Machine learning-driven design and optimization of electronic packaging: applications and future developments

Generation of data

The data is continuously generated throughout the entire lifecycle of advanced packaging, including the design phase (interconnect materials and geometric data), manufacturing phase (processing/microstructure data), characterization phase (property data), deployment phase (performance data), and recycling phase (processing/cost data). Different stages of the lifecycle generate large volumes of data through parallel and automated experiments, which are then processed for analysis^[11]. Since the Materials Genome Initiative (MGI) in 2011, an increasing amount of data has been generated in a high-throughput manner. High-throughput methods are widely used in computational and experimental materials science, leading to high-throughput computation, manufacturing, and characterization advancements. High-throughput experiments (HTE) are systematic experimental methods that can complete a large number of independent experiments in a short period of time to efficiently screen and optimize targets. The origins of HTE trace back to the early 20th century, including the discovery of the Haber-Bosch catalyst^[12] and the Hanak multi-sample concept^[13]. A landmark paper by Xiang et al. on HTE^[14] garnered significant attention in the materials field, and HTE has since made notable advancements in areas such as dielectric materials^[15], catalysis, and polymers. HTE typically combines materials science techniques to create libraries for synthesizing and characterizing materials, enabling the rapid determination of their structural, physical, and chemical properties. Because HTE can quickly establish relationships between composition, structure, and functional properties, it is an ideal experimental complement to computational simulations and modelling.

The advancements in HTE methods have been successfully demonstrated in various materials with significant technical value, proving that HTE can discover and deploy new materials at unprecedented speeds and low costs. First-principles calculations, particularly those based on more cost-effective approximation methods such as Kohn-Sham density functional theory (DFT), have facilitated the development of high-throughput techniques. High-throughput DFT (HT-DFT) calculations have become a powerful tool in new material discovery^[16,17]. Furthermore, HTE can be reliably automated to predict the performance of large numbers of materials in high-throughput scenarios. High-throughput computation is widely used in material screening, discovery, and design. For example, Shen et al. used HT-DFT techniques for the computational and intelligent design of two-dimensional (2D) functional materials^[18]. More studies exploring materials using high-throughput experimental methods are shown in Table 1^[19-35].

To meet the quantitative demands of various materials for specific performance characteristics, a range of high-throughput characterization tools is required for fast and automated evaluation. Energy-dispersive spectroscopy (EDS) systems with silicon drift detectors (SDD) can fully meet the needs of high-throughput compositional measurements when combined with other functions, such as a thermionic field emitter. X-ray fluorescence (XRF) is also used for high-throughput compositional measurements^[36,37]. Standard high-throughput characterization methods for material crystal structures include X-ray diffraction (XRD) and electron backscatter diffraction (EBSD). EBSD pattern collection times are 1 ms and offer sufficient spatial resolution to index the phases within a microstructure, enabling high-throughput characterization. Mechanical properties of materials can also now be characterized through high-throughput methods, such as micro-tensile testing to measure yield stress^[38]. Zhao et al. used the diffusion multiple methods combined with nanoindentation to test the hardness properties of multi-component alloys, achieving results three orders of magnitude faster than traditional methods^[39].

High-throughput experimental techniques can rapidly generate large amounts of experimental data, which is crucial for ML datasets. In addition, data quality is also vital. In-situ experiments provide high-quality, high-fidelity data for an in-depth understanding of the dynamic changes and damage evolution of electronic packaging during service. This data helps train reliable and trustworthy ML models. In-situ transmission electron microscopy (TEM) can characterize the evolution of microstructures in real time and is an effective tool for studying at the atomic scale^[40]. The most advanced aberration-corrected TEM can achieve a spatial resolution of 0.5 Å^[41,42]. At the same time, in-situ scanning electron microscopy (In-situ SEM) is often used to observe crack initiation and propagation on material surfaces^[43]. In contrast, In-situ EBSD can effectively reveal microstructural evolution processes, such as changes in grain orientation and recrystallization under thermal and mechanical stress^[44]. In-situ X-ray computed tomography (In-situ X-ray CT) demonstrates its unique tracking capabilities for the non-destructive observation of internal defects in packaging^[45]. Furthermore, in-situ techniques can be combined with different physical fields, such as in-situ high-temperature experiments and in-situ tensile experiments^[46]. Xu et al. recorded data related to intermetallic compound (IMC) growth and phase transition processes under Cu–Al bonding conditions through in-situ experiments, observing the dynamic evolution of the bonding interface^[47]. Malkorra et al. characterized polymer core solder ball (PCSB) coatings using in-situ micro-pillar compression experiments to obtain the local mechanical properties of Cu and Ni-P layers^[48]. Interconnection is an essential part of packaging, and researchers apply in-situ techniques to the interconnection process. Zeng et al. conducted an in-situ analysis of the solidification structure of lead-free interconnects; high-quality in-situ data guides manufacturing high-reliability lead-free micro-joints^[49].

HTEs enable the generation and screening of large datasets, while in-situ experimental techniques achieve the exploration of high-quality data. Modern electronic packaging research is generating massive and diverse data at an unprecedented speed. This data, covering multi-dimensional information from composition and microstructure to macroscopic performance, forms the fundamental cornerstone for applying ML techniques to solve challenges in the packaging field.

Data preprocessing

The importance of datasets in ML is self-evident. High-quality datasets are the cornerstone of advancing research in electronic packaging science. However, raw data is often incomplete, inconsistent, lacking certain behaviors or trends, and may even contain errors. The logic used by ML models is learned from the data rather than encoded, so the data quality is crucial for achieving good model performance^[50]. Therefore, further data processing is necessary to improve data quality and ensure the accuracy of ML model training. The primary data preprocessing methods include: data cleaning, feature selection (FS), FE, and normalization.

