Correlative, ML based and non destructive 3D analysis of intergranular fatigue cracking in SAC305 Bi solder balls

Correlative, ML based and non destructive 3D analysis of intergranular fatigue cracking in SAC305 Bi solder balls | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Correlative, ML based and non destructive 3D analysis of intergranular fatigue cracking in SAC305 Bi solder balls Roland Brunner, Charlotte Cui, Fereshteh Falah Chamasemani, Priya Paulachan, and 5 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3876312/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Apr, 2024 Read the published version in npj Materials Degradation → Version 1 posted 9 You are reading this latest preprint version Abstract Reliable connections of electrical components embody a crucial topic in the microelectronics and power semiconductor industry. This study utilises 3D nondestructive Xray tomography and specifically developed machine learning (ML) algorithms to statistically investigate crack initiation and propagation in SAC305Bi solder balls upon thermal cycling on board (TCoB). We quantitatively segment fatigue cracks and flux pores from 3D Xray tomography data utilising a multilevel MLworkflow incorporating a 3D U-Net model. The data reveals that intergranular fatigue cracking is the predominant failure mechanism during TCoB and that dynamic recrystallisation precedes crack initiation. Moreover, we find that fatigue cracks are initiated at surface notches, flux pores and printed circuit boardmetallisation intrusions. The work provides important insights regarding the underlying microstructural and mechanical mechanisms for recrystallisation and cracking, uniting the aspects of bigdata analysis with MLalgorithms and indepth understanding about the underlying materials science. Physical sciences/Materials science/Materials for devices/Electronic devices Physical sciences/Mathematics and computing Physical sciences/Engineering/Electrical and electronic engineering Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction The reliable connection of electrical components embodies a crucial topic in microelectronics and the power semiconductor industry. Hence, the intactness of a solder ball is crucial for the lifetime of the device and its functionality. The fundamental understanding of degradation mechanisms, in particular for more sustainable Pb-free solders remains a vital challenge in the field of materials science 1–5 . Solder balls serve as both electrical and thermal connections between the chip and printed circuit board (PCB) metallisations. Tin (Sn) based solder alloys have largely replaced leadbased alloys in power and microelectronics due to growing health and environmental concerns 6 . Sn – 3.0 wt.% Ag – 0.5 wt.% Cu (SAC305) is one of the most promising Snbased solder alloys. However, conventional SAC solder balls can already exhibit microstructural degradation in the asreflowed condition 7–9 . Flux pores may be formed during reflow due to outgassing of flux residues. These gasses can remain trapped within the solder after solidification and form spherical pores 8, 9 . Moreover, the solder ball may also experience thermomechanical fatigue during service 10, 11 . In operation, the current flow leads to resistive heating and further to multiple thermal loading when the device is repeatedly turned on and off. Mechanical stress emerges in the component due to the underlying coefficient of thermal expansion (CTE) mismatches, originating from the multiple materials with various CTEs present in the device 11–13 . The SAC305 solder ball represents a mechanical weak spot within the device. Here, most of the generated deformation occurs due the low hardness of the βSn matrix of approximately 0.1 GPa 14 . The plastic strain thereby introduced into the solder material may lead to recovery, polygonization and recrystallisation 15 . Consequently, the initially single or fewgrained solder balls 15–17 undergo grainrefinement in highly strained areas. These highly strained areas are located in the proximity of the interfaces to the chip and PCBsubstrates, whereat shear strain is the predominant type of strain induced 11 . The new grain boundaries that are formed during recrystallisation in those highstrain areas serve as preferred crack propagation sites 10, 11, 15, 18 . As a result, these intergranular fatigue cracks increase the thermal as well as the electrical solder resistivity and thereby impair the device’s functionality and its lifetime 11, 12 . The use of Bismuth (Bi) as an alloying element shows high potential to improve the thermo-mechanical stability of the SAC solder. The solubility limit of Bi in the βSn matrix of SACalloys is assumed to be around 2.5 wt.% 19 . Accordingly, when less than 2 wt.% Bi is added, it acts as solid solution strengthener in the βSn matrix 17, 20 . As a solid solution strengthener, Bi elevates the yield stress of the solder 14, 17, 20 and thereby retards dynamic recrystallisation and the formation of new grain boundaries, i.e. reducing crack propagation sites. The utilisation of SAC305Bialloys represents a very promising approach to diminish microstructural degradation and prolong the long-term fatigue stability of solder balls. A crucial component for the assessment of the relation between microstructural degradation and functionality is the need for characterisation of each solder ball volume on the ball grid array (BGA) in a statistical manner. Assessing entire solder ball volumes on BGAs produces large amounts of data which should be in keeping with the FAIR data principle 21 . Nevertheless, the failure assessment of a specific solder ball in complex BGAgeometries is often tedious, because daisychain measurements of electrical resistivity usually provide only information about the cumulative resistivity of all, or many, balls on the BGA. Such an approach does not reveal which particular ball has failed 11 . Light optical or electron microscopy techniques 16, 22, 23 , on the other hand, require sample preparation for each and every ball and are therefore timeconsuming and destructive. Furthermore, these techniques only give 2Dinformation of one particular crosssection, which may not be representative for the fatigue crack propagation in the solder ball volume. Xray tomography eliminates these downsides as it allows nondestructive inspection of entire BGAs and delivers full 3Dinformation. Subsequent efficient image analysis is important to retrieve statistical information from the reconstructed 3D image data. Image analysis incorporating supervised machine learning (ML) has proven to be significantly more efficient and accurate than manual feature segmentation 24, 25 . In addition to the ability of MLalgorithms to process large amounts of image data, such as the ones produced with Xray tomography, efficiently, algorithms are not subjected to volatile data evaluation noise as manual evaluation by human beings. Even data interpretation by the same person, and even the same expert, may underlie significant variability due to a number of daydependent psychological factors 26 . This variability in human judgement may lead to inaccuracies in data evaluation, which are eliminated when mathematical algorithms are applied, not to mention the benefit of the possibility for automation. The development of MLalgorithms for image analysis has been rapidly evolving in recent years 24 . Convolutional neural networks (CNNs) have proven advantageous over manual image analysis, as they are able to build highlevel features from lowlevel ones, providing accurate and efficient image recognition, object detection and image segmentation 24, 25 . CNNs have been increasingly applied to medical and biological image analysis 25, 27 and more recently, their use for image segmentation in materials science has been on the rise 28–36 . In microelectronics failure and reliability analysis, some work has been previously done on Xray tomography data 37, 38 . However, to our knowledge, the algorithms developed in these previous studies focus on the detection of flux pores. Although the CNN developed in 37 is trained on 3D data, its output is limited on a binary classification of solder balls with and without flux pores that are classified as “good” and “bad”. On the contrary, the models developed in 38 perform the pore segmentation in two consecutive binary 2D segmentation steps: first, object detection of solders is carried out and subsequently, the pores are detected using the same binary approach. None of these previous studies apply a full threedimensional segmentation to the X-ray tomography image data e.g. by a 3D UNet architecture 39 . Moreover, the previous studies are constrained to image segmentation using CNNs without considering the underlying mechanisms for defectformation and correlations with microstructural and mechanical phenomena in the material. Conversely, the implications for fatigue crack initiation by the segmented flux pores have not yet been considered. In short, the connection between MLbased image segmentation and materials science has not yet been made. Therefore, our study intends to unite the aspects of statistical fatigue analysis and the underlying microstructural and stressrelated mechanisms of fatigue crack initiation and propagation in SAC305Bi solder balls, utilising 3D imagining with 3D ML-based image analysis. We quantitatively segment fatigue cracks and flux pores from 3D Xray tomography data using a multilevel MLworkflow incorporating a 3D U-Net model. Moreover, we correlate the X-ray tomography data with microstructural features in the solder balls utilising high resolution field emission scanning electron microscopy (FESEM) and electron backscatter diffraction (EBSD). Further, we investigate the stress distribution within a solder ball during thermal cycling on board (TCoB) with finite element method (FEM) modelling. We draw connections between the simulated stress distribution, microstructural fatigue in the solder balls, i.e. recrystallisation and fatigue cracking, and statistical fatigue crack analyses from the MLworkflow. By bridging the gap between microstructural fatigue and its impact on statistically significant fatigue crack correlations, we elaborate on the importance of various smallscale mechanisms at play during TCoB. Whereat, we discuss that the rigorous understanding of the underlying small-scale mechanisms is crucial to avoid macroscopic failure within the electronic device. Based on the developed characterisation workflow we conclude that intergranular fatigue cracking is the predominant failure mechanism during TCoB and that dynamic recrystallisation precedes fatigue cracking. Moreover, we find that fatigue cracks are initiated at three kinds of notches, i.e. surface notches, flux pores and PCBmetallisation intrusions, and that crack propagation occurs along recrystallised grain boundaries which are enriched with Cu. Results 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. 1 a. The voxel size is 5.33 × 5.33 × 5.33 µm 3 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 1 b shows the correlated xy, xz and yzviews of the reconstructed 3D image from Fig. 1 a. 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. 1 b 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 1 c 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 1 c 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. 2 a. The localisation model is trained on manually labelled 2Ddata, which consists of 100 × 100 pixels 2 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 pixels 2 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. 2 a 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 pixels 3 are used, see Supp. Note 2 . Figure 2 a 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. 2 b 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. 3 a, 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. 3 b. 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 3 b 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. 3 b 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. 3 b. Statistical analysis of the crack volume. To find the primary causes for the solder fatigue, we further statistically analyse the evaluated data from Fig. 3 b. 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. 4 a–c, the flux pore volume (PV) vs. crack volume (CV), Euclidean distance from BGAcentre (d) vs. CV and number of PCBroutes times Euclidean distance (f g ) 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. 3 b. 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. 