On the quasi-steady-state assumption in modeling Czochralski crystal growth

J. J. Derby; R. A. Brown

doi:10.1016/0022-0248(88)90172-8

On the quasi-steady-state assumption in modeling Czochralski crystal growth

J. J. Derby, R. A. Brown

Chemical Engineering and Materials Science

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Abstract

The validity of the quasi-steady-state (QSS) assumption for describing conventional Czochralski crystal growth is addressed by a scaling analysis and by comparisons of numerical calculations for a QSS thermal-capillary model with results from a transient model which includes all of the dynamics associated with the growth process. The QSS model fails to accurately predict the operating states during batchwise growth when the crystal shape changes appreciably. However, the quasi-steady-state assumption is valid for describing growth runs where crystal diameter control is successfully implemented. An approximate correction for the time-averaged growth rate improves the agreement between QSS and fully transient predictions.

Original language	English (US)
Pages (from-to)	251-260
Number of pages	10
Journal	Journal of Crystal Growth
Volume	87
Issue number	2-3
DOIs	https://doi.org/10.1016/0022-0248(88)90172-8
State	Published - Feb 1988

Bibliographical note

Funding Information:
This research was supported by a grant from the United States Defense Advanced Research Project Agency. We are grateful to PD. Thomas for his assistance with the preparation of the figures in this paper.

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title = "On the quasi-steady-state assumption in modeling Czochralski crystal growth",

abstract = "The validity of the quasi-steady-state (QSS) assumption for describing conventional Czochralski crystal growth is addressed by a scaling analysis and by comparisons of numerical calculations for a QSS thermal-capillary model with results from a transient model which includes all of the dynamics associated with the growth process. The QSS model fails to accurately predict the operating states during batchwise growth when the crystal shape changes appreciably. However, the quasi-steady-state assumption is valid for describing growth runs where crystal diameter control is successfully implemented. An approximate correction for the time-averaged growth rate improves the agreement between QSS and fully transient predictions.",

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On the quasi-steady-state assumption in modeling Czochralski crystal growth

Abstract

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