多晶片模組是指將一個以上的裸晶，封裝在同一個構裝體中。其目的在於節省空間、提高性能速度、降低功率消耗、節省封裝乃至於整個模組的成本。多晶片模組由許多元件所組成，當受到溫度循環負載，由於各元件材料因熱膨脹係數的不一致而導致構裝結構變形，進而使錫球產生疲勞破壞，使構裝體失效。本文以多晶片模組為探討對象，在溫度循環負載下，探討組成元件的材料性質及幾何尺寸對其可靠度的影響。
本文以多晶片模組為研究對象，其組成元件含有散熱片、熱黏膠、晶片、底填膠、結構黏膠、基板、印刷電路板及Sn3.5Ag無鉛錫球，首先以能量法為基礎的Surface Evolver軟體計算出錫球的外型曲線，再將錫球的外型曲線資料代入ANSYS有限元素分析軟體建立三維條狀分析模型，並導入本文所發展的二階子模型(2nd order Sub-Modeling)進行分析，並簡化模型，即將晶片與基板間的底填膠與錫球的覆晶結構，以等效平板代替。在無鉛錫球材料行為方面，採用多線性等向硬化模式，並以葛拉佛拉-阿瑞尼阿斯數學模式描述無鉛錫球塑性與潛變行為模式，其他元件之材料皆以彈性模型描述之。再依JEDEC Test Method A104-B的規範，施予多晶片模組構裝由-40℃～125℃之溫度循環負載，共十個循環。由有限元素分析可得基板與印刷電路板間最外側錫球之變形、應力與應變及遲滯曲線等機械行為之變化情形，將所求得的等效應變範圍值代入Coffin-Manson計算公式中，可計算出錫球之疲勞壽命。
為驗證所發展的二階子模型分析法的精確性與效率，將其與全域精細網格模型作比較。在同溫度循環負載下，兩者的等效應變範圍差異僅有1.25%，其結果相當一致。然二階子模型僅須全域精細模型24%的計算時間，所需的硬碟容量也只要全域精細模型的38%。
其次，針對多晶片模組中基板與印刷電路板間之錫球的上錫球墊與下錫球墊半徑、印刷電路板厚度與熱膨脹係數以及基板厚度與熱膨脹係等共六個參數進一步分析對多晶片模組可靠度的影響。首先，進行單一因子分析以評估各因子對封裝結構疲勞壽命的效應。接著採用田口方法對多晶片模組進行最佳化分析，再以反應曲面法找出描述多晶片模組疲勞壽命的解析解，並得到多晶片模組的最佳設計，同時與田口方法之結果進行討論。最後，以反應曲面法分析各因子間的交互作用對錫球疲勞壽命的影響。
由單一因子分析結果顯示，同時減少上、下錫球墊半徑、固定上錫球墊而增加下錫球墊半徑、固定下錫球墊而減少上錫球墊半徑、減小印刷電路板厚度、增加印刷電路板熱膨脹係數、減小基板厚度或降低基板熱膨脹係數，皆能有效提高多晶片模組疲勞壽命。
以田口品質工程分析之最佳製程參數之等效應變範圍為0.903%，及對應的錫球疲勞壽命為5599個循環，與原始製程參數設計之等效應變範圍4.779%，對應的錫球疲勞壽命87個循環比較，等效應變範圍減少了81%，而疲勞壽命值約提昇了64倍，對構裝體可靠度有顯著之改善。
最後，以反應曲面法分析，並經統計檢定，以確認模型的配適性，而此反應曲面為一修正的立方項模型(Reduced Cubic Model)，據此可求得最佳化設計組合的等效應變範圍為0.9059%，及對應的錫球疲勞壽命為5554個循環，而經驗證實驗所得到的等效應變範圍為0.9237%，及對應的錫球疲勞壽命為5289個循環兩者相當接近，接著與田口品質工程分析所得的最佳化結果作比較，兩種方法顯示所預測出各控制因子的最佳化趨勢與錫球的可靠度都相當一致。此外，將反應曲面法所求得各控制因子對錫球疲勞壽命的影響趨勢與單因子分析及田口品質工程得到的結果進行比較，其趨勢完全一致，亦進一步驗證所建立的反應曲面之可靠性。

Multi-chip module (MCM) is a single package, which encapsulates more than one die. The purpose is to reduce the dimension, improve performance, lower power consumption and save the cost. A MCM package consists of various components, when it is under a temperature cycling load, due to the mismatch of coefficients of thermal expansion (CTE) of components, the package tends to deform and lead to fatigue failure of solder joints. Therefore, this paper focused on a MCM model under thermal cycle loading to investigate the effects of component’s material and geometry on the fatigue life of 96.5Sn3.5Ag lead-free solder joints in a MCM assembly. The components of MCM include heatsink, thermal adhesive, chips, underfill, structural adhesive, substrate, printed circuit boards (PCB) and Sn3.5Ag lead-free solder ball.
