外加Cusp磁場下柴氏法生長單晶矽之不同晶堝轉影響熱流場及氧傳輸數值分析

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阮氏懷秋(Nguyen Thi Hoai Thu) 查詢紙本館藏

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論文名稱

外加Cusp磁場下柴氏法生長單晶矽之不同晶堝轉影響熱流場及氧傳輸數值分析
(Effects of different crystal-crucible rotation conditions on flow, heat, and oxygen transport during Czochralski silicon crystal growth with a cusp magnetic field)

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摘要(中)

由於柴氏(Czochralski)長晶法具有較高的生長速度和重量控制的技術，現在成為商用矽晶片生產的主要生長方法。然而，這種技術正面臨著如何改善生長系統和操作條件以生產高質量矽單晶體的巨大挑戰。在本研究中，針對工業型柴氏長晶法在磁場環境下的二維空間熱流質傳現象進行數值模擬，我們期望找到更好的生長過程來有效控制熱量、流量、氧雜質輸送與缺陷的形成。分析在有無Cusp磁場環境下，不同晶體坩堝旋轉條件下的流動型態、溫度分佈、氧濃度和點缺陷的形成。
在本研究之結果中發現晶體與熔區界面的氧含量是由擴散和對流機制之間的競爭所決定的。在晶體和坩堝之間的低同向旋轉差異下，擴散過程對熔體中氧輸送的影響變得強於對流效應，在同向旋轉條件下可以獲得較低濃度和均勻的氧氣徑向分佈，當晶體和坩堝在同向旋轉速率（Res / Rec = 0.5842）時，在矽熔體中會發生流動轉變。在Cusp磁場的作用下，電力和磁力改變矽熔體中的速度的大小和方向。與同向旋轉情況相比，磁場對非同向旋轉情況下的氧濃度具有更強的影響。通過Cusp磁場環境下氧含量減少或增強取決於晶體和坩堝之間的旋轉差異。與使用磁場平衡的相比，使用不平衡的Cusp磁場減少了氧含量的徑向均勻性，尤其是在反向旋轉的情況下。以相同方向旋轉晶體和坩堝也產生更平坦的缺陷轉變和更低的點缺陷濃度。晶體與坩堝使用同向旋轉時，有利於生產零缺陷的矽單晶。這是因為在同向旋轉時，固液介面形狀會更凸向晶體區域。而較凸向晶體區域的介面形狀，更容易將點缺陷從晶體中心往外排出。軸向溫度梯度得到增強，這樣可以更快地從矽熔體中拉出晶體，同時可以避免組成過冷。

摘要(英)

The Czochralski process nowadays becomes a main pulling method for the production of the commercial silicon wafers due to its relatively high growth rate and possible weight control. This technique, however, is facing to the big challenges how one can improve the growth system and operation conditions to produce silicon crystals with a good quality. From this study, it is expected to find the better growth process for the effective control of the heat, flow, oxygen transport, and defect formation. 2D global numerical simulations of heat and mass transfer under the influence of magnetic field in an industrial Cz-Si growth were conducted. The flow characteristics, the distributions of temperature, oxygen concentration, and the formation of point defect under different crystal-crucible rotation conditions without and with a cusp magnetic field were analyzed.
The simulation results showed that the oxygen content along the crystal-melt interface is determined by the competition between the diffusion and convection mechanisms. At a low difference between the crystal and crucible iso-rotation rates, the effect of the diffusion process on oxygen transport in the melt becomes stronger than the effect of convection. A lower concentration and uniform radial distribution of oxygen can be obtained under the iso-rotation condition. It was found that a flow transition occurred in the silicon melt when the crystal and crucible have the same iso-rotation rate. Since that, the ratio between crystal and crucible rotational Reynolds numbers, Res/Rec, is 0.5842. Under the application of a cusp magnetic field, the electric force and the magnetic force changes the magnitude and direction of velocity in the silicon melt. The magnetic field has the stronger effect on the oxygen concentration in counter-rotation cases in comparison with iso-rotation ones. Reducing or enhancing the oxygen content by a cusp magnetic field depends on the differences between the crystal and crucible rotation rates. Using an unbalanced cusp reduces the radial uniformity of oxygen content, especially in counter-rotation cases, as compared to using a balanced one. Rotating the crystal and the crucible in the same direction also produces a flatter defect transition and a lower concentration of point defects. Producing a convex crystal-melt interface in iso-rotation cases is good for growing the defect-free crystals due to the outward diffusion of point defects from the central region to the edge of ingot. The axial temperature gradient is enhanced in iso-rotation cases. This may allow the faster pulling of crystal from the silicon melt and prevent the super-cooling during the growth.

關鍵字(中)

★ 晶體與坩堝同向及反向旋轉
★ 矽單晶生長
★ 數值模擬
★ 氧氣傳輸
★ 柴氏長晶法

關鍵字(英)

★ Crystal-crucible counter- and iso-rotation
★ Single crystal growth
★ Computer simulation
★ Oxygen transport
★ Czochralski method

論文目次

摘要 i
Abstract ii
Acknowledgements iv
Table of Contents v
List of Figures vii
List of Tables xi
Nomenclature xii
Chapter 1. Introduction 1
1.1. Motivation 1
1.2. Objectives 3
1.3. Dissertation structure 4
Chapter 2. Background 6
2.1. Introduction of Czochralski silicon crystal growth process 6
2.2. Oxygen transportation during Cz silicon growth process 9
2.3. Application of a cusp magnetic field (CMF) 14
2.4. Application of crystal-crucible rotation during the Cz silicon crystal growth 18
Chapter 3. Theoretical Formulations 21
and Computational Methods 21
3.1. Physical model 21
3.2. Theoretical formulations 22
3.2.1. Governing equations 22
3.2.2. Turbulence flow 24
3.2.3. Boundary condition for flow fields 26
3.2.4. Boundary conditions for thermal fields 27
3.2.5. Boundary condition for oxygen 28
3.2.6. Physical significance of the dimensionless numbers 29
3.3. Computational methods 31
3.3.1. Numerical methods 31
3.3.2. Grid and tolerance test 32
Chapter 4. Results and Discussions 40
4.1. Effects of crystal rotation rates on the flow, temperature, and oxygen transport under crucible counter- and iso-rotations, without a CMF 40
4.2. Effects of crystal rotation rates on the flow and oxygen transport, with a balanced and an unbalanced CMF 50
4.3. Effects of crystal-crucible counter- and iso-rotation conditions on the flow and oxygen transport at different crystal lengths under a balanced CMF 62
4.4. Effects of crystal rotation rates on defect formation and thermal stress without and with a CMF 71
4.5. Effects of crucible rotation rates on the flow, temperature and oxygen transport without a CMF 77
Chapter 5. Conclusions and Future works 83
5.1. Conclusions 83
5.2. Future works 84
References 86
Appendix A. Calculation for oxygen concentration at crucible wall and free melt surface 93
Appendix B. Modeling of initial point defect 98
Appendix C. Calculation of thermal stress 100
Appendix D. Publications during PhD study (2014-2018) 102

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指導教授

陳志臣(Chen Jyh Chen)

審核日期

2018-7-23

推文