How to provide the constant impurity distribution along the ingot
https://doi.org/10.17073/1609-3577-2018-2-69-82
Abstract
On the basis of segregation study in crystal growth from a thin melt layer in presence of the submerged heater the possibility to obtain the uniform material along the height of the ingot is shown. Numerically in modeling of solidification of 200 mm in a diameter Sb doped Ge the accurate solution with account for convection was found in the central part of the domain to coincide with the one dimension problem for the melt layer beginning from 40 mm. Condition to neglect with convection in mass transfer are to be more rigorous: the melt layer should be less than 20 mm. In this case, one may use Tiller’s equation obtained to calculate the axial impurity distribution in approach of the diffusion-control segregation. The analysis of attempts to describe experimental data of crystal growth by use of the simplified equations has shown their validity in case of account for actual crystal growth rate or change in the melt layer thickness during the run, as in expression find by Marchenko et al. The above said makes it possible for to describe analytically the axial distribution of impurity in the ingot, particularly, for B and P in silicon and to recommend the amount of its concentration over the height. The uniform material in the very end of the solidification process of the rest portion of the ingot can be obtained by the variation of the growth rate due to change in the cooling rate with time.
Keywords
directional crystallization,
the submerged into the melt heater,
multi-crystalline silicon,
characterization,
oxygen and carbon content
Supporting agencies: The authors are grateful to SIMAP for the opportunity to use the ANSYS Fluent software code in the laboratory.
About the Authors
M. A. Gonik
Centre for Material Reseaches «Photon»
Russian Federation
Russian Federation
Cheska Lipa Str., Aleksandrov, Vladimir Region 601655
Michael A. Gonik: Cand. Sci. (Eng.), Director
F. Baltaretu
Technical University of Civil Engineering of Bucharest
Romania
Romania
Lacul Tei Blvd, no. 122-124, Sector 2, Bucharest 510009
Florin Baltaretu: PhD, Professor, Head of the Department of Thermal Engineering
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For citations:
Gonik M.A., Baltaretu F. How to provide the constant impurity distribution along the ingot. Izvestiya Vysshikh Uchebnykh Zavedenii. Materialy Elektronnoi Tekhniki = Materials of Electronics Engineering. 2018;21(2):69-82. (In Russ.) https://doi.org/10.17073/1609-3577-2018-2-69-82
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