Virtual Metrology Model Research Articles

Developing the Keep-Important-Samples Scheme for Training the Advanced CNN-Based Automatic Virtual Metrology Models

Developing the Keep-Important-Samples Scheme for Training the Advanced CNN-Based Automatic Virtual Metrology Models

A novel semi-supervised robust learning framework for dynamic generative latent variable models and its application to industrial virtual metrology

Among a variety of virtual metrology models, dynamic generative latent variable models (DGLVMs) have proven to be an effective tool, owing to outstanding advantages in dealing with complicated data characteristics including temporal correlations, variable colinearities, high dimensionality, and process and measurement uncertainties. Presently, the vast majority of DGLVMs are developed upon the assumption that data are Gaussian-distributed, which is however, non-robust against outlying data and leads the DGLVMs to compromised performance, as the Gaussian distribution is susceptible to outliers that would skew the estimated parameters of DGLVMs. In view of this, this paper proposes a semi-supervised robust learning (SsRL) framework for the DGLVMs by designing an ad-hoc fully robust model structure that handles the outlying data by means of the heavy-tail properties of Student’s t distribution. In addition, the SsRL-DGLVM framework is initiated as a concrete model using probabilistic slow feature analysis (denoted RoSsPSFA) for which a rigorous training algorithm without resorting to any approximations is developed. The performance of the RoSsPSFA is thoroughly evaluated by both numerical and real-world industrial cases, showing the RoSsPSFA’s better immunity against outlying data and higher generalization accuracy.

Plasma heating characterization of the large area inductively coupled plasma etchers with the plasma information for managing the mass production

Meter-scale of the large area inductively coupled plasma etchers with the capacitive power coupling are widely applied for the mass production of OLED (organic light emitting diode) display panels. Because of the large area-to-volume ratio of the etcher, the balance between the power loss and absorption is easily located in the capacitive coupling mode rather than the ideal inductively coupled mode. Therefore, the process results are sensitively governed by the power absorption and plasma heating properties of the reactors. We have introduced a new PI (plasma information) parameter, the ratio of the stochastic heating to Ohmic heating of the plasmas, which is monitorable by using the optical emission spectroscopy data of the processing etchers. With the help of this plasma heating characteristic index, we could optimize the process recipes with the detailed control of the etched hole sidewall passivation and related species generation rate in the plasmas; thus, chamber-to-chamber matching in the huge mass production fab with the higher efficiency was possible. It was demonstrated that the introduced PI index with plasma heating mechanism characterization could be applicable to the VM (virtual metrology) modeling as one of the good information supplying core variables. This PI index has shown a very high correlation with the plasma sheath and ion flux governing phenomena for a large number of mass-produced OLED display glasses. From these results, the introduced plasma heating mechanism-based PI index is expected to be utilized as a good reference index for their performance analysis or PI-VM modelings.

Multi-source AdaBoost with cross-weight method for virtual metrology in semiconductor manufacturing

In the context of Industry 4.0, many production scenarios utilise sensors to monitor manufacturing processes, resulting in massive data that can be leveraged to build machine-learning models to improve production efficiency and quality. In semiconductor manufacturing, where many sensors are employed to monitor the production process, the resulting multi-sensor data poses challenges for constructing a virtual metrology (VM) model to assess wafer quality. Furthermore, building separate prediction models for each sensor can result in a loss of redundancy present in the multi-sensor data. Therefore, this paper proposes a multi-source AdaBoost with a cross-weight sampling method for predicting the critical dimension required in VM. Compared with the existing AdaBoost algorithm in regression, the proposed method adapts well to multi-source data by incorporating a cross-weight sampling distribution. Thus, when updating the sampling weight distribution, the impact of both individual and multi-source data is considered to re-sample high-quality observations. Based on the numerical results from the synthetic datasets and case study in semiconductor manufacturing, the proposed method outperforms benchmark methods. Additionally, owing to the redundancy of multi-sensor data, the proposed method demonstrates robust performance regardless of the noise level in the semiconductor VM data.

Multi-source adaptive thresholding adaboost with application to virtual metrology

ABSTRACT To maintain high-quality semiconductor wafer production processes, it is necessary to build high-quality virtual metrology (VM) model. Based on the result of the VM, the engineer can monitor and control the specific process. In the manufacturing process, various sources are obtained from sensor equipment. It is important to consider that these source data exhibit varying characteristics during the model construction. However, when all data sources are simply aggregated into a single model, the performance of the overall model may degrade, especially if any of the individual sources contain outliers or noise. To address this issue, we develop a data-fusion model designed to incorporate diverse data sources into a unified multi-source model. In particular, we improve an Adaboost regression algorithm to make it suitable for multi-source data in the field of VM. The algorithm combines the residuals of the models derived from each individual data source and all sources to adaptively adjust the thresholding value, which, in turn, determines whether the predicted values are accurate or not for each weak learner. Extensive practical validations on real-world processing data from semiconductor manufacturers have demonstrated that the proposed method outperforms single learning algorithms and is more robust than all benchmarks.

