Visualisation of the BGA using correlated X-ray tomography and EBSD.
The BGA package under investigation consists of solder balls sandwiched between the chip and PCB. Three SAC305Bi solder alloys with different wt.% Bi (0, 1.1, 1.9) are subjected to TCoB in ambient atmosphere, see method section for further details. TCoB is chosen as fatigue method to study the effect of mechanical stress on solder fatigue induced by CTEmismatch, dynamic recrystallisation and Bicontent, regardless of electrical current. For each Bicontent, three BGAs with 152 balls each are investigated. After TCoB, the whole BGAs are non-destructively imaged in three-dimensions utilising X-ray tomography to gain sufficient statistical yield, see method section. An exemplary 3D reconstruction from the raw data of an investigated BGA is shown in Fig. 1a. The voxel size is 5.33 × 5.33 × 5.33 µm3 and volume of interest shows the entire BGA (yellow), including the chip (blue) and PCB (brown), for all scans. The convention for the coordinate system used throughout the study is depicted in Fig. 1. Figure 1b shows the correlated xy, xz and yzviews of the reconstructed 3D image from Fig. 1a. The birdview of the BGA layout is visualised in the x-yplane, whereas the two cross-sectional views are shown in the x-zand y-zplane indicating the elevation of the solder balls in zdirection. The locations of the individual intersections are illustrated in Fig. 1b by dashed lines. Degradation features of the solder balls such as the flux pores, fatigue cracks as well as the solder ball itself can be qualitatively identified due to different material densities present. Figure 1c shows an exemplary crosssectional image in the xzplane for the 0, 1.1, 1.9 wt.% Bicontents, alongside correlated FESEM EBSD overlays, see methods and supp. note 6. The crystallographic information from the EBSDmaps allows the identification of crack propagation sites. The EBSDmaps depict the initial single and fewgrained crystal orientations of the individual solder balls, as well as the recrystallised areas which are induced by TCoB. The recrystallised areas are mainly concentrated in the vicinity of the substrate. Figure 1c qualitatively illustrates that the cracked proportion of the ball decreases with increasing Bicontent.
MLbased localisation and 3D segmentation of the BGA.
For the thorough investigation of the degradation mechanisms present within the BGA-package, the statistical representativeness is a crucial and vital factor. Via the X-ray tomography characterisation, a large amount of volumetric data is generated. The tomographic results can image, with a selected volume of interest, the entire BGA array with 152 solder balls in a nondestructive manner. Manual localisation and segmentation of each solder ball within the reconstructed threedimensional image is of course highly labour-intensive, especially if the number of BGAs is more than one. Automation is the key here, however not trivial. Contrast and brightnessgradients throughout the solder material, similar greyvalues of cracks, pores and background, cracks propagating through pores and Xray scattering artefacts at the solder surface make it difficult, if not impossible, to segment the features of interest merely via greyvalue thresholding. To overcome this obstacle, an image processing workflow is developed utilising MLalgorithms capable of providing enhanced accuracy and efficiency. This multilevel workflow with its different MLmodels is illustrated in Fig. 2. Three MLbased algorithms are developed and trained. First, the localisation of solder balls in the X-ray tomography data is performed, see Supp. Note 1. The solder ball localisation is done in one x-yslice with a sliding windowbased binary CNN. The CNN generates bounding boxes for each solder ball as an output. An exemplary output from the localisation model is shown in Fig. 2a. The localisation model is trained on manually labelled 2Ddata, which consists of 100 × 100 pixels2 xyplane clips, either depicting a solder ball or not. Hence, the localisation model utilises a binary ansatz, which is trained on positive and negative image data. In total, 1208 (628 positive + 580 negative) images are used for the training. The model is trained for 40 epochs on an Intel Core i5-8265U CPU with 16 GB RAM. The final training and validation accuracies reach 100.00% and 99.25%, respectively.