DenseNet

Highway Networks and deep residual networks (ResNet) have enabled neural networks to reach greater depths, with architectures easily exceeding 100 layers. However, as network depth increases, issues such as vanishing gradients and inefficient learning become more apparent. If shorter connections could be established between a CNN’s input and output layers, the network could train more deeply, precisely, and efficiently. Therefore, Huang et al. introduced a DenseNet, with the architecture shown in Figure 1^[90]. It connects each layer to every other layer, except itself, through a forward-feedback mechanism. Unlike traditional convolutional networks with L layers, which have L connections, DenseNets feature L(L + 1)/2 direct connections. This design reduces the number of parameters, mitigates the vanishing gradient problem, and enhances feature propagation.

Figure 1. The DenseNet architecture: a 5-layer dense block with a growth rate of k = 4. Each layer takes all preceding feature maps as input^[80]. DenseNet: Dense neural network.

Inspired by DenseNet, researchers have also proposed the DefectSegNet model for the automated identification of crystallographic defects and the TSRNet model to enhance the structural information in reconstruction outputs. Zhou et al. developed the scale-transferable detection network (STDN) for detecting multi-scale objects in images^[91]. The network is integrated with DenseNet, creating a single-stage object detector equipped with an embedded super-resolution layer to explicitly explore the inter-scale consistency across multiple detection scales.

CNNs

DenseNets are the core of ANNs, but their input and output sizes are fixed. As mentioned earlier, DenseNets are typically used as part of a larger model and are rarely used alone. CNNs are one of the most representative neural networks in ML, with their development dating back to the 1980s^[92]. The first milestone research in CNNs was LeNet-5, introduced by LeCun et al., initially used for document recognition^[93]. The network architecture, as shown in Figure 2, consists of convolutional and pooling layers, followed by fully connected layers for classification tasks. The performance of this network outperformed any other network of its time.

Figure 2. The overall architecture of the CNN includes an input layer, multiple alternating convolution and max-pooling layers, one fully connected layer, and one classification layer^[94]. CNN: Convolutional neural network.

AlexNet, introduced in 2012, is a deep CNN consisting of 5 convolutional layers and 3 fully connected layers. The network includes 650,000 neurons and 60 million parameters, achieving top performance on the large-scale ImageNet ILSVRC-2012 dataset. Building on AlexNet, Simonyan and Zisserman introduced the deep convolutional networks VGG (Oxford Visual Geometry Group) -16 and VGG-19^[95]. VGG-Net leverages its depth to learn more from the dataset, and its use of tiny convolutional filters significantly increased the network depth to 16 to 19 layers. As the network depth increases, the issue of vanishing gradients arises. To address this, He et al. designed the ResNet, which has a depth of up to 152 layers^[96]. ResNet establishes shortcut connections by skipping one or more layers, allowing the network to access the output data directly, effectively mitigating the vanishing gradient problem.

CNNs include one-dimensional CNNs, 2D CNNs, and multi-dimensional neural networks. The evaluation of electronic packaging reliability often relies on microscope data, and 2D CNNs perform exceptionally well in processing microscopic images. Therefore, this section focuses on 2D CNNs. The core computation of a 2D CNN is the cross-correlation operation between the 2D input data and the 2D convolutional kernel. Farizhandi et al.^[97] successfully processed image data of the amplitude decomposition process of Fe-Cr-Co alloys obtained through phase-field simulations using the pre-trained network EfficientNet, proposed by Tan and Le^[98]. Kondo et al. also used CNNs to extract semantic features strongly associated with macroscopic properties automatically^[99]. Kunwar et al. used CNNs to identify the presence of interface bubbles and IMCs during the hot-dip coating process of Cu strips^[100]. Due to the small training dataset, data augmentation was performed before using CNN for recognition. This data preparation process is typically implemented using GANs in ML, which we will discuss in detail later.

Convolutional encoder-decoder

The convolutional encoder-decoder architecture is closely related to CNNs. Both use convolutional layers as the fundamental building blocks. A typical CNN structure consists of convolutional layers, followed by pooling layers, and ends with fully connected layers for classification output. The convolutional encoder-decoder is an extension built upon the CNN framework.

The convolutional encoder is based on the fully convolutional network (FCN) model^[101]. In FCN, transposed convolutions or bilinear upsampling replace the traditional fully connected layers. In the convolutional encoder-decoder, the encoder is responsible for FE, while the attention module plays a key role in feature recalibration and enhancement. Attention mechanisms have shown outstanding performance in tasks such as image classification, object detection, semantic segmentation, and video understanding^[102,103]. The “header” in the decoder connects the feature maps extracted by the encoder, generating rich feature maps and extracting contextual information. With its multi-level visual perception, the decoder can interpret hierarchical visual concepts and recover details^[104,105]. Loss functions measure the difference between predictions and targets, guiding the training process. The model adjusts its parameters by minimizing the loss function to improve prediction accuracy. Different tasks require different loss functions, such as mean squared error (MSE), mean absolute error (MAE), and cross-entropy loss^[106-114]. Typical formulations for these include:

MSE:

Where N is the number of samples, y_i is the true value, and $$ \hat{y}_i $$ is the predicted value.

MAE:

Cross-entropy loss (e.g., for binary classification):

where y_i is the true label, typically 0 or 1, and $$ \hat{y}_i $$ is the predicted probability for class 1.