4 b, Fig. 4 c 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. CV chip – PV chip , CV PCB – PV PCB and CV PCB – f g exhibit positive correlation coefficients, whereas CV chip – PV PCB and CV PCB – PV chip correlate negatively. Bicontent r (CV chip – PV chip ) r (CV chip – PV PCB ) r (CV PCB – PV chip ) r (CV PCB – PV PCB ) r (CV PCB – f g ) 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 n PCB−routes denotes the number of PCBroutes leading to the ball. The correlations for the overall CV, CV chip and CV PCB are summarised in supp. Tables 1 –3, respectively. CV chip correlates negatively with f g , whereas CV PCB 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. 4 a 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 CV chip decreases parabolically with increasing Bicontent, while the maximum CV PCB does not significantly decrease between the 1.1 wt.% and 1.9 wt.% Bi balls, see Fig. 4 b and Fig. 4 c, respectively. The Spearman correlation coefficients for the investigated CV –, CV chip – and CV PCB – 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. 5 a. 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. 5 b. This is in keeping with the simulated stress distribution shown in Fig. 5 a., as recrystallisation will occur in the highly stressed (strained) areas first. Moreover, the EBSDmaps in Fig. 5 b 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 5 c 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. 5 d 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. 5 e. 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. Discussion The functionality of a solder ball in terms of its ability to conduct both electrical and thermal current from the chip to the PCB is vastly impaired when the material is interrupted by gasfilled volumes such as flux pores and fatigue cracks 11 . Hence, the non-destructive, statistically significant failure analysis of fatigue crack initiation and propagation in solder balls is essential. Furthermore, an in-depth understanding of the underlying mechanisms for solder fatigue on a microstructural scale is crucial for the design of materials scienceinformed engineering solutions to prolong the fatigue lifetime of leadfree solder balls. We statistically identify the solder properties that impact a solder balls fatigue from 3D data by conducting nondestructive X-ray tomography and applying sophisticated MLbased image analysis methods. The statistical results show a significant prolongation of solder ball lifetime by the addition of Bi to the SAC305 alloy. In order to understand the underlying mechanisms of solder fatigue, we discuss ( 1 ) the impact of the periodical stress and strain on the solder during TCoB, ( 2 ) the crack propagation through the solders and ( 3 ) the influence of Bi on the fatigue and microstructural properties of SAC305 solder balls. Due to the CTEmismatches in the multicomponent device, mechanical stress and deformation are induced in the solder during TCoB 15, 40 . Since stress and deformation occur periodically during TCoB, the predominant mechanisms of solder degradation are considered to be fatigue and the propagation of fatigue cracks into the solder balls. Figure 3 a and Fig. 5 b support this assumption and illustrate the initiation of cracks either at surface notches or at internal notches, i.e. metallisation intrusions and flux pores, and their propagation into the solder bulk. A typical characteristic of fatigue cracks 41 . As the mechanical stress in the solder during TCoB stems from CTEmismatches between the various components of the multilayer device, stress and strain are most pronounced near the interfaces to the chip and the PCB. The emerging inhomogeneous stress distribution is even more enhanced by the presence of surfacenotches and the intrusion of the PCBmetallisation into the ball. The accompanied FEM simulation illustrates how the ballshape of the solder translates the shear stress at the interfaces into an hourglassshaped stress gradient within the ball, see Fig. 5 a. This stress gradient induces a proportional strain gradient in the solder, consisting of both plastic and elastic strain. Accordingly, the dislocation density is higher near the interfaces and notches, causing the solder to dynamically recover and recrystallise there earlier compared to the rest of the solder. This hourglassshaped recrystallisation behaviour is observed in the EBSDmaps in Fig. 5 b. Further, the EBSDmaps show that the solidification structures of the balls are initially built of either single crystals or a few large grains. These observations are consistent with the findings in 15, 22, 20 . The IPFs in Fig. 5 d show that the orientations of the newly formed grains are smeared out around the initial crystal orientation. Hence, the solder balls in this study do not undergo primary recrystallisation, where statistically oriented grains would nucleate in a highly deformed crystal 41 . Rather, continuous recovery and polygonization takes place in the investigated solder balls, as rearrangement of dislocations generates smallangle grain boundaries and new grains that are slightly misoriented towards the initial crystal orientation. Furthermore, highly strained regions in the initial single crystals, visible in the KAMmaps in Fig. 5 c, are likely to undergo recrystallisation with continued cycling. The KAMdistributions are also in agreement with the FEM simulations in Fig. 5 a. Additional EBSD and KAMmaps, as well as IPFs are shown in Supp. Figure 3 to support the provided argumentation. Since the Cu PCBmetallisation is much stiffer than the solder, its intrusion into the ball acts as an additional internal notch and crack initiation site. The notch effect of the PCBintrusion is confirmed by the FEMsimulations in Fig. 5 a as well as by the EBSDmaps in Fig. 5 b, where polygonization can be seen to start in the vicinity of the PCBintrusions. This can be seen particularly clearly in the EBSDmap of the 1.9 wt.% Bi sample. The correlation of the EBSDmaps with the corresponding 3D segmented image data in Fig. 5 d confirms that the cracks visualised with X-ray tomography and analysed with the MLassisted workflow are indeed intergranular fatigue cracks. Since the cracks propagate along recrystallised grain boundaries, those are of particular interest for the understanding of fatigue crack propagation. EDX analyses of exemplary grain boundaries for each Bicontent are shown in Supp. Figure 4 . The EDXmaps show Cuenrichment along recrystallised grain boundaries. This enrichment may cause or promote intergranular fatigue cracking. Since grain boundaries are first formed in the highstrain areas near the solder interfaces, intergranular crack initiation and propagation are also expected to start there. The onset of dynamic recrystallisation, and therefore the formation of grain boundaries, requires a critical dislocation density. As no primary Biprecipitates are present in the EDXmaps, see Supp. Figure 4 , it is assumed that Bi is solved in the β-Sn matrix, acting as a solid solution strengthener and increasing the Snmatrix’ yield strength. Since the primary fatigue symptom is intergranular crack propagation, as illustrated in Fig. 5 b, Bi is therefore expected to delay both recrystallisation and subsequent intergranular fatigue cracking. This can be seen in Fig. 1 c and Fig. 5 e, where crosssectional overview of EBSDmaps of exemplary balls for 0 wt.%, 1.1 wt.% and 1.9 wt.% Bi samples are correlated with the X-ray tomography slices and 3D segmentations, respectively. This relationship is also shown in the scatter plots in Fig. 4 . Moreover, the IPFs in Fig. 5 d and Supp. Figure 3 are more localised around the initial crystal orientation(s) in the 1.9 wt.% Bi balls compared to the 0 wt.% Bi balls which indicates that dynamic recrystallisation is further advanced in 0 wt.% Bi balls. Furthermore, fatigue cracking has progressed further in balls with decreasing Bicontent, which is also in keeping with the results from the statistical analyses shown in Fig. 4 . As already mentioned, the solid solution strengthening effect of Bi delays polygonization, grain boundary formation and subsequent intergranular fatigue cracking in Bicontaining solder balls. Nonetheless, the 1.1 wt.% and 1.9 wt.% Bi samples are also recrystallised to various extents. However, intergranular cracks have not propagated to the same proportion as in the 0 wt.% Bi samples, as can be seen in Fig. 1 c and Fig. 5 b, despite the grain boundaries also being enriched with Cu, illustrated in Supp. Figure 4 . Therefore, it is assumed that Biadditions may also influence the structure of grain boundaries in SAC305, leading to strengthening of the recrystallised grain boundaries. The study of structure and elemental composition of grain boundaries in Bifree and Bicontaining solder balls is not part of this work but will be the subject of a future study. Conversely, cracks, once initiated in a ball, dampen the stress from the substrates so it cannot be efficiently transmitted to the opposing side of the crack. Accordingly, no more, or fewer, dislocations are produced in the ball and dynamic recrystallisation stops, or slows down, once a crack is initiated, since the dislocation density and rearrangement of dislocations into an energetically more favourable configuration is its driving force. Hence, recrystallisation in the 0 wt.% Bi ball in Fig. 5 b is less progressed than in the 1.1 wt.% Bi sample, as the cracks in the 0 wt.% Bi ball inhibit further recrystallisation after crack initiation and the strain energy from further cycling is invested in propagating the cracks. Apparently, however the recrystallised grains in the 0 wt.% Bi sample have undergone coarsening during the hightemperature periods of TCoB after cracking. This results in larger grains compared to the 1.1 wt.% and 1.9 wt.% Bi samples, as shown in the grain size distributions in Fig. 5 d. Moreover, the KAMmaps in Fig. 5 c show that strain is less pronounced in polygonised areas of the crosssection, compared to the initial grain. Therefore, it is assumed that recrystallisation provides stress relief in the solder. This thorough microstructural analysis, in combination with the FEM modelling results, elaborates the underlying mechanisms for fatigue cracking. Moreover, the correlations of the EBSDmaps with Xray tomography data and their segmentations prove the validity of our statistical analysis of solder fatigue. Several conclusions can be drawn from our study on solder fatigue, its statistical correlations with solder ball properties and the underlying microstructural and mechanical mechanisms. Firstly, intergranular cracks propagating along recrystallised, Cuenriched grain boundaries of solder balls constitute the predominant fatigue mechanism during thermal cycling of BGAs. Secondly, recrystallisation and grain boundary formation in highstrain areas near the chip and PCBinterfaces of the solder balls precedes crack initiation. The stress distribution in the solder ball during TCoB is simulated with FEM and it is in keeping with the shape of the recrystallisation fronts in EBSDmaps. Thirdly, fatigue cracks initiate either at notches at the solder ball surface, Cumetallisation intrusions or at internal defects, i.e. flux pores, and propagate along recrystallised grain boundaries into the surrounding solder ball matrix. These aspects could be considered in the design of BGAs to engineer the notcheffects on solder fatigue. Lastly, alloying Bi to SAC305 markedly delays recrystallisation, fatigue crack initiation and propagation, thereby prolonging the lifetime of solder balls. EDXmaps show that the investigated Biconcentrations act as solid solution strengthener in βSn rather than forming primary precipitates, thereby increasing the solder ball’s yield strength. In summary, this study proves nonequivocally that intergranular fatigue cracks and flux pores in SAC305 + x Bi (x = 0, 1.1, 1.9 wt.