Detection and Prediction of Probe Mark Damage in Wafer Testing

Abstract

In wafer testing, the test probe needs to contact the surface of the semiconductor wafer to measure electrical parameters such as resistance, capacitance, and current. The probe mark damage frequently occurs on the machine during wafer testing. This phenomenon causes inaccuracies in electrical parameter testing, significantly reducing the yield in IC packaging processes and resulting in substantial manufacturing cost losses. Therefore, this study proposed an effective probe mark damage detection and prediction method to prevent significant yield reduction due to inaccurate testing. This study uses importance analysis from random forests and correlation analysis to identify the critical parameters influencing probe mark damage. Introducing these parameters into a Sparse Transformer with hybrid normalization can successfully train an intelligent model for predicting the occurrence of probe mark damage. The model accurately predicts the probability of probe mark damage and promptly adjusts machine parameters to avoid inaccuracies in electrical parameter settings. The proposed approach can outperform other methods, achieving two very high accuracies of 95.1% (at room temperature) and 93.5% (at high temperature) and significantly reducing the occurrence of large-area probe mark damage.

1. Introduction

In modern semiconductor manufacturing, wafer testing is a crucial process affecting the final product quality and production efficiency. During this process, the probe mark is one of the essential components for inspecting wafers. It is a mark created at test points through specific techniques during wafer manufacturing, used to identify wafer locations and test points accurately. Test engineers rely on the position of the probe mark to perform high-precision measurements and evaluation of process characteristics and electrical verification tests on test points on the wafer. Suppose the probe mark position is inaccurate or unclear. In that case, the test engineer may be unable to locate the test points on the wafer, leading to test failures, increased testing time and costs, and even affecting the overall quality of the wafer. Therefore, ensuring the precision and clarity of probe marks is a core issue that wafer manufacturers must address. Manufacturers must analyze extensive machine-generated data during wafer testing to determine signs or commonalities before probe mark damage [1] occurs. If we can identify these signs, wafer manufacturers can implement preventive measures early to reduce manufacturing cost losses during IC packaging and testing.

Figure 1 is the analysis process required to predict the occurrence of probe mark damage. This study will first extract the data flow and implement the blocks of mapped data from the organized database. Then, the next step uses random forest important analysis [2] to select important parameters from the machine operation parameters. Then, the following step uses correlation analysis [3] to screen out critical parameters from the important parameters. Furthermore, the experiment uses min–max normalization [4] to scale the size of the critical parameters linearly. After that, we input the critical parameters into the prediction model for training and testing to predict the probability of probe mark damage occurrence. In wafer testing, the prober can predict the possible occurrence of probe mark damage based on the trained model and promptly adjust the critical parameters of the machine operation to reduce the occurrence of subsequent probe mark damage.

Figure 2 shows the model of the testing machine TSK3-194 used in the packaging process within the semiconductor plant. Figure 3 displays that this machine has a high-precision probe system and measurement equipment capable of controlling wafer temperature, automating test procedures, adjusting probe pressure and position, measuring electrical parameters, and collecting test data. During the testing process, the machine places the wafer on the test platform and performs tests on the wafer according to the pre-set procedures defined by the operator. It records the interactions between the probe and the wafer surface. After testing, the machine can record the corresponding test parameters and probe mark images to facilitate subsequent analysis for good product yield, ensuring better yield rates in the packaging process. Semiconductor fab provides data about the setting values of wafer testing machine parameters and the corresponding results of using probe marks in wafer testing. These data are machine log data, not images. According to these data, this study proposes a method to predict the correlation between machine parameter settings and probe marking accuracy in wafer testing.

Big data analytics often apply correlation analysis methods such as Spearman [5] and Pearson [6] when exploring how to effectively predict and prevent probe mark damage. These methods help engineers understand the correlation between different parameters, thereby identifying key factors that affect the probe mark. Choosing the appropriate correlation analysis method is crucial, depending on the nature of the data. For example, for linear and continuous data, the Pearson correlation coefficient is an ideal choice; for nonlinear or discrete data, the Spearman correlation coefficient is more suitable. However, with the rapid data volume growth in wafer manufacturing and testing processes, traditional correlation analysis methods have gradually shown their limitations. The application of modern deep learning techniques supports a novel method of solving this problem. Through deep learning models, data analysts can analyze and process large amounts of high-dimensional manufacturing and testing data to more accurately predict and prevent the occurrence of probe mark damage. This paper will discuss several commonly used deep learning models and their applications in probe mark damage analysis, including the Deep and Cross Network (DCN) [7], the Deep Neural Network (DNN) [8], Autoencoder [9], Stacked Autoencoder (SAE) [10], XLNet [11], Transformer [12], and Sparse Transformer [13].

The Deep and Cross Network (DCN) combines the advantages of Deep Neural Networks (DNN) and Cross Networks, allowing it to automatically learn high-order and low-order feature interactions. DCN is particularly suitable for handling data with complex interaction features. For example, complex nonlinear interactions may exist between different environmental and manufacturing parameters in probe mark damage analysis. Through DCN operation, these interaction features can be captured, thereby improving the model prediction accuracy. Furthermore, the Deep Neural Network (DNN) is a deep learning model composed of multiple layers of neurons capable of learning complex patterns and features from data. DNN performs excellently in handling nonlinear and high-dimensional data, making it widely used in probe mark damage analysis. Training a DNN model can effectively predict the probability of probe mark damage, allowing for timely preventive measures to reduce risk.

A Stacked Autoencoder (SAE) is an autoencoder structure that learns deep features of data through multiple Stacked Autoencoders. SAE excels in unsupervised learning and feature extraction, making it suitable for data preprocessing and dimensionality reduction. In probe mark damage analysis, we can use SAE to extract high-order features of the data, further improving the prediction model performance. XLNet is an improved Transformer model that integrates autoregressive models and bidirectional Transformers [14] to achieve higher prediction accuracy. XLNet has advantages in handling sequential data and sequence prediction and can analyze temporal changes in the manufacturing process to predict probe mark damage. This characteristic makes XLNet particularly important in wafer testing, where the case considered time factors. Autoencoders, through unsupervised learning, can learn low-dimensional representations of data. By compressing data into a low-dimensional space and then reconstructing it, Autoencoder can effectively extract the main features of the data. In probe mark damage analysis, Autoencoder can be used for dimensionality reduction and feature extraction, thereby improving the accuracy of the prediction model.

The Sparse Transformer is an improved Transformer that uses sparse attention mechanisms to reduce computational load. Since its introduction, the Transformer model has gained popularity for its excellent performance in natural language processing (NLP) tasks. However, the computational cost of standard Transformers is very high, limiting their application on large datasets. To solve this problem, the Sparse Transformer effectively reduces computational load through a sparse attention mechanism while maintaining model performance. In wafer testing, a Sparse Transformer can analyze large amounts of high-dimensional data to find critical parameters that affect the position and quality of probe marks. Finally, this study adopts a hybrid method combining batch normalization [15] and layer normalization [16] techniques in the Sparse Transformer model. As a result, the Sparse Transformer model with hybrid normalization technology outperforms all the other models mentioned above in execution performance. This study aims to significantly improve the accuracy of probe mark damage detection and prediction and provide more accurate identification of critical parameters affecting the position of the probe mark in the manufacturing process. The proposed one allows for early countermeasures to adjust machine operation modes, thereby reducing manufacturing cost losses and improving overall manufacturing yield.