Typical encoder-decoder models include SegNet^[115,116], U-Net^[117-119], and the DeepLab series. SegNet consists of an encoder network, a decoder network, and a pixel-level classification layer (The architecture of SegNet is shown in Figure 3). The encoder network’s topology is consistent with the 13 convolutional layers of VGG16. The decoder network maps the low-resolution encoder feature maps to full-resolution feature maps for pixel-level classification. U-Net is one of the most important frameworks for semantic segmentation, widely used in image segmentation^[120-123], image enhancement^[124-126], and other fields. U-Net features a symmetric encoder-decoder structure, where the encoder progressively downsamples the input image to capture feature information while the decoder progressively upsamples to recover spatial resolution. Skip connections between corresponding features in the encoder and decoder preserve high resolution, which is a key feature of U-Net. Zhou et al. proposed the U-Net++ architecture, which differs from the previous architecture by redesigning the skip paths^[118]. The encoder and decoder sub-networks are connected through a series of nested dense skip paths, reducing the semantic gap between their feature maps. This design achieved a 3.9 and 3.4-point improvement in mean IoU over U-Net and Wide U-Net, respectively. Chen et al. combined the responses of DCNN layers with conditional random fields (CRFs) to overcome the poor localization characteristics of deep networks, resulting in the DeepLab system^[127]. This system outperforms previous methods, achieving more accurate localization of object boundaries. Chen et al. later optimized the DeepLab architecture^[128-131].

Figure 3. The architecture of SegNet^[116].

The excellent performance of convolutional encoder-decoder models has led to their widespread application in materials science. Shrivastava et al. applied convolutional encoder-decoder models to predict peak stress clusters, particularly focusing on clusters’ size and other features within a heterogeneous linear elasticity framework^[132]. Konstantinova et al. extracted features from images using convolutional layers, projected them into a lower-dimensional space, and then transposed convolutional layers to reconstruct clean images from this simplified representation^[133]. Tsopanidis et al. employed the U-Net architecture to analyze the morphological features of fracture surfaces in MgAl₂O₄ samples, with experimental results demonstrating the model’s strong generalization ability and robustness^[134].

GANs

A GAN consists of a generator and a discriminator. The generator aims to learn real data distribution and generate samples that closely resemble real data. In contrast, the discriminator aims to correctly determine whether the input data comes from real data or the generator. The generator and discriminator act as adversaries: the generator improves its ability to produce data closer to real data, while the discriminator enhances its ability to differentiate. This adversarial approach is based on the concept of Nash equilibrium from game theory^[135]. The input to the generator G is a random variable z, which generates samples that follow a real data distribution. The discriminator D receives input data and labels it as 1 if it is from real data x, and 0 if it is from the output of the generator G(z).

Researchers have made improvements and theoretical extensions to the original GAN model to adapt to different analytical tasks. Goodfellow et al. first proposed GAN^[135]. Similar to other neural networks, GAN also faces the issue of vanishing gradients. Arjovsky et al. replaced the traditional Jensen-Shannon divergence with the Wasserstein distance to obtain smoother gradients and achieve stable training^[136]. Mao et al. proposed the least squares GAN (LSGAN), which replaces the cross-entropy loss function in traditional GANs with a least squares loss for the discriminator^[137]. Berthelot et al. introduced a new balance-enhancing method to better balance the generator and discriminator training process^[138]. They combined it with the Wasserstein distance loss to train autoencoder-based GANs. Furthermore, Conditional GANs (cGANs)^[139,140] have been widely used as a general solution for various image-to-image translation tasks. Both cGAN and GAN are trained using paired images with one-way translation. Researchers introduced cycleGAN^[141], DualGAN^[142], and one-to-many cGAN to overcome these limitations^[143].

GANs possess a unique game-theoretic concept, giving them significant advantages in data generation, data augmentation, and material design. Huang et al. designed a flexible Quantum GAN that generates high-dimensional feature images and utilizes quantum superposition to train multiple samples in parallel^[144]. Kench et al. designed the SliceGAN architecture, which uses easily accessible 2D images to synthesize high-fidelity 3D data, achieving uniform information density^[145]. Many researchers have leveraged GANs to assist in material design. Mao et al. used GANs to design complex materials with extreme properties in an unsupervised manner, without prior knowledge^[146]. In GAN-based design, the discriminator network learns from the dataset to map the relationship between configurations and attributes, rapidly generating new configurations with extreme attributes. Dan et al. proposed a GAN-based generative ML model (MatGAN), which efficiently generates new hypothetical inorganic materials by training on materials from the ICSD database^[147]. Narikawa et al. applied GAN-based deep convolutional GAN, cycle-consistent GAN, and super-resolution GAN techniques to generate, transform, and enhance the quality of microstructure images, reconstructing virtual microstructures that are nearly indistinguishable from real images^[148].

ML-based defect detection in electronic packaging

In the post-Moore era, electronic packaging dimensions are progressively shrinking^[149], and consequently, solder joint sizes are diminishing, now reaching micrometre and even nanometer scales. This trend leads to size-dependent changes in microstructural features, such as grain size, thickness, and IMC. The formation of these IMCs is a primary contributor to solder joint failure, and an empirical formula typically governs their growth^[150,151]:

X(t) represents the thickness of the IMC layer at time t, X₀ is the thickness of the IMC at the initial moment, t is the time of the aging experiment, D is a constant depending on the activation energy and aging time, and n is a time constant.

Recognizing the influence of size on IMC growth, Zhu et al. refined the aforementioned empirical formula by introducing two size factors: B1 and B2^[152]. These factors, which relate to the reaction rate and diffusion activation energy, respectively, account for the effect of solder joint dimensions on the growth of IMC thickness.