%) solder balls can be visualised with 3D X-ray tomography and statistically analysed with the MLalgorithms developed for this purpose. The MLbased segmentation workflow developed in this study can be used to efficiently and nondestructively inspect solder balls on BGAlevel with high statistical yield. The developed workflow provides the possibility for efficient and advanced failure analysis. The gained data reveals the crack initiation at surface notches and at internal notches, i.e. flux pores and PCB-metallisation intrusions, a typical feature of fatigue cracks. Further, intergranular propagation paths of the fatigue cracks represent a major issue. The work provides important insights regarding the underlying mechanisms for recrystallisation and crack propagation, as well as the effects of Bi on the microstructural fatigue in the solder alloys. The analysis of microstructural features and the simulation of the stress distribution is utilised to understand the statistically evaluated solder fatigue, thereby uniting the aspects of bigdata analysis with MLalgorithms and indepth understanding about the underlying materials science. Methods The experimental and methodological approaches of this study are described in the following. More details can be found in the supplementary notes. Sample Production and TCoB Three solder materials are investigated: Sn – 3.0 wt.% Ag – 0.5 wt.% Cu (SAC305), SAC305 + 1.1 wt.% Bi and SAC305 + 1.9 wt.% Bi. Bi acts as a solidsolution strengthener in βSn. No primary precipitation of Bi is expected for this content 20, 17 . The investigated solder balls are produced by droplet spraying in an inert N 2 atmosphere and subsequently soldered between the Cumetallisations of the chip and the PCB. Reflow is done at a peak temperature of 240°C and with a mean heating rate of 44°C/min in inert N 2 atmosphere, followed by rapid air cooling to 90°C with a mean cooling rate of 107°C/min and ambient air cooling to room temperature. The 3D BGA layout is shown in Fig. 1 a, alongside with its coordinate system for the subsequent analysis. Figure 1 b shows the xylayout of the BGA. Thermal cycling is conducted between − 40–125°C with ramp and dwelltimes of 15 mins, respectively. Hot and cold air is alternately injected into a furnace in order to obtain heating rates as linear as possible. The furnace temperature during thermal cycling is homogenised by air circulation. The 0 wt.% Bi sample is thermally cycled for 1764 cycles, the 1.1 wt.% Bi samples and the 1.9 wt.% Bi samples for 2914 and 2570 cycles, respectively. The BGAs with Bicontent underwent larger numbers of cycles, since the amount of Biadditions provide solid solution strengthening effects of the βSn matrix and hence delay recrystallisation and subsequent intergranular cracking. Nondestructive 3D X-ray tomography scans Nondestructive X-ray tomography has the capability to scan entire BGAs in less than an hour. Hence, this method is suitable for the generation of the large amount of image data that is necessary for ML and statistical statements regarding solder fatigue. The X-ray tomography scans are done with a GE Phoenix Nanotom M (research edition) using a cone beam. By using a cone beam, the achievable magnification is limited by the lateral size of the BGA (~ 10 × 7 mm 2 ). The achievable voxelsize results to 5.33 × 5.33 × 5.33 µm 3 for scanning entire BGAs. The interaction of an Xray beam with matter is described by the BeerLambertlaw: $$\frac{\text{I}}{{\text{I}}_{0}}=\text{e}\text{x}\text{p}(-\frac{{\mu }}{{\rho }} {\rho } \text{d})$$ , where \(\text{I}\) denotes the transmitted Xray intensity, \({\text{I}}_{0}\) the incident Xray intensity, \(\frac{{\mu }}{{\rho }}\) the attenuation coefficient, \({\rho }\) the material density and \(\text{d}\) the penetrated sample thickness. Due to the dependency of Xray attenuation on the density, more specifically the atomic number, of the penetrated material, airfilled defects, i.e. cracks and pores, appear darker in the Xray tomography scans than βSn and Cumetallisations. This allows the distinction of pores and cracks based on their greyvalues. FESEM EBSD FESEM overview EBSD maps are used to verify X-ray tomography imaging, i.e. to assess whether its resolution is sufficient for the investigation of solder fatigue. Moreover, EBSD maps provide crystallographic information about the solder balls. The final solder ball crosssections for EBSD are prepared with a Hitachi IM4000 + ion-slicer, which yields deformationfree surfaces. The accelerating voltage for ionslicing is set to 6 kV and the swing angle to 30° with 3 swings per minute. Overview EBSDmaps are acquired with a Zeiss 450 Gemini FESEM. An accelerating voltage of 10 kV, a step size of 400 nm and an Oxford Symmetry detector are used for EBSDmapping. Oxford Instrument AZtecCrystal 5.1 is used for the evaluation of EBSD data. IPFs are used to extract information about the polygonization behaviour of the solder balls and grain size distributions are plotted in order to determine their recrystallisation stage. Neighbouring grains with misorientations > 10° are considered in the grain size distributions. Since the polygonised grains are quasicircular, their equivalent circle diameter is used as size metric. The grain size distribution is plotted as the areaweighted fraction of grains with a particular diameter in proportion to the entire solder crosssection. More details can be found in supp. note 6. ML-algorithms Due to the large amount of 3Dimage data produced by X-ray tomography, supervised MLalgorithms are used for the quantitative image analysis. The analysis is done in two steps: xylocalisation followed by 3D feature segmentation. The localisation algorithm is based on a binary, sequential, feedforward slidingwindow convolutional neural network (CNN) adapted from 30 . Its schematic architecture is shown in Supp. Figure 1 and described in detail in supp. note 1, alongside exemplary training images, the model’s accuracy and loss histories and its testing accuracy. The 3D segmentation model is a U-Net CNN. Its architecture, training and validation accuracy and loss histories are shown in detail in Supp. Figure 1 and its architecture is elaborated in supp. note 2. In order to efficiently produce a large amount of training data for the 3D segmentation model, a 2D segmentation U-Net model was used. Details about the 2D segmentation model are also shown in Supp. Figure 1 and described in supp. note 3. All ML models that are developed in this study are described in detail in Supp. Notes 1–3 . Calculation of separation distance and crack distribution on the BGA In order to visualise the crack initiation sites in the solder balls, the segmented cracks and pores obtained from the 3D UNet are projected into 2Dplanes, i.e. xz and xyprojections. The respective voxels, associated with either cracks or pores, are summed up along the yaxis for the xzprojections and along the zaxis for the xyprojections. Additionally, the outlines of the solder ball and metallisations are thresholded and overlaid onto the projections. The visualisation of the crack volume distribution on the BGA allows fast identification of particularly fatigued solder balls. To that end, the crack volumes gained from the 3D segmentation are put into relation with the solder volume to obtain the volume percentage of cracks in the respective balls. These crack volume proportions are then schematically plotted into heatmaps which exhibit the BGAlayout. This is done by utilising the localisation outputs. FEM simulation During TCoB, mechanical stresses are introduced into the solder balls. These mechanical stresses stem from misfits in CTE between the various components in the multimaterial device. In order to visualise the stress distribution in the solder ball, 3D FEM simulations were done with Ansys MAPDL 2022R2 for one exemplary heating and cooling cycle, considering the 2D plane in the centre of 3D geometry, see supp. note 5. The 3D geometry is extracted from an .stl file from Xray tomography imaging. The geometry and the results of the FEM simulation are shown in Fig. 5 a and in Supp. Figure 2 . The simulated heating cycle is implemented with the same parameters as the TCoB cycling done in this study: Heating from − 40°C to 125°C, followed by cooling to -40°C. Both the ramp times and dwell times are set to 15 minutes, respectively. A thermal transient analysis is carried out based on the heating cycle. The temperature profile of the FEM simulation is shown in Supp. Figure 2 , alongside crosssectional in plane stress distributions for a selection of timesteps. The elastic tensor of β-Sn and the thermal expansion coefficient are taken from 42 . Boundary conditions for the FEM analysis are implemented considering the following. Firstly, the surface notches on the chip-side are represented by fixed nodes, which account for the attachment of the ball to the chipmetallisation. The PCB-metallisation intrusion is implemented with the mechanical and thermal expansion values of Cu from 43 . Lastly, like the chip-side, the bottom nodes of the metallisation are rigidly fixed. More details about the FEM simulation are given in Supp. note 5. Declarations Acknowledgement The authors gratefully acknowledge the financial support under the scope of the COMET program within the K2 Center “Integrated Computational Material, Process and Product Engineering (IC-MPPE)” (Project No 886385). This program is supported by the Austrian Federal Ministries for Climate Action, Environment, Energy, Mobility, Innovation and Technology (BMK) and for Labour and Economy (BMAW), represented by the Austrian Research Promotion Agency (FFG), and the federal states of Styria, Upper Austria and Tyrol, P. No. P2.22 ECOSolder. We acknowledge the support from J. Wosik for the EBSD and EDX measurements and B. Sartory for fruitful discussions regarding EBSD and EDX experiments. Contribution C.C. performed under the supervision of R.B. the image‑and data‑analysis work and the data interpretation and evaluation. R.S. performed the simulations. F.F. developed and trained the U‑Net models. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3876312","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":268410535,"identity":"2694f7b6-9141-416b-bb2a-cbd3c9f71841","order_by":0,"name":"Roland Brunner","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIiWNgGAWjYFAC5gYGBjaGBCjPhoGBnaAWRhQtaUAzgNQBErQcJqzFvL2x8XNBGUOe+YzcYw8+7jkfzd/MwPj5Ax4tMmcONkvPOMdQLHMjL91wxrPbuTMOMzBL4LNFQiKxQZq3jSFxhkSOmTTPgdu5G4AOI6Sl+Tdcy58D50BamH8Q0NKGsIXhwAGQFjb8tvAcbLPmOSdRLMHzxkyy50Ay0C+MbRZn8Glhbz58m6fMJk+CPcdM4scBu9z+9ubDNyrwaIHpROaAYmoUjIJRMApGAUUAAOPbSWGjmh3iAAAAAElFTkSuQmCC","orcid":"","institution":"Materials Center Leoben Forschung GmbH (MCL)","correspondingAuthor":true,"prefix":"","firstName":"Roland","middleName":"","lastName":"Brunner","suffix":""},{"id":268410536,"identity":"560b57b0-c702-45bd-b057-b046bac9bb3a","order_by":1,"name":"Charlotte Cui","email":"","orcid":"","institution":"Materials Center Leoben Forschung GmbH (MCL)","correspondingAuthor":false,"prefix":"","firstName":"Charlotte","middleName":"","lastName":"Cui","suffix":""},{"id":268410537,"identity":"31bea915-a9ba-48d4-950f-cb4518227fb2","order_by":2,"name":"Fereshteh Falah Chamasemani","email":"","orcid":"","institution":"Materials Center Leoben Forschung GmbH (MCL)","correspondingAuthor":false,"prefix":"","firstName":"Fereshteh","middleName":"Falah","lastName":"Chamasemani","suffix":""},{"id":268410538,"identity":"96cb334f-8be7-49ec-97a2-de0fe65adf6e","order_by":3,"name":"Priya Paulachan","email":"","orcid":"","institution":"Materials Center Leoben Forschung GmbH (MCL)","correspondingAuthor":false,"prefix":"","firstName":"Priya","middleName":"","lastName":"Paulachan","suffix":""},{"id":268410539,"identity":"aa1fb240-6f5b-47a4-82cf-b2ca9e1fb76d","order_by":4,"name":"Rahulkumar Sinoijya","email":"","orcid":"","institution":"Materials Center Leoben Forschung GmbH (MCL)","correspondingAuthor":false,"prefix":"","firstName":"Rahulkumar","middleName":"","lastName":"Sinoijya","suffix":""},{"id":268410540,"identity":"8f117069-ebe0-402f-a38f-21546b33650d","order_by":5,"name":"Jördis Rosc","email":"","orcid":"","institution":"Materials Center Leoben Forschung GmbH (MCL)","correspondingAuthor":false,"prefix":"","firstName":"Jördis","middleName":"","lastName":"Rosc","suffix":""},{"id":268410541,"identity":"4338dc6b-bc39-4858-8d8d-012fda86c6a6","order_by":6,"name":"Walter Hartner","email":"","orcid":"","institution":"Infineon Technologies AG","correspondingAuthor":false,"prefix":"","firstName":"Walter","middleName":"","lastName":"Hartner","suffix":""},{"id":268410542,"identity":"c118d394-cce1-4639-9f70-479b648e49e8","order_by":7,"name":"Michael Reisinger","email":"","orcid":"","institution":"Kompetenzzentrum für Automobil und Industrieelektronik GmbH","correspondingAuthor":false,"prefix":"","firstName":"Michael","middleName":"","lastName":"Reisinger","suffix":""},{"id":268410543,"identity":"b10902ec-6cc1-4da1-ad2d-c122bde893fd","order_by":8,"name":"Peter Imrich","email":"","orcid":"","institution":"Kompetenzzentrum für Automobil und Industrieelektronik GmbH","correspondingAuthor":false,"prefix":"","firstName":"Peter","middleName":"","lastName":"Imrich","suffix":""}],"badges":[],"createdAt":"2024-01-18 16:20:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3876312/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3876312/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41529-024-00456-8","type":"published","date":"2024-04-20T04:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":50050870,"identity":"da630b7a-c676-4875-8e91-46036ea2fc7d","added_by":"auto","created_at":"2024-01-23 16:44:04","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":2916933,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCorrelated X-ray tomography and EBSD.