2. Related Work

2.1. Literature Review

In semiconductor manufacturing, it is common practice to evaluate the effects of different parameters on process outcomes in advance to reduce the likelihood of damage. These studies typically focus on the relationships between process parameters, equipment parameters, test conditions, and process stability and use methods such as correlation analysis and random forest to identify critical factors that may affect product yield. By incorporating these parameters into models, it becomes possible to predict the occurrence of damage more accurately.

Firstly, Chang et al. [17] demonstrated the correlation between process parameters and product yield. They evaluated how factors such as temperature, pressure, and chemical concentration during the process affected semiconductor product yield and identified vital process parameters for optimization through correlation analysis. Their findings showed that the interaction between process parameters significantly impacted the final product quality, and the fab can apply such discoveries in-process adjustments to improve yield. Various process parameters also influence wafer testing, and through correlation analysis, the relationship between these parameters and probe damage can be identified, thereby improving overall product yield during the wafer testing phase. Secondly, Kim et al. [18] explored the relationship between equipment parameters and process stability, emphasizing the importance of equipment parameters (e.g., machine operating speed) in maintaining process consistency. Variations in equipment parameters often lead to instability in the process, affecting product quality and yield. The study indicated that deeply analyzing equipment parameters makes identifying factors significantly impacting process stability possible, which can help optimize equipment adjustments. In addition, Li et al. [19] focused on analyzing damage parameters. They examined the relationship between different process parameters and damage occurrence rates and proposed a model to predict damage risk. This method is directly applicable to the current study, as it provides a point of reference for comparing their analysis of process parameters with the model predictions in this study, which can help improve the accuracy of the model the authors of the current work use.

Furthermore, random forest provides a powerful tool for feature selection and model optimization when dealing with multidimensional parameters in industrial processes. By constructing multiple decision trees, random forest calculates the impact of each feature on the model prediction accuracy, allowing for the accurate identification of the most influential parameters, thereby improving the model prediction accuracy and interpretability. Moreover, Sandri et al. [20] employed the permutation method within random forests to assess feature importance, offering a stable and effective variable selection method even in complex industrial environments. Further, Strobl et al. [21] discussed the stability of feature ranking in random forest, which is crucial for process optimization involving many parameters. Finally, Chen et al. [22] explained the correlation between the model and parameters, especially in the context of improving test efficiency. They successfully identified key parameters by conducting correlation analysis on experimental parameters, which helped to reduce the time required for testing.

2.2. The Deep and Cross Network

Figure 4 illustrates the Deep and Cross Network (DCN) [7] architecture, which is a novel model that combines traditional Deep Neural Networks (DNN) and Cross Networks. First, we input a feature map (left blue area), and then a convolution operation generates an offset field (middle part of the figure). This offset field determines the sampling positions of each convolution kernel. After developing these offset fields, the deformable convolution dynamically adjusts its sampling points based on these offsets, allowing the convolution process to capture irregular shapes or highly variable features, thereby enhancing the ability to capture complex data. The advantage of deformable convolution lies in its ability to learn and dynamically adjust the sampling positions of the convolution kernel, adapting to different shapes and structures of the input data. This part allows the network to accurately capture valuable features when dealing with irregular shapes. The network mainly uses the deformable convolution architecture to learn high-order nonlinear relationships between features. It can capture complex patterns and feature combinations in the data through multiple layers of neurons with linear transformations and nonlinear activation functions. Finally, the outputs of these two paths are fused in the final layer of the model to produce the prediction results.

2.3. The Deep Neural Network

Figure 5 shows a standard and powerful deep learning model, the Deep Neural Network (DNN) [8], widely used to address various machine learning problems. The DNN model consists of multiple neuron layers, often called hidden layers. Neurons in each hidden layer transmit signals and extract features through weights and activation functions. In a DNN, data first pass through the input layer and then progress layer by layer to the hidden layers. Each neuron in a hidden layer performs a weighted sum of the outputs from the previous layer and transforms this sum using a nonlinear activation function (such as ReLU or Sigmoid). This process enables the DNN to capture nonlinear features and complex patterns in the data. The number of hidden layers and the number of neurons in each layer are crucial parameters in designing a DNN, as these choices impact the model learning capacity and computational complexity. Increasing the number of layers of DNN can learn higher-level abstract features. Still, it also faces the risk of overfitting, which needs mitigation through regularization techniques (such as dropout or L2 regularization).

The training process of a DNN typically involves the backpropagation algorithm and Gradient Descent. The backpropagation algorithm calculates the gradient of the loss function, propagates the error backward from the output layer to the input layer, and updates the weights to minimize the loss function. This iterative update process is repeated on the training data until the model performance meets expectations. The DNN component is primarily responsible for learning high-level nonlinear representations of the input features. By constructing a multi-layer hidden structure, the model can capture complex patterns in the data and effectively enhance predictive performance. During this process, we adopted appropriate regularization techniques and optimization algorithms to ensure the stability and generalization ability of the model.

2.4. The Autoencoder

An Autoencoder [9] is an unsupervised learning model explicitly designed for learning compact representations of data, and we can use it to reconstruct the original data, as illustrated in Figure 6. This model comprises two main components: the encoder and the decoder. The primary function of the encoder is to take the input data and transform it into a latent representation or encoding, which is typically a lower-dimensional vector that captures the essential features of the input data. This process is achieved through a series of linear and nonlinear transformations, aiming to extract the core information of the data while reducing redundancy.

In this experimental process, the Autoencoder minimizes the reconstruction error between the input and reconstructed data, using Mean Squared Error (MSE) as the loss function. By learning an adequate representation of the data, the model can significantly reduce the dimensionality of the data while preserving its essential features, which is particularly useful for handling high-dimensional data.

2.5. The Stacked Autoencoder

The Stacked Autoencoder (SAE) [10] comprises multiple Autoencoders stacked layer by layer, with each Autoencoder input being the hidden representation from the previous Autoencoder, as shown in Figure 7. This multi-layered structure allows the SAE to learn multi-level feature representations of the data. In our study, the primary role of the SAE model is to perform feature extraction and dimensionality reduction on the input data, providing more representative features for subsequent machine learning tasks. Stacking multiple Autoencoders can capture complex structures and patterns within the data, thereby enhancing the model prediction performance and stability.

2.6. XLNet

XLNet [11] is a natural language processing model based on the Transformer architecture, developed by the Google research team and released in 2019. The Google research team designed it to improve the BERT (Bidirectional Encoder Representations from Transformers) [23] model, addressing some of the limitations inherent in BERT, as illustrated in Figure 8. XLNet enhances model performance and effectiveness by introducing autoregressive properties and Permutation Language Modeling.