The IMC proportion is also affected by solder joint size. Magnien et al. studied the thickness and proportion of IMC in solder joints of different sizes^[153]. The results indicate that the IMC thickness is directly proportional to the solder joint size, while the IMC proportion is inversely proportional to the solder joint size. As the solder joint size decreases, the diffusion of Cu from the boundary remains unchanged. This results in a higher concentration of dissolved copper in smaller solder joints, leading to a higher formation rate of the Cu₃Sn phase. Huang et al. found that the growth rate of the IMC Cu₆Sn₅ is faster on fine-grained Cu than on coarse-grained Cu^[154]. This is because fine grains provide more grain boundary channels, which promote rapid atomic diffusion. Therefore, solder joint size affects IMC morphology, which in turn affects IMC growth, ultimately leading to defects in the solder joint. The solder microstructure also changes with the decrease in size, especially for lead-free solders, where β-Sn is the main component. When the solder joint size decreases from the millimetre scale to the micrometre scale, the number of β-Sn grains that can be accommodated inside the joint gradually decreases. In extreme cases, the solder joint exhibits a single-crystal or near-single-crystal structure. β-Sn shows significant anisotropy in its diffusion, thermal expansion, mechanical, and electrical properties. This strong anisotropy significantly impacts the reliability of micro-solder joints during use^[155-157]. The reduced solder joint size inevitably makes the impact of size-related local effects (such as current crowding, stress concentration, etc.) on the overall solder joint reliability more severe. Detecting solder joint defects becomes particularly important to ensure the overall reliability of solder joints. Manual visual inspection for defect detection is inefficient and lacks stability. Traditional image processing methods achieve high detection accuracy through image subtraction, but they are time-consuming. With the rise of deep learning-based defect detection techniques, many classical ML algorithms have been applied to defect detection in electronic packaging^[158].

CNNs have been widely applied in image processing, object detection, and segmentation. The image preprocessing process is simplified by automatically extracting image features, leading to improved detection speed^[159-162]. The essence of defect detection is identifying and locating defects or anomalies, which can be abstracted as an object detection task in deep learning. Therefore, object detection algorithms can be employed to perform defect detection tasks. Currently, object detection algorithms based on CNNs are most widely used in this field. They can be mainly divided into two categories: two-stage detectors represented by Region-based CNNs (such as Faster R-CNN), which are generally known for their high accuracy, and single-stage detectors represented by the “You Only Look Once (YOLO)” series, which are famous for their high-speed detection capabilities. Ren et al. integrated the region proposal network (RPN) with the Fast R-CNN object detection network, resulting in the new object detection system, Faster R-CNN^[163]. The system is a unified object detection network consisting of two modules: the deep FCN (RPN) module for generating region proposals, and the Fast R-CNN detector that uses the proposed regions. Specifically, the RPN module indicates the areas on which the Fast R-CNN module should focus (The system architecture is shown in Figure 4A). Faster R-CNN enables a unified deep learning-based object detection system to operate at 5-17 frames per second (fps). The Faster R-CNN model has been widely applied to defect detection tasks^[164-167]. Li et al. employed Faster R-CNN to detect five different types of printed circuit board (PCB) defects, achieving a mean average precision (mAP) of 60%, with approximately 90% accuracy in detecting Bridge and Empty type defects^[168]. Ma et al. proposed an improved Faster R-CNN deep learning network^[169]. The original Faster R-CNN performs multiple downsampling operations, making it challenging to achieve high-precision detection of minor defects on chip surfaces. Ma et al. replaced the original VGG16 backbone network with ResNet50, alleviating the gradient vanishing issue during model training and improving the accuracy of small defect FE. The improved system performs better in detecting and identifying chip surface defects, increasing the mAP of the original Faster R-CNN algorithm from 91.49% to 94.92% (The architecture of the improved system and the actual detection results are shown in Figure 4B-D). Hu et al. proposed a defect detection deep learning method more suitable for production environments^[170], which is based on Faster R-CNN and incorporates the guided anchor (GA) introduced by Wang et al.^[171]. In addition to using ResNet50 for FE, GARPN is employed to predict more accurate anchor points, and the residual units of ShuffleNetV2 replace the basic residual units to reduce the overall computational load of the network. To address the challenges of detecting small objects and objects with extreme aspect ratios on the surface of flexible printed circuit boards (FPC), Shen et al. proposed a new algorithm based on Faster R-CNN, called GA-Faster-RCNN^[172]. The algorithm replaces the RPN network in the original Faster R-CNN with the GA module, leverages the feature pyramid network (FPN)^[173] to enhance the FE capability for multi-scale defects, and substitutes ResNet-101 for VGG16 in the original Faster R-CNN. Overall, Faster R-CNN and its improved versions, as representatives of two-stage detectors, demonstrate high detection accuracy in electronic packaging defect detection tasks, especially when dealing with complex backgrounds and tiny defects, thanks to their RPN and fine-grained FE. However, this accuracy advantage often comes with relatively high computational complexity and slower detection speeds, which can be challenging in some production environments requiring real-time online inspection.

Figure 4. (A) Original Faster R-CNN architecture; (B) Improved Faster R-CNN architecture; (C) Detection results of the original architecture; (D) Detection results of the improved architecture^[163,169]. R-CNN: Region-based convolutional neural network.

