Virtual Metrology Model Research Articles

DBAM: Making Virtual Metrology/Soft sensing with time series data scalable through Deep Learning

Machine Learning (ML) based technologies, like Virtual Metrology (VM)/Soft Sensing, Predictive Maintenance and Fault Detection, have been successfully applied in the past recent years in data intensive manufacturing industries, like semiconductor manufacturing, to improve process monitoring and related operations. Standardization and alignment over multiple equipment is a key element to ensure industry-wide adoption and scalability for ML-based technologies in complex production environment. In this work we address the topic of VM/Soft Sensing – a particular ML-based technology for process control – in the context of equipment matching and scalability. We present a Deep Learning-based domain adaptation approach, called DANN-Based Model Alignment (DBAM), that provides a common VM model for two identical-in-design systems whose data are following different distributions. The proposed approach has the merit of (i) exploiting directly raw sensor data (that typically present themselves in the form of time series) and (ii) offering interpretability of the features. The proposed approach is compared against other approaches in the literature for VM/Soft Sensing on a real-world case study from semiconductor manufacturing.

Rapid Resolution of Parametric Failures in the Process Development Period by Integrating Device Physics and Big Data

This paper describes a method for rapid resolution of parametric failure during the development period. Since the number of samples is small, it is not possible to carry out general big data analysis of white defect failures of CMOS image sensors (CISs) during the development period in the same way as can be done during the mass production period. Our feature value analysis of white defects based on device physics revealed that both a development product and mass products using big data show similar fluctuations in dark current spectroscopy and in-plane distribution in the wafer. Process step/tool identification and tool sensor data analysis revealed the degree of vacuum within the implantation tool to have a strong correlation with white defect count. We developed a virtual metrology (VM) model for white defect count and varied the degree of vacuum. As a result of our experiments, we were able to reduce white defect count during the development period by 75%. The time required for resolution of failures was 10% that of the conventional method. This paper describes a detailed explanation of how the potential causative process step/tool was identified in addition to the conference paper presented in ISSM2020.

Machine learning-based virtual metrology on film thickness in amorphous carbon layer deposition process

A stringent manufacturing process control is important to achieve reliable process control in nanoscale semiconductor manufacturing processes. Based on the advanced process control mechanisms in advanced semiconductor manufacturing, virtual metrology (VM) can be used to reduce the time and cost incurred in conventional metrology. This paper proposes a VM model based on the neural network (NN) architecture for predicting film thickness in amorphous carbon layer deposition processes, which is used for etch hard mask in high-aspect-ratio etch processes. A series of deposition experiments was conducted using the Box–Behnken design. The equipment status data and in situ optical emission spectroscopy (OES) sensor data were collected. Conventional recipe-based process modeling with the equipment status data showed a reasonable correlation with the deposited film thickness, and the augmentation of in situ plasma chemistry information through OES improved the machine learning accuracy with artificial neural networks. Consequently, our model’s prediction accuracy was approximately 99.5% for R2 when both equipment status data and OES sensor data were used as training data, as compared to when only equipment status data were used to train the model. Therefore, we recommend that in situ OES sensor data, as well as equipment status data, should be used in training NN-based VM models for high prediction accuracy.

A Realizable Overlay Virtual Metrology System in Semiconductor Manufacturing: Proposal, Challenges and Future Perspective

Integrated circuits (IC) are fabricated on a wafer through stacked layers of circuit patterns. To ensure proper functionality, the overlay of each pattern layer must be within the tolerance. Inspecting each wafer’s overlay is unrealistic and impractical. Hence, wafers are selectively inspected at metrology stations through sampling strategies. With virtual metrology (VM), the metrology quality of the uninspected wafers can be estimated. Motivated by a real-world production environment of a 200mm semiconductor manufacturing plant (fab), a VM to estimate the overlay of the photolithography process is envisioned. Past researches on overlay VM leveraged fault detection and classification (FDC) data to estimate the overlay errors. As such, for fabs in the progress of completing their FDC development for photolithography equipment, a different modeling approach is required to realize an overlay VM that sustains the production line until FDC data can be leveraged for VM. With practical gaps that must be addressed in real fabs, this paper focuses on realizing an overlay VM for the photolithography process without leveraging FDC data. Therefore, the objectives of this paper are two folds: First, to identify the research challenges towards realizing the overlay VM. Second, to propose the future research perspectives of the envisioned overlay VM. Based on the future research perspectives, a two-steps overlay VM modeling approach utilizing data mining techniques is proposed toward realizing the envisioned overlay VM system. The proposed approach first classifies the process stability at the wafer lot level, and subsequently, performs overlay error estimations for wafers in the wafer lots classified with stable process. Linear regression models are proposed to perform overlay error estimations in this work to augment the interpretability of the overlay VM.

