Stability and bifurcation analysis of flow field in Bridgman crystal growth

• Main Authors: Chen, Ming-kuan, 陳明寬
• Other Authors: Chung-wen Lan
• Format: Others
• Language: zh-TW
• Published: 1997
• Online Access: http://ndltd.ncl.edu.tw/handle/03032598187407015570

碩士 === 國立中央大學 === 化學工程學系 === 85 === The Bridgman method has been widely used in semiconductor crystal growth.Two configurations the method, horizontal and vertical, are often used. For the vertical mode with the melt on the bottom, the so-calledinverse Bridgman method, in particularly, thecomplicate due to flow bifurcationsimilar to two-phase Rayleigh-Benard (RB) problem. For the horizontal mode, unstabletime dependent flows are often observed for low-Prandtl- number semiconductors.In order to better understand such interesting and complicate phenomena, numericalnonlinear analysis is necessary.In this thesis, a numerical nonlinear analysis tool is developed. Themethoda finite-volume/Newton's methodusing a numerical Jacobian matrix and an iterative matrix solver.In addition to the construction of bifurcation diagrams, the stabilityof various solution families is further examined by their leadingeigenvalues based on linear stability analysis.Form the result of RB problem, with the unknow interface, the bifurcation behavior is quitedifferent from the one without the interface.The interface not only destabilizes the system and leads to slightlyasymmetric bifurcation, but also makes the bifurcation more complicatedue to boundary deformation. With a smaller aspect ratio, the firstprimary bifurcation is supercritical, but it may become transcriticalas the aspect ratio increase.When the system is tilted, the bifurcation becomes imperfect and simpler.For horizontal Bridgman system, with the presence of the interface, the Hopf point appears earlier as comparedwith one-phase one, and its freqency is smaller.Fully transient calculations are also performed. Near the Hopf point, thefreqency evaluated leading eigenvalues are consistent with the onesmeasured directly from the transient calculations.