A hierarchical model-based method for wafer level virtual metrology under process information deficiency

Online inspection is one of the most critical processes of quality control in semiconductor manufacturing. The physical inspection methods for wafers are time-consuming and unable to achieve wafer level metrology. In order to improve production efficiency and expand inspection coverage, virtual metrology (VM) methods have recently received widespread attention; they utilize process parameters to estimate wafer metrology results. However, due to process drift and other reasons, the process information contained in real-time signal data (RTS data) used for VM modeling in industrial production is insufficient. This work proposed a hierarchical modeling method for machine learning-based virtual wafer metrology, leveraging RTS and post-process quality characteristics. The hierarchical model consists of an multiway principle analysis (MPCA) sub-model for RTS feature extracting and two separate long short-term memory (LSTM) networks for wafer-to-wafer dynamics in RTS and quality characteristics, respectively. A case study on the thickness VM of chemical vapor deposition thin film is conducted, and the proposed method has achieved better results than other methods in comparison.

Virtual Metrology Modeling for Wafer Edges via Graph Attention Networks

Quality monitoring is an essential element of defect detection in semiconductor manufacturing processes, but semiconductor companies use virtual metrology (VM) in addition to actual metrology to prevent productivity degradation due to the time and costs required to obtain measurements. Past VM studies aimed to predict average wafer measurement values via equipment sensor data and focused on achieving improved predictive performance by selecting or extracting important variables among high-dimensional variables such as equipment sensor data. However, the management of wafer chip quality requires not only average measurement values but also measurement value predictions for chips located at the edges, which are vulnerable to defects. In this paper, we therefore propose a graph attention (GAT) network-based VM model that predicts the measurement values of chips located at wafer edges by constructing graph data with measurement data (i.e., the measurement location information in wafers and the measurement values). To verify the performance of the proposed model, we conduct a comparative experiment with conventional machine learning methods. The experimental results show that the proposed VM model contributes to a predictive performance improvement in terms of the measurement values of chips located at wafer edges.

Semi-Supervised Deep Kernel Active Learning for Material Removal Rate Prediction in Chemical Mechanical Planarization.

The material removal rate (MRR) is an important variable but difficult to measure in the chemical-mechanical planarization (CMP) process. Most data-based virtual metrology (VM) methods ignore the large number of unlabeled samples, resulting in a waste of information. In this paper, the semi-supervised deep kernel active learning (SSDKAL) model is proposed. Clustering-based phase partition and phase-matching algorithms are used for the initial feature extraction, and a deep network is used to replace the kernel of Gaussian process regression so as to extract hidden deep features. Semi-supervised regression and active learning sample selection strategies are applied to make full use of information on the unlabeled samples. The experimental results of the CMP process dataset validate the effectiveness of the proposed method. Compared with supervised regression and co-training-based semi-supervised regression algorithms, the proposed model has a lower mean square error with different labeled sample proportions. Compared with other frameworks proposed in the literature, such as physics-based VM models, Gaussian-process-based regression models, and stacking models, the proposed method achieves better prediction results without using all the labeled samples.

Methodology for Plasma Diagnosis and Accurate Virtual Measurement Modeling Using Optical Emission Spectroscopy

In this study, we diagnose and monitor the plasma process in real time using optical emission spectroscopy (OES). Notably, this method is inexpensive and can effectively diagnose the plasma state without plasma interference. The virtual metrology (VM) model based on machine learning can successfully predict the thickness of a ZrO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> thin film deposited via plasma-enhanced atomic layer deposition (PE-ALD). The neural network model predicts the thickness by recording the emission light information generated during PE-ALD using OES. The prediction accuracy can be improved by including the maximum possible number of process variables, such as the radiofrequency power, pressure, and gas sensing data, in modeling. However, the complexity of the system may increase owing to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">requirement</i> of physical knowledge on the system and result interpretation. Therefore, herein, we perform predictive modeling using variables with a high correlation and OES data, focusing on the importance of each process variable. Additionally, we use plasma data with minimized variability for variable optimization of the PE-ALD process. Consequently, we design an enhanced VM model with high prediction accuracy. The methodology adopted in this study is based on the PE-ALD process; however, it can also be extended to other processes using plasma.

