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  • 1
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    Thermal-capillary analysis of Czochralski and liquid encapsulated Czochralski crystal growth (1986)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: Results are presented from finite element analysis of the Czochralski (CZ) and Liquid Encapsulated Czochralski (LEC) crystal growth processes based on a thermal-capillary model which governs the heat transfer in the system simultaneously with setting the shapes of the melt/solid interface, the melt and encapsulant menisci, and the radius of a steadily growing crystal. Calculations are performed for the small-scale growth of silicon (CZ) and gallium arsenide (LEC). The effects of melt volume and crucible position relative to the heater on the radius of the crystal and the shape of the melt/solid interface are predicted for the CZ system, and the importance of including an accurate representation of the melt meniscus for modeling the process is demonstrated. The additional effect of an encapsulant layer on heat transfer is treated for the LEC method for the cases of totally transparent and opaque encapsulant. The responses of these LEC prototype systems are examined for changes in pull rate and encapsulant volume.
    Keywords: SOLID-STATE PHYSICS
    Type: Journal of Crystal Growth (ISSN 0022-0248); 74; 605-624
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  • 2
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    Thermal-capillary analysis of Czochralski and liquid encapsulated Czochralski crystal growth. II - Processing strategies (1986)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: The pseudosteady-state heat transfer model developed in a previous paper is augmented with constraints for constant crystal radius and melt/solid interface deflection. Combinations of growth rate, and crucible and bottom-heater temperatures are tested as processing parameters for satisfying the constrained thermal-capillary problem over a range of melt volumes corresponding to the sequence occuring during the batchwise Czochralski growth of a small-diameter silicon crystal. The applicability of each processing strategy is judged by the range of existence of the solution, in terms of melt volume and the values of the axial and radial temperature gradients in the crystal.
    Keywords: SOLID-STATE PHYSICS
    Type: Journal of Crystal Growth (ISSN 0022-0248); 75; 227-240
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  • 3
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    Thermal-capillary analysis of small-scale floating zones Steady-state calculations (1986)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: Galerkin finite element analysis of a thermal-capillary model of the floating zone crystal growth process is used to predict the dependence of molten zone shape on operating conditions for the growth of small silicon boules. The model accounts for conduction-dominated heat transport in the melt, feed rod and growing crystal and for radiation between these phases, the ambient and a heater. Surface tension acting on the shape of the melt/gas meniscus counteracts gravity to set the shape of the molten zone. The maximum diameter of the growing crystal is set by the dewetting of the melt from the feed rod when the crystal radius is large. Calculations with small Bond number show the increased zone lengths possible for growth in a microgravity environment. The sensitivity of the method to the shape and intensity of the applied heating distribution is demonstrated. The calculations are compared with experimental observations.
    Keywords: SOLID-STATE PHYSICS
    Type: Journal of Crystal Growth (ISSN 0022-0248); 75; 367-389
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  • 4
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    Fluid mechanics and mass transfer in melt crystal growth: Analysis of the floating zone and vertical Bridgman processes (1986)
    In:  CASI
    Details
    Publication Date: 2013-08-31
    Description: This research program focuses on analysis of the transport mechanisms in solidification processes, especially one of interest to the Microgravity Sciences and Applications Program of NASA. Research during the last year has focused on analysis of the dynamics of the floating zone process for growth of small-scale crystals, on studies of the effect of applied magnetic fields on convection and solute segregation in directional solidification, and on the dynamics of microscopic cell formation in two-dimensional solidification of binary alloys. Significant findings are given.
    Keywords: SOLID-STATE PHYSICS
    Type: The materials processing research base of the Materials Processing Center; p 27-48
    Format: application/pdf
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  • 5
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    Thermal-capillary model for Czochralski growth of semiconductor materials (1985)
    In:  CASI
    Details
    Publication Date: 2016-06-07
    Description: The success of efficiently calculating the temperature field, crystal radius, melt mensicus, and melt/solid interface in the Czochralski crystal growth system by full finite-element solution of the government thermal-capillary model is demonstrated. The model predicts realistic response to changes in pull rate, melt volume, and the thermal field. The experimentally observed phenomena of interface flipping, bumping, and the difficulty maintaining steady-state growth as the melt depth decreases are explained by model results. These calculations will form the basis for the first quantitative picture of Cz crystal growth. The accurate depiction of the melt meniscus is important in calculating the crystal radius and solidification interface. The sensitivity of the results to the equilibrium growth angle place doubt on less sophisticated attempts to model the process without inclusion of the meniscus. Quantitative comparison with experiments should be possible once more representation of the radiation and view factors in the thermal system and the crucible are included. Extensions of the model in these directions are underway.
