The present status of numerical simulation of crystal growth processes, especially by the Czochra... more The present status of numerical simulation of crystal growth processes, especially by the Czochralski technique, is discussed by comparison of numerical and experimental results. It is shown in which cases the convective heat transport in the melt has to be considered in order to give realistic numerical results. Furthermore, examples were presented in which 2-dimensional simulations agree with experiments and cases where a 3-dimensional simulation is necessary. Finally, it will be shown that for a simulation of doping distribution in the crystal, i.e. segregation, the crystal melt interface has to be treated as a “moving boundary”.
ABSTRACT Melt growth is the most important growth method for the production of bulk single crysta... more ABSTRACT Melt growth is the most important growth method for the production of bulk single crystals of semiconductors, oxides, metals and other materials. Its technology can only be understood or improved by a profound knowledge of the underlying fundamentals, like phase diagrams, growth kinetics, heat and species transport. This article treats relevant aspects of these fundamentals in close correlation to the most important melt growth processes, the Czochralski and Gradient Freeze (Bridgman) methods.
We have theoretically analyzed buoyancy-driven convection in directional solidification configura... more We have theoretically analyzed buoyancy-driven convection in directional solidification configurations under the influence of additional forces acting on flow on a centrifuge, the centrifugal and the Coriolis forces. The influence of centrifugation on buoyancy-driven convection in the melt depends on the following conditions: the geometrical orientation of the melt cylinder on the centrifuge, the presence of radial temperature gradients in the melt (curved crystal-melt interface), the centrifuge radius, and the rotation rate of the centrifuge. The behaviour of convection depends on the complex interaction of buoyancy and Coriolis forces. It is demonstrated by theoretical considerations and experiments that a suppression of the vigor of convection up to one order of magnitude is possible under certain conditions on the centrifuge.
Proceedings of 8th International Conference on Indium Phosphide and Related Materials, 1996
The potential of the VGF process is analysed by using a flat bottom crucible for the growth of In... more The potential of the VGF process is analysed by using a flat bottom crucible for the growth of InP crystals with 2" diameter. Results of numerical simulations are used to design a set-up which can be run in a LEC facility. The EPD ≈3·103 cm-2 of the grown crystals is in accordance with calculated results based on an analysis of
Convective flows in water in a vertical cylindrical test cell heated from below were studied. A s... more Convective flows in water in a vertical cylindrical test cell heated from below were studied. A sequence of different stable flow configurations is found. The time dependent convection is characterized by well defined frequencies. Water results were compared with results of the directional solidification of InSb by the vertical Bridgman technique. A clear correlation of material inhomogeneities and unsteady thermal convection is possible using theoretical results of the critical Rayleigh number (Ra). The first flow configuration which occurs at slightly supercritical Ra is a steady unicellular antisymmetric roll. At higher Ra staggering of rolls occurs only in vertical direction. The shape and aspect ratio of the container can influence the flow transitions.
ABSTRACT The low-loss and the favorable dispersion characteristics of silica monomode fibers for ... more ABSTRACT The low-loss and the favorable dispersion characteristics of silica monomode fibers for wavelength of 1.3 μm and 1.55 μm have selected the materials for sources and detectors in terms of epitaxial layers of Ga1-xInxAs1-yPy lattice matched to InP substrates. InP has in addition also remarkable electronic properties and is also used as an active material for various types of electronic devices (FETs). However, to make this technological conception with a combination of sophisticated optoelectronic and electronic devices reliable and effective for optical fiber communication, it is absolutely necessary to work towards integration, i.e., optoelectronic integrated circuits (OEICs). The fabrication of these OEICs needs large diameter wafers with a high resistivity (semi-insulating material) and with a high material quality which is presently not available. The paper discusses the requirements concerning the physical properties of the InP-material and gives a perspective in how far these requirements can be met in the near future by the various InP crystal growth methods.
