Probabilistic Design and Reliability Analysis of Flip-Chip Chip Scale Packages under Accelerated Environmental Conditions

對於電子封裝體受熱循環負荷下之疲勞壽命預估，以往研究所得的結果通常為一定値，然而觀察實際實驗或測試結果，封裝體之疲勞壽命往往具有相當的離散性。為使模擬分析能反映並呈現實際實驗或測試結果，本研究利用有限元素法，並特別納入「機率設計系統」(Probabilistic Design System, PDS)，以探討尺寸和材料之不確定性及疲勞壽命估算公式之參數變異性對封裝體疲勞壽命分佈與可靠度評估所造成的影響。本研究概分為兩大部份，在第一部份的研究中，選定一特定覆晶晶片尺寸封裝體(Flip-chip Chip Scale Package, FCCSP)，針對前述所提各參數的不確定性設定合理的假設與機率分佈，進行力學分析與疲勞壽命評估。本研究也藉由機率圖紙、卡方適合度檢定與其他機率及統計相關的數學推導與演算，比較其結果與有限元素軟體內建「機率設計系統」分析所得結果的異同性，作為分析流程修正的依據，以保證分析結果的準確性。在第二部份的研究中，針對一般加速環境試驗中藉由大量試驗手法獲得嚴苛環境下與正常環境下的加速因子(Acceleration Factor, AF)模型，由數值模擬方式探討加速因子模型的適用性，並同時驗證本研究中模擬結果的準確性，以求爾後能快速、經濟的預測封裝體於正常環境下之壽命分佈、可靠度與失效率。本研究結果顯示，封裝體尺寸和材料之不確定性，確實對封裝體疲勞壽命預估產生影響；在研究中也發現，疲勞壽命預估公式中之參數變異對封裝體之壽命與可靠度評估會造成相當程度的影響。另外，「機率設計系統」雖然可以概略得出封裝體疲勞壽命的累積分佈函數曲線(Cumulative Distribution Function Curve)，但透過研究中自行開發之分析架構，可獲得更圓滑且為封閉型式(Closed Form)的累積分佈函數曲線，增進封裝體疲勞壽命與可靠度預估之準確性。在加速試驗分析中，可以發現在選擇合宜的加速因子模型並確認其適用性後，即可依據該模型建構一標準分析流程，估算封裝體於特定環境下之平均失效時間(Mean Time to Failure, MTTF)與失效率等可靠度有關量度。Considering the fatigue life of electronic packages under thermal-cyclic loading, the real test outcome reflects the fatigue life of an electronic package is, in fact, not deterministic but a random variable following a certain probability distribution. The outcome has been paid attention to and become an important issue that needs to be investigated furthermore. Therefore, in the present study, a finite element analysis and a Monte Carlo simulation-based parametric study of a flip-chip chip scale package (FCCSP) subjected to thermal cyclic loading is carried out by using Probabilistic Design System (PDS) of ANSYS. In the first stage of the analysis, a few parameters involved in the package dimension, material property and life prediction formula are assumed to be random to account for their uncertainties. Moreover, to improve the accuracy of the probabilistic life distribution obtained from PDS, a refined probabilistic design procedure which includes probability paper and chi-square goodness-of-fit test is proposed in particular. In the second stage of the analysis, emphasis is placed on the confirmation of an acceleration model in which the accelerated thermal-cyclic tests are carried out numerically based on the analytical model established previously. The analytical result indicates that random geometric configuration, material property and random life prediction formula may cause fatigue life of the package to have scattered distribution as those observed from experiments. The result also indicates that PDS can indeed be employed to find the cumulative fatigue life distribution of the electronic package owing to parameter uncertainties, and the proposed refined procedure can further improve the smoothness of the cumulative fatigue life distribution curve and transform this curve into a closed form expression. Finally, a confirmed acceleration model can be used for the prediction of mean time to failure (MTTF), reliability and failure rate of the package under different thermal-cyclic conditions including the field or field-used one