Roughness prediction of end milling surface for behavior mapping of digital twined machine tools

Background: The quality of machined parts is considered as a relevant factor to evaluate the production performance of machine tools. For mapping the production performance into a digital twin machine tool, a virtual metrology model for surface roughness prediction, which affects products' mechanical capacity and aesthetic performance, is proposed in this paper. Methods: The proposed model applies a three-layer backpropagation neural network by using real-time vibration, force, and current sensor data collected during the end milling machining process. A grid search plan is used to settle down the number of neurons in the middle layer of the backpropagation neural network. Results: The experimental results indicate that the model with multiple signals as input performs better than it with a single signal. In detail, when the model input is the combination of force, vibration, and current sensor data, the prediction accuracy reaches the optimum with the mean absolute percentage error of 1.01%. Conclusions: Compared with the state-of-the-art convolutional neural network method with automatic feature extraction ability and other commonly used traditional machine learning methods, the proposed data preprocessing procedure integrated with a three-layer backpropagation neural network has a minimum prediction error.

Data-Driven Adaptive Virtual Metrology for Yield Prediction in Multibatch Wafers

Virtual metrology (VM) is widely used for yield management and control in semiconductor manufacturing owing to its high real-time inspection, low cost, and convenient maintenance. However, the multimodal characteristics of batch processes are ignored in the existing yield VM models. The adaptive multimodal division and modal sample imbalance have also not been considered. Therefore, a data-driven adaptive VM model based on the Gath–Geva fuzzy clustering (GGFC) and multitask learning deep belief network (MLDBN) is proposed to solve the problems above. First, the GGFC model is designed to realize the feature extraction of the batch direction and the modal division of the time and variable directions. Second, the partition coefficient and classification entropy indexes are designed to determine the modal categories automatically and establish the SMOTE model to deal with the imbalance of multimodal samples. Third, the local features of multimodal are extracted by the designed MLDBN models. After that, the batch direction features and the multi-features extracted from multimodal are used as the improved MLDBN parameters to realize the fusion prediction. Finally, experiments are carried out by the accurate industrial data from a multibatch wafer fabrication process. The efforts show that the proposed VM model presents better performances in the result of different indicators and has higher accuracy and robustness than the traditional models.

Product-to-Product Virtual Metrology of Color Filter Processes in Panel Industry

The current thin film transistor liquid crystal display (TFT-LCD) panel industry evolves in transition from volume production to customized production service as a major competition strategy. Owing to the highly mixed production type of small batch sizes and high varieties, metrology data are usually collected too infrequently for building accurate virtual metrology (VM) models. In this paper, a new product-to-product (P2P) VM model to predict photoresist spacer heights in the color filter process of the array sector is developed. First, a position-based random forests model is proposed for the base product. Second, an ensemble model combining the base model and a biased estimation random forests model for the new product of small batch size is proposed to perform P2P VM between different products on the same tool. The real datasets of photoresist spacer heights for different products are used to illustrate the accuracy of the new P2P VM framework in the experimental study. Note to Practitioners—As global competition intensifies, production management needs to be adjusted to adapt swiftly to changes in the time-varying and competitive market. For manufacturing firms, how to operate the manufacturing system effectively and efficiently plays a crucial role in quality and yield improvements. The color filter process in the array sector is of critical importance in the TFT-LCD practice since it essentially dictates the quality level of subsequent processing steps in the cell and assembly sectors. Virtual metrology is a state-of-the-art measure that can be used for monitoring and controlling purposes to maintain the yield and productivity of the color filter process in the highly mixed production environment. An immediate challenge to be faced by the data scientists is how to build accurate virtual metrology models for a variety of product lines separately in color filter manufacturing. A new proposal of product-to-product virtual metrology is first addressed between products, enabling to build appropriate virtual metrology models for new products with small-sized production batches.

