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Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik × Subject: numerical simulation ×

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Now showing 1 - 3 of 3
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    3D-Simulation von Halbleiterdetektoren : Schlussbericht
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2001) Gajewski, Herbert
    [no abstract available]
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    Mathematical modeling of Czochralski type growth processes for semiconductor bulk single crystals
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Dreyer, Wolfgang; Druet, Pierre-Étienne; Klein, Olaf; Sprekels, Jürgen
    This paper deals with the mathematical modeling and simulation of crystal growth processes by the so-called Czochralski method and related methods, which are important industrial processes to grow large bulk single crystals of semiconductor materials such as, e.,g., gallium arsenide (GaAs) or silicon (Si) from the melt. In particular, we investigate a recently developed technology in which traveling magnetic fields are applied in order to control the behavior of the turbulent melt flow. Since numerous different physical effects like electromagnetic fields, turbulent melt flows, high temperatures, heat transfer via radiation, etc., play an important role in the process, the corresponding mathematical model leads to an extremely difficult system of initial-boundary value problems for nonlinearly coupled partial differential equations ...
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    Spin coating of an evaporating polymer solution
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Münch, Andreas; Please, Colin P.; Wagner, Barbara
    We consider a mathematical model of spin coating of a single polymer blended in a solvent. The model describes the one-dimensional development of the thin layer of the mixture as the layer thins due to flow created by a balance of viscous forces and centrifugal forces and due to evaporation of the solvent. In the model both the diffusivity of the solvent in the polymer and the viscosity of the mixture are very rapidly varying functions of the solvent volume fraction. Guided by numerical solutions an asymptotic analysis reveals a number of different possible behaviours of the thinning layer dependent on the nondimensional parameters describing the system. The main practical interest is in controlling the appearance and development of a ``skin'' on the polymer where the solvent concentration reduces rapidly on the outer surface leaving the bulk of the layer still with high concentrations of solvent. The critical parameters controlling this behaviour are found to be eps the ratio of the diffusion to advection time scales, delta the ratio of the evaporation to advection time scales and exp(-gamma), the ratio of the diffusivity of the initial mixture and the pure polymer. In particular, our analysis shows that for very small evaporation with delta ll exp(-3/(4gamma)) eps^3/4 skin formation can be prevented