Simulation of Industrial Crystal Growth by the Vertical Bridgman Method
Single crystals of Cadmium-Zinc-Telluride are used as a substrate material for the production of infrared detectors and are usually grown by the vertical Bridgman method. We present a simulation of the whole growth process in two steps: In the first step,
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Kristallographisches Institut, Universitat Freiburg, Hebelstr. 25, 79104 Freiburg, Germany http://www.krist.uni-freiburg.de Institut fiir Angewandte Mathematik, Universitat Freiburg, Hermann-Herder-Str. 10, 79104 Freiburg, Germany http://www.mathematik.uni-freiburg.de/IAM Zentrum fiir Technomathematik, Universitat Bremen, Postfach 330440, 28334 Bremen, Germany http://www.math.uni-bremen.de/zetem
Abstract. Single crystals of Cadmium-Zinc-Telluride are used as a substrate material for the production of infrared detectors and are usually grown by the vertical Bridgman method. We present a simulation of the whole growth process in two steps: In the first step, the (stationary) heat transport in the furnace is modeled and calculated for different positions of the ampoule. This provides information about the most important parameter during this process: the temperature distribution in furnace and ampoule. The obtained temperatures are then used in the second step as boundary conditions for the (time dependent) simulation of temperature and convection in the ampoule. Only the use of adaptive finite element methods allows an efficient numerical simulation of the moving phase boundary, the convection in the melt and the temperature distribution in melt and crystal. Numerical results are presented for both furnace and ampoule simulations.
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Introduction
Single crystals of the semiconductor Cadmium-Zinc-Telluride (Cd,Zn)Te are excellent substrate materials for growth of thin Mercury-Cadmium-Telluride (Hg,Cd)Te layers, which are used as detector material for infrared radiation, see [7]. Such (Cd,Zn)Te crystals are usually grown by the vertical Bridgman method, where an ampoule with material melt is moved in a temperature field such that the material slowly crystallizes. Fig. 1 shows the schematics of the furnace with ampoule and heating distribution. The material, which is placed in a sealed quartz-glass ampoule, is molten in the hot area of the crystal growth furnace. To start the crystallization process, a relative motion between the furnace and the ampoule is started resulting in a temperature reduction at the lower end of the growth ampoule. When the temperature at the bottom falls below the melting temperature the crystallization process starts. With further movement more and more W. Jäger et al. (eds.), Mathematics - Key Technology for the Future © Springer-Verlag Berlin Heidelberg 2003
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Fig. 1. Schematics of growth furnace and heating distribution material solidifies until finally the whole crystal is grown. The most important parameter during this process is the temperature distribution in furnace and ampoule. In the industrial production of infrared detectors, a significant dependence of the efficiency of the manufactured detectors on the quality of the substrate material is observed. Therefore an investigation of the growth conditions for the substrate material becomes necessary, to optimize the production process. Key param
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