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Flip-chip plastic ball grid array (FC-PBGA) packages are widely used in high performance components. However, its die back is normally under tensile stress at low temperatures. This paper presents a probabilistic mechanics approach to predict the die failure probability in the FC-PBGA qualification process. The methodology consists of three parts: i) die strength test using four-point bending (4PB) method, ii) the radius of curvature (ROC) measurement of the assembled FC-PBGA at room temperature, and iii) finite element method (FEM) stress analysis. In the first part, a specially modified three-parameter Weibull function is used to fit the 4PB die strength data. The three parameters of the Weibull distribution are used as the sole description of the cracking characteristics for a specific die process in the late analysis. In the second part, the measured ROC of FC-PBGA at room temperature is used as a calibration input to determine the effective stress-free temperature of the FC-PBGA. It is used to overcome the difficulty caused by process-induced residual stress and unknown material properties. This effective stress-free temperature can be used in the stress analysis in the third part of the mentioned methodology. In the third part, the FEM is used to calculate the die stress distribution under most critical stage of certain qualification process. The calculated stress distribution is combined with the Weibull distribution parameters of die strength test to predict the die failure percentage.