紅外線光彈技術於矽晶圓應力檢測之開發應用

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：15

、訪客IP：3.148.227.92

姓名

鍾翔宇(Xiang-Yu Zhong) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

紅外線光彈技術於矽晶圓應力檢測之開發應用
(Research on the Development and Application of Infrared Photoelastic Technique for Stress Measurement in Silicon Wafers.)

相關論文

★ 應用機器視覺於機械手臂隨機物件夾取與三維人體姿態偵測	★ 矩形平板施加點質量陣列的振動特性與暫態波傳分析與波源歷時反算應用
★ 矩形平板部分埋沒於顆粒體之動態反應與振動特性	★ 透過質量陣列控制撓曲波傳之理論分析及設計應用
★ 基底運動引發板結構動態反應之理論分析與實驗量測	★ 以雙向耦合離散元素法與有限元素法模擬顆粒體在矩形板振動下產生的克拉尼圖與反克拉尼圖

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

至系統瀏覽論文 (2030-1-23以後開放)

摘要(中)

近年因應產業及製程需求，半導體產業所使用之矽晶圓厚度趨於薄化，在加工時產生的殘留應力容易使矽晶圓在後端加工製程時破損。而使用常見之接觸式或破壞式應力量測方式容易使得晶圓破裂，且量測效率較低，因此本研究採用光彈法(Photoelastic Method)來量測矽晶圓內部應力，其非接觸式且可全場量測的特性十分適合用於量測此類高單價且硬脆之材料。本技術透過紅外光光彈法量測非透明材料矽晶圓內部應力，搭配實驗量測及有限元素法模擬對應，以及分析在多種不同波長光源下，等向性光彈材料與矽晶圓試片之光彈條紋數量及分佈之變化與應力關係。本文使用光彈法架構作為基礎，利用偏振後的偏極光，通過具有雙折射性質(Birefringence)的材料試片，藉由分析試片折射率與入射光波長的關係來測定試片面內應力，並使用四步移相法(Four-Step Phase-Shifting Method)與六步移相法(Six-Step Phase-Shifting Method)，透過拍攝不同相位圖像的方式，計算出矽晶圓試片之主應力方向角及內部應力差值。藉由實驗量測之等色線條紋(Isochromatic fringes)與有限元素分析軟體模擬試片受力結果比對，確認此技術之量測系統與解條方法之準確及可行性。本文的主要貢獻為：(1)建構一紅外光彈系統，整合自組型雙軸向位移平台，以拍攝大範圍全域之矽晶圓光彈圖像(2)分析矽晶圓異向性之光彈結構與矽晶圓晶格方向之關係，並透過四步及六步移相法計算試片之主應力方向角及內部應力差值，可直接對應得到試片內部各位置之量值，無須再細數條紋數以計算量值。(3)運用實驗量測結果與有限元素模擬比對，提供可全場量測非透明矽晶圓試片應力量測方法。本研究運用實驗量測與有限元素模擬比對，提供可全場量測非透明矽晶圓試片應力量測方法，預期可供半導體產業領域殘留應力檢測方面相關的運用價值。

摘要(英)