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea. \u003c/strong\u003eRendered X-ray tomography image of the entire BGA\u003cstrong\u003e \u003c/strong\u003ewith the chip (blue), the PCB (brown) and the solder balls (yellow). \u003cstrong\u003eb.\u003c/strong\u003e X-ray tomography slice image of the BGA from the reconstructed three-dimensional raw data, for the x‑y‑ (bird view), x‑z- (cross-section 1) and y-z- (cross-section 2) plane. The location of the cross-section 1 and 2 is indicated by view A-A (red dashed line) and view B-B (green dashed line), respectively. For the location of the bird view a blue dashed line (0-0) is shown in cross-section (view A-A and view B‑B). \u003cstrong\u003ec.\u003c/strong\u003e Correlated cross-sectional X-ray tomography and FESEM EBSD maps for SAC305 with 0 wt.% Bi, 1.1 wt.% Bi and 1.9 wt.% Bi, respectively are presented. Grain orientation data from the FESEM EBSD characterisation is projected on the X‑ray tomography data. The illustrated X‑ray tomography cross-sections correspond to the view A-A.\u003c/p\u003e","description":"","filename":"Fig1CorrelatedXraytomographyandEBSD.png","url":"https://assets-eu.researchsquare.com/files/rs-3876312/v1/14ab9569576343fa129ca046.png"},{"id":50050089,"identity":"602d1af2-4e9e-470f-9ae0-fd207f79429a","added_by":"auto","created_at":"2024-01-23 16:36:04","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":3976824,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eML-based localisation and segmentation workflow.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea.\u003c/strong\u003e ML-based segmentation workflow, illustrating both training (grey) and analysis (purple). Input is provided from the X-ray tomography data. First, a 2D localisation ML-model is trained to extract the positions of the solder balls in the x-y‑plane. Second, the balls are extracted from the X-ray tomography using the generated bounding boxes from the ML-localisation model. For the training of the 2D U‑Net‑segmentation model, tomography slices from the x-z‑plane are manually labelled. Label refinement is performed on re‑assembled x-z‑slices obtained from the 2D U‑Net segmentation model. The refined 2D‑labels are further used as training data for the 3D U‑Net segmentation model. In the final analysis workflow, raw 3D tomography data is used as an input, the 2D localisation performed, the individual solder balls are extracted based on the localisation, the 3D‑segmentation is performed and the segmented balls are placed into the BGA‑layout based on the localisation outputs. \u003cstrong\u003eb.\u003c/strong\u003e Comparison of 2D U‑Net and 3D U‑Net segmentation results for representative solder balls with a Bi-content of 0, 1.1 and 1.9 wt.%, overlaid on the normalised raw tomography data. The segmentation colour code is the same as in a. Scale bar with 100 µm is valid for all images.\u003c/p\u003e","description":"","filename":"Fig2MLbasedlocalisationandsegmentationworkflow.png","url":"https://assets-eu.researchsquare.com/files/rs-3876312/v1/0d32c78ba35d2886078a1060.png"},{"id":50050088,"identity":"b9e8798b-4d71-4c70-aad5-ba66bdfc8692","added_by":"auto","created_at":"2024-01-23 16:36:04","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1139243,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSeparation distance and visualisation of the crack distribution on the entire BGA.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea.\u003c/strong\u003e From left to right: Representative 3D segmentations, accumulated crack‑ and pore‑projections in x-z and x‑y (chip‑ and PCB‑sides) plane for each Bi content with the respective outlines of the solder bulk. The brighter the pixel in the respective projection, the larger the separation distance between the adjacent solder‑surfaces along the projection axis in the given position. Scale bar with 100 mm is valid for all images. \u003cstrong\u003eb.\u003c/strong\u003e Heatmaps of the crack volumes of the entire BGAs for the different Bi‑contents of 0 (first row), 1.1 (second row) and 1.9 (third row) wt.%, respectively. Each square represents a single solder ball on the BGA. The darker the square, the larger the crack volume in the corresponding ball.\u003c/p\u003e","description":"","filename":"Fig3SeparationdistanceandvisualisationofthecrackdistributionontheentireBGA.png","url":"https://assets-eu.researchsquare.com/files/rs-3876312/v1/cc1a36439a1950ad44698313.png"},{"id":50050086,"identity":"458105fa-86ab-4579-81c9-744ea53f0693","added_by":"auto","created_at":"2024-01-23 16:36:04","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1176822,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eStatistical analysis of the crack volume.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eStatistical analysis of the crack volume (CV) and its correlation with various solder ball properties for the various Bi‑contents with 0\u0026nbsp;wt.%\u0026nbsp;(pink), 1.1\u0026nbsp;wt.%\u0026nbsp;(blue) and 1.9\u0026nbsp;wt.%\u0026nbsp;(green). The spearman correlation coefficients (r) are calculated for each Bi‑content. All properties are correlated for the crack volume in the entire ball, as well as for the chip‑ and PCB‑side. \u003cstrong\u003ea.\u003c/strong\u003e\u0026nbsp;Correlation between the CV of the entire ball with the (from left to right): flux pore volumes on the chip‑side (PV\u003csub\u003eChip\u003c/sub\u003e), flux pore volumes on the PCB-side (PV\u003csub\u003ePCB\u003c/sub\u003e), Euclidian distance form BGA-centre (d), number of PCB routes times Euclidean distance (f\u003csub\u003eg\u003c/sub\u003e) and Bi- content. \u003cstrong\u003eb.\u003c/strong\u003e Correlation between CV\u003csub\u003echip\u003c/sub\u003e with (from left to right): PV\u003csub\u003echip\u003c/sub\u003e, PV\u003csub\u003ePCB\u003c/sub\u003e, d, f\u003csub\u003eg\u003c/sub\u003e and Bi- content. \u003cstrong\u003ec.\u003c/strong\u003e\u0026nbsp;Correlation between CV\u003csub\u003ePCB\u003c/sub\u003e with (from left to right): PV\u003csub\u003echip\u003c/sub\u003e, PV\u003csub\u003ePCB\u003c/sub\u003e, d, f\u003csub\u003eg\u003c/sub\u003e and Bi- content.\u003c/p\u003e","description":"","filename":"Fig4Statisticalanalysisofthecrackvolume.png","url":"https://assets-eu.researchsquare.com/files/rs-3876312/v1/38e0e73629caec2183f896fa.png"},{"id":50050090,"identity":"238e7461-39dc-4ec1-96e7-859a69880b15","added_by":"auto","created_at":"2024-01-23 16:36:04","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":5632980,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMicrostructure characterisation and FEM.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFEM geometry, FEM stress distribution during TCoB, cross‑sectional FESEM EBSDs, IPFs, grain size distributions and correlation of EBSD‑maps with ML‑based 3D‑segmentation. \u003cstrong\u003ea.\u003c/strong\u003e FEM geometry (3D and 2D) and stress distribution in the solder ball cross‑section during one exemplary TCoB‑cycle. The plane of the 2D‑geometry is shown in grey in the 3D‑geometry. Simulated stress distributions for 125 and -40°C are exemplarily demonstrated for the 2D cross‑section. Colour bar is scaled from ‑160 MPa (blue) to 90 MPa (red). Scale bar with 100 µm for all images. \u003cstrong\u003eb\u003c/strong\u003e. Cross‑sectional EBSD‑maps for representative solder balls, one for each Bi‑content. Scale bar with 200 µm for all images. \u003cstrong\u003ec\u003c/strong\u003e. KAM‑maps for 0 wt.%, 1.1 wt.% and 1.9 wt.% Bi. Scale bar with 200 µm for all images. \u003cstrong\u003ed.\u003c/strong\u003e IPFs and grain size distributions for the EBSD‑maps illustrated in b. \u003cstrong\u003ee.\u003c/strong\u003e The EBSD‑maps are correlated with the respective 3D segmentation. Scale bar with 100 µm for all images.\u003c/p\u003e","description":"","filename":"Fig5MicrostructurecharacterisationandFEM.png","url":"https://assets-eu.researchsquare.com/files/rs-3876312/v1/da750b8f605b95f08fec8715.png"},{"id":55691206,"identity":"ca9138dc-4d88-402f-96d7-62eda1f05577","added_by":"auto","created_at":"2024-05-01 23:09:05","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4198607,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3876312/v1/768e7216-793e-4077-a3d4-084a094d94b4.pdf"},{"id":50050091,"identity":"4ddd1cf4-23cd-4238-82c0-d14956d04763","added_by":"auto","created_at":"2024-01-23 16:36:04","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":11528703,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"Supplementarysubmitted.docx","url":"https://assets-eu.researchsquare.com/files/rs-3876312/v1/7627ea24044f25ec22e5b2b2.docx"}],"financialInterests":"(Not answered)","formattedTitle":"Correlative, ML based and non destructive 3D analysis of intergranular fatigue cracking in SAC305 Bi solder balls","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe reliable connection of electrical components embodies a crucial topic in microelectronics and the power semiconductor industry. Hence, the intactness of a solder ball is crucial for the lifetime of the device and its functionality. The fundamental understanding of degradation mechanisms, in particular for more sustainable Pb-free solders remains a vital challenge in the field of materials science\u003csup\u003e1\u0026ndash;5\u003c/sup\u003e. Solder balls serve as both electrical and thermal connections between the chip and printed circuit board (PCB) metallisations. Tin (Sn) based solder alloys have largely replaced leadbased alloys in power and microelectronics due to growing health and environmental concerns\u003csup\u003e6\u003c/sup\u003e. Sn \u0026ndash; 3.0 wt.% Ag \u0026ndash; 0.5 wt.% Cu (SAC305) is one of the most promising Snbased solder alloys. However, conventional SAC solder balls can already exhibit microstructural degradation in the asreflowed condition\u003csup\u003e7\u0026ndash;9\u003c/sup\u003e. Flux pores may be formed during reflow due to outgassing of flux residues. These gasses can remain trapped within the solder after solidification and form spherical pores\u003csup\u003e8, 9\u003c/sup\u003e. Moreover, the solder ball may also experience thermomechanical fatigue during service\u003csup\u003e10, 11\u003c/sup\u003e. In operation, the current flow leads to resistive heating and further to multiple thermal loading when the device is repeatedly turned on and off. Mechanical stress emerges in the component due to the underlying coefficient of thermal expansion (CTE) mismatches, originating from the multiple materials with various CTEs present in the device\u003csup\u003e11\u0026ndash;13\u003c/sup\u003e. The SAC305 solder ball represents a mechanical weak spot within the device. Here, most of the generated deformation occurs due the low hardness of the βSn matrix of approximately 0.1 GPa\u003csup\u003e14\u003c/sup\u003e. The plastic strain thereby introduced into the solder material may lead to recovery, polygonization and recrystallisation\u003csup\u003e15\u003c/sup\u003e. Consequently, the initially single or fewgrained solder balls\u003csup\u003e15\u0026ndash;17\u003c/sup\u003e undergo grainrefinement in highly strained areas. These highly strained areas are located in the proximity of the interfaces to the chip and PCBsubstrates, whereat shear strain is the predominant type of strain induced\u003csup\u003e11\u003c/sup\u003e. The new grain boundaries that are formed during recrystallisation in those highstrain areas serve as preferred crack propagation sites\u003csup\u003e10, 11, 15, 18\u003c/sup\u003e. As a result, these intergranular fatigue cracks increase the thermal as well as the electrical solder resistivity and thereby impair the device\u0026rsquo;s functionality and its lifetime\u003csup\u003e11, 12\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe use of Bismuth (Bi) as an alloying element shows high potential to improve the thermo-mechanical stability of the SAC solder. The solubility limit of Bi in the βSn matrix of SACalloys is assumed to be around 2.5 wt.