After the localisation step, the segmentation of the solder balls is performed. The segmentation process consists of two deep learning models based on UNet architectures. A 2D UNet model is trained at first on 4992 manually labelled 96 × 96 pixels2 slices (x-z-plane), utilising the extracted bounding boxes from the localisation model, see Supp. Note 3. Here, the training was performed on a NVIDIA A40 GPU with 48GB RAM. A representative segmentation result is shown in Fig. 2a for each Bicontent. Since the 2D UNet performs the segmentation on one xzslice at a time, the outputted xzslices need to be reassembled into the 3D ball volume for each ball. For the same reason, without consideration of previous or subsequent xzslices, the 2D UNet may misclassify or oversegment cracks and pores or undersegment the Cumetallisations. Hence, manual label refinement is further performed on the reassembled segmentations from the 2D UNet which are then utilised for training of the developed 3D UNet. Here, 61 images from each ball with 96 × 96 × 96 pixels3 are used, see Supp. Note 2. Figure 2a exemplarily illustrates segmentation results obtained from the 3D U-Net model for each Bicontent. The final step concerns the 3D reconstruction of the full BGA, wherein each segmented ball is reassigned its position according to the localisation outputs. We highlight the accuracy of the developed 3D segmentation method in Fig. 2b by comparing the segmentation results for representative solder balls utilising the 2D and 3D UNet models. As illustrated, an accurate distinction between cracks and pores is not achieved by the 2D UNet in nontrivial cases. The superiority of the 3D UNet model is further highlighted by its ability for a fully automatic segmentation based on the voxel information, eliminating the need for the reassembly of 2D segmentations, as well as its prediction precision on trainingset independent data. Therein, the 2D UNet segmentation model achieves a precision of 76.20%, whereas the 3D UNet model reaches a precision of 91.90%, see also Supp. Figure 1. The segmentation result provides enhanced possibilities for further statistical analysis of the degraded solder balls in terms of the quantification of flux pore and fatigue crack volume, as well as the sites of fatigue crack initiation.
Visualisation of crack initiation sites and the crack distribution.
Here, the segmented features in each ball, which are generated by the 3D UNet model, are further utilised to gain a comprehensive insight into fatigue crack initiation. To that end, the segmented crack and pore labels are summed up and projected into the x-z and x-yplane. Whereby the resulting projections are performed for the chip and PCBside, separately, see Supp. Note 4. Representative projections for each Bicontent are illustrated in Fig. 3a, alongside with the 3D segmentations of the corresponding solder ball. The higher the intensity of the pixel value in the projections, the larger is the separation distance of the solder–to–solder surfaces. For a better evaluation of the fatigue crack initiation sites, the corresponding outlines of the solders as well as the metallisations are also illustrated in the x-zprojections. The outlines of the solder bulk near the interfaces are overlaid on the x-yprojections. The overlays of the respective outlines visualise the progression of the fatigue cracks with regards to the solder. Zero intensity (black) within these outlines represents fully connected solder material, whereas zerovalues outside of the outlines correspond to the background. Two mechanisms can be identified with respect to crack initiation and propagation from the obtained data. It becomes apparent from the generated xzprojections, that cracks on the chipside start from a notchlike geometry feature at the solder surface and propagate inward, as can be seen in the xyprojections. Furthermore, the x-yprojections indicate that cracks can also be initiated at flux pores, i.e. from internally formed notches, as illustrated in the xyprojections of the 1.1 wt.% Bi balls.
For the visualisation of the fatigue crack volume distribution on the entire BGA, BGAheatmaps are extracted from the segmented X-ray tomography data, see Fig. 3b. Here, heatmaps for the entire ball, chip- and PCB-side with 0 wt.%, 1.1 wt.% and 1.9 wt.% Bi, respectively, are exhibited, see method section and Supp. Note 4 for more details. The crack volume is evaluated from the segmented voxels associated with a crack. Figure 3b reveals how the fatigue crack volume proportions in the solder balls are distributed on the BGAs of exemplary 0 wt.%, 1.1 wt.% and 1.9 wt.% Bi samples. The visualisation of the crack volume distribution of the entire BGA provides insights about potential fatigue cracking patterns. The approach for the construction of these heatmaps is further described in Supp. Note 4. With the heatmaps, the crack volume of the individual solder ball can be evaluated based on the colour shading. This illustration can be easily interpreted by humans and can be incorporated into quality and reliability control for a fast identification of badly fatigued solder balls. Based on the heatmap, solder balls can be selected and further prepared for high resolution characterisation, e.g. crosssectional SEM analysis. For instance, Fig. 3b reveals, according to the colour shading illustrated in the heatmaps for the 0 wt.% Bi solder, that the fatigue crack distribution is rather homogeneous on the chipside, compared to a more inhomogeneous distribution for the crack volume in the PCBside. For the 1.9 wt.% Bi balls, the crack volume is rather low for the entire array, as illustrated by the shading in the heatmap of Fig. 3b.