One of the core innovations of XLNet is Permutation Language Modeling [24]. This approach considers bidirectional context and learns the language model by considering all possible permutations of the input sequence. During training, XLNet randomly shuffles the order of the input sequence, allowing the model to learn from different permutation orders. This technique helps better capture long-range dependencies between words, effectively overcoming the limitations of BERT and enhancing the expressiveness of the model.

2.7. The Transformer

The Transformer [12] primarily aims to deal with natural language processing (NLP) and other tasks involving sequential data, as illustrated in Figure 9. The Transformer model mainly comprises the encoder and the decoder. The left half represents the encoder, composed of Nx = 6 identical blocks. Each layer contains two sub-layers. The first sub-layer is a multi-head attention layer [14], as shown in Figure 9. In this multi-head attention layer, the critical parameter sequence X is linearly transformed and projected into query, key, and value matrices. The query matrix extracts the Important parameters from the input sequence, the key matrix records all parameters in the input sequence, and the value matrix corresponds to the weighted values of each parameter. Finally, all attention results are combined to produce the final output matrix W.

Additionally, the encoder part of the Transformer model includes a self-attention sublayer [25], where the query, key, and value matrices are the same as those in the multi-head attention. A simple, fully connected sublayer [26] follows this sublayer. The right half of the Transformer model represents the decoder, which is also composed of Nx = 6 identical blocks. Each layer comprises a self-attention sublayer, an encoder–decoder attention sublayer, and a fully connected sublayer. The exact attention mechanism is applied in the self-attention sublayer, performing masked multi-head attention on the input sequence. The encoder–decoder attention sublayer then applies multi-head attention to the self-attention sublayer output and the encoder production to capture the relationship between the two. Finally, the fully connected sublayer maps the result of the multi-head attention calculation to the final prediction output.

3. Research Methods

The signals generated during the wafer testing process can produce numerous datasets. People can identify trends in data distribution using data visualization, and wafer testing can apply random forest importance analysis [2] to search important parameters. Afterward, this study uses Pearson correlation analysis [3] to check dependencies among important parameters and finally screen out critical ones (i.e., critical parameters). The wafer testing stage can monitor them to discover patterns of critical parameter changes before and after probe mark damage. Timely adjustments to critical parameters can help prevent probe mark damage and improve the yield of wafer testing. Therefore, this section will propose methods for building predictive models and implementing processes to solve the large-scale probe mark damage issue.

3.1. Probe Marking Illustration in Wafer Testing

A few probe mark images provided by a semiconductor fab in Taiwan, where the cross marks in the images indicate the traces or marks left by the probes on the wafer surface, as shown in Figure 10. The probes usually mark specific areas on the surface to facilitate subsequent wafer testing. The machines generated these images in the wafer factory during wafer testing. However, factors such as machine voltage settings, environmental contamination, and other factors may cause probe misalignment or damage, as illustrated in Figure 11. Inspectors first analyze the probe mark images of a single wafer to assess the contact condition and pressure distribution between the probe and the wafer surface. This analysis helps identify potential probe misalignment or damage, which can guide subsequent troubleshooting or adjustment of testing parameters.

3.2. Random Forest and Importance Analysis

We collected wafer testing related machine log data with 2713 data points at room temperature where the parameters included Count by Lot, Number of Contacts, Needle Tip Min, Needle Tip Max, Probing Overdrive, Chuck Temperature, Die Interval, Overdrive Value, Needle Tip Ave, Cleaning Unit Height, Cleaning Overdrive, pb_height, and Probe Card Clean Cnt. Similarly, at high temperatures, machines have parameters such as Probing Overdrive, Needle Tip Min, Needle Tip Max, Needle Tip Ave, Alignment End Position, Number of Contacts, Probing Overdrive, and pb_height. The label pb_height denotes the height of suspended probes and probe pads. Machines collected 1452 data points at room and 1261 high temperatures. We analyzed data using a random forest and importance analyses of these data points. Then, we examined the decision criteria for each Important parameter in different decision trees [27], as shown in Figure 12. We observed the various parameter values corresponding to normal and abnormal conditions based on the decision criteria at each node in the decision tree.

In Figure 12a, we found that the Needle Tip Min parameter in the room temperature decision tree had 1415 data points with values less than 210.5 µm, identified as damage. Therefore, the Needle Tip Min parameter is critical for determining whether probe mark damage occurs under room-temperature conditions. In Figure 12b, we observed that the Probing Overdrive parameter in the high temperatures decision tree had 247 data points with values less than 22.5 µm, identified as damage. Consequently, the Probing Overdrive parameter is crucial for assessing whether probe mark damage occurs under high temperatures.

Finally, the analysis results allowed us to rank the importance of several key parameters in the random forest model for both room and high temperatures, as shown in Table 1 and Table 2. This study makes the quantitative criterion for important parameters: the importance out of random forest importance analysis must be greater than 0.01. The analysis reduced the original set of 13 room-temperature parameters and seven high-temperature parameters to 8 important room-temperature and five high-temperature important parameters through random forest selection. These Important parameters, listed in Table 1 and Table 2, will serve as a critical basis for the next step in correlation analysis to identify key parameters.

3.3. Correlation Analysis

Using the important parameters filtered through the random forest and importance analysis from the previous section, we introduced correlation analysis to identify the critical parameters needed to build a predictive model. Before the random forest and importance analysis, Figure 13a shows that the correlation matrix [25] and reveals parameters highly correlated with damage, including Number of Contacts, Needle Tip Ave, Needle Tip Min, Needle Tip Max, pb_height, Probing Overdrive, Count by Lot, Alignment end position, Probe Card Clean Cnt, and Overdrive Value.

After the random forest and importance analysis, Figure 13b demonstrates that the correlation matrix can identify the key parameters highly correlated with damage, precisely Number of Contacts, Needle Tip Ave, Needle Tip Min, Needle Tip Max, pb_height, Probing Overdrive, and Alignment end position.

Under room-temperature conditions, Figure 13c shows that the correlation between Number of Contacts, Needle Tip Min, and pb_height is low, indicating that their mutual influence is limited. Therefore, these three parameters are considered independent critical parameters. Additionally, under high-temperature conditions, Figure 13d illustrates that the correlation between Number of Contacts and Probing Overdrive is low, suggesting limited mutual influence between these parameters. Thus, the analysis result considered them independent critical parameters.

3.4. Batch Normalization

The Sparse Transformer has employed the normalization module [28] in it, a commonly used technique in deep learning models. As the depth of a neural network increases, the distribution of inputs and outputs can change, which may lead to issues such as vanishing or exploding gradients during training. The normalization module not only addresses these problems but also accelerates the convergence of the model during training, enhancing both the training efficiency and generalization capability of the model. Figure 14 illustrates the batch normalization (BN) method, which normalizes the size of channel data. BN not only improves the training efficiency of the model but also allows the use of a higher learning rate during training, thereby speeding up convergence.

