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Title: Stability Analysis Of The First-order Steady- State Solution In The Czochralski Crystal Growth Process Using Perturbation Techniques
Authors: Gerges, Najib N. 
Snider, Arthur David
Issa, Camille
Affiliations: Department of Civil and Environmental Engineering 
Keywords: Czochralski crystal growth
Finite differences
Periodic fluctuations
Perturbation theory
Steady-state solution
Issue Date: 2016
Part of: International journal of computational methods and experimental measurements
Volume: 4
Issue: 4
Start page: 604
End page: 614
The Czochralski crystal growth manufacturing process results in small periodic and undesirable fluctuations in the crystal diameter under certain conditions. These fluctuations have strong, non-linear characteristics and are likely to appear at combinations of critical values of certain parameters, such as the rotational velocity, the ratio of crystal radius to crucible radius, and the temperature gradient. This paper uses perturbation theory to try to identify the critical combinations of parameters that lead to these fluctuations. Firstly, the zero and first-order equations are obtained. Secondly, numerically-based steady-state solutions of these equations are calculated, and finally, the stability of the steady-state solutions is examined. It is observed that the steady-state solutions do not exhibit any unusual patterns for any values of the configuration parameters. Furthermore, all the steady-state solutions are found to be stable for all initial conditions; therefore, the steady-state solutions and the analysis of their stability did not indicate the source of the observed fluctuations. This analysis suggests that a better approximation of the equations such as second order perturbation analysis may be needed to identify the conditions that lead to the observed fluctuations.
DOI: 10.2495/CMEM-V4-N4-604-614
Open URL: Link to full text
Type: Journal Article
Appears in Collections:Department of Civil and Environmental Engineering

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