YOLO, a novel object detection method, was introduced in 2015. It offers good accuracy and fast computational speed by utilizing a single-stage network architecture to process images^[174]. Unlike the two-stage detectors (such as Faster R-CNN) discussed earlier, YOLO integrates object localization and classification into a single network, significantly improving detection speed and making it a preferred choice for real-time applications. The first version of YOLO laid the foundation for real-time applications in machine vision systems^[175]. Subsequently, researchers continuously improved YOLO, updating it from YOLOv1 to YOLOv10^[176-182]. The YOLO series models, with their exceptional automatic detection capabilities, have been effectively applied in autonomous driving, particularly in scenarios that require efficient and accurate real-time detection systems^[183-187]. YOLO demonstrates excellent real-time capability and accuracy performance. While early versions might have slightly lower accuracy than two-stage methods, subsequent versions have significantly improved accuracy through various optimizations while maintaining high speed. Mao et al.^[188], based on the YOLOv7 model, utilized ConSinGAN^[189] for data augmentation during the preprocessing stage and designed a dual in-line pin (DIP) defect detection system, achieving a detection accuracy of 95.5%. Cao et al. constructed a chip packaging surface defect dataset consisting of 2,919 images, the first dataset designed to detect defects across multiple chips simultaneously^[190]. At the same time, the YOLOv7 model was optimized by incorporating the Carbon Border Adjustment Mechanism (CBAM) attention mechanism and the Receptive Field Block (RFB) module. New anchor boxes were designed for chip surface defect detection, and a novel post-processing method called CP-Cluster was introduced to replace the commonly used nonmaximum suppression (NMS). These improvements eliminated redundant structures in YOLO, enhancing detection accuracy and speed and reducing the number of parameters and computational workload. Lin et al. developed a system based on the YOLO algorithm for detecting capacitors assembled on PCBs^[191]. In electronic packaging, the interconnection area is also a high-defect region. Many researchers have applied YOLO series models to solder joint defect detection, achieving high detection accuracy. Zou et al. created the Weld Defect Dataset (WDD) and trained a YOLOv3 object detection network on this dataset, achieving a detection accuracy of 75.5%^[192]. Liao et al. adopted an improved deep learning algorithm, ConvNeXt-YOLOX, based on the YOLOX neural network^[193]. This algorithm is primarily used for high-precision and high-speed detection of solder joint defects on surface mount technology (SMT) production line PCB assemblies (PCBA). Testing on the constructed dataset showed that the improved ConvNeXt-YOLOX model outperformed the original YOLOX model and the lightweight YOLOX-s model, achieving an average detection accuracy (mAP) of 97.21% (The architectures of the original YOLOX and ConvNeXt-YOLOX, along with their results in the test experiments, are shown in Figure 5).

Figure 5. (A) Detailed structure of the original YOLOX model; (B) Detailed structure of ConvNeXt-YOLOX; (C) ConvNeXt-YOLOX results in PCBA solder joint defect detection; (D) YOLOX results in PCBA solder joint defect detection; (E) YOLOX-s results in PCBA solder joint defect detection^[193]. PCBA: Printed circuit board assemblies.

The Faster R-CNN and YOLO frameworks are powerful tools for solving the defect detection problem. However, whether to pursue the typical high precision of a two-stage system or prioritize the pure speed of a single-stage system required for real-time detection is a matter that needs to be weighed. The scarcity of high-quality and labelled datasets remains a significant bottleneck. Meanwhile, the decreasing size of defects also brings difficulties in detection. Another major challenge is ensuring the model can operate stably in different environments. Considering these issues, future work is likely to promote more efficient data utilization methods, such as unsupervised learning and advanced data augmentation techniques, while also focusing on building network architectures that are both lightweight and intelligent enough to adapt to real factory environments.

ML-based optimization of electronic packaging materials

As electronic components continue to miniaturize, this trend leads to higher power density, which significantly increases the internal heat generation of the components. At the same time, the increased current density may reduce the functionality of electronic devices and adversely affect their long-term reliability. Therefore, selecting appropriate materials is crucial for enhancing the lifespan and reliability of electronic packaging^[194]. ML methods offer scalability, automation, and cost-effectiveness when screening candidate materials with potential applications.

The combination of HT-DFT calculations and ML models facilitates precise atomic-level property estimation and the virtual screening of promising materials^[195-197]. Tsymbalov et al. proposed a physics-based CNN model [Figure 6A and B] to promote autonomous deep learning of the electronic band structure of crystalline solids^[198]. The model consists of a fully connected component and a CNN component. The strain components are processed through the fully connected layers and reshaped into a five-dimensional tensor. After several convolutional layers with residual connections to improve convergence, the network outputs the band structure, which matches the target band structure obtained from DFT calculations. Na et al. proposed a hybrid method that combines the graphical representation of materials and the crystal-level properties of the generalized gradient approximation (GGA) bandgap with a newly designed tuple graph neural network (TGNN) (the overall architecture of TGNN is shown in Figure 6C)^[199]. This method leverages a given material’s crystal structure and GGA bandgap information to achieve accurate bandgap prediction. This research is essential for designing, developing, and applying semiconductor materials in electronic packaging. The traditional band gap calculation using the GW approximation and band gap estimation using the TGNN model are shown in Figure 6D. To validate the applicability of this approach, the researchers provided a dataset of G0W0 bandgaps for 45,835 materials predicted by TGNN. The input features for the GNN are the crystal structures of compounds and GGA bandgap data collected from the Materials Project dataset^[200]. As shown in Figure 6E, the prediction error between the G0W0 bandgap and experimental bandgap is significantly smaller than the error between the calculated GGA bandgap and experimentally measured bandgap. Beyond these specific examples, ML is being broadly applied to tackle other critical aspects of semiconductor material optimization. Researchers are, for instance, using neural networks to bridge the gap between PBE calculations and experimental band gap measurements^[201], employing ML to guide the design of novel nitrides based on first-principles data^[202], and leveraging GANs for the inverse design and discovery of stable semiconductor materials^[203]. Furthermore, ML frameworks are being developed to predict various physical potentials across diverse material classes with experimental-level accuracy^[204]. These diverse applications underscore ML’s versatility in predicting known properties and actively guiding the search for and design of next-generation electronic materials.

Figure 6. (A) CNN architecture for band structure prediction; (B) Tensor representation and physical insights incorporated into the CNN model; (C) Overall architecture of the TGNN and the crystal property prediction process based on TGNN; (D) a: Traditional band gap calculation using the GW approximation. b: Band gap estimation using the TGNN model; (E) Comparison between PBE-GGA (blue squares) and predicted G₀W₀ band gaps (red circles)^[198,199]. CNN: Convolutional neural network; TGNN: tuple graph neural network; GW: GW approximation; PBE-GGA: Perdew-Burke-Ernzerhof generalized gradient approximation.