Equation (1) describes batch normalization, where x is the input, y is the output, and γ is the channel scaling parameter for normalization (ranging from 0 to 1), with an initial setting of 1. The value of γ is then updated based on the model loss function, fine-tuned within the range of 0.1 to 10. The larger the loss function, the smaller the value of γ, reducing its influence to help the model achieve better performance on the training data.

Equation (2) shows the weight values for batch normalization, where ${\mathsf{\omega }}_i$ represents the weight of the $i$th element. The numerator ${\gamma }_i$ is the scaling parameter for the $i$th normalization channel, and the denominator is the sum of the values of all elements. The goal is to normalize the metric of each element into a weight, ensuring that the sum of the weights of all elements equals 1, thereby ensuring an appropriate distribution of attention to each element.

(1)$y={\displaystyle \frac{x·\gamma -E\left[x·\gamma \right]}{\sqrt{Var\left[x·\gamma \right]}}}$

(2)${\mathsf{\omega }}_i={\displaystyle \frac{{\gamma }_i}{{\sum }_{j=0}{\gamma }_j}}$

3.5. Layer Normalization

Figure 15 illustrates the method of layer normalization (LN), which normalizes the features across a batch rather than normalizing the entire batch. This approach reduces the instability in training caused by varying data distributions within the batch due to changes in value sizes. LN helps improve the training effectiveness of the model, making it more stable and accurate compared to batch normalization.

Equation (3) explains layer normalization, where x is the input, y is the output, $\gamma$ is the channel scaling parameter for normalization, and β is the shift parameter. The primary purpose of β is to adjust the normalized value when the calculated normalization value equals zero, thereby improving the generalization capability of the model.

Equation (4) displays the weight values for layer normalization, where ${\gamma }_k$ represents the scaling parameter for the $k$th normalization channel, ${\mathsf{\omega }}_k$ stands for the weight of the ${\gamma }_k$, and the denominator is the sum of the values of all elements. The goal is to normalize the metric of each element into a weight, ensuring that the sum of the weights of all elements equals 1. Equation (4) provides an appropriate distribution of attention to each element.

(3)$y={\displaystyle \frac{x-E\left[x\right]}{\sqrt{Var\left[x\right]+ϵ}}}\times \gamma +\beta$

(4)${\mathsf{\omega }}_k={\displaystyle \frac{{\gamma }_k}{{\sum }_{l=0}{\gamma }_l}}$

3.6. Hybrid Normalization

Although batch normalization effectively addresses the issue of exploding gradients, it may still lead to training instability due to vanishing or exploding gradients. On the other hand, while layer normalization increases stability, it tends to be more time-consuming than batch normalization, resulting in lower efficiency. To combine the strengths of both methods, we propose a hybrid normalization (HN) approach, as illustrated in Figure 16. This method considers both batch and layer-level statistical information. By integrating the outputs of batch normalization and layer normalization, HN achieves excellent stability and efficiency when handling feature parameters across different batches.

Equation (5) denotes the loss function cross-entropy loss [29], where $N$ represents the number of samples, $C$ stands for the number of classes, $y_{i,c}$ indicates the label of the $i$th sample in the c class (using one-hot encoding), and $z_{i,c}$ is the model predicted probability for the $c$ class. Equation (6) means hybrid normalization, where $x$ is the input, $y$ is the output, and $\alpha$ is the weight adjustment coefficient. If the loss is greater than 0.5, then $\alpha =0$; otherwise, if the loss is less than or equal to 0.5, then $\alpha =1$.

(5)$loss=-{\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{\sum }_{c=1}^C{y}_{i,c}·log\left(z_{i,c}\right)$

(6)$y=\alpha \times BN\left(x\right)+\left(1-\alpha \right)\times LN\left(x\right),\hspace{0.17em}\left\{\begin{array}{l}\alpha =0,\hspace{0.17em}loss>0.5\\ \alpha =1,\hspace{0.17em}loss\le 0.5\end{array}\right.$

3.7. Build Sparse Transformer with Hybrid Normalization

In this experiment, we construct a Sparse Transformer model [13] with hybrid normalization, denoted as the HN Sparse Transformer model, as shown in Figure 17. Figure 17a illustrates that the model comprises two main components: an encoder and a decoder. On the left side, the encoder consists of Nx = 6 identical blocks containing two sublayers: a sparse multi-head attention sublayer with a normalization module and a simple, fully connected sublayer. The sparse multi-head attention sublayer linearly transforms the key parameter sequence X into query, key, and value matrices. The normalization module employs hybrid normalization to prevent gradient explosion or vanishing issues. Finally, all the attention results are combined to produce the output matrix W. The decoder is on the right half and consists of Nx = 6 identical blocks. Each layer contains three sublayers: the self-attention sublayer, the encoder–decoder attention sublayer, and the fully connected sublayer. This one uses the exact attention mechanism in the self-attention layer to perform masked multi-head attention and hybrid normalization on the input sequence. Additionally, Figure 17b illustrates the model input–output relationship at room temperature, while Figure 17c shows the input–output relationship at high temperature.

We also replaced the attention mechanism in the Transformer model with a sparse attention mechanism [30,31]. The original attention mechanism has a computational complexity of O(n²), which requires significant memory and computation time when processing long sequences. Sparse attention can reduce the computational complexity to O(n), which decreases memory usage and solves the problem of excessive computation time when handling long sequences. The main advantages of the sparse attention mechanism are as follows:

1. Increased computational efficiency: Sparse attention [30,31] significantly reduces computational and storage costs. In traditional self-attention mechanisms, computing attention scores between all inputs can become expensive, especially when dealing with long sequences. Sparse attention, however, only computes attention scores for a few critical positions with high attention scores, drastically reducing computation and improving efficiency.

2. Suitability for long sequences: Sparse attention outperforms traditional self-attention mechanisms when processing long sequences. The relative distances are large in long sequences, and long-term dependencies may limit self-attention. Sparse attention introduces a mechanism for selecting intervals, allowing the model to ignore unimportant or redundant information, which helps better capture long-term dependencies.

3. Improved generalization: Sparse attention helps reduce the risk of overfitting [32] because it focuses more on essential features. This portion is particularly beneficial when the sample size is small, as it enables the model to generalize new data better.

This method also introduces hybrid normalization. In Deep Neural Networks, as the number of layers increases, the distribution of input and output signals may change, potentially leading to issues such as gradient vanishing or explosion during training. Hybrid normalization can address these issues, making the model more accurate when processing long sequence data.

Algorithm 1 describes the steps for handling normalization in the HN Sparse Transformer. First, this algorithm calculates the sparse multi-head attention between the decoder current layer output X and the encoder final output, generating the context vector. Hybrid normalization is performed on this output, combining the advantages of batch and layer normalization. Next step adds the hybrid normalized output to the input X and normalize it to obtain the result. Then, this result is passed through the feedforward neural network to obtain the output. We calculate the right-shifted masked sparse multi-head attention to ensure the decoder does not see future positions and obtain the result. The following step maps the final output of the decoder to the output space through a linear transformation. Finally, this algorithm converts the result of the linear transformation into a probability distribution using the Softmax function, generating the final output probability sequence Y.