Statistical analysis of the crack volume.
To find the primary causes for the solder fatigue, we further statistically analyse the evaluated data from Fig. 3b. Figure 4 exhibits scatter plots, for 0 wt.% Bi, 1.1 wt.% Bi and 1.9 wt.% Bi balls with pink, blue and green dots, respectively. Here, we plot, see Fig. 4a–c, the flux pore volume (PV) vs. crack volume (CV), Euclidean distance from BGAcentre (d) vs. CV and number of PCBroutes times Euclidean distance (fg) vs. CV. Each relationship is plotted for the entire ball, as well as for the chip and PCBside. Moreover, Spearman correlation coefficients (r) are calculated for each Bicontent. Lastly, the Bicontent vs. CV relationship is also depicted in Fig. 4. The balls with 0 wt.% Bi exhibit a higher crack volume than the solder balls with 1.1 and 1.9 wt.%, as also illustrated in Fig. 3b. We argue, according to the observations, that crack initiation may originate from notches induced by the geometry of the package, as well as by the flux pores within the solder ball. The statistically significant crack volume correlations from Fig. 4 are summarised in Table 1. The correlation coefficients in Fig. 4b, Fig. 4c and Table 1 show a weak positive correlation for pores on the same side as the crack. Therefore, it is assumed that flux pores impact fatigue crack initiation in solder balls by acting as internal notches. Conversely, the correlations are negative for pores on the opposite side of the crack. This indicates that flux pores on one side initiate cracks on the same side, which decreases the probability of crack initiation on the opposing side.
Table 1
Spearman correlation coefficients for the crack volume – property relationships. Here, the statistically significant correlations between crack volume and solder properties are listed. CVchip – PVchip, CVPCB – PVPCB and CVPCB – fg exhibit positive correlation coefficients, whereas CVchip – PVPCB and CVPCB – PVchip correlate negatively.
Bicontent
|
r (CVchip – PVchip)
|
r (CVchip – PVPCB)
|
r (CVPCB – PVchip)
|
r (CVPCB – PVPCB)
|
r (CVPCB – fg)
|
0 wt.%
|
0.149
|
-0.103
|
-0.083
|
0.277
|
0.502
|
1.1 wt.%
|
0.253
|
-0.050
|
-0.047
|
0.404
|
0.293
|
1.9 wt.%
|
0.216
|
-0.046
|
-0.052
|
0.239
|
0.458
|
Considering the BGAlayout and under the assumption of isotropic thermal expansion of the multi-material substrates, solder balls located farther from the BGAcentre experience higher stresses during TCoB. Hence, fatigue of solder balls may have progressed faster for balls further away from the centre, since they experience larger stresses during TCoB compared to balls close to the centre. The correlations of the crack volume with the Euclidean distance of the ball centre from the BGAcentre are also shown in Fig. 4. The overall crack volume correlates positively with increasing distance. However, the correlations of cracks on the chipside with d show signrelated inconsistencies between the Bicontents. The cracks on the PCBside, on the other hand, correlate positively with increasing distance d. Since the PCBcopper (Cu) metallisations intrude into the solder ball and since Cu is much stiffer than the solder ball, the PCBroutes may act as additional notches in the solder. Therefore, the number of PCBroutes leading away from each ball are incorporated in the analysis, in addition to the BGAcentre distance. This relationship is described by the geometryfactor, calculated as \({\text{f}}_{\text{g}}=\left(1+{\text{n}}_{\text{P}\text{C}\text{B}\text{r}\text{o}\text{u}\text{t}\text{e}\text{s}}\right)\bullet \text{d}\), where nPCB−routes denotes the number of PCBroutes leading to the ball. The correlations for the overall CV, CVchip and CVPCB are summarised in supp. Tables 1–3, respectively. CVchip correlates negatively with fg, whereas CVPCB correlates positively, see Table 1. Hence, it is assumed that the combined effect of PCBintrusions and centredistance plays a significant role in the fatigue crack initiation and propagation in solder balls. Lastly, Fig. 4a shows that all 0 wt.% Bi balls are cracked to some extent, whereas some balls with 1.1 wt.% and 1.9 wt.% are still fully intact after TCoB. The maximum CVchip decreases parabolically with increasing Bicontent, while the maximum CVPCB does not significantly decrease between the 1.1 wt.% and 1.9 wt.% Bi balls, see Fig. 4b and Fig. 4c, respectively. The Spearman correlation coefficients for the investigated CV –, CVchip– and CVPCB – property relationships are presented in Supp. Tables 1, 2 and 3 respectively.
