| Summary: | 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.
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