The Implementation of a Smart Sampling Scheme C2O Utilizing Virtual Metrology in Semiconductor Manufacturing

Virtual metrology (VM) is an enabling technology capable of performing virtual inspection on the metrology quality of wafers. Instead of physically acquiring the metrology measurements, VM applies conjecture models on the process data of wafers to estimate the measurements of the targeted metrology variables. Prior works on overlay VM system utilized fault detection and classification (FDC) data as the process data for the conjecture models. Hence, when FDC data are unavailable owing to FDC system enhancement works, FDC-based VM models would be rendered inefficacious. During such events, a competent VM system using a different modeling approach is required to sustain the production line until FDC data resumes availability and FDC-based VM reaches production state. Motivated by a real-world production environment of a 200mm semiconductor manufacturing plant (fab), a novel wafer lot-level modeling approach for overlay VM was proposed in our prior work. Using the proposed modeling, a smart sampling scheme was also designed in the same work. The smart sampling scheme consists of two conjecture tasks, with the first task classifies the overlay quality of the wafers, and the second task estimates the overlay errors of the wafers classified with normal overlay quality. The abnormal ones are diverted to the physical metrology station. In this paper, the implementation of a smart sampling system, C2O, using the designed scheme and its experimental results are presented. The experimental results showed that C2O is capable to achieve a true positive rate (TPR) of 71.34% for the classification task and mean absolute scaled error (MASE) of 9.59 for the regression task. The obtained results set the baseline to measure the efficacy of future enhancement works, which have been enlisted and underway to augment the performance of the system so that its competency meets the requirements of real fab.

Parameters Adjustment Optimization for Prepreg of Copper Clad Laminate Based on Virtual Metrology

In this research, virtual metrology models, which can estimate the quality characteristics based on the given manufacturing parameters, were developed by lasso regression and support vector regression. Then, the virtual metrology (VM) models were integrated into a mathematical model to minimize the adjustment of manufacturing parameters and ensure the corresponding quality characteristics that would meet the customers’ needs. According to the results of the experiment, it was found that developing the virtual metrology model by using integration of lasso regression and support vector regression and taking second order terms into consideration produces the best performance for estimating the quality characteristics. Moreover, the integrated mathematical model can provide manufacturing parameters that minimize the amount of adjustment and ensure that the quality characteristics equal their corresponding target values. The proposed methodology can reduce the setup times and consequently increase productivity.

Adaptive virtual metrology method based on Just-in-time reference and particle filter for semiconductor manufacturing

The prediction of the average Material Removal Rate (MRR) for Chemical Mechanical Planarization (CMP) process has been recognized to be a critical factor of Virtual Metrology (VM) modeling as well as wafer-to-wafer process control. In this paper, a novel method is proposed to dynamically predict MRR in CMP process by using a Just-in-time (JIT) model-based strategy. First, the proposed method applies a reference search procedure to query similar data samples from the historical dataset. Second, a Support Vector Regression (SVR) model is used to fuse the similar data samples with the past MRR. Finally, Particle Filter (PF) is employed to estimate and update the fusion result. The application of PF ensures that the method can track the CMP process change and continuously learn from the current dataset. Compared with static models, the proposed method, named JIT-PF model is an online dynamic method with enhanced accuracy. Compared with pure JIT model, JIT-PF model keeps the historical knowledge in the process. A public dataset is used to validate JIT-PF model with the benchmarks from the recent literature. The model outperforms other peer dynamic models and some static models from the literature.

A virtual metrology method with prediction uncertainty based on Gaussian process for chemical mechanical planarization

The prediction of the average material removal rate (MRR) in chemical mechanical planarization (CMP) process has been recognized to be a critical factor of virtual metrology (VM) modeling for advanced process control (APC). This paper proposes a Gaussian process regression (GPR)-based model to dynamically predict MRR in CMP process. The proposed method uses K-nearest neighbor (KNN) to search for reference MRR samples in the historical dataset. Furthermore, a GPR model is trained to fuse the information from reference samples. Finally, the proposed method employs multi-task Gaussian process (MTGP) to predict the final MRR and quantify the prediction uncertainty based on the historical and the reference MRR. Compared with other methods in the recent literature, the proposed method, named KNN-MTGP model, yields better prediction accuracy than ensemble models, and comparable accuracy with deep neural networks (NN). Besides, KNN-MTGP model is capable to demonstrate the behavior of the past MRR changing with time and provide quantified prediction uncertainties. In this paper, the feasibility and advantages of KNN-MTGP model are evaluated based on the dataset of 2016 prognostic and health management (PHM) data challenge.