Epoxy resins are widely used in electronic encapsulation due to their excellent adhesive properties, thermal stability, electrical insulation, and mechanical strength. Pruksawan et al. addressed this issue by combining laboratory experimental design, an active learning process, and Bayesian optimization to predict and optimize adhesive materials^[205]. The approach was implemented in two phases: in the first phase, an accurate ML model was developed for active learning; in the second phase, experimental conditions were improved to enhance Bayesian optimization. This two-stage data-driven approach successfully identified adhesive materials with exceptionally high adhesive strength from a minimal dataset. Jin et al. proposed an optimization method for multi-component epoxy resin systems based on molecular dynamics (MD) and ML^[206]. The method uses MD simulations to generate a training dataset, then applies ML to determine the optimal component ratio, and finally validates the results experimentally. The optimized composition ratio of diglycidyl ether of bisphenol A / tetraglycidyl diaminodiphenyl methane / diaminodiphenyl sulfone / polyethersulfone was 10.5/51.23/29.63/8.64. Compared to the designed average values, the glass transition temperature (T_g) increased by 17.3%, the modulus of elasticity (E) increased by 15%, the ultimate tensile strength (UTS) increased by 32.7%, and the elongation at break (δ) increased by 85.5%. These two studies showcase different ML strategies for polymer optimization: Pruksawan et al. employ an active learning approach to minimize costly experiments, while Jin et al. leverage computationally intensive MD simulations to generate rich datasets for ML-driven multi-objective optimization, demonstrating the adaptability of ML to both data-scarce and data-rich scenarios^[205,206].

ML is rapidly becoming an indispensable tool in electronic packaging. It accelerates the prediction of the core properties of semiconductors to help design complex mixtures such as epoxy resin. However, some significant obstacles remain before ML can thoroughly guide material design. One major challenge is bridging the scale gap - reliably converting atomic simulation or experimental data into predictions of fundamental macroscopic properties, achieving reverse design, and creating entirely new materials on demand. Ultimately, the close integration of ML and material design will likely determine the pace of future innovation in advanced packaging materials.

ML-based reliability analysis of electronic packaging

The reliability of electronic packaging directly determines the overall performance and lifespan of electronic products. As electronic devices continue to become smaller and more integrated, the reliability of electronic packaging faces increasingly stringent challenges. Reliability analysis helps identify potential failure modes, preventing device malfunctions or performance degradation caused by packaging failures. Reliability analysis of electronic packaging has always been based on powerful experimental techniques [such as EBSD, digital image correlation (DIC)] and physics-based models [such as crystal plasticity finite element (CPFE)]. Although these mature methods provide deep physical insights, they face challenges regarding computational cost and large and complex data analysis. This presents an opportunity for ML to serve as a complementary tool by accelerating simulations, interpreting experimental data, and creating novel predictive models, which are the focus of this section.

Non-uniform heat flux and temperature distribution often compromise the reliability of advanced packaging and heterogeneous integration. Physics-based models are widely used to predict package-level reliability. MD and first-principles calculations are indispensable simulation tools for analysis at the microscopic and atomic scales. First-principles calculations are algorithms that directly solve the Schrödinger equation based on the principles of quantum mechanics^[207]. These calculations are founded on the interactions between atomic nuclei and electrons and their fundamental laws of motion, with certain approximations applied. Zhang et al. employed first-principles calculations to analyze Ni-Sn-based IMCs used in high-power device packaging^[208]. This work guides the microstructural design and process development of all IMC solder joints in the Ni-Sn system. Based on first-principles calculations, Fu et al. analyzed the formation difficulty of Cu₆Sn₅ and Cu₃Sn from a microscopic perspective^[209]. They also investigated the interfacial failure mechanism from an energetic standpoint. Increasing chip integration density has led to a continuous reduction in package dimensions. This makes interfacial observation extremely difficult, for instance, with barrier layers in through-silicon vias (TSVs) that are only 100 nanometers thick or thinner. MD, a vital simulation method for addressing issues at the atomic and molecular level, is highly effective for analyzing the dynamic properties of nanoscale materials^[210]. Therefore, it is also well-suited for analysing and predicting materials in such small-scale packages. Using MD simulations, Gao et al. analyzed different Cu/Ta interface models and performed tensile simulations^[211]. Their findings showed that the critical strain energy release rates for rough and tilted interfaces were higher than those of a perfect interface. They also found that interfacial voids significantly reduced the energy release rate. Ji et al. utilized MD to investigate the influence of IMCs on the Cu/Si interface^[212]. They evaluated the interfacial fracture performance based on stress, strain, and critical strain energy release rate, ultimately finding that an IMC layer of a specific thickness can improve the fracture properties. The anti-corrosion performance of two organic encapsulation materials, polydimethylsiloxane (PDMS) and hexamethyldisilane (HMDSO), on copper surfaces was investigated by Zhang et al. using MD^[213]. This research provides valuable insights into the corrosion-related reliability of electronic packages.

Physics-based models have long been indispensable tools in electronic packaging reliability analysis. They provide a fundamental understanding of the physics of failure and enable detailed, multi-scale observations. However, their significant computational cost, both in time and resources, severely limits their application for macro-scale system analysis, large-scale parameter optimization, and real-time health monitoring. Researchers increasingly turn to data-driven ML methods to overcome these shortcomings and establish rapid mappings from experimental or simulation data to system performance.