Restricted Relevance Vector Machine for Missing Data and Application to Virtual Metrology

In semiconductor manufacturing, virtual metrology (VM) is a method of predicting physical measurements of wafer qualities using in-process information from sensors on production equipment. The relevance vector machine (RVM) is a sparse Bayesian kernel machine that has been widely used for VM modeling in semiconductor manufacturing. Missing values from equipment sensors, however, preclude training an RVM model due to missing kernels from incomplete instances. Moreover, imputation for such kernels can lead to a loss of model sparsity. In this work, we propose a restricted RVM (RRVM) that selects its basis functions from only complete instances to handle incomplete data for VM. We conduct the experiments using toy data and real-life data from an etching process for wafer fabrication. The results indicate the model’s competitive prediction accuracy with massive missing data while maintaining model sparsity. Note to Practitioners—In recent decades, virtual metrology (VM) has focused on wafer fabrication in semiconductor manufacturing due to its advantages for process monitoring and automation. Typically, signals from production process equipment can predict wafer qualities in VM, which often leads to high data dimensionality. The relevance vector machine (RVM) is an algorithm that can provide a sparse solution to a Bayesian kernel method for a prediction model. Missing components in incomplete data due to sensor failures in wafer fabrication processes, however, hinder model training, and the existing approaches to handling missing data using imputation may lead to a loss of model sparsity. This article proposes a new method for RVM with incomplete data to train a model built on fully available instances by incorporating the available components of incomplete instances into model training. Using the proposed method, one can predict wafer qualities building a model trained to maintain its sparsity. Experiments indicate that the proposed model achieves competitive prediction performance and maintains model sparsity when incomplete instances are used.

Decision-based virtual metrology for advanced process control to empower smart production and an empirical study for semiconductor manufacturing

Virtual metrology (VM) has been employed to improve the performance of advanced process control for semiconductor manufacturing. A number of VM models have been proposed to predict the quality characteristics for the wafers that have not been sampled and measured. However, little research has been done to address the interrelations between the VM model and associated decisions for advanced process control and yield enhancement. There is a research need for developing a framework that can integrate the confidence level of VM prediction and domain knowledge to derive appropriate decisions for real-time control. To fill the gaps, this study aims to develop a decision-based virtual metrology framework that integrates clustering and regression models to enhance the prediction and ensure the decision quality for the R2R controller. In particular, Isolation Forest is employed to cluster the data group for multi-recipes and multi-tools. Random Forest Regression is developed for the prediction model for each category respectively to enhance the accuracy of predicted results. Furthermore, this approach designs an overall confidence score based on data integrity and predicted results to suggest the optimal decision rules for R2R control in real time. This approach is validated with an empirical study in a leading semiconductor manufacturing company in Taiwan. Indeed, the results have demonstrated practical viability and the developed solution has been implemented.

Virtual Metrology for Etch Profile in Silicon Trench Etching With SF₆/O₂/Ar Plasma

This study practiced virtual metrology (VM) for the etch profile and depth in the deep silicon trench etching with SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> /O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /Ar plasma. Machine learning-based VM models constitute the classification models of etch profile and the prediction models of etch depth from the silicon trench etch. Machine learning algorithms of random forest and Xgboost were used for classifying etch profiles by employing recipe-based equipment status variable identification (SVID) data. Predictive etch depth models constructed with neural network models employed both equipment SVID data and optical emission spectroscopy (OES) data, which provide chemistry information of the plasma during the etch process. Plasma VM model, augmenting OES data to SVID data presented improved accuracy in predicting etch profile. The augmented phenomenological plasma information during the etch process helped to establish a more accurate VM model in the plasma process. The importance of variables was identified through the permutation importance of each model. Additionally, the actual process results of the variables with high importance were analyzed with the etching reaction of SF <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> /O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /Ar plasma.

Virtual Metrology in Semiconductor Fabrication Foundry Using Deep Learning Neural Networks

Physical metrology inspections are crucial in semiconductor fabrication foundry to ensure wafers are fabricated within the production specification limits and prevent faulty wafers from being shipped and installed in customers&#x2019; devices. However, it is not possible to examine every wafer as such inspection would incur impractical cost on manpower, finances, and production cycle time (CT) of fabrication foundries (fabs). Virtual metrology (VM) presents an alternate approach to perform metrology inspection without incurring high costs by using machine learning (ML) models. By leveraging historical equipment and process data, ML models can be calibrated to estimate the targeted metrology variables to estimate the quality of wafers, thereby performing virtual inspection on wafers. Recently, VM researchers begin introducing deep learning (DL) into VM research works to examine its capability. Specifically, the VM researchers experimented on the convolutional neural network (CNN). The targeted metrologies are metrologies of plasma-based processes in both etching and chemical vapor deposition. Initial success has been reported by the VM researchers. While various CNN-based VM models have been proposed plasma-based fabrication processes, it has yet to be experimented in photolithography process. Motivated by the initial successes of CNN in plasma-based processes, this work is an initiative to experiment CNN&#x2019;s performance in predicting the overlay errors of photolithography process. Using data from a real fab, this work first establishes a baseline using the methodology of a prior work. Then, the prediction results of the proposed CNN model are compared with the baseline. The results showed that CNN is able to further reduce the prediction errors.