Development of convolutional neural network based Gaussian process regression to construct a novel probabilistic virtual metrology in multi-stage semiconductor processes

Manufacturing of semiconductor chips involves hundreds of process steps. For high-throughput semiconductor manufacturers, it is not feasible to get all the quality measurements of wafers at each step because of expensive costs. Based on the limited measurements of sampled wafers, virtual metrology (VM) allows predicting the relevant quality variables without increasing the number of physical measurements. Traditional data-driven VM methods are constructed using a predefined model along with feature extractions in data pre-processing. Often the identified VM model is not reliable if the constructed model and the extracted features are improper. In this paper, the convolutional neural network (CNN) based Gaussian process regression (GPR) VM mode (CNN-GPR) calibrated by maximization of the Bayesian posterior density distribution is systematically developed. CNN is used to extract information from massive wafer data through layers of the cascade-connected convolving filters. With the extracted features, the GPR model associates the stochastic nature of the operating steps with the quality variables to obtain the predicted means as well as the quantitated uncertainty levels. Unlike the traditional VM models where the extracted features and the prediction models are generated separately, the CNN-GPR model is sensitive to the variations of the quality variables and the features are determined simultaneously through the covariance matrices with information from both of the process and the quality variables. The proposed CNN-GPR model performs better as it represents the complex process of the whole set of measured variables. Through the studies on a real semiconductor process, the effectiveness of the proposed algorithm is demonstrated and compared against the regular regression algorithms.

Advanced Process Control Using Virtual Metrology to Cope With Etcher Condition Change

In the semiconductor, an advanced process control (APC) system using virtual metrology (VM) for plasma etching is required to achieve further device miniaturization. VM is a method to predict process outputs such as the critical dimension (CD) from equipment data indicating the etcher condition. The prediction model for VM is called VM model. Although a highly accurate VM model is necessary to realize the APC system, the prediction accuracy can be worse when the correlations between the CD and equipment data change because of changes in etcher conditions. To solve the problem, we propose a multiple VM model selection APC system. The proposed APC builds: 1) multiple local VM models that are built using a series of lot data to cope with the correlation change and 2) a global VM model that is built using all of the lot data to improve the robustness of CD prediction. When APC is applied, the proposed APC selects the optimal VM model among the multiple VM models that have been built. This paper shows that the proposed system contributes to improving prediction accuracy even though the correlation change occurs by simulation based on actual etcher experimental data.

Virtual Metrology Model Robustness Against Chamber Condition Variation Using Deep Learning

Virtual metrology (VM) predicts the actual measurement for ongoing semiconductor process. Optical emission spectroscopy (OES) data is often used to build up VM models, since it has a lot of information on process quality. However, it also includes significant redundant information, so it is important how to select only meaningful features. Deep learning (DL) techniques have been very successful in analyzing image data and it is tempting to apply those techniques to the OES data. In this paper, we propose DL configurations specific to OES data that outperform those used for image analysis. Specifically, our proposed method accounts for variable size data, chamber to chamber differences, condition drift due to accumulation, observation data drift due to an accumulation of deposition on a window, and the effects of maintenance. We evaluated our method on a real, mass-production dataset and compared our results with those obtained by using state-of-the-art image analysis DL techniques in the famous contest, ImageNet large-scale visual recognition challenge (ILSVRC).

Prediction of the Number of Defects in Image Sensors by VM Using Equipment QC Data

This paper describes methods and evaluation results of predicting the number of defects in image sensors using equipment QC data. Virtual metrology (VM) models are mainly used for measurable values such as dimensions and electrical characteristics. Herein, to predict countable values, we used a regression tree and stepwise AIC for variable selection as well as the “hockey-stick regression model” and generalized linear model for regression, instead of the partial least squares (PLS) regression. The results showed an improved prediction performance in comparison with the conventional method. This method can be used to predict other countable values such as defects or dust particles.

