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研究生： 納迪爾
Salazar, Nadir
論文名稱： 基於 COMSOL 的 BF33 玻璃通孔 (TGV) 熱機械可靠度分析.
COMSOL-Based Thermo-Mechanical Reliability Analysis of Through-Glass Via (TGVs) in BF33 Glass.
指導教授： 李文熙
Wen-Hsi, Lee
學位類別： 碩士
Master
系所名稱： 智慧半導體及永續製造學院 - 半導體製程學位學程
Program on Semiconductor Manufacturing Technology
論文出版年： 2026
畢業學年度： 114
語文別： 英文
論文頁數： 113
中文關鍵詞： 玻璃穿孔（TGV） 、COMSOL Multiphysics 、熱機械可靠度 、BF33 玻璃 、應力緩解 、高分子襯層 、Gibson-Ashby 模型 、均質化
外文關鍵詞： Through-Glass Via (TGV), COMSOL Multiphysics, thermo-mechanical reliability, BF33 glass, stress mitigation, polymeric liner, Gibson-Ashby model, homogenization
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    • 隨著半導體產業持續突破摩爾定律的限制，2.5D 與 3D 封裝技術對於滿足更高效能、更低延遲以及更小尺寸的需求，正變得日益重要。在此背景下，玻璃穿孔（TGV）憑藉其固有的電氣絕緣特性與較低的介電損耗，逐漸成為矽穿孔（TSV）的一項極具吸引力的替代方案。然而，熱機械可靠度仍是一大隱憂：電鍍銅核心與 BF33 玻璃之間的熱膨脹係數不匹配，會在熱負載下產生顯著的介面應力。

    本論文於 COMSOL Multiphysics 軟體中開發了一套完整的多物理場有限元素分析（FEA）架構，用以評估並降低沙漏型 TGV 結構中的熱機械應力，此模型涵蓋基板厚度、通孔開口與頸部直徑等關鍵幾何參數。在以已發表之多物理場基準資料校準模擬架構後，本研究進一步在不同熱邊界條件下驗證了焦耳熱、熱傳導與固體力學三者的耦合效應。結構可靠度則以延性銅材的馮米塞斯應力，以及相對於脆性 BF33 玻璃抗彎強度的第一主應力來評估。

    為降低介面應力集中現象，本研究探討了多種以設計為導向的緩衝策略。採用 Gibson-Ashby 模型對多孔銅－空氣晶種層進行建模，結果顯示提高空氣體積分率可降低有效楊氏模數並減少玻璃中的應力——但僅靠此方式，仍不足以在高熱負載下將應力降至斷裂門檻以下。相較之下，高分子緩衝層則展現出更具潛力的結果：本研究評估了 SU-8、Parylene C 與 Ph-yne-BCB 等單層襯層，以及均質化銅－有機複合層與多層混合結構；其中 SU-8 表現最為突出，展現出最高的柔順性，並能在所研究條件下將玻璃中的最大第一主應力降低至斷裂極限以下。不過，其中也浮現出一種取捨：襯層越厚，有效銅半徑越小，進而導致電阻與焦耳熱增加。因此，本研究確立了一個適當的 SU-8 襯層厚度，作為兼顧機械應力釋放與熱／電性能表現的最佳設計區間。

    相對地，均勻幾何縮放僅使主要應力響應產生有限的變化——顯示可靠度主要受材料不匹配程度支配，而非單純取決於幾何形狀。整體而言，本研究建立了 TGV 可靠度的量化基準，並證實柔順的高分子緩衝層是降低下一代玻璃中介層熱失配應力最有效的途徑。

    As the semiconductor industry pushes beyond Moore’s Law, 2.5D and 3D packaging have become increasingly important for meeting the demand for higher performance, lower latency, and smaller form factors. In this context, through-glass vias (TGVs) have emerged as an attractive alternative to through-silicon vias (TSVs) because of their inherent electrical insulation and lower dielectric loss. However, thermo-mechanical reliability remains a major concern, since the mismatch in thermal expansion between the electroplated copper core and BF33 glass generates significant interfacial stress during thermal loading.

    This thesis develops a comprehensive multiphysics finite element analysis (FEA) framework in COMSOL Multiphysics to evaluate and mitigate thermo-mechanical stresses in an hourglass-shaped TGV structure. The model incorporates key geometric parameters such as substrate thickness, via opening, and neck diameter. After calibrating the simulation framework against published multiphysics baseline data, I validated the coupled effects of Joule heating, heat transfer, and solid mechanics under different thermal boundary conditions. Structural reliability was then assessed using von Mises stress for ductile copper and first principal stress relative to the bending strength of brittle BF33 glass.

