本論文提出一準確且有效率之解析幾何法，以分析結合晶片直接接合(DCA)技術之控制塌陷晶片接合(C4)型態銲錫接點於迴銲過後之幾何形狀。在建立解析幾何法時，首先將熔融共晶銲錫自由表面之經線切割成一系列有限且足夠精細的小圓弧，並由力平衡分析得到熔融共晶銲錫內部與環境之壓力差，進而由Laplace-Young方程式求得熔融共晶銲錫自由表面任意點之曲率半徑，再由解析幾何可依序求得熔融共晶銲錫自由表面經線上各小圓弧節點之位置，而得到熔融共晶銲錫自由表面之形狀。舉凡如銲錫體積、外加負載、墊片尺寸、熔融共晶銲錫表面張力、熔融共晶銲錫與高鉛凸塊間之界面張力等影響熔融銲錫形狀的因子均將予以有系統的探討。此外，銲錫凸塊、防銲定界(SMD)/非防銲定界(NSMD)墊片型態銲錫接點及部分覆蓋高鉛凸塊之銲錫倒角的幾何形狀亦將予以分析。此解析幾何法之計算結果與Surface Evolver軟體、以Heinrich分析模型為基礎之衍生模型及實驗等所得到之結果相比較均相當脗合。
由於近來電子構裝採用超細密腳距構裝技術以提升電子產品之效能，錫橋成為電子構裝常見缺陷之一。本論文接著利用Surface Evolver軟體建立一計算模型以分析面積型態構裝錫橋之穩定性。錫橋穩定性之影響因子，如墊片尺寸、銲錫凸塊總體積、相鄰墊片腳距、熔融銲錫與墊片間之接觸角、熔融銲錫與防銲層間之接觸角以及熔融銲錫之表面張力等均分別予以有系統之探討。臨界銲錫凸塊總體積及臨界相鄰墊片腳距可分別定義為錫橋由穩定狀態變成不穩定(消失)狀態時，銲錫凸塊總體積及相鄰墊片腳距。本論文亦予以分析橫跨多墊片如三或四個墊片之錫橋穩定性。本論文分析所得錫橋臨界銲錫凸塊總體積與文獻中所得分析結果相比較相當脗合，顯示本論文所建立之分析模型相當適合用於分析錫橋之穩定性。
本論文最後利用Surface Evolver軟體分析上下墊片非對齊之SMD及C4型態銲錫接點之自我對位機制。並將銲錫接點自我對位運動簡化類比為元件質量、彈簧及阻尼之動態系統。並藉由基礎動態分析，可初步得到自我對位運動系統之自然頻率、阻尼比及元件振幅降低至小於 時所需時間(稱為對位時間)。此外，舉凡自我對位機制之影響因子，如上下墊片偏移量、銲錫接點高度、墊片尺寸、銲錫接點體積、外加負載、黏滯係數及熔融銲錫表面張力等均分別予以有系統之探討。本論文所得上下墊片非對齊SMD型態銲錫接點之自我對位運動計算結果與文獻中所得分析結果相比較相當契合。
本論文準確且有效率的分析銲錫接點於迴銲過後之形狀、錫橋的穩定性及銲錫接點之自我對位機制，並提供各設計參數之影響，以供電子構裝設計之參考。本論文所提各分析方法亦可進一步應用於其他先進構裝技術，如晶圓級構裝、光電元件構裝等。

An accurate and efficient analytical geometric method is presented for predicting the geometric parameters of the Controlled Collapse Chip Connection (C4) type solder joint using Direct Chip Attach (DCA) technology in area array type package after a reflow process. By this method, the meridian of the solder joint is first discretized as a series of sufficiently fine fragmental arcs. After calculating the internal pressure inside the molten eutectic solder from the forces balance, the meridional and circumferential curvature radii of each arc are then obtained from the Laplace-Young equation. As a result, the coordinates of each node of the arc and the solder joint geometry can be determined in turn. The factors that affect the final shape of the molten eutectic solder joints, including the solder volumes, the external loading, the pad size, the surface tension of molten eutectic solder, and the interfacial surface tension between molten eutectic solder and solid high-lead bump are considered herein. Moreover, liquid formation of solder bump constrained by a circular pad, SMD/NSMD solder joint and eutectic solder fillet partially spreading cover the high-lead bump is also conducted. The results computed by the analytical geometric method are also compared with those obtained using the Surface Evolver program, the extended Heinrich’s model, and the experimental results. The results of the various approaches are mutually consistent.
As ultra-fine-pitch technologies are adopted to enhance the performance of electronic packaging, solder bridging becomes an urgently serious defect. This work also presents a computational model using the Surface Evolver program to analyze the stability of solder bridging for area array type package. Several factors that affect the stability of solder bridging spanning two identical circular pads are considered herein, including the pad size, the total volume of solder bumps, the pitch between adjacent pads, the contact angle between the molten solder alloy and the pad, the contact angle between the molten solder alloy and the solder mask and the surface tension of the molten solder alloy, respectively. The critical total volume of solder bumps and the critical pitch between adjacent pads are defined as the corresponding critical values to determine the solder bridging from a stable state to an unstable (vanishing) state. The stability of solder bridging spanning three and four identical circular pads is also discussed. Good agreement between the computed critical total volume of solder bumps for solder bridging and that available in the literature exhibits that the model developed in this work can be practically applied to predict the stability of solder bridging.
The mechanism of self-alignment for the SMD and C4 type solder joints with misaligned upper/lower pads is analyzed using the Surface Evolver program. The self-aligning motion is then simplified by analogy to the component mass with a spring and a damper. Fundamental dynamic analysis is used to obtain preliminary results, such as natural frequency, damping ratio and alignment time, which is the time taken for the amplitude of self-aligning motion to decay to less than . The factors that affect the mechanism of self-alignment, such as the misalignment between the upper/lower pads, the solder joint height, the pad size, the solder volumes, the external loading and the viscosity and surface tension of molten eutectic solder are all taken into account. The results for a SMD solder joint calculated using the model proposed herein and those available in the literature are in good agreement.
This work analyzes the geometric parameters of the solder joints after a reflow process, the stability of the solder bridging and the self-alignment for the solder joints with misaligned upper/lower pads accurately and efficiently. The results provide the influences of various design factors and should be helpful for the electronic packaging design. The proposed approaches can also be applied to other advanced packaging technologies, such as wafer level packaging and optoelectronic device packaging, etc.

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