An Online Virtual Metrology Model With Sample Selection for the Tracking of Dynamic Manufacturing Processes With Slow Drift

Modeling of dynamic manufacturing processes with slow drift using data-driven approaches is challenging because most data-driven models are trained by off-line data. In this paper, we propose to track slow drift of manufacturing processes using an online Bayesian Auto-Regression eXogenous (ARX) model with time-variant parameters. The model parameters are trained off-line and are updated online using Bayes’ rule. To avoid the frequent online model update, a Sample Importance (SI) test is proposed to screen online samples and only the sample that passes SI test is incremented to the VM model. The SI test decides the importance of the sample by collectively considering sample freshness, model prediction error and prediction uncertainty. Furthermore, the SI test is applied to off-line Data Base (DB) and an iteration algorithm is devised for off-line sample selection. The off-line sample selection algorithm can effectively reduce the sample redundancy in off-line DB while maintaining the model performance. To validate the effectiveness of the proposed method, Prognostics and Health Management (PHM) data challenge 2016 dataset is employed to predict material removal rate of chemical-mechanical planarization process. The validation results indicate that the proposed method outperforms existing state-of-art approaches in literature such as Just-in-Time (JIT) and deep learning models.

A Novel Method for Deposit Accumulation Assessment in Dry Etching Chamber

Particle contamination in the dry etching chamber is one of the major issues in the semiconductor manufacturing. Particles on the wafer surface may cause wafer defects and yield loss. Therefore, particle monitoring is important to support contamination control and predictive maintenance activities. To achieve this goal, this paper proposes a virtual metrology (VM) method to estimate the deposit accumulation on the chamber wall, which can be a major root cause of the particle contamination. In the proposed method, the piecewise linear approximation (PLA) is employed and modified to derive a general segmentation template for the trace signals. Based on the trace segmentation template, important features that relate to the deposit accumulation are better extracted and modeled. To justify the effectiveness of the proposed method, we validate our method on the etching data from three different maintenance cycles. In the results, the proposed method with trace segmentation has improved performance compared to the VM model that does not segment the data, as well as the VM model that partitions the trace data by step number. The deposit accumulation indicator given by the proposed method demonstrates a slow trend over etching cycles and it matches well with the off-line metrology measurements.

A Structure Data-Driven Framework for Virtual Metrology Modeling

Virtual metrology (VM) has been widely studied in the semiconductor industry with the purpose of decreasing the cycle time and reducing the expensive metrology measurements. Ideally, a VM model should not only be able to provide accurate predictions but also present an interpretable and rational structure to accommodate fundamental restrictions and relationships that are known to be present in the process. The last aspects have been missing in the VM models proposed hitherto. Therefore, in this article, we propose a novel framework by combining in a single VM model the capability to learn from data with the ability to incorporate the domain knowledge on the process. Thus, the new methodology can use the best of both information sources: data and the subject-matter expert (SME) knowledge. The framework consists of two phases. In the first phase, a Gaussian Bayesian network (GBN) is used to extract the implicit relationships between the metrology and production/process variables. In the second phase, the target response variable is defined, the predictors are selected through the associated Markov blanket, and finally, an empirical model is estimated to accurately predict the response. The proposed framework was tested and its effectiveness was confirmed through a real industrial data from a chemical–mechanical polishing (CMP) process in semiconductor fabrication. The physical meaning of the model obtained was also scrutinized by an SME. Note to Practitioners— Unlike the conventional virtual metrology (VM) techniques that model the x–y relationship based only on process data, the proposed method aims at consolidating the process knowledge from experts into an extensive relational structure. Not only the x–y model is inferred but also the relationships among the predictors are revealed. The structure is illustrated in a form of a connected graph so that the correlation between parameters can be expressed explicitly, which is also compatible with the physical laws. With the clear visualization of the correlation structure of variables, the practitioners are able to utilize the result in different applications. The learned structure can be further integrated into the plant advanced process control system, including VM, process monitoring and diagnosis, and run-to-run (R2R) control.

Application of PI-VM for management of the metal target plasma etching processes in OLED display manufacturing

Generation of the defect particles during the plasma-assisted metal dry etching process is induced by the various mechanisms. Most of these mechanisms are caused by the non-volatility of metal-halide compounds generated during the etching process. Degeneration of the metal etching process chamber condition is observed as the frequent process fault caused by the defects, but the worse condition is not recovered by itself. Because of this property of the metal etching process, proper work of the preventive maintenance (PM) to restore the process chamber or the addition of a discharge cleaning step is required periodically. However, inadequate PM or discharge cleaning by the uncertain cause analysis of the defect generation should be a just temporary remedy, and might lead the repetition of similar problems. To solve this problem, the virtual metrology (VM) model based on the plasma information (PI) parameters, known as PI-VM, was developed and applied for the defect control of the metal layer dry etching processes in organic light emitting diode (OLED) display manufacturing. To obtain the information about the generation rates of non-volatile compounds and their removal rates by the exhaustion system, PI parameters are designed with the consideration of the reaction kinetics in the metal etching plasma volume, sheath, and reacting surface using the big data of equipment engineering system (EES) and optical emission spectroscopy (OES) accumulated during the mass production process. The developed PI-VM index could be applied to a 2–3 h earlier alarm system for the defect occurrence, and had succeeded over 90% of alarm rate. This PI-VM alarm was applied to predictive control of the process by the early substitution of the discharge cleaning step or by the repair of the proper parts in the process chamber. By the control of processes based on the predicted results of the PI-VM, management of the mass production line with about 30% decreased defect was possible in OLED display manufacturing.

