Mathematical modeling of Czochralski type growth processes for semiconductor bulk single crystals

DOI10.1007/s00032-012-0184-9zbMath1257.35181OpenAlexW2056719481MaRDI QIDQ1932782

Olaf Klein, Juergen Sprekels, Wolfgang Dreyer, Pierre-Étienne Druet

Publication date: 21 January 2013

Published in: Milan Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00032-012-0184-9

zbMATH Keywords

optimal controlNavier-Stokes equationsCzochralski methodwell-posednessMaxwell's equationsnumerical simulationcrystal growthradiative heat transferMHD equationsfirst-order necessary optimality conditionsnonlinear PDE systemstraveling magnetic fields

Mathematics Subject Classification ID

Related Items (2)

Higher \(L^p\) regularity for vector fields that satisfy divergence and rotation constraints in dual Sobolev spaces, and application to some low-frequency Maxwell equations ⋮ Optimal control of semiconductor melts by traveling magnetic fields

Uses Software

• PARDISO
• pdelib
• Triangle

Cites Work

• Noncompactness of integral operators modeling diffuse-gray radiation in polyhedral and transient settings
• Weak solutions to a time-dependent heat equation with nonlocal radiation boundary condition and arbitrary \(p\)-summable right-hand side.
• Existence of weak solutions to the time-dependent MHD equations coupled to the heat equation with nonlocal radiation boundary conditions
• Modeling and simulation of sublimation growth of SiC bulk single crystals
• Existence for the stationary MHD-equations coupled to heat transfer with nonlocal radiation effects
• Optimal Control of Three-Dimensional State-Constrained Induction Heating Problems with Nonlocal Radiation Effects
• Optimal Control of a Semilinear PDE with Nonlocal Radiation Interface Conditions
• State-Constrained Optimal Control of Semilinear Elliptic Equations with Nonlocal Radiation Interface Conditions
• Conductive-radiative heat transfer in grey materials
• TRANSIENT CONDUCTIVE–RADIATIVE HEAT TRANSFER: DISCRETE EXISTENCE AND UNIQUENESS FOR A FINITE VOLUME SCHEME
• Weak solutions to a stationary heat equation with nonlocal radiation boundary condition and right‐hand side in L^p (p⩾1)
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