ABSTRACT Electrical resistance measurements were evaluated as a method to study phase transformat... more ABSTRACT Electrical resistance measurements were evaluated as a method to study phase transformations and reactions during thermal processing of metallic thin film precursors for chalcopyrite solar cells. The CuInSe2 (CIS) absorbers were formed by the stacked elemental layer (SEL) process. Pure Cu films were investigated, as well as sequentially evaporated Cu–In and Cu–Ga thin film stacks. According to Kissinger the activation energy of a chemical reaction can be determined by evaluating the temperature of maximum reaction rate depending on the (constant) heating rate of the samples. The Kissinger-evaluation of the activation energy of the Cu11In9 formation derived from the resistance measurements in this work was in good match with prior calorimetric results. The speed of the electric measurements (up to 50/s) was high enough to resolve even fast melting reactions. Very slow reactions could be measured reproducibly. Variations in the temperature-dependent behaviour of different samples could be correlated to the influence of the precursor morphology on the reaction kinetics; i.e. the dewetting of an elemental layer in the precursor led to a higher diffusion length, and therefore, delayed reactions. The substrate temperature during Cu-deposition had an influence on the Cu–Ga reaction kinetics. To conclude, electric resistance measurements during the thermal processing of thin film SEL-precursors could serve to determine kinetic parameters and to analyse the influence of different deposition processes on the reaction behaviour.
The dissolution of the silica crucible by the silicon melt acts as a source of oxygen doping in t... more The dissolution of the silica crucible by the silicon melt acts as a source of oxygen doping in the growth of silicon single crystals by the Czochralski-method. Literature data on the dissolution rate of silica in silicon melts are available up to now only from ex-situ measurements. These data were obtained by measuring the decrease of the diameter of silica rods or plates dipped into a silicon melt. In the present work, the silica dissolution rate is measured for the first time by an in-situ technique. The decrease of the thickness of the wall of a silica crucible of a laboratory-scale Czochralski crucible containing silicon melt is measured by optical laser interferometry. The obtained results are compared quantitatively to literature data obtained by the above-mentioned ex-situ technique.
ABSTRACT Oxygen concentration and distribution in Czochralski silicon melts were investigated by ... more ABSTRACT Oxygen concentration and distribution in Czochralski silicon melts were investigated by an electrochemical oxygen sensor, based on the solid ionic conductor zirconia. Crucible rotation was found to have a strong influence on the oxygen distribution in the silicon melt. The forced convection driven by the crucible rotation dominates the oxygen transport in the melt compared to diffusion. Concentration variations in the melt measured during crystal growth were subsequently compared with changes of the oxygen content of the grown crystal.
The present status of numerical simulation of crystal growth processes, especially by the Czochra... more The present status of numerical simulation of crystal growth processes, especially by the Czochralski technique, is discussed by comparison of numerical and experimental results. It is shown in which cases the convective heat transport in the melt has to be considered in order to give realistic numerical results. Furthermore, examples were presented in which 2-dimensional simulations agree with experiments and cases where a 3-dimensional simulation is necessary. Finally, it will be shown that for a simulation of doping distribution in the crystal, i.e. segregation, the crystal melt interface has to be treated as a “moving boundary”.
ABSTRACT Melt growth is the most important growth method for the production of bulk single crysta... more ABSTRACT Melt growth is the most important growth method for the production of bulk single crystals of semiconductors, oxides, metals and other materials. Its technology can only be understood or improved by a profound knowledge of the underlying fundamentals, like phase diagrams, growth kinetics, heat and species transport. This article treats relevant aspects of these fundamentals in close correlation to the most important melt growth processes, the Czochralski and Gradient Freeze (Bridgman) methods.
We have theoretically analyzed buoyancy-driven convection in directional solidification configura... more We have theoretically analyzed buoyancy-driven convection in directional solidification configurations under the influence of additional forces acting on flow on a centrifuge, the centrifugal and the Coriolis forces. The influence of centrifugation on buoyancy-driven convection in the melt depends on the following conditions: the geometrical orientation of the melt cylinder on the centrifuge, the presence of radial temperature gradients in the melt (curved crystal-melt interface), the centrifuge radius, and the rotation rate of the centrifuge. The behaviour of convection depends on the complex interaction of buoyancy and Coriolis forces. It is demonstrated by theoretical considerations and experiments that a suppression of the vigor of convection up to one order of magnitude is possible under certain conditions on the centrifuge.
