Validation of strong magnetic field asymptotic models for dopant transport during semiconductor crystal growth

N. Ma; J. S. Walker

doi:10.1016/S0022-0248(97)00236-4

Validation of strong magnetic field asymptotic models for dopant transport during semiconductor crystal growth

N. Ma, J. S. Walker

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

15 Scopus citations

Abstract

This paper presents a numerical solution for the unsteady transport of a dopant during the growth of a semiconductor crystal from a melt with an externally applied magnetic field. This solution confirms the results of an asymptotic model. Both solutions show that at every time during the growth of the crystal, the dopant distribution (1) is very nonuniform throughout the melt, and (2) is far from the instantaneous steady state. The present numerical solution for an arbitrary mass Péclet number Pe_m and an arbitrary Hartmann number Ha predicts a dopant distribution in the crystal, which agrees remarkably well with the dopant distribution predicted by the asymptotic solution for Pe_m ≫ 1 and Ha ≫ 1. The maximum difference between the crystal compositions predicted by these two different approaches is less than 4% for the range of magnetic field strengths considered.

Original language	English
Pages (from-to)	401-409
Number of pages	9
Journal	Journal of Crystal Growth
Volume	180
Issue number	3-4
DOIs	https://doi.org/10.1016/S0022-0248(97)00236-4
State	Published - Oct 1997
Externally published	Yes

Funding

This research was supported by the National Aeronautics and Space Administration under Cooperative Research Agreement NCC8-90, by the National Science Foundation under Grant CTS 94-19484, and by the Division of International Programs of the National Science Foundation. The calculations were performed on the SGI Power Challenge at the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign under Grant CTS 96-0024N.

Funders	Funder number
National Science Foundation	CTS 94-19484
National Aeronautics and Space Administration	NCC8-90

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10.1016/S0022-0248(97)00236-4

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title = "Validation of strong magnetic field asymptotic models for dopant transport during semiconductor crystal growth",

abstract = "This paper presents a numerical solution for the unsteady transport of a dopant during the growth of a semiconductor crystal from a melt with an externally applied magnetic field. This solution confirms the results of an asymptotic model. Both solutions show that at every time during the growth of the crystal, the dopant distribution (1) is very nonuniform throughout the melt, and (2) is far from the instantaneous steady state. The present numerical solution for an arbitrary mass P{\'e}clet number Pem and an arbitrary Hartmann number Ha predicts a dopant distribution in the crystal, which agrees remarkably well with the dopant distribution predicted by the asymptotic solution for Pem ≫ 1 and Ha ≫ 1. The maximum difference between the crystal compositions predicted by these two different approaches is less than 4% for the range of magnetic field strengths considered.",

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AU - Walker, J. S.

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N2 - This paper presents a numerical solution for the unsteady transport of a dopant during the growth of a semiconductor crystal from a melt with an externally applied magnetic field. This solution confirms the results of an asymptotic model. Both solutions show that at every time during the growth of the crystal, the dopant distribution (1) is very nonuniform throughout the melt, and (2) is far from the instantaneous steady state. The present numerical solution for an arbitrary mass Péclet number Pem and an arbitrary Hartmann number Ha predicts a dopant distribution in the crystal, which agrees remarkably well with the dopant distribution predicted by the asymptotic solution for Pem ≫ 1 and Ha ≫ 1. The maximum difference between the crystal compositions predicted by these two different approaches is less than 4% for the range of magnetic field strengths considered.

AB - This paper presents a numerical solution for the unsteady transport of a dopant during the growth of a semiconductor crystal from a melt with an externally applied magnetic field. This solution confirms the results of an asymptotic model. Both solutions show that at every time during the growth of the crystal, the dopant distribution (1) is very nonuniform throughout the melt, and (2) is far from the instantaneous steady state. The present numerical solution for an arbitrary mass Péclet number Pem and an arbitrary Hartmann number Ha predicts a dopant distribution in the crystal, which agrees remarkably well with the dopant distribution predicted by the asymptotic solution for Pem ≫ 1 and Ha ≫ 1. The maximum difference between the crystal compositions predicted by these two different approaches is less than 4% for the range of magnetic field strengths considered.

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Validation of strong magnetic field asymptotic models for dopant transport during semiconductor crystal growth

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