%\u003csup\u003e19\u003c/sup\u003e. Accordingly, when less than 2 wt.% Bi is added, it acts as solid solution strengthener in the βSn matrix\u003csup\u003e17, 20\u003c/sup\u003e. As a solid solution strengthener, Bi elevates the yield stress of the solder\u003csup\u003e14, 17, 20\u003c/sup\u003e and thereby retards dynamic recrystallisation and the formation of new grain boundaries, i.e. reducing crack propagation sites. The utilisation of SAC305Bialloys represents a very promising approach to diminish microstructural degradation and prolong the long-term fatigue stability of solder balls. A crucial component for the assessment of the relation between microstructural degradation and functionality is the need for characterisation of each solder ball volume on the ball grid array (BGA) in a statistical manner. Assessing entire solder ball volumes on BGAs produces large amounts of data which should be in keeping with the FAIR data principle\u003csup\u003e21\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eNevertheless, the failure assessment of a specific solder ball in complex BGAgeometries is often tedious, because daisychain measurements of electrical resistivity usually provide only information about the cumulative resistivity of all, or many, balls on the BGA. Such an approach does not reveal which particular ball has failed\u003csup\u003e11\u003c/sup\u003e. Light optical or electron microscopy techniques\u003csup\u003e16, 22, 23\u003c/sup\u003e, on the other hand, require sample preparation for each and every ball and are therefore timeconsuming and destructive. Furthermore, these techniques only give 2Dinformation of one particular crosssection, which may not be representative for the fatigue crack propagation in the solder ball volume. Xray tomography eliminates these downsides as it allows nondestructive inspection of entire BGAs and delivers full 3Dinformation. Subsequent efficient image analysis is important to retrieve statistical information from the reconstructed 3D image data.\u003c/p\u003e \u003cp\u003eImage analysis incorporating supervised machine learning (ML) has proven to be significantly more efficient and accurate than manual feature segmentation\u003csup\u003e24, 25\u003c/sup\u003e. In addition to the ability of MLalgorithms to process large amounts of image data, such as the ones produced with Xray tomography, efficiently, algorithms are not subjected to volatile data evaluation noise as manual evaluation by human beings. Even data interpretation by the same person, and even the same expert, may underlie significant variability due to a number of daydependent psychological factors\u003csup\u003e26\u003c/sup\u003e. This variability in human judgement may lead to inaccuracies in data evaluation, which are eliminated when mathematical algorithms are applied, not to mention the benefit of the possibility for automation. The development of MLalgorithms for image analysis has been rapidly evolving in recent years\u003csup\u003e24\u003c/sup\u003e. Convolutional neural networks (CNNs) have proven advantageous over manual image analysis, as they are able to build highlevel features from lowlevel ones, providing accurate and efficient image recognition, object detection and image segmentation\u003csup\u003e24, 25\u003c/sup\u003e. CNNs have been increasingly applied to medical and biological image analysis\u003csup\u003e25, 27\u003c/sup\u003e and more recently, their use for image segmentation in materials science has been on the rise\u003csup\u003e28\u0026ndash;36\u003c/sup\u003e. In microelectronics failure and reliability analysis, some work has been previously done on Xray tomography data\u003csup\u003e37, 38\u003c/sup\u003e. However, to our knowledge, the algorithms developed in these previous studies focus on the detection of flux pores. Although the CNN developed in\u003csup\u003e37\u003c/sup\u003e is trained on 3D data, its output is limited on a binary classification of solder balls with and without flux pores that are classified as \u0026ldquo;good\u0026rdquo; and \u0026ldquo;bad\u0026rdquo;. On the contrary, the models developed in\u003csup\u003e38\u003c/sup\u003e perform the pore segmentation in two consecutive binary 2D segmentation steps: first, object detection of solders is carried out and subsequently, the pores are detected using the same binary approach. None of these previous studies apply a full threedimensional segmentation to the X-ray tomography image data e.g. by a 3D UNet architecture\u003csup\u003e39\u003c/sup\u003e. Moreover, the previous studies are constrained to image segmentation using CNNs without considering the underlying mechanisms for defectformation and correlations with microstructural and mechanical phenomena in the material. Conversely, the implications for fatigue crack initiation by the segmented flux pores have not yet been considered. In short, the connection between MLbased image segmentation and materials science has not yet been made.\u003c/p\u003e \u003cp\u003eTherefore, our study intends to unite the aspects of statistical fatigue analysis and the underlying microstructural and stressrelated mechanisms of fatigue crack initiation and propagation in SAC305Bi solder balls, utilising 3D imagining with 3D ML-based image analysis. We quantitatively segment fatigue cracks and flux pores from 3D Xray tomography data using a multilevel MLworkflow incorporating a 3D U-Net model. Moreover, we correlate the X-ray tomography data with microstructural features in the solder balls utilising high resolution field emission scanning electron microscopy (FESEM) and electron backscatter diffraction (EBSD). Further, we investigate the stress distribution within a solder ball during thermal cycling on board (TCoB) with finite element method (FEM) modelling. We draw connections between the simulated stress distribution, microstructural fatigue in the solder balls, i.e. recrystallisation and fatigue cracking, and statistical fatigue crack analyses from the MLworkflow. By bridging the gap between microstructural fatigue and its impact on statistically significant fatigue crack correlations, we elaborate on the importance of various smallscale mechanisms at play during TCoB. Whereat, we discuss that the rigorous understanding of the underlying small-scale mechanisms is crucial to avoid macroscopic failure within the electronic device. Based on the developed characterisation workflow we conclude that intergranular fatigue cracking is the predominant failure mechanism during TCoB and that dynamic recrystallisation precedes fatigue cracking. Moreover, we find that fatigue cracks are initiated at three kinds of notches, i.e. surface notches, flux pores and PCBmetallisation intrusions, and that crack propagation occurs along recrystallised grain boundaries which are enriched with Cu.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e\u003cstrong\u003eVisualisation of the BGA using correlated X-ray tomography and EBSD.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe 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. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea. The voxel size is 5.33 \u0026times; 5.33 \u0026times; 5.33 \u0026micro;m\u003csup\u003e3\u003c/sup\u003e 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. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. Figure \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb shows the correlated xy, xz and yzviews of the reconstructed 3D image from Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea. 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. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb 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 \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec 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 \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec qualitatively illustrates that the cracked proportion of the ball decreases with increasing Bicontent.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMLbased localisation and 3D segmentation of the BGA.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFor 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. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. Three MLbased algorithms are developed and trained. First, the localisation of solder balls in the X-ray tomography data is performed, see \u003cstrong\u003eSupp. Note 1\u003c/strong\u003e. 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. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea. The localisation model is trained on manually labelled 2Ddata, which consists of 100 \u0026times; 100 pixels\u003csup\u003e2\u003c/sup\u003e 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\u0026thinsp;+\u0026thinsp;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.\u003c/p\u003e\n\u003cp\u003eAfter 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 \u0026times; 96 pixels\u003csup\u003e2\u003c/sup\u003e slices (x-z-plane), utilising the extracted bounding boxes from the localisation model, see \u003cstrong\u003eSupp. Note 3\u003c/strong\u003e. Here, the training was performed on a NVIDIA A40 GPU with 48GB RAM. A representative segmentation result is shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea 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 \u0026times; 96 \u0026times; 96 pixels\u003csup\u003e3\u003c/sup\u003e are used, see \u003cstrong\u003eSupp. Note 2\u003c/strong\u003e. Figure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea 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. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eb 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 \u003cstrong\u003eSupp.\u003c/strong\u003e Figure \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. 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.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eVisualisation of crack initiation sites and the crack distribution.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eHere, 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 \u003cstrong\u003eSupp. Note 4\u003c/strong\u003e. Representative projections for each Bicontent are illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea, 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\u0026ndash;to\u0026ndash;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.\u003c/p\u003e\n\u003cp\u003eFor the visualisation of the fatigue crack volume distribution on the entire BGA, BGAheatmaps are extracted from the segmented X-ray tomography data, see Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb. 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 \u003cstrong\u003eSupp. Note 4\u003c/strong\u003e for more details. The crack volume is evaluated from the segmented voxels associated with a crack. Figure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb 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 \u003cstrong\u003eSupp. Note 4\u003c/strong\u003e. 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. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb 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. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStatistical analysis of the crack volume.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo find the primary causes for the solder fatigue, we further statistically analyse the evaluated data from Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb. Figure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e 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. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea\u0026ndash;c, the flux pore volume (PV) vs. crack volume (CV), Euclidean distance from BGAcentre (d) vs. CV and number of PCBroutes times Euclidean distance (f\u003csub\u003eg\u003c/sub\u003e) 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. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e. 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. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb. 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. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e are summarised in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The correlation coefficients in Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eb, Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ec and Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e 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.\u0026nbsp;\u003c/p\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003e\u003cstrong\u003eSpearman correlation coefficients for the crack volume \u0026ndash; property relationships.