Algorithm 1: HN Sparse Transformer Algorithm

Input: High-dimensional parameter vector sequence XOutput: Sequence of probabilities for Probe Mark Damage occurrence Y Sparse Multi-Head Attention This step calculates the attention weights for each decoder output position by combining the current layer output X from the decoder with the final output from the encoder, generating the context vector A. Hybrid Normalization Apply hybrid normalization to the output of the sparse multi-head attention. AddNorm Add the hybrid normalized output to the input X and perform normalization. FeedForward Process the output from the addition and normalization through a feedforward neural network. Masked Sparse MultiHead Attention Calculate the right-shifted masked sparse multi-head attention to ensure that the decoder cannot see future positions. Linear Map the final output of the decoder to the output space through a linear transformation. Softmax Convert the result of the linear transformation into a probability distribution using the Softmax function, generating the final output probability sequence Y.

4. Experimental Results and Discussion

This section first introduces the sources of company characteristic data and the software packages used for the experiment. It then presents the results of using key probe mark parameters to adjust and improve the wafer probe mark. Finally, by aggregating the critical parameters into a high-dimensional parameter vector, we can input this information into a Sparse Transformer model to predict potential probe mark damage and compare the accuracy and parameter predictions among them.

4.1. Experimental Environment

Table 3 shows the hardware specifications used in this experiment. Table 4 describes the software packages used in the experiment applications. Data preprocessing uses the Pandas and Numpy software packages [33] in applications. Building deep learning models utilizes TensorFlow and Keras for modeling. Finally, visualizing and displaying the experimental results applies the Matplotlib or Pyplot software packages [34].

4.2. Data Collection

First, machines have logged various signal data generated by the wafer testing equipment, including machine voltage, the number of probe contact points, temperature, testing time, and test results. For instance, Figure 18 and Figure 19 can help illustrate these signals provide valuable information, which can help us analyze and predict the likelihood of probe mark damage. In the next step, we collected the machine log data and saved it in tabular format for easy processing and analysis. Next, this study will preprocess these sampled data. Preprocessing includes cleaning data, filling in missing values, normalizing data, and feature engineering. These steps ensure the completeness and consistency of the data, thereby improving the effectiveness of model training. For instance, data clearing can filter and correct outliers in the data using statistical methods or machine learning algorithms. Different normalization methods, such as min–max or z-score normalization, will be applied to various signal data types to ensure the data values fall within an appropriate range.

After data preprocessing, data transformation will organize the collected data into input and output formats suitable for detection and prediction models. The input data in the experiment consists of feature vectors of critical parameters, while the output data represents the predicted probability of probe mark damage. Specifically, we need to collect various signal data generated by the wafer testing equipment, including 13 signals—Count by Lot, Number of Contacts, Needle Tip Min, Needle Tip Max, Probing Overdrive, Chuck Temperature, Die Interval, Overdrive Value, Needle Tip Ave, Cleaning Unit Height, Cleaning Overdrive, pb_height, and Probe Card Clean Cnt. Data collection received a total of 1452 data points at room temperature and 1261 data points at high temperature. This data helps analyze and predict the probability of probe mark damage occurrence. We stored the data in tabular format for easy processing and analysis.

4.3. Settings for Probe Mark Damage Prediction

This study employs a Sparse Transformer model to predict probe mark damage. The original model consists of a Transformer Encoder and a Transformer Decoder, each with three layers: Multi-Head Attention, dropout, and Layer Normalization. We replaced the self-attention mechanism with sparse attention, as illustrated in Figure 17a. This modification reduces the computational and storage costs associated with the traditional self-attention mechanism, shortens training time, and effectively enhances the model prediction accuracy.

In the training, data allocation used 80% of the 1452 room-temperature data points as the training set (1161 points) and 20% as the validation set (291 points). Similarly, we used 80% of the 1261 high-temperature data points as the training set (1008 points) and 20% as the validation set (253 points). Cross-validation [35] was employed with the chosen k = 5 folds during training and validation to provide a more comprehensive evaluation, helping us better understand the model performance and generalization capabilities. In the testing, data assignment used a test dataset consisting of 2000 room-temperature and 2000 high-temperature data points, each containing the corresponding front-end and back-end probe mark signals, to evaluate the performance of the trained HN Sparse Transformer model. This approach expects to increase the accuracy and efficiency of predicting the probability of probe mark damage through these adjustments and optimizations.

Regarding the parameter settings of the prediction model, each Transformer Decoder also includes a Dense layer. The Mean Squared Error (MSE) is the loss function, and Adam is the optimizer. Setting an early stopping criterion can prevent overfitting, where training would terminate if accuracy did not improve after 10 iterations. This experiment set the batch size to 64 and the maximum number of training iterations to 50. For model tuning, the experiment employed hyperparameter tuning techniques to optimize model performance. This case defined a set of hyperparameter ranges, including 14 layers, 4 attention heads, and a dropout rate of 0.1. For the model architecture, this study experimented with different Transformer configurations, such as increasing the number of layers, adjusting the number of attention heads, and altering hidden layer dimensions. We also considered enhancing the model expressiveness by using different activation functions like ReLU and the sparse attention mechanism. In this experiment, we also used a hybrid normalization method, which considers batch and layer statistics by combining batch and layer normalization outputs. This approach improves the model convergence speed and overall efficiency when processing feature parameters across different batches. Additionally, we replaced the attention mechanism in the Transformer model with sparse attention, which reduces computational and storage costs, shortens training time, and effectively enhances model accuracy.

4.4. Experimental Results

After aggregating the critical parameters into a high-dimensional parameter vector, we input this information into a pre-trained prediction model to predict potential probe mark damage and evaluate the model prediction accuracy. Therefore, the experiment used a pre-trained prediction model to predict probe marks and reduce potential probe mark damage.

In wafer testing, data formation aggregated the critical parameters into a high-dimensional parameter vector, fed into a pre-trained prediction model to predict potential probe mark damage. This study proposed a control experiment approach: in the first process, the machine conducted wafer testing without adjusting the critical parameters. In the second process, once the predicted potential probe mark damage may occur in wafer testing, the on-site engineer can then adjust the machine’s critical parameters in a timely manner. Hopefully, this adjustment can effectively reduce the number of probe mark damages on the probe pad afterward.

We tested the trained models through a test dataset. Loss represents a root-mean-square value, and Accuracy is the ratio of the number of samples correctly classified by the classifier to the total number of samples. It indicated that the loss decreased and the accuracy increased, indicating that the more tests conducted, the better the model improved its fit and inference accuracy with the data. At room temperature, in Figure 20 and Figure 21, after testing with the DCN, DNN, SAE, XLNet, AE, Transformer, Sparse Transformer, and hybrid normalization Sparse Transformer models, the model prediction accuracy were 82.7%, 87.1%, 88.6%, 85.3%, 89.4%, 91.7%, 93.9%, and 95.1%, respectively. On the other hand, at high temperature, the model prediction accuracy were 83.2%, 84.8%, 86.3%, 85.5%, 85.3%, 88.1%, 91.4%, and 93.5%, respectively. Following these, this study can confirm that we trained all models successfully. In Figure 20 and Figure 21, dnn represents DNN, dcn stands for DCN, sae denotes SAE, xlnet implies XLNet, ae means AE, tf indicates Transformer, stf shows Sparse Transformer, and hnstf is hybrid normalization Sparse Transformer.

