Modeling the linkages between heat transfer and microdefect formation in crystal growth : examples of Czochralski growth of silicon and vertical Bridgman growth of bismuth germanate
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2000.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2005
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| Online Access: | http://hdl.handle.net/1721.1/9113 |
| _version_ | 1826193434861371392 |
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| author | Mori, Tatsuo, 1961- |
| author2 | Robert A. Brown. |
| author_facet | Robert A. Brown. Mori, Tatsuo, 1961- |
| author_sort | Mori, Tatsuo, 1961- |
| collection | MIT |
| description | Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2000. |
| first_indexed | 2024-09-23T09:39:11Z |
| format | Thesis |
| id | mit-1721.1/9113 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T09:39:11Z |
| publishDate | 2005 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/91132019-04-11T06:08:41Z Modeling the linkages between heat transfer and microdefect formation in crystal growth : examples of Czochralski growth of silicon and vertical Bridgman growth of bismuth germanate Mori, Tatsuo, 1961- Robert A. Brown. Massachusetts Institute of Technology. Dept. of Chemical Engineering. Massachusetts Institute of Technology. Dept. of Chemical Engineering. Chemical Engineering. Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2000. Includes bibliographical references (p. 367-387). Microdefect formation in crystalline material is strongly correlated to the processing conditions for growth of crystals important in microelectronic processing. The geometry and operation conditions for crystal growth systems affect the temperature profile in the crystal and melt, which influences microdefect formation. The objectives of this thesis are to formulate the computational framework to establish the linkage between microdefect formation in crystal and proce5sing conditions of crystal growth system. The research focuses on two industrially important crystal growth problems: Czochralski (CZ) growth of single-crystal silicon and growth of bismuth germanium oxide (Bi4Ge30 12:BGO) by the vertical Bridgman method. A sequential, two-step approach is taken for linking mathematical modeling between processing conditions and microdefect formation in crystals. An accurate model of heat transfer in CZ growth of silicon is developed by including all the components in the system. Microdefoct formation in the crystal is then modEled by imposing the temperature profile obtained by the global heat transfer simulation. The integrated hydrodynamics thermal-capillary model (IHTCM) of CZ crystal growth includes radiative and conductive heat transfer between all components of the system. An important component of this simulation is the incorporation of a model of turbulence in the melt. A low Reynolds number k-c model is incorporated into the IHTCM for CZ system. The coupled k-c/IHTCM is applicable to any CZ system geometry and operating conditions because of the self-consistency of the model. Also a robust numerical solution method is developed to solve numerically unstable k-c equations by a finite-element approximation. The comparison between simulations and experiments for CZ growth of an 8" diameter crystal shows semi-quantitative agreement in melt/crystal interface, oxygen concentration in the crystal, and the location of a neutral zone, where the concentrations of two intrinsic point defects balance, in the crystal. Microdefect formation in CZ silicon is modeled with intrinsic point defects (vacancies and self-interstitials) and their agglomerates. The model is two-dimensional in space and predicts the radial profiles of point defects, which are determined near the melt/crystal interface, and the axial development of size distribution of voids and self-interstitial agglomerates, which is a function of point defect supersaturation and the temperature profile. The model provides quantitative links between operating conditions and microdefect distribution in the entire crystal. An effective numerical method with parallel processing is developed using a mixed local discontinuous Galerkin method. The predicted agglomeration temperatures and densities for vacancy and self-interstitial clusters are within the ranges of experimental data. The predictions also include the location for ring-like oxidation-induced stacking fault (OSF) formation, assuming the OSF-ring is formed at the radial location with the peak in residual vacancy concentration after the onset of vacancy agglomeration. The simulations clearly reproduce the radial distribution of microdefects observed by experiments. Starting from the crystal center and moving to the edge, the simulations predict a void region, the OSF-ring as a region of locally high vacancy concentration, a defect free region, a region dominated by self-interstitial clusters, and finally a defect free region near the crystal edge. The defect free region at the crystal edge results from the radial diffusion of point defects caused by reactions at the crystal surface. The heat transfer model in the vertical Bridgman system for BGO crystal growth incorporates internal radiation in the semi-transparent BGO crystal and conduction and radiation for all components of the heat transfer system. A band approximation is used to model internal radiation in the crystal. The global heat transfer model provides quantitative understanding of the heat transfer within the semi-transparent BGO crystal as well as in the entire system. Comparison of the temperature profile at the crucible wall between simulations and experiments for the large 11 cm diameter BGO crystal growth shows good agreement. The detailed analysis of heat transfer near the solidification interface gives insight for the control of bubble defects in BGO crystal formed by constitutional supercooling. The framework for numerical simulations developed in this thesis quantitatively demonstrates the linkage between processing conditions and microdefect formation in crystalline material. The linkage is established by the coupling of self-consistent modeling of global heat transfer in the crystal growth systems and microdefect formation in crystals. by Tatsuo Mori. Ph.D. 2005-08-22T22:50:43Z 2005-08-22T22:50:43Z 2000 2000 Thesis http://hdl.handle.net/1721.1/9113 45131922 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 387 p. 24136144 bytes 24135896 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Chemical Engineering. Mori, Tatsuo, 1961- Modeling the linkages between heat transfer and microdefect formation in crystal growth : examples of Czochralski growth of silicon and vertical Bridgman growth of bismuth germanate |
| title | Modeling the linkages between heat transfer and microdefect formation in crystal growth : examples of Czochralski growth of silicon and vertical Bridgman growth of bismuth germanate |
| title_full | Modeling the linkages between heat transfer and microdefect formation in crystal growth : examples of Czochralski growth of silicon and vertical Bridgman growth of bismuth germanate |
| title_fullStr | Modeling the linkages between heat transfer and microdefect formation in crystal growth : examples of Czochralski growth of silicon and vertical Bridgman growth of bismuth germanate |
| title_full_unstemmed | Modeling the linkages between heat transfer and microdefect formation in crystal growth : examples of Czochralski growth of silicon and vertical Bridgman growth of bismuth germanate |
| title_short | Modeling the linkages between heat transfer and microdefect formation in crystal growth : examples of Czochralski growth of silicon and vertical Bridgman growth of bismuth germanate |
| title_sort | modeling the linkages between heat transfer and microdefect formation in crystal growth examples of czochralski growth of silicon and vertical bridgman growth of bismuth germanate |
| topic | Chemical Engineering. |
| url | http://hdl.handle.net/1721.1/9113 |
| work_keys_str_mv | AT moritatsuo1961 modelingthelinkagesbetweenheattransferandmicrodefectformationincrystalgrowthexamplesofczochralskigrowthofsiliconandverticalbridgmangrowthofbismuthgermanate |