## 3 Results and Discussion
### Thermal Simulation Analysis of Packaging Defects
In terms of heating rate, the solder ball missing condition exhibits the fastest rate at 41.9 \({}^{\circ}\)C/s, followed by the solder ball bridging condition at 32.3 \({}^{\circ}\)C/s, while the normal  
Figure 7: Simulated temperature distributions on the package substrate under different defect conditions: (**a**) normal package with uniform temperature; (**b**) missing solder ball resulting in localized hot spots; (**c**) missing solder ball and pad producing similar hot spots without boundary features; (**d**) bridging causing localized cold zones due to altered heat flow. packaging condition is the slowest at 28.5 \({}^{\circ}\)C/s. When evaluated based on temperature saturation time, the solder ball missing condition again shows the fastest response, reaching saturation in just 1.4 s, followed by the bridging condition at 17.0 s, with the normal condition being the slowest at 37.5 s.  
These differences among the three cases are fundamentally attributed to variations in heat transfer paths. Specifically, solder ball loss results in a rapid temperature rise due to circumferential heat flow around the defect. Solder ball bridging, on the other hand, partially compensates for heat transfer efficiency through an alternative lateral conduction channel. Meanwhile, the effect of solder pad absence is essentially masked by the low thermal conductivity of the substrate, as the missing pad does not contribute to effective thermal coupling. To complement the simulation analysis and further validate the physical observations, representative experimental results are presented prior to neural network-based detection evaluation. Figure 9 shows real infrared thermal images and corresponding optical images of the defective BGA samples introduced in Section 2.2. These images capture the surface temperature distribution and physical structure under different defect conditions, including bridge and missing solder ball. Figure 9 presents the temperature distribution of a bridged solder ball. The normal solder ball appears in blue, indicating a relatively low temperature at its center. In contrast, the bridged solder ball exhibits an elongated high-temperature region, with the central area showing lower temperature than the surroundings, reflecting lateral heat conduction between bridged solder balls. Figure 9 shows the infrared thermal response of a missing solder ball. A red hotspot appears at the missing center, indicating elevated temperature due to disrupted lateral heat conduction. The temperature distribution within individual solder balls is visibly uneven, with a gradual cooling trend from the periphery toward the center. Moreover,  
Figure 8: Transient temperature rise profiles at the package center under different defect conditions, comparing heating rates and temperature saturation times among normal, missing solder ball, and bridging scenarios, highlighting the impact of defect-induced heat transfer path alterations. the isothermal regions vary among different solder balls, highlighting the influence of defect-induced heat flow distortion. Figure 9b,d display optical images of the actual solder ball structures corresponding to the thermal images. The normal solder balls appear silver, smooth, and uniformly spherical, with consistent size and surface quality. In contrast, at the location without solder ball, the exposed copper pad is clearly visible. These experimental observations further support the accuracy of the thermal simulation and provide a real-data foundation for training and evaluating the neural network in the next section.