4.5. Performance Comparison

By comparing the performance indexes of Accuracy and RMSE of various deep learning models and the computing efficiency of Time-Complexity [36], we can evaluate the performance of each model in this experiment. At room and high temperatures, the performance evaluation showcases the Accuracy, Loss, and Time-Complexity metrics of eight models, including DCN, DNN, SAE, XLNet, Autoencoder, Transformer, Sparse Transformer, and HN Sparse Transformer. These metrics are presented separately in Table 5 and Table 6.

4.6. Discussion

The experimental results show that the proposed hybrid normalization Sparse Transformer model can accurately predict probe mark damage. The proposed approach achieved the accuracy of 95.1% (at room temperature) and 93.5% (at high temperature) in predicting probe mark damage, significantly outperforming other methods. This fact demonstrates that using Sparse Transformer technology combined with a hybrid normalization strategy can notably improve the model prediction accuracy and stability. Examining the performance of various models finds that the approach proposed in this study can predict probe mark damage more accurately, providing real-time warnings that enable timely adjustments to machine parameters during the process, which is highly beneficial for improving wafer test yield. In addition, the method shows adaptability to different environmental conditions based on training and testing results under both room temperature and high temperature. The model maintains its prediction accuracy and efficiency under normal or high-temperature conditions. This adaptability further overcomes the limitations of traditional models that may be restricted to specific temperatures, ensuring that we can widely apply the model across various manufacturing environments.

Chang et al. [17] emphasized the influence of process parameters on product yield. Through correlation analysis, they identified critical factors, such as temperature, pressure, and chemical concentration, which impact the final product quality. Similarly, this experiment also found that parameters play a critical role in cases of high probe mark damage occurrence, with specific parameters significantly affecting predicting damage. Moreover, Kim et al. [18] argued that equipment parameters are crucial for experimental stability and emphasized that optimizing equipment can reduce the likelihood of probe mark damage. However, our experiment found that even when equipment remains stable, probe mark damage still occurs, suggesting that other potential factors have a more significant influence than equipment adjustments. This case indicates that optimizing equipment alone is not the only solution to reducing the occurrence of damage. Li et al. [19] conducted a correlation analysis of process parameters. They found that the interaction between parameters significantly impacted experimental prediction results, which was highly beneficial for our experiment. Sandri et al. [20] introduced the use of random forest for feature importance analysis to identify key parameters, and we employed a similar approach in this experiment to determine critical process parameters that significantly impacted the prediction results for probe mark damage. Strobl et al. [21] proposed a classification tree method based on the Gini Index, and we also adopted a similar classification method to select key parameters and evaluate their impact on probe mark damage. Chen et al. [22] explored the correlation of testing parameters in semiconductor experiments. They noted that specific parameters significantly affect the final prediction results during the product testing phase. This outcome aligns with part of our experimental findings. However, our experiment emphasizes critical parameters, unlike Chen et al., who focused on testing phase parameters. The results show a strong correlation between key process parameters and testing parameters in influencing the occurrence of probe mark damage.

The experiment of this study also encountered some limitations. First, during the probe mark process on the machinery, the completeness and time range of the data are crucial for ensuring the reliability and accuracy of the experimental results. Since the fab uses machines purchased earlier, some of the data generated by the machines were incomplete, requiring manual intervention to fill in the missing values. Additionally, the amount of high-temperature data collected was smaller than the normal-temperature data, leading to imbalanced training data and varying reliability in the models created. Furthermore, this study only utilized data from two consecutive months rather than data covering a complete product manufacturing cycle or an entire year. The limited period of the data may not adequately reflect long-term trends in the production process. To address this, further expanding the scale and diversity of collected data is necessary to enhance training effectiveness and improve prediction accuracy. In addition, while we employed hybrid normalization techniques to process the data, the appropriate selection of normalization methods is crucial. Currently, the proposed approach checks whether the loss value is a threshold for selecting the normalization technique. This binary division may not fully capture the different characteristics within the data. For instance, when the data are simple, excessive use of batch normalization may lead to poor training results. In contrast, overusing layer normalization on relatively complex datasets might decrease efficiency. To improve this situation, we must look for novel optimization strategies for parameter normalization to enhance the model training efficiency and overall performance.

5. Conclusions

This study proposes a hybrid normalization Sparse Transformer model to rapidly and accurately predict probe mark damage occurrences in wafer testing at room and high temperatures. The hybrid normalization method introduced in this study combines the advantages of both batch normalization and layer normalization. Batch normalization addresses vanishing or exploding gradients, accelerating model training convergence. On the other hand, layer normalization reduces the instability in training caused by the distributional shifts induced by batch normalization, leading to more stable training convergence. By employing the Sparse Transformer approach, this study successfully provides stable and efficient predictions of probe mark damage occurrences at room and high temperatures.

In future work, we aim to improve the performance and stability of the hybrid normalization Sparse Transformer model. We will explore ways to increase or decrease the number of layers in the encoder and decoder, adjust the number of hidden units or attention heads in each layer, and other strategies to enhance predictive accuracy. Additionally, studying how to increase the scale and diversity of the dataset, including data under different manufacturing conditions such as room temperature and high temperature, will help the model better adapt to changes in real-world application environments. We also plan to develop online learning algorithms, allowing the model to update and learn from real-time data streams continuously. This manner will enable the model to quickly adapt to changes in the manufacturing process and maintain efficient and accurate anomaly detection capabilities. While improving model performance, we will also focus on research into the interpretability and explainability of the model. By incorporating visualization techniques and interpretative methods, we hope to reveal the internal mechanisms of the model, helping engineers better understand and utilize the model, thus improving the accuracy and trustworthiness of anomaly detection results. Finally, we hope to collaborate with wafer manufacturing companies to validate the effectiveness of the trained model in natural production environments. Through practical application, we aim to gather more feedback and data to refine and optimize the model further, thereby enhancing its value in predicting probe mark damage.

Author Contributions

B.R.C. and Y.-R.W. conceived and designed the experiments; H.-F.T. collected the data and proofread this manuscript; and B.R.C. wrote this paper. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The Sample Codes for Sample Code.zip data are used to support the findings of this study. https://drive.google.com/file/d/1EHHIRz-jZ3UObaXWTb_1FAbvkfhsUA3w/view?usp=sharing (accessed on 16 September 2024).

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. The workflow of probe mark damage prediction.

Figure 2. Wafer testing machine.

Figure 3. On-site process personnel operating the machine manually.

Figure 4. Deep and Cross Network architecture.

Figure 5. Deep Neural Network architecture.

Figure 6. Autoencoder architecture.

Figure 7. Stacked Autoencoder architecture.

Figure 8. XLNet architecture.