    Keywords: SOLID-STATE PHYSICS
    Type: JPL Proceedings of the Flat-Plate Solar Array Project Workshop; p 195-214
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  • 6
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    Mathematical Modelling of High-speed Ribbbon Systems: a Case Study of Edge-defined Film-fed Growth (1984)
    In:  CASI
    Details
    Publication Date: 2014-09-12
    Description: Finite element numerical analysis was used to solve the coupled problem of heat transfer and capillarity to describe low and high speed silicon sheet growth in meniscus defined systems. Heat transfer models which neglect the details of convective heat flow in the melt are used to establish operating limits for an EFG system in terms of the growth rate, die temperature and the static head acting on the meniscus. It is shown that convective heat transfer in the melt becomes important only at high growth rates or for materials with low thermal conductivities.
    Keywords: SOLID-STATE PHYSICS
    Type: JPL Proc. of the Flat-Plate Solar Array Proj. Res. Forum on the High-Speed Growth and Characterization of Crystals for Solar Cells; p 311-329
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  • 7
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    Fluid flow in crystallization processes (1982)
    In:  Other Sources
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    Publication Date: 2011-08-18
    Description: Investigations of the interactions of heat, mass, and momentum transport in crystal growth from the melt are described. Studies of the mall-scale floating zone process and on a prototype of the vertical Bridgman growth system were emphasized. In both systems detailed numerical calculations are used to dissect the interplay between fluid convection and dopant segregation. These calculations are based on finite element techniques that make feasible the complete solution of solidification problems which include convection. Other numerical methods were developed for solving thermal models of crystal growth processes with melt/gas menisci and for simulating the microscale instabilities in solidification interfaces.
    Keywords: SOLID-STATE PHYSICS
    Type: The Mater. Process. Res. Base of the Mater. Process. Center; p 97-116
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  • 8
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    Radial segregation induced by natural convection and melt/solid interface shape in vertical Bridgman growth (1983)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: The roles of natural convection in the melt and the shape of the melt/solid interface on radial dopant segregation are analyzed for a prototype of vertical Bridgman crystal growth system by finite element methods that solve simultaneously for the velocity field in the melt, the shape of the solidification isotherm, and the temperature distribution in both phases. Results are presented for crystal and melt with thermophysical properties similar to those of gallium-doped germanium in Bridgman configurations with melt below (thermally destabilizing) and above (stabilizing) the crystal. Steady axisymmetric flow are classified according to Rayleigh number as either being nearly the growth velocity, having a weak cellular structure or having large amplitude cellular convention. The flows in the two Bridgman configurations are driven by different temperature gradients and are in opposite directions. Finite element calculations for the transport of a dilute dopant by these flow fields reveal radial segregation levels as large as sixty percent of the mean concentration. Segregation is found most severe at an intermediate value of Rayleigh number above which the dopant distribution along the interface levels as the intensity of the flow increases.
    Keywords: SOLID-STATE PHYSICS
    Type: NASA-CR-173627 , NAS 1.26:173627
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  • 9
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    Segregation effects during growth of pseudo-binary system with large liquidus-solidus separation (1982)
    In:  Other Sources
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    Publication Date: 2019-07-27
    Description: Results are reported for an experimental study of the seeded growth, of PbSnTe single crystals in a vertical Bridgman-Stockbarger (B-S) furnace. Profiles of axial and radial segregation of Sn are presented for crystal growth from melts with aspect ratios of 15 and 6.8; the profiles indicate intense convective mixing. A one-dimensional model of heat and mass transfer in an idealized B-S furnace with diffusion control is used to examine the importance of liquidus-solidus separation in determining growth-rate and composition transients in a pseudobinary system. It is shown that the coupling of heat and mass transfer in a pseudobinary system with a large liquidus-solidus separation causes the transient behavior in a nondilute system to differ markedly from such behavior in a dilute system and that PbSnTe crystals with a reasonable diameter can be grown under nearly convectionless conditions in a microgravity environment.
    Keywords: SOLID-STATE PHYSICS
    Type: IAF PAPER 82-130
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  • 10
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    Natural convection in melt crystal growth - The influence of flow pattern on solute segregation (1982)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: The results of two lines of research aimed at calculating the structure of the flows driven by buoyancy in small-scale crystal growth systems and at understanding the coupling between these flows, the shape of the solidification interface, and dopant segregation in the crystal are reviewed. First, finite-element methods are combined with computer-aided methods for detecting multiple steady solutions to analyze the structure of the buoyancy-driven axisymmetric flows in a vertical cylinder heated from below. This system exhibits onset of convection, multiple steady flows, and loss of the primary stable flow beyond a critical value of the Rayleigh number. Second, results are presented for calculations of convection, melt/solid interface shape, and dopant segregation within a vertical ampoule with thermal boundary conditions that represent a prototype of the vertical Bridgman growth system.
    Keywords: SOLID-STATE PHYSICS
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