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研究生： 胡永毅
Wu, Weng-Ngai
論文名稱： 利用COMSOL進行碳化矽物理氣相長晶之全域數值模擬
Numerical Global Simulation of Silicon carbide PVT growth with COMSOL®
指導教授： 許文東
Hsu, Wen-Dung
學位類別： 碩士
Master
系所名稱： 工學院 - 材料科學及工程學系
Department of Materials Science and Engineering
論文出版年： 2022
畢業學年度： 110
語文別： 英文
論文頁數： 135
中文關鍵詞： 碳化矽 、物理氣相長晶 、大塊單晶成長
外文關鍵詞： Silicon Carbide, PVT growth, Bulk crystal growth
相關次數： 點閱：110  下載：15 
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    • 本研究主要是以通用模擬軟體COMSOL®，耦合磁場、熱場、流場、物質輸送現象和相場逵行碳化矽物理氣相傳輸之長晶模擬。在當中會討論到感應生熱線圈之幾何設計、輻射熱在長晶爐腔內之傳播、固–氣體間之揮發–凝華模型(赫茲–克努森模型)、碳化矽粉末在粉末填充區之揮發情況等一系列碳化矽物理氣相傳輸長晶之相關議題。在前提條件準備完成後，模型會耦合相場進行暫態的長晶模擬，並最終會預測出以論文內坩鍋設計所長出的結晶型狀。本研究的核心是建立一個具可塑性的碳化矽長晶爐模擬之模型，為日後加入摻雜、冷卻和缺陷分析等功能提供基礎可靠的參考。

    In this study, simulation of SiC PVT growth has been done by coupling magnetic field, heat transfer, fluid dynamics, mass transports and phase field modules to present a precise growth simulation in COMSOL®. To perform the simulation, serval topic, such as, design of coil and geometry, radiation in growth chamber, Hertz Knudsen model for SiC growth, powder evolution during the growth process, phase field coupling issues have been discussed. Finally, different couple methods of phase field and other modules are shown in result. The goal of this work is to create a flexible model, which can further develop for doping, dislocation analysis for SiC PVT growth.

    摘要 i ABSTRACT ii Acknowledgement iii Content iv List of figures viii List of tables xiii Nomenclature xiv Material properties xxi 1 Introduction to SiC growth 1 2 Simulation of PVT method 8 2.1 Heat transfer model 8 2.1.1 Heat induction 8 2.1.2 Heat radiation 10 2.1.3 Heat conduction and convection in porous media 18 2.2 Fluid dynamics model 21 2.2.1 Flow condition 21 2.2.2 Fluid dynamics in the growth chamber 24 2.3 Interaction between gaseous species and chamber component 26 2.3.1 Species generation and its behavior 26 2.4 Thermodynamic data calculation 27 2.4.1 Vapor pressure calculation with JANAF database 29 2.4.2 Species equilibrium in powder source 30 2.4.3 Species equilibrium on seed surface 31 2.4.4 Species kinetics and thermal equilibrium 37 2.4.5 Theoretical approach for kinetic parameters 39 2.4.6 Ab-initial calculation of reaction kinetics between SiC gas species 40 2.4.7 Sticking coefficient on seed surface 42 2.4.8 Consistency check for growth model 44 2.5 Mass transport model 45 2.5.1 Mass transportation in source powder 45 2.5.2 Mass transportation on seed layer surface 50 2.5.3 Mass transport in graphite crucible 51 2.5.4 Mass transport in gas room 52 2.6 Phase field model 52 2.6.1 Basic of phase field method 53 2.6.2 Interface coupling for phase field model 60 2.6.3 Preparation for phase field coupling 61 3 Numerical modeling 63 3.1 Introduction to Finite Volume Method and Finite Element Method 63 3.2 Building blocks of numerical method 66 3.2.1 Node and mesh 67 3.2.2 Shape function 67 3.3 Matrix formation 69 3.4 System matrix and coupling 70 3.5 Geometry of the PVT growth chamber 71 3.5.1 Coil geometry 73 3.5.2 Crucible geometry 77 3.6 Moving mesh and Phase field 78 3.7 Mesh settings 80 3.8 Boundary conditions of simulation 82 3.9 Discretization of element 84 3.10 Convergence conditions 85 4 Results and discussions 86 4.1 Magnetic field of growth chamber 86 4.1.1 Skin depth calculation from simulation 86 4.1.2 Frequency analysis for growth chamber 89 4.2 Temperature field of growth chamber 92 4.2.1 Nusselt number in the growth chamber 92 4.2.2 Temperature evolution during the growth process 93 4.2.3 Geometry changes effect 93 4.2.4 Temperature on seed layer 97 4.2.5 Temperature profile of the growth chamber 98 4.3 Fluid dynamics of growth chamber 98 4.3.1 Reynold’s number in the growth chamber 99 4.3.2 Knudsen number in the growth chamber 100 4.3.3 Partial pressure of species in growth chamber 101 4.4 Species concentration in growth chamber 104 4.4.1 Species concentration distribution 104 4.4.2 Si/C ratio distribution 106 4.4.3 Growth rate on seed layer 108 4.4.4 Time evolution of powder 110 4.5 Crystal growth simulation with phase field 113 4.5.1 Time dependent simulation of SiC crystal growth 113 4.5.2 Time dependent growth rate and growth front temperature of SiC seed 116 5 Conclusions 121 A Appendix 123 A.1 Derivation of differential volume dV to radius dr 123 A.2 Using test variable to solve weak form equation 124 References 125

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