Please use this identifier to cite or link to this item:
Title: Stability analysis of the first order steady-state solution in the czochralski crystal growth process
Authors: Gerges, Najib N. 
Fares, Nabil
Snider, Arthur David
Affiliations: Department of Civil and Environmental Engineering 
Department of Civil and Environmental Engineering 
Keywords: Czochralski crystal growth
Periodic fluctuations
Steady-state solution
Perturbation theory
Finite differences
Issue Date: 2010
Part of: NED university journal of research
Volume: 7
Issue: 2
Start page: 85
End page: 98
The Czochralski crystal growth manufacturing process results in small periodic and undesirable fluctuations in the crystal diameter under certain conditions. These fluctuations have strongly nonlinear characteristics and seem 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 were obtained. Secondly, numerically-based steady-state solutions of these equations were calculated, and finally, the stability of the steady-state solutions was examined. It was 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 were 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 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.
Ezproxy URL: Link to full text
Type: Journal Article
Appears in Collections:Department of Civil and Environmental Engineering

Show full item record

Record view(s)

checked on Jun 4, 2023

Google ScholarTM


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.