# Research on Lifespan Prediction Methods Using Ultrasonic Microimaging for Electronic Packaging
## 4 Solder Joint Failure Modeling and Lifespan Prediction
### Solder Joint Lifespan Prediction  
In the actual aging process of solder joints, due to their varied positions on the chip, the extent of stress and thermal cycling impact differs, leading to variations in aging rates. These differences are primarily manifested in two ways: the rate of progression of solder joint failure and the timing of the failure's onset and termination. The failure timing not only serves as a critical indicator for determining the stages of defect-free, defect initiation, and defect-caused failure but also as a crucial basis for lifespan prediction. The failure curve of solder joint number 107 on the second flip chip of sample board number 1 reveals that during accelerated thermal cycling life tests, the intensity of the damaged area of the solder joint significantly increases around the 50 th cycle, the rate of increase slows down after about 130 cycles, and it stabilizes after 150 cycles. To precisely define the failure process, the inflection points of the curve are determined using the second derivative, identified as the initial failure point A and the termination point B. The second derivative of the cumulative failure model F(\(t\)) based on the two-parameter Weibull distribution, \(F^{\prime\prime}(t)\), is:  
\[F^{\prime\prime}(t)=\frac{k}{\lambda}[(k-1)(\frac{t-\gamma}{\lambda})^{k-2} \frac{1}{\lambda}exp[-(\frac{t-\gamma}{\lambda})^{k}]-k(\frac{t-\gamma}{ \lambda})^{2k-2}\frac{1}{\lambda}exp[-(\frac{t-\gamma}{\lambda})^{k}]] \tag{6}\]  
By setting \(F^{\prime\prime}(t)=0\), we identified two temporal inflection points, A and B, on the failure curve, as shown in Figure 14b. Points A and B are defined as the initiation and termination points of solder joint failure, respectively, then the health status of the solder joint is classified into the following three stages. 1. Healthy and Defect-Free Solder Joint Stage (from cycle 0 to cycle A of the accelerated thermal cycling test): During this phase, the solder joint exhibits excellent mechanical and thermal properties, with no visible or functional defects. The structure and material properties of the solder joint remain in their initial state, fully meeting design and functional requirements. The reliability of the solder joint in this stage is exceptionally high. \begin{table}
\begin{tabular}{l c} \hline
**Test Sample Number** & **Maximum Absolute Value of Fitting Residuals \(|e_{i}|\)** \\ \hline Sample 1 & 0.23 \\ Sample 2 & 0.24 \\ Sample 3 & 0.20 \\ Sample 4 & 0.20 \\ \hline \end{tabular}
\end{table} 
Table 3: Maximum absolute values of fitting residuals \(|e_{i}|\) for various experimental samples. Defective but Non-Failure Solder Joint Stage (from cycle A to cycle B of the accelerated thermal cycling test):  
As the number of test cycles increases, the solder joint begins to show signs of structural fatigue or material degradation. Although these initial defects do not yet lead to a complete loss of function, they do impact performance, evidenced by increased electrical resistance or decreased thermal conductivity. While the solder joint can still meet basic operational requirements, its performance stability and long-term reliability begin to be compromised. Failed Solder Joint Stage (after cycle B of the accelerated thermal cycling test):  
Once the test cycles exceed point B, the performance of the solder joint significantly deteriorates, failing to meet the minimum design standards and marking the entrance into a failure state. At this point, the physical and chemical properties of the solder joint may have undergone irreversible changes, such as crack propagation or poor contact, resulting in the loss of its original function. In the assessment of solder joint lifespan, point B is defined as the critical time node for solder joint failure. This node marks a significant decline in solder joint performance to a state where it no longer meets the minimum design standards.