ML methods can achieve high accuracy in forecasting reliability issues caused by junction temperature variations^[214-217]. Researchers are increasingly focusing on using ML methods to predict and optimize the thermal reliability of electronic packaging systems. A junction temperature prediction method based on the back propagation (BP) neural network is proposed, with prediction accuracy superior to traditional polynomial fitting methods^[218]. Other researchers have combined BP neural networks, interpolation methods, and Kalman filtering for junction temperature prediction. Although the accuracy has been improved, the high computational complexity may limit its practical applicability^[219]. Wang et al. proposed an enhanced multi-feature electro-chemo-thermal coupling modelling method, combined with an improved decoupled modified bias extended Kalman filter method, for iterative state of charge (SOC) prediction, achieving more robust prediction results^[220]. They also proposed an improved multi-head bidirectional long short-term memory (LSTM) temporal convolutional model for lithium-ion battery SOC estimation^[221]. In addition, they established a back propagation neural network - square-root cubature kalman filter (BPNN-SRCKF) estimation model based on fusion dual-factor parameter identification to achieve accurate and reliable online SOC estimation^[222]. Gharaibeh et al. optimized an ANN deep learning model by adjusting the number of hidden layers and the number of neurons in each layer to predict the temperature distribution of four chips in a multi-chip module (MCM) under both uniform and non-uniform heat flux^[223]. In the case of uniform heat flux, the neural network has one hidden layer with 10 neurons, while in the case of non-uniform heat flux, the network has three hidden layers, each containing 4 neurons. In both scenarios, the model’s prediction R² value was 0.99. This model successfully predicted the temperature distribution under different heat flux conditions, aiding in the real-time evaluation of the thermal reliability of MCMs. Djedidi et al. conducted a study on the reliability of systems on chip (SoC) in applications, using a nonlinear auto-regressive (NAR) neural network to model the temperature drift trend^[224]. When the estimated error of the actual drift exceeds a predefined threshold, the model is updated, enabling real-time prediction of the SoC’s remaining useful life (RUL). ELM is a ML model known for its strong fitting and classification capabilities, and it offers faster learning speeds than traditional feedforward neural networks^[225]. Liu et al. proposed an ICS-ELM model based on an improved Cuckoo Search optimization method for ELM^[226]. This model takes saturation voltage drop, collector current, and aging cycle count as inputs and predicts junction temperature as the output, establishing a multi-input, single-output insulated-gate bipolar transistor (IGBT) junction temperature prediction model with high accuracy. Majd et al. collected temperature, shear stress, and differential stress time series data from multiple electronic packages using piezoresistive silicon-based strain sensors in a thermal shock chamber and then analyzed the data using various neural network models^[227].

In electronic packaging, solder joints provide electrical interconnection and mechanical support for electronic devices. Therefore, evaluating the reliability and predicting the lifetime of solder joints has always been a significant challenge for researchers^[228-230]. While traditional statistical models such as Weibull regression and the Cox proportional hazards model (Cox-PHM) have long been employed for reliability analysis due to their simplicity^[231-235], they often struggle to capture the complex, multi-factor interactions inherent in modern packaging failures, thus paving the way for ML approaches.

The reliability of solder joints is influenced by multiple factors, including thermal variations, the mechanical properties of the solder joint itself, electromigration during service, and the formation of IMCs^[236-239]. ML methods can comprehensively capture the interactions between these competing factors, enabling high-fidelity predictions of solder joint lifetime while accelerating the development of predictive models for reliability assessment. Samavatian et al. proposed a correlation-driven neural network (CDNN) model that captures correlations between candidate features and accurately predicts lifetime based on material properties, device configuration, and thermal cycling, with a root mean square error of just 5.71%^[240]. The model also analyzed the effects of solder material and thickness on joint failure evolution and estimated the optimal solder layer thickness balancing creep and fatigue damage. The reliability of 3D integrated circuits (ICs) faces more significant challenges. Hsu et al. used AI deep learning based on CNNs for non-destructive analysis of typical 3D IC chips with solder micro-bumps using 3D X-ray tomography images (Figure 7 shows the test samples, the training/testing procedure, and performance of the CNN model)^[241]. Training the model with a collected image database can quickly predict solder joint interconnection failures based on non-destructive 3D X-ray tomography images with an accuracy of up to 89.9%. The study identified key features determining the “good” or “faulty” conditions of reflowed micro-bumps, such as the percentage of area loss in the middle cross-section. Yuan et al. combined sequential ANNs with finite element modelling to generate datasets based on finite element analysis (FEA)^[242]. They trained the datasets using recurrent neural networks (RNN) and LSTM architectures to evaluate the thermal cycling performance of solder joints in glass wafer-level chip-scale packaging (G-WLCSP). Reihanisaransari et al. considered the effects of BGA chip position, PCB thickness, solder alloy composition, and solder ball volume on solder joint reliability^[243]. They obtained training data for a neural network model through 480 finite element simulations and 20 experimental tests. Using the trained neural network model, they successfully predicted the solder joint reliability with an accuracy of 97.55%. The above content summarizes different ML strategies for solder joint reliability: some use neural networks to learn directly from experimental or simulated data [such as CDNN or NN+finite element method (FEM)], while others use CNNS to analyze non-destructive imaging data (such as 3D X-rays). They can handle high-dimensional inputs and discover hidden correlations that traditional models might overlook. However, the breadth and high quality of the training data (whether from FEM or experiments) remain one of the challenges to be overcome, and it is also necessary to ensure that the ML model captures the underlying mechanisms of faults rather than just statistical correlations. Effective integration of multimodal data (such as thermal, mechanical, and imaging) remains an important goal.

Figure 7. (A) Overall image of the test sample; (B) CNN model training/testing procedure and performance^[241]. CNN: Convolutional neural network.

In conclusion, ML is transforming the reliability analysis of electronic packaging, moving beyond traditional statistics and towards predictive, data-driven approaches. However, the path forward requires overcoming key obstacles: generating high-fidelity life cycle data, integrating physical knowledge into ML, and developing interpretable models suitable for the working environment. The “Digital Twins” concept combines real-time data, physics-based simulation, and ML and may represent the future direction of comprehensive reliability management in this field.

