Transient global modeling for the pulling process of Czochralski silicon crystal growth. I. Principles, formulation, and implementation of the model

Xin Liu, Hirofumi Harada, Yoshiji Miyamura, Xue feng Han, Satoshi Nakano, Shin ichi Nishizawa, Koichi Kakimoto

Research output: Contribution to journalArticle

Abstract

A transient global model for the crystal pulling process was developed for magnetic-field-applied Czochralski silicon (CZ-Si) growth. Heat transfer by solid conduction, melt convection, and diffuse gray radiation is taken into account for the crystal, melt, and other components in the furnace. The mesh adaption and view factor updating for the dynamic pulling process were realized by the structured grid deformations for different domains. By imposing the thermal boundary conditions in the vicinity of the triple point, the inverse control by the virtual proportional integral derivative controller and heat flux is acceptable for the transient global simulation of the pulling process in CZ-Si crystal growth. The applied cusp-shaped magnetic field (CMF) suppressed the turbulent melt flow and stabilized the heat and mass transport. CMF with different zero-Gauss-plane locations resulted in different flow patterns, which could affect the impurity transport during the pulling process. This developed transient global model can be applied for the segregation predictions of impurities (oxygen and carbon) and dopants in the CZ-Si growing process.

Original languageEnglish
Article number125405
JournalJournal of Crystal Growth
Volume532
DOIs
Publication statusPublished - Feb 15 2020

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pulling
Silicon
Crystallization
Crystal growth
crystal growth
Magnetic fields
formulations
silicon
cusps
Impurities
Crystals
magnetic fields
impurities
Flow patterns
Heat flux
Furnaces
Carbon
Mass transfer
Doping (additives)
Boundary conditions

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Inorganic Chemistry
  • Materials Chemistry

Cite this

Transient global modeling for the pulling process of Czochralski silicon crystal growth. I. Principles, formulation, and implementation of the model. / Liu, Xin; Harada, Hirofumi; Miyamura, Yoshiji; Han, Xue feng; Nakano, Satoshi; Nishizawa, Shin ichi; Kakimoto, Koichi.

In: Journal of Crystal Growth, Vol. 532, 125405, 15.02.2020.

Research output: Contribution to journalArticle

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AU - Nakano, Satoshi

AU - Nishizawa, Shin ichi

AU - Kakimoto, Koichi

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