Domain-adaptive active learning for cost-effective virtual metrology modeling

Virtual metrology (VM) is a promising solution for wafer-to-wafer quality monitoring in the semiconductor manufacturing process. VM alternates physical metrology with a prediction model trained using previous metrology data. Active learning can be used to build a VM model for new equipment efficiently with reduced metrology costs. However, conventional active learning is limited by a low prediction accuracy at its initial stage, which is referred to as the cold-start problem. In this study, we propose a domain-adaptive active learning method to address this issue. Using existing equipment as the source domain, the proposed method initializes the VM model through unsupervised domain adaptation from the source domain to the target domain. Active learning is then performed to iteratively update the VM model toward improving the prediction accuracy. Thus, the metrology cost required to obtain a VM model that satisfies the desired prediction accuracy for the target metrology task can be reduced. The effectiveness of the proposed method is demonstrated experimentally using real-world data from a semiconductor manufacturer.

Virtual metrology modeling of reactive ion etching based on statistics-based and dynamics-inspired spectral features

Due to increasing demand on the fabrication yield and throughput in micro/nanoscale manufacturing, virtual metrology (VM) has emerged as an effective data-based approach for real-time process monitoring. In this work, a novel automated methodology, without the need for domain knowledge and experience, for extracting useful features from raw optical emission spectroscopy (OES) data is presented. Newly proposed OES features are combined with other types of data, which include tool settings, sensor readings, physical measurements, non-numerical data, and process control parameters. Using partial least squares and support vector regression, VM models for predicting the critical dimension after reactive ion etching are built. The results from the VM model indicate that the coefficient of determination of up to 0.65 and the root mean square Error of 0.08 can be achieved. Compared to the traditional features obtained by the current solution in industry, the performances of VM models via the proposed methodology can enhance the coefficient of determination by 62.5% and reduce the root mean square error by 23.1%.

Machine Learning Prediction of Electron Density and Temperature from Optical Emission Spectroscopy in Nitrogen Plasma

We present a non-invasive approach for monitoring plasma parameters such as the electron temperature and density inside a radio-frequency (RF) plasma nitridation device using optical emission spectroscopy (OES) in conjunction with multivariate data analysis. Instead of relying on a theoretical model of the plasma emission to extract plasma parameters from the OES, an empirical correlation was established on the basis of simultaneous OES and other diagnostics. Additionally, we developed a machine learning (ML)-based virtual metrology model for real-time Te and ne monitoring in plasma nitridation processes using an in situ OES sensor. The results showed that the prediction accuracy of electron density was 97% and that of electron temperature was 90%. This method is especially useful in plasma processing because it provides in-situ and real-time analysis without disturbing the plasma or interfering with the process.

Machine learning virtual SEM metrology and SEM-based OPC model methodology

Background: E-beam metrologies, both critical dimension scanning electron microscope metrology and defect scan metrology, have been playing a very critical role in gating patterning quality. SEM images can provide rich visual information for engineers to do qualitative and quantitative analyses. However, the low e-beam metrology tool throughput makes it impossible to obtain SEM images for larger area. Monte Carlo-based SEM image simulations or other SEM image simulations require postlithography or postetch pattern three-dimensional structures as prerequisite, and the simulation speed is not sufficiently fast for full chip implementation. Aim: We aim to develop machine learning SEM models with sufficient accuracy and speed for full chip application in semiconductor manufacturing environment. Approach: We have proposed a virtual SEM metrology solution based on U-Net neural network with physics-based feature maps as model input. With information in aerial image space encoded properly, SEM images of both postlithography and postetch can be predicted accurately enough for practical applications using our proposed virtual SEM metrology models. Equipped with GPUs, the machine learning-based SEM image models are fast enough to make it possible to realize full chip SEM generation from post-OPC data. Results: Our machine learning SEM image models can predict SEM images with normalized cross correlation around 0.95 in reference to ground truth SEM images, each SEM image (512 × 512 in size) takes about 800 ms using single CPU, and the speed can be accelerated to about 10 ms with single GPU. Conclusions: Using U-Net structure and physics-based feature maps as model inputs, machine learning-based SEM image models can be developed. The models are sufficiently accurate and fast to find their applications in semiconductor manufacturing, and they can be used as independent model for OPC data verification or generate SEM images as reference for SEM defect scan metrology.