\u003c/strong\u003e Here, the statistically significant correlations between crack volume and solder properties are listed. CV\u003csub\u003echip\u003c/sub\u003e \u0026ndash; PV\u003csub\u003echip\u003c/sub\u003e, CV\u003csub\u003ePCB\u003c/sub\u003e \u0026ndash; PV\u003csub\u003ePCB\u003c/sub\u003e and CV\u003csub\u003ePCB\u003c/sub\u003e \u0026ndash; f\u003csub\u003eg\u003c/sub\u003e exhibit positive correlation coefficients, whereas CV\u003csub\u003echip\u003c/sub\u003e \u0026ndash; PV\u003csub\u003ePCB\u003c/sub\u003e and CV\u003csub\u003ePCB\u003c/sub\u003e \u0026ndash; PV\u003csub\u003echip\u003c/sub\u003e correlate negatively.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBicontent\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003er\u0026nbsp;(CV\u003csub\u003echip\u003c/sub\u003e \u0026ndash; PV\u003csub\u003echip\u003c/sub\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003er\u0026nbsp;(CV\u003csub\u003echip\u003c/sub\u003e \u0026ndash; PV\u003csub\u003ePCB\u003c/sub\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003er\u0026nbsp;(CV\u003csub\u003ePCB\u003c/sub\u003e \u0026ndash; PV\u003csub\u003echip\u003c/sub\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003er\u0026nbsp;(CV\u003csub\u003ePCB\u003c/sub\u003e \u0026ndash; PV\u003csub\u003ePCB\u003c/sub\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003er\u0026nbsp;(CV\u003csub\u003ePCB\u003c/sub\u003e \u0026ndash; f\u003csub\u003eg\u003c/sub\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003e0 wt.%\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.149\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.103\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.083\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.277\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.502\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003e1.1 wt.%\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.253\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.050\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.047\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.404\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.293\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003e1.9 wt.%\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.216\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.046\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.052\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.239\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.458\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eConsidering 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. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e. 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 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\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}\\)\u003c/span\u003e\u003c/span\u003e, where n\u003csub\u003ePCB\u0026minus;routes\u003c/sub\u003e denotes the number of PCBroutes leading to the ball. The correlations for the overall CV, CV\u003csub\u003echip\u003c/sub\u003e and CV\u003csub\u003ePCB\u003c/sub\u003e are summarised in supp. Tables \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e\u0026ndash;3, respectively. CV\u003csub\u003echip\u003c/sub\u003e correlates negatively with f\u003csub\u003eg\u003c/sub\u003e, whereas CV\u003csub\u003ePCB\u003c/sub\u003e correlates positively, see Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. 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. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea 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 CV\u003csub\u003echip\u003c/sub\u003e decreases parabolically with increasing Bicontent, while the maximum CV\u003csub\u003ePCB\u003c/sub\u003e does not significantly decrease between the 1.1 wt.% and 1.9 wt.% Bi balls, see Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eb and Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ec, respectively. The Spearman correlation coefficients for the investigated CV \u0026ndash;, CV\u003csub\u003echip\u003c/sub\u003e\u0026ndash; and CV\u003csub\u003ePCB\u003c/sub\u003e \u0026ndash; property relationships are presented in \u003cstrong\u003eSupp.\u003c/strong\u003e Tables \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, 2 and 3 respectively.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStress distribution, recrystallisation and intergranular cracking.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe 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. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea. The plane of the 2Dgeometry is shown in grey in the 3Dgeometry. Simulation results for the \u0026beta;Sn matrix are shown, during exposure to a TCoB-cycle with a temperature increase from \u0026minus;\u0026thinsp;40\u0026deg;C to 125\u0026deg;C and a subsequent cooling to -40\u0026deg;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 \u003cstrong\u003eSupp.\u003c/strong\u003e Figure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. 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.\u003c/p\u003e\n\u003cp\u003eAs 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. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003eb. This is in keeping with the simulated stress distribution shown in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea., as recrystallisation will occur in the highly stressed (strained) areas first. Moreover, the EBSDmaps in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003eb 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 \u003cstrong\u003eSupp. Note 7\u003c/strong\u003e and \u003cstrong\u003eSupp.\u003c/strong\u003e Figure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e. No primary Bi-precipitates can be seen for either alloy.\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ec 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.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ed 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.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ee. 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.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe functionality of a solder ball in terms of its ability to conduct both electrical and thermal current from the chip to the PCB is vastly impaired when the material is interrupted by gasfilled volumes such as flux pores and fatigue cracks\u003csup\u003e11\u003c/sup\u003e. Hence, the non-destructive, statistically significant failure analysis of fatigue crack initiation and propagation in solder balls is essential. Furthermore, an in-depth understanding of the underlying mechanisms for solder fatigue on a microstructural scale is crucial for the design of materials scienceinformed engineering solutions to prolong the fatigue lifetime of leadfree solder balls.\u003c/p\u003e \u003cp\u003eWe statistically identify the solder properties that impact a solder balls fatigue from 3D data by conducting nondestructive X-ray tomography and applying sophisticated MLbased image analysis methods. The statistical results show a significant prolongation of solder ball lifetime by the addition of Bi to the SAC305 alloy. In order to understand the underlying mechanisms of solder fatigue, we discuss (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) the impact of the periodical stress and strain on the solder during TCoB, (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e) the crack propagation through the solders and (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e) the influence of Bi on the fatigue and microstructural properties of SAC305 solder balls.\u003c/p\u003e \u003cp\u003eDue to the CTEmismatches in the multicomponent device, mechanical stress and deformation are induced in the solder during TCoB\u003csup\u003e15, 40\u003c/sup\u003e. Since stress and deformation occur periodically during TCoB, the predominant mechanisms of solder degradation are considered to be fatigue and the propagation of fatigue cracks into the solder balls. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea and Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb support this assumption and illustrate the initiation of cracks either at surface notches or at internal notches, i.e. metallisation intrusions and flux pores, and their propagation into the solder bulk. A typical characteristic of fatigue cracks\u003csup\u003e41\u003c/sup\u003e. As the mechanical stress in the solder during TCoB stems from CTEmismatches between the various components of the multilayer device, stress and strain are most pronounced near the interfaces to the chip and the PCB. The emerging inhomogeneous stress distribution is even more enhanced by the presence of surfacenotches and the intrusion of the PCBmetallisation into the ball. The accompanied FEM simulation illustrates how the ballshape of the solder translates the shear stress at the interfaces into an hourglassshaped stress gradient within the ball, see Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea. This stress gradient induces a proportional strain gradient in the solder, consisting of both plastic and elastic strain. Accordingly, the dislocation density is higher near the interfaces and notches, causing the solder to dynamically recover and recrystallise there earlier compared to the rest of the solder. This hourglassshaped recrystallisation behaviour is observed in the EBSDmaps in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb. Further, the EBSDmaps show that the solidification structures of the balls are initially built of either single crystals or a few large grains. These observations are consistent with the findings in\u003csup\u003e15, 22, 20\u003c/sup\u003e. The IPFs in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed show that the orientations of the newly formed grains are smeared out around the initial crystal orientation. Hence, the solder balls in this study do not undergo primary recrystallisation, where statistically oriented grains would nucleate in a highly deformed crystal\u003csup\u003e41\u003c/sup\u003e. Rather, continuous recovery and polygonization takes place in the investigated solder balls, as rearrangement of dislocations generates smallangle grain boundaries and new grains that are slightly misoriented towards the initial crystal orientation. Furthermore, highly strained regions in the initial single crystals, visible in the KAMmaps in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec, are likely to undergo recrystallisation with continued cycling. The KAMdistributions are also in agreement with the FEM simulations in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea. Additional EBSD and KAMmaps, as well as IPFs are shown in \u003cb\u003eSupp.\u003c/b\u003e Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e to support the provided argumentation. Since the Cu PCBmetallisation is much stiffer than the solder, its intrusion into the ball acts as an additional internal notch and crack initiation site. The notch effect of the PCBintrusion is confirmed by the FEMsimulations in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea as well as by the EBSDmaps in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb, where polygonization can be seen to start in the vicinity of the PCBintrusions. This can be seen particularly clearly in the EBSDmap of the 1.9 wt.% Bi sample.\u003c/p\u003e \u003cp\u003eThe correlation of the EBSDmaps with the corresponding 3D segmented image data in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed confirms that the cracks visualised with X-ray tomography and analysed with the MLassisted workflow are indeed intergranular fatigue cracks. Since the cracks propagate along recrystallised grain boundaries, those are of particular interest for the understanding of fatigue crack propagation. EDX analyses of exemplary grain boundaries for each Bicontent are shown in \u003cb\u003eSupp.\u003c/b\u003e Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. The EDXmaps show Cuenrichment along recrystallised grain boundaries. This enrichment may cause or promote intergranular fatigue cracking. Since grain boundaries are first formed in the highstrain areas near the solder interfaces, intergranular crack initiation and propagation are also expected to start there. The onset of dynamic recrystallisation, and therefore the formation of grain boundaries, requires a critical dislocation density. As no primary Biprecipitates are present in the EDXmaps, see \u003cb\u003eSupp.