Figure 9. Transformer architecture.

Figure 10. Images of the traces or marks left by the probes.

Figure 11. Images of probe misalignment or damage.

Figure 12. Condition at a node in a decision tree. (a) Condition at a node in a decision tree at room temperature. (b) Condition at a node in a decision tree at high temperature.

Figure 13. Correlation of important parameters. (a) Correlation of all parameters before random forest analysis. (b) Correlation of important parameters after random forest analysis. (c) Correlation of important parameters at room temperature. (d) Correlation of important parameters at high temperature.

Figure 13. Correlation of important parameters. (a) Correlation of all parameters before random forest analysis. (b) Correlation of important parameters after random forest analysis. (c) Correlation of important parameters at room temperature. (d) Correlation of important parameters at high temperature.

Figure 14. Batch normalization.

Figure 15. Layer normalization.

Figure 16. Hybrid normalization.

Figure 17. Sparse Transformer with hybrid normalization. (a) Architecture of HN Sparse Transformer. (b) Model diagram at room temperature. (c) Model diagram at high temperature.

Figure 18. The correct location of the probe mark.

Figure 19. The incorrect location of the probe mark.

Figure 20. Model loss and accuracy at room temperature. (a) Loss at room temperature. (b) Accuracy at room temperature.

Figure 21. Model loss and accuracy at high temperature. (a) Loss at high temperature. (b) Accuracy at high temperature.

Table 1

Important parameters at room temperature.

Feature	Importance
Count by Lot	0.445951
Number of Contacts	0.325416
Needle Tip Min	0.245873
Probing Overdrive	0.239127
Overdrive Value	0.138109
Needle Tip Ave	0.039399
pb_height	0.026661
Probe Card Clean Cnt	0.022967

Table 2

Important parameters at high temperature.

Feature	Importance
Probing Overdrive	0.552812
Needle Tip Min	0.261571
Alignment End Position	0.172564
Number of Contacts	0.136161
Needle Tip Max	0.041341

Table 3

Hardware specifications.

Component	GPU Workstation
GPU	NVIDIA Geforce RTX3070
CPU	Intel® Xeon® Silver 4316
Memory	32 GB DDR4
Storage	256 GB × 1 (SSD) 1 TB × 1 (HDD)

Table 4

Recipe of package.

Software	Version
Anaconda® Individual Edition	4.9.2
Jupyter Notebook	2.5.4
Tensorflow	2.6.0
Keras	2.6.0
Pandas	1.3.3
Numpy	1.21.1
Matplotlib	3.4.3
Pyplot	2.5.4

Table 5

Performance indexes at room temperature.

Metrics	DCN	DNN	SAE	XLNet	AutoEncoder	Transformer	SparseTransformer	HN Sparse Transformer
Accuracy (%)	82.7	87.1	88.6	85.3	89.4	91.7	93.9	95.1
Loss (RMSE)	0.1945	0.1847	0.1882	0.177	0.1872	0.1645	0.1566	0.1423
Inference Time (ms)	20	24	35	41	22	37	19	16
Time-Complexity	O($n$)	O($n$)	O($n$)	O($n^2$)	O($n$)	O($n^2$)	O($nlogn$)	O($nlogn$)

Table 6

Performance indexes at high temperature.

Metrics	DCN	DNN	SAE	XLNet	AutoEncoder	Transformer	SparseTransformer	HN Sparse Transformer
Accuracy (%)	83.2	84.8	86.3	85.5	85.3	88.1	91.4	93.5
Loss (RMSE)	0.1863	0.1743	0.1729	0.1776	0.1637	0.1687	0.1603	0.1571
Inference Time (ms)	19	26	32	37	23	45	22	17
Time-Complexity	O($n$)	O($n$)	O($n$)	O($n^2$)	O($n$)	O($n^2$)	O($nlogn$)	O($nlogn$)

References

1. Jiao, Y.; Vert, J. The Kendall and Mallows Kernels for Permutations. IEEE Trans. Pattern Anal. Mach. Intell.; 2018; 40, pp. 1755-1769. [DOI: https://dx.doi.org/10.1109/TPAMI.2017.2719680] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/28981406]

2. Genuer, R.; Poggi, J.M.; Tuleau-Malot, C. Variable selection using random forests. Pattern Recognit. Lett.; 2010; 31, pp. 2225-2236. [DOI: https://dx.doi.org/10.1016/j.patrec.2010.03.014]

3. Benesty, J.; Chen, J.; Huang, Y.; Cohen, I. Pearson correlation coefficient. Noise Reduction in Speech Processing; Springer: Berlin/Heidelberg, Germany, 2009; pp. 1-4.

4. Raffel, C.; Shazeer, N. Exploring the limits of transfer learning with a unified text-to-text transformer. Proceedings of the IEEE International Conference on Communications and Information Systems (ICCIS); Chongqing, China, 4–6 December 2020; pp. 5485-5551.

5. Sangwan, A.; Zhu, W.-P.; Ahmad, M.O. Design and performance analysis of Bayesian, Neyman–Pearson, and competitive Neyman–Pearson voice activity detectors. IEEE Trans. Signal Process.; 2007; 55, pp. 4341-4353. [DOI: https://dx.doi.org/10.1109/TSP.2007.896118]

6. Zhang, Q.T.; Song, S.H. Model selection and estimation for lognormal sums in Pearson’s framework. Proceedings of the IEEE 63rd Vehicular Technology Conference (VTC); Melbourne, VIC, Australia, 7–10 May 2006; pp. 2823-2827. [DOI: https://dx.doi.org/10.1109/VETECS.2006.1683383]

7. Vos, K.; Peng, Z. Vibration-based anomaly detection using LSTM approaches. Mech. Syst. Signal Process.; 2022; 169, 108752. [DOI: https://dx.doi.org/10.1016/j.ymssp.2021.108752]

8. Thiry, L.; Zhao, H.; Hassenforder, M. Categorical models for big data. Proceedings of the 2018 IEEE International Congress on Big Data (BigData Congress); San Francisco, CA, USA, 2–7 July 2018; pp. 272-275. [DOI: https://dx.doi.org/10.1109/BigDataCongress.2018.00049]

9. Yamaki, S.; Seki, S.; Sugita, N.; Yoshizawa, M. Performance evaluation of cross-correlation functions based on correlation filters. Proceedings of the 2021 20th International Symposium on Communications and Information Technologies (ISCIT); Tottori, Japan, 19–22 October 2021; pp. 145-149. [DOI: https://dx.doi.org/10.1109/ISCIT52804.2021.9590596]

10. Rosa-Zurera, M.; Jarabo-Amores, P.; Lopez-Ferreras, F.; Sanz-Gonzalez, J.L. Comparative analysis of importance sampling techniques to estimate error functions for training neural networks. Proceedings of the IEEE/SP 13th Workshop on Statistical Signal Processing; Bordeaux, France, 17–20 July 2005; pp. 121-126. [DOI: https://dx.doi.org/10.1109/SSP.2005.1628576]