Proceedings of 8th International Conference on Indium Phosphide and Related Materials, 1996
The potential of the VGF process is analysed by using a flat bottom crucible for the growth of In... more The potential of the VGF process is analysed by using a flat bottom crucible for the growth of InP crystals with 2" diameter. Results of numerical simulations are used to design a set-up which can be run in a LEC facility. The EPD ≈3·103 cm-2 of the grown crystals is in accordance with calculated results based on an analysis of
Convective flows in water in a vertical cylindrical test cell heated from below were studied. A s... more Convective flows in water in a vertical cylindrical test cell heated from below were studied. A sequence of different stable flow configurations is found. The time dependent convection is characterized by well defined frequencies. Water results were compared with results of the directional solidification of InSb by the vertical Bridgman technique. A clear correlation of material inhomogeneities and unsteady thermal convection is possible using theoretical results of the critical Rayleigh number (Ra). The first flow configuration which occurs at slightly supercritical Ra is a steady unicellular antisymmetric roll. At higher Ra staggering of rolls occurs only in vertical direction. The shape and aspect ratio of the container can influence the flow transitions.
ABSTRACT The low-loss and the favorable dispersion characteristics of silica monomode fibers for ... more ABSTRACT The low-loss and the favorable dispersion characteristics of silica monomode fibers for wavelength of 1.3 μm and 1.55 μm have selected the materials for sources and detectors in terms of epitaxial layers of Ga1-xInxAs1-yPy lattice matched to InP substrates. InP has in addition also remarkable electronic properties and is also used as an active material for various types of electronic devices (FETs). However, to make this technological conception with a combination of sophisticated optoelectronic and electronic devices reliable and effective for optical fiber communication, it is absolutely necessary to work towards integration, i.e., optoelectronic integrated circuits (OEICs). The fabrication of these OEICs needs large diameter wafers with a high resistivity (semi-insulating material) and with a high material quality which is presently not available. The paper discusses the requirements concerning the physical properties of the InP-material and gives a perspective in how far these requirements can be met in the near future by the various InP crystal growth methods.
ABSTRACT Electrical resistance measurements were evaluated as a method to study phase transformat... more ABSTRACT Electrical resistance measurements were evaluated as a method to study phase transformations and reactions during thermal processing of metallic thin film precursors for chalcopyrite solar cells. The CuInSe2 (CIS) absorbers were formed by the stacked elemental layer (SEL) process. Pure Cu films were investigated, as well as sequentially evaporated Cu–In and Cu–Ga thin film stacks. According to Kissinger the activation energy of a chemical reaction can be determined by evaluating the temperature of maximum reaction rate depending on the (constant) heating rate of the samples. The Kissinger-evaluation of the activation energy of the Cu11In9 formation derived from the resistance measurements in this work was in good match with prior calorimetric results. The speed of the electric measurements (up to 50/s) was high enough to resolve even fast melting reactions. Very slow reactions could be measured reproducibly. Variations in the temperature-dependent behaviour of different samples could be correlated to the influence of the precursor morphology on the reaction kinetics; i.e. the dewetting of an elemental layer in the precursor led to a higher diffusion length, and therefore, delayed reactions. The substrate temperature during Cu-deposition had an influence on the Cu–Ga reaction kinetics. To conclude, electric resistance measurements during the thermal processing of thin film SEL-precursors could serve to determine kinetic parameters and to analyse the influence of different deposition processes on the reaction behaviour.
The dissolution of the silica crucible by the silicon melt acts as a source of oxygen doping in t... more The dissolution of the silica crucible by the silicon melt acts as a source of oxygen doping in the growth of silicon single crystals by the Czochralski-method. Literature data on the dissolution rate of silica in silicon melts are available up to now only from ex-situ measurements. These data were obtained by measuring the decrease of the diameter of silica rods or plates dipped into a silicon melt. In the present work, the silica dissolution rate is measured for the first time by an in-situ technique. The decrease of the thickness of the wall of a silica crucible of a laboratory-scale Czochralski crucible containing silicon melt is measured by optical laser interferometry. The obtained results are compared quantitatively to literature data obtained by the above-mentioned ex-situ technique.
ABSTRACT Oxygen concentration and distribution in Czochralski silicon melts were investigated by ... more ABSTRACT Oxygen concentration and distribution in Czochralski silicon melts were investigated by an electrochemical oxygen sensor, based on the solid ionic conductor zirconia. Crucible rotation was found to have a strong influence on the oxygen distribution in the silicon melt. The forced convection driven by the crucible rotation dominates the oxygen transport in the melt compared to diffusion. Concentration variations in the melt measured during crystal growth were subsequently compared with changes of the oxygen content of the grown crystal.
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