Stress distribution, recrystallisation and intergranular cracking.
We simulate the stress-distribution within the solder ball during TCoB by using ANSYS MAPDL 2022R2. Here, we utilise the geometry data obtained from the X-ray tomography, see supp. note 5 and method section. Since the stiffness of the Cumetallisations is much higher than that of the solder, the metallisations are represented as fixed nodes at the top and bottom of the ball. The metallisation intrusion from the PCB is implemented with the properties of Cu. The 3D and 2D geometries used for FEM are shown in Fig. 5a. The plane of the 2Dgeometry is shown in grey in the 3Dgeometry. Simulation results for the βSn matrix are shown, during exposure to a TCoB-cycle with a temperature increase from − 40°C to 125°C and a subsequent cooling to -40°C. Both ramp and dwelltimes are set to 15 minutes, respectively. The parameters of the simulated thermal cycle correspond to the ones from the real TCoBtesting conditions. The simulation results for one exemplary TCoBcycle are shown in Supp. Figure 2. The highest stress in the solder is present near the interfaces to the substrates, since the effects of CTEmismatch are most pronounced here. More specifically, the stresses are concentrated at the surface notches on the chipside and the notches created by the intrusion of the PCBmetallisation into the solder. It can also be seen that the ballshape of the solder causes an hourglassshaped stress distribution over the solder crosssection.
As fatigue crack propagation impairs the remaining functionality of the solder during TCoB, the propagation paths of those cracks are of interest. In order to visualise these crack propagation paths within the solder microstructure, crosssectional FESEM EBSD scans are performed for representative solder balls with different Bicontents. Hourglassshaped recrystallisation fronts in the initially single or fewgrained balls are visible in the EBSDmaps, see Fig. 5b. This is in keeping with the simulated stress distribution shown in Fig. 5a., as recrystallisation will occur in the highly stressed (strained) areas first. Moreover, the EBSDmaps in Fig. 5b show that recrystallisation starts at the surfacenotches on the chipside and the metallisation intrusion on the PCBside, which matches the stress concentrations in those areas seen in the FEM modelling results. In the recrystallised areas near the interfaces, intergranular cracks can be seen in the 0 wt.% Bi sample. The same is true for the 1.1 wt.% Bi sample, although the intergranular crack seen there is less gaping than in the 0 wt.% Bi sample. The 1.9 wt.% Bi sample only exhibits a small crack at the chipinterface, but it does also show the hourglassshaped recrystallisation front, albeit in much earlier stages than the 0 wt.% Bi and the 1.1 wt.% Bi samples. In order to understand the effect of Bi-additions in the solder microstructure after TCoB, FESEM EDX analysis is done for exemplary regions for each Bi-content, see Supp. Note 7 and Supp. Figure 4. No primary Bi-precipitates can be seen for either alloy.
Figure 5c depicts the kernel average misorientation (KAM) maps for the respective EBSDmaps. From the KAMmaps, highstrain areas in the solder crosssections can be qualitatively deduced. Recrystallised areas appear less strained than singlecrystalline regions. In Fig. 5d we present the inverse pole figures (IPFs) for the ydirection and the grain size distributions for each crosssection. The IPFs appear smeared out, indicating distorted orientations around the initial crystal orientation(s) of the balls. In order to correlate the fatigue cracks from the 3D segmentation with their propagation paths in the solder microstructure, exemplary EBSDmaps are overlaid with corresponding X-ray tomography segmentations in Fig. 5e. The correlated overlays clearly reveal that the cracks visible in the segmented X-ray tomography data are indeed intergranular fatigue cracks. Hence, the 3D MLanalysis based on X-ray tomography data describes the intergranular fatigue crack propagation in the solder balls. Not only does the developed MLsegmentation workflow allow a fully automated, nondestructive 3D failure analysis of entire BGAs, but also the underlying microstructural and mechanical mechanisms for fatigue crack initiation and propagation are correlatively established.