluded that the effective segregation coefficient is not constant during the growth process but rather increases for larger melt diameters due to less intensive melt mixing.

**Keywords:** silicon single crystals; floating zone; effective segregation coefficient; numerical modelling

**Citation:** Surovovs, K.; Surovovs, M.; Sabanskis, A.; Virbulis, J.; Dadzis, K.; Menzel, R.; Abrosimov, N. Numerical Simulation of Species Segregation and 2D Distribution in the Floating Zone Silicon Crystals. *Crystals* **2022**, *12*, 1718. https://doi.org/10.3390/ cryst12121718

Academic Editors: Mingyang Chen, Jinbo Ouyang and Dandan Han

Received: 31 October 2022 Accepted: 19 November 2022 Published: 26 November 2022

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