\u003c/b\u003e Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, it is assumed that Bi is solved in the β-Sn matrix, acting as a solid solution strengthener and increasing the Snmatrix\u0026rsquo; yield strength. Since the primary fatigue symptom is intergranular crack propagation, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb, Bi is therefore expected to delay both recrystallisation and subsequent intergranular fatigue cracking. This can be seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec and Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ee, where crosssectional overview of EBSDmaps of exemplary balls for 0 wt.%, 1.1 wt.% and 1.9 wt.% Bi samples are correlated with the X-ray tomography slices and 3D segmentations, respectively. This relationship is also shown in the scatter plots in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Moreover, the IPFs in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed and Supp. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e are more localised around the initial crystal orientation(s) in the 1.9 wt.% Bi balls compared to the 0 wt.% Bi balls which indicates that dynamic recrystallisation is further advanced in 0 wt.% Bi balls. Furthermore, fatigue cracking has progressed further in balls with decreasing Bicontent, which is also in keeping with the results from the statistical analyses shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. As already mentioned, the solid solution strengthening effect of Bi delays polygonization, grain boundary formation and subsequent intergranular fatigue cracking in Bicontaining solder balls. Nonetheless, the 1.1 wt.% and 1.9 wt.% Bi samples are also recrystallised to various extents. However, intergranular cracks have not propagated to the same proportion as in the 0 wt.% Bi samples, as can be seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec and Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb, despite the grain boundaries also being enriched with Cu, illustrated in Supp. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Therefore, it is assumed that Biadditions may also influence the structure of grain boundaries in SAC305, leading to strengthening of the recrystallised grain boundaries. The study of structure and elemental composition of grain boundaries in Bifree and Bicontaining solder balls is not part of this work but will be the subject of a future study. Conversely, cracks, once initiated in a ball, dampen the stress from the substrates so it cannot be efficiently transmitted to the opposing side of the crack. Accordingly, no more, or fewer, dislocations are produced in the ball and dynamic recrystallisation stops, or slows down, once a crack is initiated, since the dislocation density and rearrangement of dislocations into an energetically more favourable configuration is its driving force. Hence, recrystallisation in the 0 wt.% Bi ball in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb is less progressed than in the 1.1 wt.% Bi sample, as the cracks in the 0 wt.% Bi ball inhibit further recrystallisation after crack initiation and the strain energy from further cycling is invested in propagating the cracks. Apparently, however the recrystallised grains in the 0 wt.% Bi sample have undergone coarsening during the hightemperature periods of TCoB after cracking. This results in larger grains compared to the 1.1 wt.% and 1.9 wt.% Bi samples, as shown in the grain size distributions in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed. Moreover, the KAMmaps in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec show that strain is less pronounced in polygonised areas of the crosssection, compared to the initial grain. Therefore, it is assumed that recrystallisation provides stress relief in the solder. This thorough microstructural analysis, in combination with the FEM modelling results, elaborates the underlying mechanisms for fatigue cracking. Moreover, the correlations of the EBSDmaps with Xray tomography data and their segmentations prove the validity of our statistical analysis of solder fatigue.\u003c/p\u003e \u003cp\u003eSeveral conclusions can be drawn from our study on solder fatigue, its statistical correlations with solder ball properties and the underlying microstructural and mechanical mechanisms. Firstly, intergranular cracks propagating along recrystallised, Cuenriched grain boundaries of solder balls constitute the predominant fatigue mechanism during thermal cycling of BGAs. Secondly, recrystallisation and grain boundary formation in highstrain areas near the chip and PCBinterfaces of the solder balls precedes crack initiation. The stress distribution in the solder ball during TCoB is simulated with FEM and it is in keeping with the shape of the recrystallisation fronts in EBSDmaps. Thirdly, fatigue cracks initiate either at notches at the solder ball surface, Cumetallisation intrusions or at internal defects, i.e. flux pores, and propagate along recrystallised grain boundaries into the surrounding solder ball matrix. These aspects could be considered in the design of BGAs to engineer the notcheffects on solder fatigue. Lastly, alloying Bi to SAC305 markedly delays recrystallisation, fatigue crack initiation and propagation, thereby prolonging the lifetime of solder balls. EDXmaps show that the investigated Biconcentrations act as solid solution strengthener in βSn rather than forming primary precipitates, thereby increasing the solder ball\u0026rsquo;s yield strength.\u003c/p\u003e \u003cp\u003eIn summary, this study proves nonequivocally that intergranular fatigue cracks and flux pores in SAC305\u0026thinsp;+\u0026thinsp;x Bi (x\u0026thinsp;=\u0026thinsp;0, 1.1, 1.9 wt.%) solder balls can be visualised with 3D X-ray tomography and statistically analysed with the MLalgorithms developed for this purpose. The MLbased segmentation workflow developed in this study can be used to efficiently and nondestructively inspect solder balls on BGAlevel with high statistical yield. The developed workflow provides the possibility for efficient and advanced failure analysis. The gained data reveals the crack initiation at surface notches and at internal notches, i.e. flux pores and PCB-metallisation intrusions, a typical feature of fatigue cracks. Further, intergranular propagation paths of the fatigue cracks represent a major issue. The work provides important insights regarding the underlying mechanisms for recrystallisation and crack propagation, as well as the effects of Bi on the microstructural fatigue in the solder alloys. The analysis of microstructural features and the simulation of the stress distribution is utilised to understand the statistically evaluated solder fatigue, thereby uniting the aspects of bigdata analysis with MLalgorithms and indepth understanding about the underlying materials science.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eThe experimental and methodological approaches of this study are described in the following. More details can be found in the supplementary notes.\u003c/p\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eSample Production and TCoB\u003c/h2\u003e \u003cp\u003eThree solder materials are investigated: Sn \u0026ndash; 3.0 wt.% Ag \u0026ndash; 0.5 wt.% Cu (SAC305), SAC305\u0026thinsp;+\u0026thinsp;1.1 wt.% Bi and SAC305\u0026thinsp;+\u0026thinsp;1.9 wt.% Bi. Bi acts as a solidsolution strengthener in βSn. No primary precipitation of Bi is expected for this content\u003csup\u003e20, 17\u003c/sup\u003e. The investigated solder balls are produced by droplet spraying in an inert N\u003csub\u003e2\u003c/sub\u003e atmosphere and subsequently soldered between the Cumetallisations of the chip and the PCB. Reflow is done at a peak temperature of 240\u0026deg;C and with a mean heating rate of 44\u0026deg;C/min in inert N\u003csub\u003e2\u003c/sub\u003e atmosphere, followed by rapid air cooling to 90\u0026deg;C with a mean cooling rate of 107\u0026deg;C/min and ambient air cooling to room temperature. The 3D BGA layout is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea, alongside with its coordinate system for the subsequent analysis. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb shows the xylayout of the BGA. Thermal cycling is conducted between \u0026minus;\u0026thinsp;40\u0026ndash;125\u0026deg;C with ramp and dwelltimes of 15 mins, respectively. Hot and cold air is alternately injected into a furnace in order to obtain heating rates as linear as possible. The furnace temperature during thermal cycling is homogenised by air circulation. The 0 wt.% Bi sample is thermally cycled for 1764 cycles, the 1.1 wt.% Bi samples and the 1.9 wt.% Bi samples for 2914 and 2570 cycles, respectively. The BGAs with Bicontent underwent larger numbers of cycles, since the amount of Biadditions provide solid solution strengthening effects of the βSn matrix and hence delay recrystallisation and subsequent intergranular cracking.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eNondestructive 3D X-ray tomography scans\u003c/h2\u003e \u003cp\u003eNondestructive X-ray tomography has the capability to scan entire BGAs in less than an hour. Hence, this method is suitable for the generation of the large amount of image data that is necessary for ML and statistical statements regarding solder fatigue. The X-ray tomography scans are done with a GE Phoenix Nanotom M (research edition) using a cone beam. By using a cone beam, the achievable magnification is limited by the lateral size of the BGA (~\u0026thinsp;10 \u0026times; 7 mm\u003csup\u003e2\u003c/sup\u003e). The achievable voxelsize results to 5.33 \u0026times; 5.33 \u0026times; 5.33 \u0026micro;m\u003csup\u003e3\u003c/sup\u003e for scanning entire BGAs. The interaction of an Xray beam with matter is described by the BeerLambertlaw:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\frac{\\text{I}}{{\\text{I}}_{0}}=\\text{e}\\text{x}\\text{p}(-\\frac{{\\mu }}{{\\rho }} {\\rho } \\text{d})$$\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{I}\\)\u003c/span\u003e\u003c/span\u003e denotes the transmitted Xray intensity, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{I}}_{0}\\)\u003c/span\u003e\u003c/span\u003e the incident Xray intensity, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{{\\mu }}{{\\rho }}\\)\u003c/span\u003e\u003c/span\u003e the attenuation coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }\\)\u003c/span\u003e\u003c/span\u003e the material density and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{d}\\)\u003c/span\u003e\u003c/span\u003e the penetrated sample thickness. Due to the dependency of Xray attenuation on the density, more specifically the atomic number, of the penetrated material, airfilled defects, i.e. cracks and pores, appear darker in the Xray tomography scans than βSn and Cumetallisations. This allows the distinction of pores and cracks based on their greyvalues.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003eFESEM EBSD\u003c/h2\u003e \u003cp\u003eFESEM overview EBSD maps are used to verify X-ray tomography imaging, i.e. to assess whether its resolution is sufficient for the investigation of solder fatigue. Moreover, EBSD maps provide crystallographic information about the solder balls. The final solder ball crosssections for EBSD are prepared with a Hitachi IM4000\u0026thinsp;+\u0026thinsp;ion-slicer, which yields deformationfree surfaces. The accelerating voltage for ionslicing is set to 6 kV and the swing angle to 30\u0026deg; with 3 swings per minute. Overview EBSDmaps are acquired with a Zeiss 450 Gemini FESEM. An accelerating voltage of 10 kV, a step size of 400 nm and an Oxford Symmetry detector are used for EBSDmapping. Oxford Instrument AZtecCrystal 5.1 is used for the evaluation of EBSD data. IPFs are used to extract information about the polygonization behaviour of the solder balls and grain size distributions are plotted in order to determine their recrystallisation stage. Neighbouring grains with misorientations\u0026thinsp;\u0026gt;\u0026thinsp;10\u0026deg; are considered in the grain size distributions. Since the polygonised grains are quasicircular, their equivalent circle diameter is used as size metric. The grain size distribution is plotted as the areaweighted fraction of grains with a particular diameter in proportion to the entire solder crosssection. More details can be found in supp. note 6.