    Several design-driven buffer strategies were investigated to reduce interfacial stress concentrations. Gibson-Ashby modeling of porous copper-air seed layers showed that increasing air volume fraction lowers the effective Young’s modulus and reduces stress in the glass, although this reduction alone is not enough to bring the stress below the fracture threshold under elevated thermal loads. Polymer-based buffers showed more promising results. Single-layer liners of SU-8, Parylene C, and Ph-yne-BCB, along with homogenized copper-organic composite layers and multi-layer hybrid structures, were evaluated. Among these, SU-8 stood out because it offered the highest compliance and reduced the maximum first principal stress in the glass enough to remain below the fracture limit under the studied conditions. A trade-off was also observed: thicker liners reduce the effective copper radius, which increases electrical resistance and Joule heating. Based on this result, an optimal SU-8 liner thickness was identified to balance mechanical stress relief with thermal and electrical performance.

    Uniform geometric scaling, by contrast, produced only limited change in the primary stress response, suggesting that reliability is governed more strongly by material mismatch than by geometry alone. Overall, this work establishes a quantitative baseline for TGV reliability and shows that compliant polymer buffer layers offer the most effective route for reducing thermal mismatch stress in next-generation glass interposers.

    Abstract II 摘要 IV Acknowledgement VI Chapter 1: Introduction 1 1.1 Research Background 1 1.2 Research Motivation 5 1.3 Contributions of This Work 9 Chapter 2: Literature Review 10 2.1 Literature Review 10 2.2 Base Material Characteristics and Parametric Selection 13 2.2.1 Borosilicate Glass (BF33) Substrate 13 2.2.2 Electroplated Copper Core 14 2.2.3 Polymeric Liner Materials (Ph-yne-BCB, Parylene C, and SU-6) 14 2.2.4 The Physics of Mechanical Buffering 15 2.3 Effective Material Modeling 16 2.3.1 The Gibson-Ashby Model for Porous Media 17 2.3.2 Rule of Mixture for Thermal and Volumetric Properties 17 2.3.3 Voigt-Reuss-Hill (VRH) Average for Composite Stiffness 18 2.4 Thermo-Mechanical Failure Criteria 20 2.4.1 Ductile Behavior: Copper Interconnects 20 2.4.2 Brittle Behavior: BF33 Glass Substrate 21 Chapter 3: Model Methodology 23 3.0 Simulation Environment and Software Framework 23 3.0.1 Workflow and Design Logic 23 3.1 Model Formulation and Baseline Replication 25 3.1.1 Baseline Material Properties 25 3.1.2 Baseline Geometry 25 3.1.3 Boundary Conditions (Physics) 26 3.1.4 Addressing Missing or Assumed Parameters 28 3.2 Simulation Methodology and Experimental Roadmap 31 3.2.1 Physics Boundary Settings 31 3.2.2 Buffer Material Properties Parameter Run 35 3.2.3 Glass Geometry Size Parameter Run 35 3.2.4 Mesh Sensitivity Test 36 3.3 Mesh Validation and Parameter Validation Results 38 3.3.1 Mesh Validation Results 38 3.3.2 Thermal Buffer Layer Material Sweep 40 3.3.3 Current Parametric Sweeps 42 3.3.4 Boundary Condition Validation 45 3.3.5 Glass Size Validation 47 3.4 Replicated Model vs Qu Et Al. Reference Paper’s Baseline Results 49 3.4.1 Temperature Gradient Comparison 49 3.4.2 Displacement and Von Mises Stress Comparison 51 3.4.3 Defect Sensitivity Analysis 52 3.5 Introduction To The Lab’s TGV Structure 54 3.5.1 Geometry Structure 54 3.5.2 Material Selection 54 3.5.3 Boundary Conditions 55 3.5.4 Mesh Refinements for The Lab’s TGV Structure 56 3.6 The Comparison Results Between The Reference Paper’s Glass Vs BF33 Glass 57 3.7 Simulation Roadmap and Parametric Design Space 58 3.7.1 Phase 2.0: Baseline Dense Electroplated Copper 58 3.7.2 Phase 2.1: Porous Interface Investigation 59 3.7.3 Phase 3.0–3.2: Buffer and Liner Architecture Optimization 60 3.7.4 Phase 4.0: Via Geometric Sensitivity 63 Chapter 4 Results and Discussion 64 4.1 Introduction to Results 64 4.2 Phase 2.0: Baseline Performance Analysis 64 4.3 Phase 2.1: Interfacial Porosity and Gibson-Ashby Modeling 68 4.4 Phase 3.0–3.2: Buffer and Liner Architecture Optimization 74 4.4.1 Phase 3.0: Single-Layer Resin Liner Optimization 74 4.4.2 Phase 3.1: Homogenized Cu–Organic Mixture Framework 80 4.4.3 Phase 3.2: Multi-Layer Architecture and Fabrication Realities 86 4.5 Phase 4.0: Geometric Scaling and Sensitivity 90 Chapter 5 92 5.1 Conclusion 92 5.2 Future Work 94 References 96

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