11. Zhang, Z.; Wang, H. Within wafer & wafer to wafer thickness uniformity controllable study on ILD-CMP via polishing pad’s physical property analysis and linear interval feedback APC’s implementation. Proceedings of the 2019 China Semiconductor Technology International Conference (CSTIC); Shanghai, China, 18–19 March 2019; pp. 1-3. [DOI: https://dx.doi.org/10.1109/CSTIC.2019.8755719]

12. Liu, D.; Guo, T.; Chen, M. Fault detection based on modified t-SNE. Proceedings of the 2019 CAA Symposium on Fault Detection, Supervision and Safety for Technical Processes (SAFEPROCESS); Xiamen, China, 5–7 July 2019; pp. 269-273. [DOI: https://dx.doi.org/10.1109/SAFEPROCESS45799.2019.9213365]

13. Chatzimparmpas, A.; Martins, R.M.; Kerren, A. t-viSNE: Interactive assessment and interpretation of t-SNE projections. IEEE Trans. Vis. Comput. Graph.; 2020; 26, pp. 2696-2714. [DOI: https://dx.doi.org/10.1109/TVCG.2020.2986996] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/32305922]

14. Devlin, J.; Chang, M.W.; Lee, K.; Toutanova, K. BERT: Pre-training of deep bidirectional transformers for language understanding. arXiv; 2019; arXiv: 1810.04805

15. Kang, S.; Cho, S.; An, D.; Rim, J. Using wafer map features to better predict die-level failures in final test. IEEE Trans. Semicond. Manuf.; 2015; 28, pp. 431-437. [DOI: https://dx.doi.org/10.1109/TSM.2015.2443864]

16. Chen, Y.; Yinglan, F. Research on PCA data dimension reduction algorithm based on entropy weight method. Proceedings of the 2020 2nd International Conference on Machine Learning, Big Data and Business Intelligence (MLBDBI); Taiyuan, China, 23–25 October 2020; pp. 392-396. [DOI: https://dx.doi.org/10.1109/MLBDBI51377.2020.00084]

17. Chang, Y.-H.; Lee, J. Correlation analysis between process parameters and yield in semiconductor manufacturing. J. Semicond. Manuf. Technol.; 2015; 9, pp. 113-122.

18. Kim, J.; Park, C.; Hwang, S. Equipment parameter analysis and optimization for stable semiconductor production. IEEE Trans. Semicond. Manuf.; 2018; 31, pp. 510-520.

19. Li, X.; Zhang, Y. Correlation analysis of process defects in semiconductor manufacturing. Int. J. Adv. Manuf. Technol.; 2020; 102, pp. 3121-3132.

20. Sandri, M.; Zuccolotto, P. Variable selection using random forests. Data Analysis, Classification, and the Forward Search; Zani, S.; Cerioli, A.; Riani, M.; Vichi, M. Springer: Berlin/Heidelberg, Germany, 2006; pp. 263-270.

21. Strobl, C.; Boulesteix, A.L.; Zeileis, A.; Hothorn, T. Unbiased split selection for classification trees based on the Gini index. Comput. Stat. Data Anal.; 2007; 52, pp. 483-501. [DOI: https://dx.doi.org/10.1016/j.csda.2006.12.030]

22. Chen, M.; Liu, Z. Test parameter correlation analysis for semiconductor reliability testing. Microelectron. Reliab.; 2021; 116, 113896.

23. Li, K.S.-M.; Jiang, X.-H.; Chen, L.L.-Y.; Wang, S.-J.; Huang, A.Y.-A.; Chen, J.E.; Liang, H.-C.; Hsu, C.-L. Wafer defect pattern labeling and recognition using semi-supervised learning. IEEE Trans. Semicond. Manuf.; 2022; 35, pp. 291-299. [DOI: https://dx.doi.org/10.1109/TSM.2022.3159246]

24. Fan, S.-K.S.; Hsu, C.-Y.; Tsai, D.-M.; He, F.; Cheng, C.-C. Data-driven approach for fault detection and diagnostic in semiconductor manufacturing. IEEE Trans. Autom. Sci. Eng.; 2020; 17, pp. 1925-1936. [DOI: https://dx.doi.org/10.1109/TASE.2020.2983061]

25. Vaswani, A.; Shazeer, N.; Parmar, N.; Uszkoreit, J.; Jones, L.; Gomez, A.N.; Kaiser, Ł.; Polosukhin, I. Attention is all you need. Proceedings of the Advances in Neural Information Processing Systems; Long Beach, CA, USA, 4–9 December 2017; Volume 30, pp. 5998-6008.

26. Press, O.; Shazeer, N. Improving Transformer Models by Reordering their Sublayers. arXiv; 2019; arXiv: 1911.03862

27. Child, R.; Gray, S.; Radford, A.; Sutskever, I. Generating long sequences with sparse transformers. arXiv; 2019; arXiv: 1904.10509

28. Huang, G.; Liu, Z.; van der Maaten, L.; Weinberger, K.Q. Densely connected convolutional networks. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR); Honolulu, HI, USA, 21–26 July 2017; pp. 4700-4708.

29. Yao, Q.; Hu, F.; Zhang, Y.; Xu, S.; Zhu, H. Spatiotemporal multi-graph convolution network for ride-hailing demand forecasting. Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (KDD); Anchorage, AK, USA, 4–8 August 2019; pp. 2752-2761.

30. Zhou, B.; Khosla, A.; Lapedriza, A.; Oliva, A.; Torralba, A. Learning deep features for discriminative localization. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR); Las Vegas, NV, USA, 27–30 June 2016; pp. 2921-2929.

31. Bhatia, K.; Ajanthan, T.; Torr, P. Sparse attentive backtracking: Temporal credit assignment through reminding. Proceedings of the Advances in Neural Information Processing Systems; Online, 6–12 December 2020; pp. 1918-1930.

32. Zur, R.M.; Jiang, Y.; Pesce, L.L.; Drukker, K. Noise injection for training artificial neural networks: A comparison with weight decay and early stopping. Med. Phys.; 2009; 36, pp. 4810-4818. [DOI: https://dx.doi.org/10.1118/1.3213517] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/19928111]

33. Wu, Y.; Burda, Y.; Salakhutdinov, R.; Grosse, R. Simplified VAEs with improved training and generalization. Proceedings of the Advances in Neural Information Processing Systems; Vancouver, BC, Canada, 8–14 December 2019; pp. 1019-1029.

34. Chan, W.; Jaitly, N.; Le, Q.; Vinyals, O. Listen, attend and spell: A neural network for large vocabulary conversational speech recognition. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP); Shanghai, China, 20–25 March 2016; pp. 4960-4964.

35. Ioffe, S.; Szegedy, C. Batch normalization: Accelerating deep network training by reducing internal covariate shift. arXiv; 2015; arXiv: 1502.03167

36. Chang, B.R.; Tsai, H.-F.; Chen, G.-R. Self-adaptive server anomaly detection using ensemble meta-reinforcement learning. Electronics; 2024; 13, 2348. [DOI: https://dx.doi.org/10.3390/electronics13122348]