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eML-algorithms\u003c/h2\u003e \u003cp\u003eDue to the large amount of 3Dimage data produced by X-ray tomography, supervised MLalgorithms are used for the quantitative image analysis. The analysis is done in two steps: xylocalisation followed by 3D feature segmentation. The localisation algorithm is based on a binary, sequential, feedforward slidingwindow convolutional neural network (CNN) adapted from\u003csup\u003e30\u003c/sup\u003e. Its schematic architecture is shown in \u003cb\u003eSupp.\u003c/b\u003e Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and described in detail in supp. note 1, alongside exemplary training images, the model\u0026rsquo;s accuracy and loss histories and its testing accuracy. The 3D segmentation model is a U-Net CNN. Its architecture, training and validation accuracy and loss histories are shown in detail in \u003cb\u003eSupp.\u003c/b\u003e Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and its architecture is elaborated in supp. note 2. In order to efficiently produce a large amount of training data for the 3D segmentation model, a 2D segmentation U-Net model was used. Details about the 2D segmentation model are also shown in \u003cb\u003eSupp.\u003c/b\u003e Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and described in supp. note 3. All ML models that are developed in this study are described in detail in \u003cb\u003eSupp. Notes 1\u0026ndash;3\u003c/b\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eCalculation of separation distance and crack distribution on the BGA\u003c/h2\u003e \u003cp\u003eIn order to visualise the crack initiation sites in the solder balls, the segmented cracks and pores obtained from the 3D UNet are projected into 2Dplanes, i.e. xz and xyprojections. The respective voxels, associated with either cracks or pores, are summed up along the yaxis for the xzprojections and along the zaxis for the xyprojections. Additionally, the outlines of the solder ball and metallisations are thresholded and overlaid onto the projections.\u003c/p\u003e \u003cp\u003eThe visualisation of the crack volume distribution on the BGA allows fast identification of particularly fatigued solder balls. To that end, the crack volumes gained from the 3D segmentation are put into relation with the solder volume to obtain the volume percentage of cracks in the respective balls. These crack volume proportions are then schematically plotted into heatmaps which exhibit the BGAlayout. This is done by utilising the localisation outputs.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eFEM simulation\u003c/h2\u003e \u003cp\u003eDuring TCoB, mechanical stresses are introduced into the solder balls. These mechanical stresses stem from misfits in CTE between the various components in the multimaterial device. In order to visualise the stress distribution in the solder ball, 3D FEM simulations were done with Ansys MAPDL 2022R2 for one exemplary heating and cooling cycle, considering the 2D plane in the centre of 3D geometry, see supp. note 5. The 3D geometry is extracted from an .stl file from Xray tomography imaging. The geometry and the results of the FEM simulation are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea and in Supp. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The simulated heating cycle is implemented with the same parameters as the TCoB cycling done in this study: Heating from \u0026minus;\u0026thinsp;40\u0026deg;C to 125\u0026deg;C, followed by cooling to -40\u0026deg;C. Both the ramp times and dwell times are set to 15 minutes, respectively. A thermal transient analysis is carried out based on the heating cycle. The temperature profile of the FEM simulation is shown in \u003cb\u003eSupp.\u003c/b\u003e Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, alongside crosssectional in plane stress distributions for a selection of timesteps. The elastic tensor of β-Sn and the thermal expansion coefficient are taken from\u003csup\u003e42\u003c/sup\u003e. Boundary conditions for the FEM analysis are implemented considering the following. Firstly, the surface notches on the chip-side are represented by fixed nodes, which account for the attachment of the ball to the chipmetallisation. The PCB-metallisation intrusion is implemented with the mechanical and thermal expansion values of Cu from\u003csup\u003e43\u003c/sup\u003e. Lastly, like the chip-side, the bottom nodes of the metallisation are rigidly fixed. More details about the FEM simulation are given in Supp. note 5.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors gratefully acknowledge the financial support under the scope of the COMET program within the K2 Center \u0026ldquo;Integrated Computational Material, Process and Product Engineering (IC-MPPE)\u0026rdquo; (Project No 886385). This program is supported by the Austrian Federal Ministries for Climate Action, Environment, Energy, Mobility, Innovation and Technology (BMK) and for Labour and Economy (BMAW), represented by the Austrian Research Promotion Agency (FFG), and the federal states of Styria, Upper Austria and Tyrol, P. No. P2.22 ECOSolder. We acknowledge the support from J.\u0026nbsp;Wosik for the EBSD and EDX measurements and B. Sartory for fruitful discussions regarding EBSD and EDX experiments.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eContribution\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eC.C. performed under the supervision of R.B. the image‑and data‑analysis work and the data interpretation and evaluation. R.S. performed the simulations. F.F. developed and trained the U‑Net models. P.P. and C.C. developed the localisation model. W.H. and fabricated and provided the samples, with support from M.R. and P.I. R.B. and C.C. planned the FESEM‑EBSD, FESEM‑EDX and X-ray tomography measurements. \u0026nbsp;C.C. and R.B. wrote the paper. All authors discussed the results and commented on the paper.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCode availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll code that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBieler TR, Jiang H, Lehman LP et al. Influence of Sn Grain Size and Orientation on the Thermomechanical Response and Reliability of Pb-free Solder Joints:1462\u0026ndash;1467. https://doi.org/10.1109/ECTC.2006.1645849\u003c/li\u003e\n\u003cli\u003eChung CK, Duh J-G, Kao CR (2010) Direct evidence for a Cu-enriched region at the boundary between Cu6Sn5 and Cu3Sn during Cu/Sn reaction. Scripta Materialia 63:258\u0026ndash;260. https://doi.org/10.1016/j.scriptamat.2010.04.011\u003c/li\u003e\n\u003cli\u003eGong J, Conway PP, Liu C et al. (2009) Heterogeneous Intragranular Inelastic Behavior of a Sn-Ag-Cu Alloy. Journal of Elec Materi 38:2429\u0026ndash;2435. https://doi.org/10.1007/s11664-009-0871-7\u003c/li\u003e\n\u003cli\u003eHuang YL, Lin KL, Liu DS (2010) Microstructure evolution and microimpact performance of Sn\u0026ndash;Ag\u0026ndash;Cu solder joints under thermal cycle test. J Mater Res 25:1312\u0026ndash;1320. https://doi.org/10.1557/JMR.2010.0162\u003c/li\u003e\n\u003cli\u003eKariya Y, Williams N, Gagg C et al. 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Journal of Elec Materi 41:283\u0026ndash;301. https://doi.org/10.1007/s11664-011-1811-x\u003c/li\u003e\n\u003cli\u003eSayyadi R, Naffakh-Moosavy H (2019) The Role of Intermetallic Compounds in Controlling the Microstructural, Physical and Mechanical Properties of Cu-Sn-Ag-Cu-Bi-Cu Solder Joints. Sci Rep 9:8389. https://doi.org/10.1038/s41598-019-44758-3\u003c/li\u003e\n\u003cli\u003eCHANTARAMANEE S, SUNGKHAPHAITOON P (2021) Influence of bismuth on microstructure, thermal properties, mechanical performance, and interfacial behavior of SAC305-xBi/Cu solder joints. Transactions of Nonferrous Metals Society of China 31:1397\u0026ndash;1410. https://doi.org/10.1016/S1003-6326(21)65585-1\u003c/li\u003e\n\u003cli\u003eBoeckhout M, Zielhuis GA, Bredenoord AL (2018) The FAIR guiding principles for data stewardship: fair enough? Eur J Hum Genet 26:931\u0026ndash;936. https://doi.org/10.1038/s41431-018-0160-0\u003c/li\u003e\n\u003cli\u003eBen Romdhane E, Gu\u0026eacute;don-Gracia A, Pin S et al. 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Springer, Berlin Heidelberg\u003c/li\u003e\n\u003cli\u003eThe Materials Project (2020) Materials Explorer: Sn (mp-55), database version v2022.10.28. https://doi.org/10.17188/1267399. https://next-gen.materialsproject.org/materials/mp-55?_limit=75\u0026amp;formula=Sn#how_to_cite\u003c/li\u003e\n\u003cli\u003eRoss RB (1992) Metallic Materials Specification Handbook, 4th edn. 1. Ross Materials Technology Ltd, East Kilbride, Glasgow\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-materials-degradation","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"npjmatdeg","sideBox":"Learn more about [npj Materials Degradation](http://www.nature.com/npjmatdeg/)","snPcode":"41529","submissionUrl":"https://submission.springernature.com/new-submission/41529/3","title":"npj Materials Degradation","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3876312/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3876312/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eReliable connections of electrical components embody a crucial topic in the microelectronics and power semiconductor industry. This study utilises 3D nondestructive Xray tomography and specifically developed machine learning (ML) algorithms to statistically investigate crack initiation and propagation in SAC305Bi solder balls upon thermal cycling on board (TCoB). We quantitatively segment fatigue cracks and flux pores from 3D Xray tomography data utilising a multilevel MLworkflow incorporating a 3D U-Net model. The data reveals that intergranular fatigue cracking is the predominant failure mechanism during TCoB and that dynamic recrystallisation precedes crack initiation. Moreover, we find that fatigue cracks are initiated at surface notches, flux pores and printed circuit boardmetallisation intrusions. The work provides important insights regarding the underlying microstructural and mechanical mechanisms for recrystallisation and cracking, uniting the aspects of bigdata analysis with MLalgorithms and indepth understanding about the underlying materials science.\u003c/p\u003e","manuscriptTitle":"Correlative, ML based and non destructive 3D analysis of intergranular fatigue cracking in SAC305 Bi solder balls","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-01-23 16:35:59","doi":"10.21203/rs.3.rs-3876312/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"revise","date":"2024-02-13T12:15:59+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-02-12T18:55:05+00:00","index":2,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-01-29T15:13:39+00:00","index":2,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-01-25T13:04:06+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-01-21T21:16:56+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewersInvited","content":"","date":"2024-01-21T21:15:29+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-01-21T21:12:34+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-01-19T08:16:33+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Materials Degradation","date":"2024-01-18T16:15:26+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-materials-degradation","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"npjmatdeg","sideBox":"Learn more about [npj Materials Degradation](http://www.nature.com/npjmatdeg/)","snPcode":"41529","submissionUrl":"https://submission.springernature.com/new-submission/41529/3","title":"npj Materials Degradation","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"dac6f251-d68c-4c0f-adc8-72f28dc4a0a6","owner":[],"postedDate":"January 23rd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":28270874,"name":"Physical sciences/Materials science/Materials for devices/Electronic devices"},{"id":28270875,"name":"Physical sciences/Mathematics and computing"},{"id":28270876,"name":"Physical sciences/Engineering/Electrical and electronic engineering"}],"tags":[],"updatedAt":"2024-05-01T23:00:48+00:00","versionOfRecord":{"articleIdentity":"rs-3876312","link":"https://doi.org/10.1038/s41529-024-00456-8","journal":{"identity":"npj-materials-degradation","isVorOnly":false,"title":"npj Materials Degradation"},"publishedOn":"2024-04-20 04:00:00","publishedOnDateReadable":"April 20th, 2024"},"versionCreatedAt":"2024-01-23 16:35:59","video":"","vorDoi":"10.1038/s41529-024-00456-8","vorDoiUrl":"https://doi.org/10.1038/s41529-024-00456-8","workflowStages":[]},"version":"v1","identity":"rs-3876312","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3876312","identity":"rs-3876312","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}