Just-In-Time Modeling With Variable Shrinkage Based on Gaussian Processes for Semiconductor Manufacturing

Virtual metrology (VM) is often applied in semiconductor manufacturing when process measurements cannot be obtained without delay or without impacting the cycle time. When the process condition is varying, the modeling results can be inaccurate if a single VM model is adopted. Also, the large number of variables in the process data increases the difficulty of obtaining good predictions. To improve the accuracy of the metrology value prediction, it is necessary to select and apply only the significant variables in modeling. This paper proposes a just-in-time approach for VM modeling, along with a variable shrinkage and selection method that uses Gaussian process regression. The proposed method is validated using semiconductor process data and found to be superior compared to conventional methods.

Recurrent feature-incorporated convolutional neural network for virtual metrology of the chemical mechanical planarization process

In semiconductor manufacturing, the chemical mechanical planarization (CMP) process produces higher thickness variability in the edge area of the wafer than that in the center area due to the characteristics of the polishing operation. To address this problem, advanced CMP equipment includes a function that controls the removal rate of each area. However, to take full advantage of this capability, effective advanced process control systems must be implemented with a virtual metrology (VM) model. However, the prediction performance of the VM model often deteriorates due to process drift. Here, we present a deep learning-based VM model that demonstrates high performance in the presence of nonlinear process drift. The proposed model combines a recurrent neural network and a convolutional neural network to extract time-dependent and time-independent features. A two-stage model training method is proposed that alternately updates the weights of each network to improve prediction performance. In the experiments using on-site CMP process data, the performance of the deep learning models exceeded that of standard machine learning models. The proposed model showed an 8.48% decrease in process variability relative to the best-performing machine learning model, which was elastic nets.

Multitask learning for virtual metrology in semiconductor manufacturing systems

Abstract Virtual metrology (VM) estimates the real metrology of wafers from process data collected from multiple chambers. In semiconductor manufacturing, independent models for each process chamber are limited because the number of sampled wafers measured at each chamber are too few to build a reliable model. One potential solution to this problem is to pool the data from all chambers to create a model capable of learning and serving as a global predictive model. However, even with chambers that perform the same operation, the condition of their semiconductor tools may vary because of various factors. This study uses, for the first time, various multitask methods to develop VM models. By learning multiple related tasks simultaneously, multitask methods effectively increase the number of observations included in the prediction model. In addition, by identifying the related task, the method can make a prediction using only similar tasks. This property of multitask learning can be useful to account for lack of information in a single chamber and for diversity among the chambers. The experimental results indicate that multitask models consistently outperformed independent and pooled models regardless of the size of the training set used. Among the multitask methods, a multitask tree-based ensemble model outperformed the others in every case. This implies that the problem of wafer quality prediction can be better addressed with a form of multitask learning.

On Effectiveness of Transfer Learning Approach for Neural Network-Based Virtual Metrology Modeling

Virtual metrology (VM) technologies have been successfully developed to enable wafer-to-wafer quality monitoring with reduced costs in the semiconductor manufacturing process. VM estimates an inspection task by predicting metrology variables as a function of process variables using prediction models trained with previous wafer records collected from the involved set of equipment. However, it is difficult to obtain accurate prediction models, in particular for a newly adopted equipment set, if the number of wafer records for the target equipment set are insufficient. While collecting more records is time-consuming and costly, the abundant data of related equipment sets are fruitful sources to improve VM modeling for an equipment set. Here, we investigate the effectiveness of a transfer learning approach based on neural networks to circumvent data insufficiency. This approach exploits knowledge acquired from previously established VM models of other equipment sets to improve the VM modeling on the target equipment set. Experimental results of the implementation with neural networks on actual datasets demonstrate its superiority in both aspects of metrology accuracy and computational efficiency compared with a traditional independent learning approach.