In recent years, to meet the demands of the semiconductor industry and manufacturing processes, the thickness of silicon wafers used in the semiconductor industry has been trending towards thinning. The residual stress generated during processing can easily cause the silicon wafer to break during subsequent processing. Conventional contact or destructive stress measurement methods are prone to wafer breakage and have lower measurement efficiency. Therefore, this study adopts the photoelastic method to measure the internal stress of silicon wafers. Its non-contact and full-field measurement characteristics are particularly suitable for measuring such high-value and brittle materials. This technique measures the internal stress of non-transparent silicon wafers using infrared photoelasticity, combined with experimental measurements and finite element method simulations, and analyzes the changes in the number and distribution of isochromatic fringes of isotropic photoelastic materials and silicon wafer specimens under different wavelength light sources and their relationship with stress. Based on the photoelasticity framework, this paper uses polarized polarized light, which passes through a material specimen with birefringence, to determine the in-plane stress of the specimen by analyzing the relationship between the refractive index of the specimen and the incident light wavelength. Images of the specimen under different light fields are captured, and the four-step phase-shifting method and six-step phase-shifting method are used to calculate the principal stress direction angle and internal stress difference of the silicon wafer specimen by capturing images with different phases. By comparing the experimental isochromatic fringe patterns with the results of finite element analysis simulation of the specimen under load, the accuracy and feasibility of the measurement system and fringe analysis method are confirmed.
The primary contributions of this research: (1) Develop an infrared photoelasticity system integrated with a custom-built biaxial displacement platform to capture full-field photoelastic images of large-area silicon wafers. (2) Investigate the correlation between the photoelastic structure of anisotropic silicon wafers and their crystallographic orientations. Employ four-step and six-step phase-shifting techniques to calculate the principal stress direction angles and internal stress differences within the specimens. This direct approach eliminates the need for manual fringe counting to obtain quantitative stress values at each point within the specimen. (3) Compare experimental measurement results with finite element simulation to provide a comprehensive method for full-field stress measurement of opaque silicon wafer specimens. This study uses experimental measurement and finite element simulation comparison to provide a full-field measurement method for the stress measurement of non-transparent silicon wafer specimens, which is expected to have application value in the residual stress inspection of the semiconductor industry.

關鍵字(中)

★ 紅外光
★ 矽晶圓
★ 光彈法
★ 移相法
★ 應力量測

關鍵字(英)

★ Infrared light
★ silicon wafer
★ photoelasticity
★ phase-shifting method
★ stress measurement

論文目次

中文摘要 i
Abstract ii
致謝 iv
目錄 vi
圖目錄 x
表目錄 xvi
第一章緒論 1
1-1 研究背景與目的 1
1-2 文獻回顧 2
1-3 內容簡介 4
第二章光彈理論與實驗方法 7
2-1 光彈法(Photoelastic Method) 7
2-1-1 應力-光學定律(Stress-Optic Law) 7
2-1-2 光學元件介紹 11
2-1-3 平面偏光系統(Plane Polariscope) 14
2-1-4 圓偏光系統(Circular Polariscope) 15
2-2 移相法(Phase-Shifting Method) 17
2-2-1 四步移相法(Four-Step Phase-Shifting Method) 18
2-2-2 六步移相法(Six-Step Phase-Shifting) 19
2-2-3 移相法之實驗步驟 21
2-3 矽晶圓之光彈係數 22
2-3-1 矽晶圓之晶格結構描述 22
2-3-2異向性材料光彈係數分析 23
2-4 局部光彈圖像拼接方法 27
2-4-1 位移平台設計 28
2-4-2 位移平台校正與影像裁切拼接 28
第三章可見光光彈系統實驗架設與實驗結果討論 51
3-1 實驗架設 51
3-1-1 實驗設備 51
3-1-2 試片規格 52
3-1-3 試片加壓機構與力量量測設備 52
3-2 模擬設定 53
3-3 圓環光彈試片實驗與模擬驗證 53
3-3-1 主應力方向分析 54
3-3-2 主應力差分析 54
3-4 板型光彈試片實驗與模擬驗證 55
3-4-1 主應力方向分析 55
3-4-2 主應力差分析 56
第四章紅外線光彈系統實驗架設與實驗結果討論 75
4-1 實驗架設 75
4-1-1 實驗設備 75
4-1-2 試片規格 76
4-1-3 試片加壓機構與力量量測設備 76
4-2 模擬設定 77
4-3 圓環光彈試片實驗與模擬驗證 78
4-3-1 主應力方向分析 78
4-3-2 主應力差分析 79
4-4 矽晶圓試片實驗與模擬驗證 80
4-4-1 主應力方向分析 80
4-4-2 主應力差分析 81
第五章結論與未來展望 99
5-1 結論 99
5-2 未來展望 100
參考文獻 101