ML-based structural design optimization for electronic packaging

A well-designed structure significantly influences electronic packaging systems’ reliability, thermal management, electrical performance, and mechanical strength^[244-246]. Researchers have extensively studied micro-bump layout design, packaging design under plastic encapsulation, flip-chip interconnection design, and high-power multi-chip structure design in electronic packaging^[247-249]. However, due to limitations in experimental costs and computational capacity, a systematic approach for packaging structure optimization has yet to be established, hindering chip designers from effectively determining the optimal design parameters for their products.

Flip-chip packaging technology is widely used in the electronics packaging industry, eliminating the need for wire connections and achieving the shortest connection paths. Compared to wire bonding (WB) and tape automated bonding (TAB), it offers higher packaging density, smaller package size, superior electrical and thermal properties, and lighter weight^[250-253]. However, this technology still faces specific challenges. As mentioned earlier, selecting the appropriate materials is crucial for improving packaging reliability, and additionally, the design of the interconnection structure layout plays a significant role. Wu et al. developed a FEA model, varying chip thickness, width, and PCB board thickness to obtain the corresponding maximum first principal stress, which was used as training data for ML models^[254]. The models were trained using ordinary least squares linear regression, lasso regression, ridge regression, Poisson regression, bagging regression, support vector regression (SVR), KNN, and random forest (RF) algorithms for prediction. The comparison revealed that the RF algorithm provided the best stress prediction capability for chip packaging integration design. However, FEA-based ML methods typically rely on temporary data generation procedures, which are less efficient and struggle to handle increasing chip design parameters. Chu et al. adopted an efficient statistical sampling method for generating training data using computer models^[255]: the Latin hypercube sampling (LHS) scheme^[256]. This method was used to create the initial dataset for training the ML model, and an ANN model was developed for ERR prediction, applied to reliability prediction, and design optimization of ultra-low-k chip packaging. To capture the nonlinear data patterns and input-output electrical relationships of analogue circuits, Lai et al. employed ML techniques to improve the packaging and testing processes of analogue ICs^[257]. This approach enabled rapid prediction of resistance (R), inductance (L), and capacitance (C) values, thereby providing a basis for improvements in structural design.

High-performance PCB designs have evolved to 12 to 20 layers. Each layer contains various signals sensitive to the stacked physical design, which significantly increases the complexity of the stacking design^[258]. Long et al. proposed a method that uses ML to rapidly generate models and analyze electronic packaging structures’ mechanical behavior^[259]. Chae et al. proposed a reverse stacking optimization method for advanced packaging design (ISOP+), which utilizes an automatic search algorithm and a ML surrogate model to generate stacking designs optimized for performance requirements directly^[260]. Experimental results indicate that the ISOP+ framework reduces the design cycle from several hours to just a few minutes and significantly outperforms other baseline optimization methods and manual designs.

ML facilitates the design of three-dimensional electronic packaging structures, effectively addressing the growing complexity of packages. The increasing intricacy of 3D electronic packaging poses significant inspection challenges. While physical cross-sectional analysis is destructive, 3D X-ray microscopy (XRM) offers a non-destructive alternative, generating comprehensive volumetric data via full-angle tomography for reconstructing detailed internal architectures^[261]. Figure 8A shows the workflow. Given the substantial spatial information involved, ML techniques are crucial for efficiently processing these datasets and facilitating 3D reconstruction and defect identification. Deep learning high-resolution reconstruction (DLHRR) methods^[262] can significantly accelerate 3D X-ray scans for complex packages and overcome significant field-of-view limitations^[263].

Figure 8. (A) Workflow for 3D XRM measurement; (B) Deep learning network model: reconstruct a high-quality 3D XRM volume dataset with low noise and minimal artefacts through a small amount of X-ray projection and/or exposure time; (C) XRM data for lens components of smartphone cameras: FDK and DeepRecon comparison^[264]. XRM: X-ray microscopy; FDK: Feldkamp-Davis-Kress.

ML offers a novel approach to the design of packaging structures and integrates with 3D X-ray technology to analyze these structures, thereby enhancing analytical efficiency, accelerating development processes, and assisting in identifying and rectifying potential defects in packaging structures within practical applications. By establishing a CNN bridging 2D projection and 3D reconstruction (as depicted in Figure 8B), the network can be trained to disregard noise within the data and emphasize small-scale features. This approach mitigates noise and artefacts in the reconstruction outcomes while retaining edge characteristics and fine surface details^[264]. Carl Zeiss X-ray Microscopy (XRM) Inc. has recently incorporated a deep learning-based CT reconstruction workflow, called DeepRecon, into its 3D XRM workflow. Compared with the conventional standard algorithm, this approach enhances image quality by up to four times [Figure 8C] and, in specific scenarios, increases throughput by as much as tenfold^[265,266]. Certain materials, such as metal foam, can only be subjected to 3D scanning with a minimal field of view, thereby impeding the reconstruction process. Zhang et al. used optimized neuroimplicit X-ray imaging (ONIX)^[267]. This DL algorithm can retrieve continuous 3D object representations from limited views, to enhance the volumetric information and capabilities of 3D X-ray stereoscopic imaging.

The application of ML in designing and optimising electronic packaging structures is gaining momentum. ML offers powerful new approaches, from optimizing PCB stacking to enhancing 3D structure analysis through X-rays. However, the main difficulties are seamlessly integrating ML into complex CAD and FEA workflows and embedding key physics-based constraints into data-driven models. Furthermore, generating sufficient high-quality data and ensuring the interpretability of ML-driven designs are also persistent issues. The future direction may involve more complex generative design methods (using GANs or reinforcement learning), multi-objective optimization frameworks that balance thermal, mechanical, and electrical performance, and closer integration between ML-driven design and advanced destructive analysis.