Surface Evolver, an energy-based approach software is applied to calculate the shape of the solder ball, then bring this data into ANSYS, a finite element analysis software, to generate a 3-D finite element sliced bar-like model and use Second-order Sub-Modeling to perform the analysis in order to simplify numerical simulation of the model, an effective substitution for solder joints/underfill between the chip and the substrate is adopted turning the complex geometry to a simple isotropic layer. About the material behavior of the lead-free solder, the multi-linear isotropic hardening model is selected, using Garofalo-Arrhenius mathematical model to describe its plastic and creep behavior. The material’s properties for other components are assumed to be linear elastic.
According to JEDEC Test Method A104-B thermal cycle loading between 40℃ to 125℃ up to 10 cycles is applied to the MCM package. Hereby, we computed the deformation, stress, strain and hysterisis curve of the outermost solder joint (between substrate and PCB) by finite element analysis. The equivalent strain range is substituted into Coffin-Mansion formula to estimate the fatigue life of solder joint. For efficiently running numerical simulation Second-Order Sub-model is developed for a simpler simulation. For verifying the accuracy and efficiency of Second-Order Sub-model we compare it with fine mesh global model under same thermal cycle loading, the results show that the difference of equivalent strain range between these two models is only 1.25%. The calculation time and hard disk capacity required for Second-Order Sub-Modeling is only about 24% and 38% compare to fine mesh global modeling.
The single-factor experiment was adopted to predict the impact on the fatigue life of MCM by following 6 factors: The upper and lower pad radii of the solder ball,The PCB thickness and CTE,the substrate thickness and CTE. First, the single factor analysis is performed to evaluate the effect of each parameter with the solder ball reliability. Then both Taguchi method and the Response Surface Method (RSM) are applied to obtain an optimal parameter combination to improve the reliability of MCM package. Results from the Single-factor experiment show that the reduction of both upper and lower solder pad radius, fixing the upper solder pad and increasing the lower solder pad radius, fixing the lower solder pad and reducing the upper solder pad radius, reducing the thickness of the PCB, increasing the CTE of PCB, reducing substrate thickness or lower the CTE of substrate, promises to improve the fatigue life of MCM package.
The optimal design of Taguchi method shows significant improvement, the equivalent strain range is 0.903%. And the fatigue life is 5599 cycles, compare to the original design with equivalent strain range 4.779 %.and the fatigue life 87 cycles, the equivalent strain range reduced about 81% and the fatigue life enhanced about 64 times.
Response Surface Method is employed to derive a closed-form function in polynomial format to predict the fatigue life for the solder ball. The RSM model predicts a set of optimal design with equivalent strain range 0.9059% and the fatigue life 5554 cycles. And the certified experiment with this optimal design shows that the equivalent strain range is 0.9237% and the fatigue life is 5289 cycles. The RSM model could successfully predict the reliability of the MCM package.

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