Physically-based, lumped-parameter models for the prediction of oxygen concentration during Czochralski growth of silicon crystals

Kerry Wang; Holger Koch; Matthias Trempa; Christian Kranert; Jochen Friedrich; Jeffrey J. Derby

doi:10.1016/j.jcrysgro.2021.126384

Physically-based, lumped-parameter models for the prediction of oxygen concentration during Czochralski growth of silicon crystals

Kerry Wang, Holger Koch, Matthias Trempa, Christian Kranert, Jochen Friedrich, Jeffrey J. Derby

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Lumped-parameter models are derived from boundary layer and other physical arguments to describe oxygen concentration levels during the Czochralski (CZ) growth of silicon. These models are assessed against predictions from a detailed, high-fidelity 2D-3D numerical simulation of the entire CZ puller, whose solutions are realistic but require intense computational effort. Comparisons of predictions show that the lumped-parameter model captures the correct trends of melt oxygen levels influenced by melt height, crucible rotation, and crystal rotation. A simple fitting of coefficients provides reasonably good quantitative predictions by the lumped-parameter model, and its near-instantaneous computations make it an interesting candidate for real-time growth optimization and control. Possible model improvements and extensions are discussed.

Original language	English (US)
Article number	126384
Journal	Journal of Crystal Growth
Volume	576
DOIs	https://doi.org/10.1016/j.jcrysgro.2021.126384
State	Published - Dec 15 2021
Externally published	Yes

Bibliographical note

Funding Information:
The authors would like to acknowledge partial support of this work from the University of Minnesota and the CZ3003 project, funded partly by the German Federal Ministry for Economic Affairs and Energy (BMWi) under contract number 0324357A. The authors would like to thank Dr. Thomas Jung for significant, original contributions. We also wish to thank an anonymous reviewer, whose comments substantially improved the paper.

Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

A1. Computer simulation
A1. Convection
A2. Czochralski method
A2. Single Crystal Growth
B2. Semiconducting silicon

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title = "Physically-based, lumped-parameter models for the prediction of oxygen concentration during Czochralski growth of silicon crystals",

abstract = "Lumped-parameter models are derived from boundary layer and other physical arguments to describe oxygen concentration levels during the Czochralski (CZ) growth of silicon. These models are assessed against predictions from a detailed, high-fidelity 2D-3D numerical simulation of the entire CZ puller, whose solutions are realistic but require intense computational effort. Comparisons of predictions show that the lumped-parameter model captures the correct trends of melt oxygen levels influenced by melt height, crucible rotation, and crystal rotation. A simple fitting of coefficients provides reasonably good quantitative predictions by the lumped-parameter model, and its near-instantaneous computations make it an interesting candidate for real-time growth optimization and control. Possible model improvements and extensions are discussed.",

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note = "Funding Information: The authors would like to acknowledge partial support of this work from the University of Minnesota and the CZ3003 project, funded partly by the German Federal Ministry for Economic Affairs and Energy (BMWi) under contract number 0324357A. The authors would like to thank Dr. Thomas Jung for significant, original contributions. We also wish to thank an anonymous reviewer, whose comments substantially improved the paper. Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

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T1 - Physically-based, lumped-parameter models for the prediction of oxygen concentration during Czochralski growth of silicon crystals

AU - Wang, Kerry

AU - Koch, Holger

AU - Trempa, Matthias

AU - Kranert, Christian

AU - Friedrich, Jochen

AU - Derby, Jeffrey J.

N1 - Funding Information: The authors would like to acknowledge partial support of this work from the University of Minnesota and the CZ3003 project, funded partly by the German Federal Ministry for Economic Affairs and Energy (BMWi) under contract number 0324357A. The authors would like to thank Dr. Thomas Jung for significant, original contributions. We also wish to thank an anonymous reviewer, whose comments substantially improved the paper. Publisher Copyright: © 2021 Elsevier B.V.

PY - 2021/12/15

Y1 - 2021/12/15

N2 - Lumped-parameter models are derived from boundary layer and other physical arguments to describe oxygen concentration levels during the Czochralski (CZ) growth of silicon. These models are assessed against predictions from a detailed, high-fidelity 2D-3D numerical simulation of the entire CZ puller, whose solutions are realistic but require intense computational effort. Comparisons of predictions show that the lumped-parameter model captures the correct trends of melt oxygen levels influenced by melt height, crucible rotation, and crystal rotation. A simple fitting of coefficients provides reasonably good quantitative predictions by the lumped-parameter model, and its near-instantaneous computations make it an interesting candidate for real-time growth optimization and control. Possible model improvements and extensions are discussed.

AB - Lumped-parameter models are derived from boundary layer and other physical arguments to describe oxygen concentration levels during the Czochralski (CZ) growth of silicon. These models are assessed against predictions from a detailed, high-fidelity 2D-3D numerical simulation of the entire CZ puller, whose solutions are realistic but require intense computational effort. Comparisons of predictions show that the lumped-parameter model captures the correct trends of melt oxygen levels influenced by melt height, crucible rotation, and crystal rotation. A simple fitting of coefficients provides reasonably good quantitative predictions by the lumped-parameter model, and its near-instantaneous computations make it an interesting candidate for real-time growth optimization and control. Possible model improvements and extensions are discussed.

KW - A1. Computer simulation

KW - A1. Convection

KW - A2. Czochralski method

KW - A2. Single Crystal Growth

KW - B2. Semiconducting silicon

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Physically-based, lumped-parameter models for the prediction of oxygen concentration during Czochralski growth of silicon crystals

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Keywords

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