參考文獻

[1] A. Kumar, R. G. R. Prasath, V. Pogue, K. Skenes, C. Yang, S. N. Melkote and S. Danyluk, “Effect of Growth Rate and Wafering on Residual Stress of Diamond Wire Sawn Silicon Wafers.” Procedia Manufacturing, Vol 5, 2016, pp. 1382-1393.
[2] K. T. Turner, S. Veeraraghavan and J. K. Sinha, “Relationship between Localized Wafer Shape Changes Induced by Residual Stress and Overlay Errors.” Journal of Micro/Nanolithography, MEMS, and MOEMS, Vol 11(1), 2012, 013001-013001.
[3] C. Yang, F. Mess, K. Skenes, S. Melkote and S. Danyluk, “On the Residual Stress and Fracture Strength of Crystalline Silicon Wafers.” Applied Physics Letters, Vol 102(2), 2013, 021909.
[4] L. Zhang, R. Barrett, P. Cloetens, C. Detlefs and M. Sanchez del Rio, “Anisotropic Elasticity of Silicon and its Application to the Modelling of X-Ray Optics.” Journal of synchrotron radiation, Vol 21(3), 2014, pp. 507-517.
[5] H. D. Geiler, H. Karge, M. Wagner, M. Jurisch, U. Kretzer and M. Scheffer-Czygan, “Photoelastic Characterization of Residual Stress in Gaas-Wafers.” Materials science in semiconductor processing, Vol 9(1-3), 2006, pp. 345-350.
[6] H. D. Geiler, M. Wagner, H. Karge, M. Paulsen and R. Schmolke, “Photoelastic Stress Evaluation and Defect Monitoring in 300-mm-Wafer Manufacturing.” Materials Science in Semiconductor Processing, Vol 5(4-5), 2002, pp. 445-455.
[7] J. W. Dally and W. F. Rilley, Experimental Stress Analysis, New York: McGraw-Hill Companies, 1978.
[8] R. V. South, “A Treatise on Photo-Elasticity” , The Mathematical Gazette , Vol 16, 1932, pp.277-279.
[9] 洪光民、馬劍清:〈圓盤與長條樑之理論解析與實驗光學全場量測〉。博士論文，國立台灣大學，民國91年6月。
[10] 楊婷雅、黃育熙:〈利用光彈法研究光學薄膜之應力光學係數量測〉。碩士論文，國立臺灣科技大學，民國106年7月。
[11] N. J. Renidler and I. Vigness, “Hole-Drilling Strain-Gage Method of Measuring Residual Stresses: Authors Indicate that this Method Permits the Magnitudes and Principal Directions of Residual Stresses at the Hole Location to Be Determined.” Experimental Mechanics, Vol 6, 1966, pp. 577-586.
[12] ASTM E837-13a, “Standard Test Method for Determining Residual Stresses by the Hole-Drilling Stress-Gage Method.”, 2013.
[13] 劉美丞、黃育熙:〈利用反射式光彈量測與分析銲接殘留應力〉。碩士論文，國立臺灣科技大學，民國107年7月。
[14] 周禹廷、趙振綱、黃育熙:〈利用反射式光彈法量測與分析圓管環縫填料對接殘留應力〉。碩士論文，國立臺灣科技大學，民國108年7月。
[15] V. G. Gorshkov, Y. K. Danileiko, et.al. “Mechanical Microstresses in Dislocation-Free Floating-Zone Silicon Monocrystals.” Physica Status Solidi (a), Vol. 106, 1988, pp. 363-369.
[16] Y. Niitsu, K. Ichinose, K. Ikegami, “Mechanics and Materials for Electronic Packaging: Vol 2—Thermal and Mechanical Behavior and Modeling.” ASME, Vol. 187, 1994, pp. 29–35.
[17] E. A. Patterson and Z. F. Wang, “Towards Full Field Automated Photoelastic Analysis of Complex Components.” Strain, Vol 27(2), 1991, pp. 49-53.
[18] Z. F. Wang and E. A. Patterson, “Use of Phase-Stepping with Demodulation and Fuzzy Sets for Birefringence Measurement.” Optics and Lasers in Engineering, Vol 22(2), 1995, pp. 91-104.
[19] A. Asundi, L. Tong and C. G. Boay, “Phase-Shifting Method with a Normal Polariscope.” Applied optics, Vol 38(28), 1999, 5931-5935.
[20] K. Ramesh, Digital Photoelasticity: Advanced Techniques and Applications. Berlin: Springer, 2000.
[21] H. Liang, Y. Pan, S. Zhao, G. Qin, and K. K. Chin, “Two-Dimensional State of Stress in a Silicon Wafer.” Journal of Applied Physics, Vol 71(6), 1992, 2863-2870.
[22] M. Yamada, K. Ito and M. Fukuzawa, “Residual Strain as a Measure of Wafer Quality in Indium Phosphide Crystals.” In Conference Proceedings. 1997 International Conference on Indium Phosphide and Related Materials, IEEE, 1997, pp. 209-212.
[23] T. Zheng and S. Danyluk, “Study of Stresses in Thin Silicon Wafers with Near-Infrared Phase Stepping Photoelasticity.” Journal of materials research, Vol 17, 2002, pp. 36-42.
[24] F. Jagailloux, V. Valle, J. C. Dupre, J. D. Penot and A. Chabli, “Applied Photoelasticity for Residual Stress Measurement Inside Crystal Silicon Wafers for Solar Applications.” Strain, Vol 52(4), 2016, pp. 355-368.
[25] F. Jagailloux, V. Valle, “Analysis and Comparison of Different Methods Used to Extract Isoclinic and Isochromatic Parameters. Application to the Determination of the Residual Stresses Inside Crystal Silicon Wafers.” Strain, Vol 54(4), 2018, e12275.
[26] H. Wang, Z. Jiang, F. Xu, Q. Kemao, “Estimating Residual Stresses of Silicon Wafer from Measured Full-Field Deflection Distribution.” Optics and Lasers in Engineering, Vol 148, 2022, 106781.
[27] T. Zheng, A study of residual stresses in thin anisotropic (silicon) plates. Georgia Institute of Technology, 2000.
[28] S. He, T. Zheng and S. Danyluk, “Analysis and Determination of the Stress-Optic Coefficients of Thin Single Crystal Silicon Samples.” Journal of applied physics, Vol 96(6), 2004, 3103-3109.
[29] E. J. Boyd and D. Uttamchandani, “Measurement of the Anisotropy of Young′s Modulus in Single-Crystal Silicon.” Journal of Microelectromechanical Systems, Vol 21(1), 2011, pp. 243-249.
[30] M. A. Hopcroft, W. D. Nix and T. W. Kenny, “What is the Young′s Modulus of Silicon?” Journal of microelectromechanical systems, Vol 19(2), 2010, pp. 229-238.
[31] 高郁倫、吳先晃:〈以高動態數位影像作光彈四步相移法之改善〉。碩士論文，國立雲林科技大學，民國104年6月。
[32] 周侑成、陳元方:〈各種自動化光彈分析方法之比較〉。碩士論文，國立成功大學，民國104年6月。
[33] Yuriy V. Tokovyy, Y. H. Huang, C. Y. Yen and C. C. Ma, “Analytical and Experimental Evaluation of Stresses in Elastic Annuli Subjected to Three-Point Loading on the Outer Surface.” Applied mathematical modelling, Vol 73, 2019, pp. 442-458.
[34] M. Tariq, M. Abdelhamid, Y. Li, M. Omar and Y. Zhou, “Fusion of Thermal and Visible Acquisitions for Evaluating Production-Borne Scratches and Shunts in Photo-Voltaic PV Cells.” Journal of Materials Science Research, Vol 1(4), 2012, 57.
[35] 國科會精密儀器中心:《微機電系統技術與應用》，財團法人國家實驗研究院台灣儀器科技研究中心，2005年3月。

指導教授

廖展誼(Chan-Yi Liao)

審核日期

2025-1-22

推文