Virtual metrology of semiconductor PVD process based on combination of tree-based ensemble model

In semiconductor manufacturing processes, virtual metrology (VM) has been investigated as a promising tool to predict important characteristics of products. Although partial least squares (PLS) is a well-known modeling technique that can cope with collinearity and therefore applied to construction of VM, its prediction performance deteriorates due to changes in process characteristics. In particular, maintenance of equipment strongly affects the process characteristics and the prediction performance. In this paper, VM was developed by using locally weighted PLS (LW-PLS), which is a type of just-in-time modeling technique, and it was used to predict the etching conversion differential of an actual dry etching process. The industrial application results have shown that the developed VM based on LW-PLS is superior to the conventional VM based on the sequential update model and artificial neural network model. In particular, it has been confirmed that the LW-PLS-based VM can keep its high prediction performance even after the maintenance, i.e., replacement of parts.

Virtual metrology (VM) is the prediction of end-of-batch properties (i.e., metrology data) using process variables and other information available for the process and/or the product (i.e., machine data) without physically conducting property measurement. VM (sometimes augmented with existing metrology) has been utilized in semiconductor process monitoring and control. Besides the economic benefit of replacing or reducing metrology tools, due to the instant availability of high frequency machine data, a good VM can actually provide better process monitoring and control performance compared to the same monitoring and control schemes based on the physical metrology data which often obtained at lower frequencies and usually with delays. In this paper, we propose a statistics pattern analysis (SPA) based VM approach for predicting sheet resistance using optical emission spectroscopy (OES) data. The advantageous properties of the SPA based VM are discussed. And the performance of the SPA based VM is compared with several commonly used VM algorithms in terms of prediction accuracy.

Plasma etch is a complex semiconductor manufacturing process in which material is removed from the surface of a silicon wafer using a gas in plasma form. As the process etch rate cannot be measured easily during or after processing, virtual metrology is employed to predict the etch rate instantly using ancillary process variables. Virtual metrology is the prediction of metrology variables using other easily accessible variables and mathematical models. This paper investigates the use of Gaussian process regression as a virtual metrology modelling technique for plasma etch data.

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.

In TSV fabrication process, TSV depth measurement of all wafers is essential to maintain high yield and wafer quality. However, there are limits such as high cost and (low throughput using an actual metrology, i.e. scanning electron microscope (SEM), and only few wafers in a lot are monitored in practice. In this research, we presented a virtual metrology (VM) system for TSV depth measurement after etching process. The proposed VM system is based on PLS regression (PLSR) and neural networks (NN) using OES data to predict TSV depth. Real operational data taken during TSVs etching process along with 80 and 25 μm diameter TSVs are used in order to verify the quality of the prediction accuracy of the proposed VM model.

This paper proposes a novel highly accurate virtual metrology (VM) method based on adaptive online time-series learning. The method comprises a novel time-series prediction algorithm robust against data drifts and shifts observed in semi-conductor manufacturing. The prediction algorithm incorporates time-aware data normalization and adaptive online learning. The time-aware normalizer transforms the data to suppress the effect of drifts. The adaptive online learner captures the time-varying relationship between response and inputs caused by shifts. On both simulated and real process data our approach outperforms conventional VM approaches. When applied to advanced process control (APC) on high-volume production lines at a major semiconductor manufacturer, our VM method substantially reduced variability of process outcomes.

In semiconductor manufacturing, as some of the variables in processes cannot be easily measured during or after the production, virtual metrology (VM) is employed to predict metrology outputs using ancillary process variables. However, because of changeable processes and high-dimensional inputs, VM can be expensive or difficult to implement. In this work, just-in-time (JIT) modeling is used to cope with changes in process characteristics and to automatically update the statistical model. In addition, owing to the non-uniform data distribution, Gaussian process regression (GPR) as a probabilistic approach is a typical method to enhance the robustness of the system in the probability density space. With high-dimensional input variables in deposition processes, a variable shrinkage and selection method for GPR is proposed. It is superior to the conventional methods. The features of the proposed method are shown by way of illustrative examples and the proposed method is compared to conventional work based on real semiconductor process data.

Multi-step virtual metrology for semiconductor manufacturing: A multilevel and regularization methods-based approach

Plasma etch is a key process in modern semiconductor manufacturing facilities as it offers process simplification and yet greater dimensional tolerances compared to wet chemical etch technology. The main challenge of operating plasma etchers is to maintain a consistent etch rate spatially and temporally for a given wafer and for successive wafers processed in the same etch tool. Etch rate measurements require expensive metrology steps and therefore in general only limited sampling is performed. Furthermore, the results of measurements are not accessible in real-time, limiting the options for run-to-run control. This paper investigates a Virtual Metrology (VM) enabled Dynamic Sampling (DS) methodology as an alternative paradigm for balancing the need to reduce costly metrology with the need to measure more frequently and in a timely fashion to enable wafer-to-wafer control. Using a Gaussian Process Regression (GPR) VM model for etch rate estimation of a plasma etch process, the proposed dynamic sampling methodology is demonstrated and evaluated for a number of different predictive dynamic sampling rules.

Advanced Process Control (APC) is an important research area in Semiconductor Manufacturing (SM) to improve process stability crucial for product quality. In low-volume-high-mixture fabrication plants (fabs), Knowledge Discovery in Databases is extremely challenging due to complex technology mixtures and reduced availability of data for comparable process steps. High Density Plasma Chemical Vapor Deposition (HDP CVD) appears to be a process area in SM predestinated for application of Data Mining (DM). Enhancing physical metrology by predictive models leads to smart future fabs. Actual research focuses on Virtual Metrology (VM) using high sophisticated Machine Learning (ML) methods to model unknown functional interrelations and to predict the thickness of dielectric layers deposited onto a metallization layer of the manufactured wafers. Decision Trees (DT), Neural Networks (NN) and Support Vector Regression (SVR) have been investigated to maximize the accuracy of the regression. For data of various logistical granularities promising results have been achieved by implementing these statistical models.

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.

This paper discussed the virtual metrology (VM) modelling of multi-class quality to describe the relationship between the variables of a production machine's condition and the estimated/forecasted product quality soon after finishing the machine processing. Applications of PCA and LASSO technique of the Sparse modelling were introduced to define the multi-dimensional quality. Because the high accuracy and quick computations are required for the VM modelling, in this study, the PCA-LASSO combination was applied before building the VM models based on the kernel SVM (kSVM), particularly the linear kernel for real-time use. As the result of evaluation of a CVD (Chemical vapor deposition) process in an actual semiconductor factory, LASSO and linear-SVM could reduce the scale of the machine variable's set and calculation time by almost 57% and 95% without deterioration of accuracy even without PCA. In addition, as the PCA-LASSO, the multi-dimensional quality was rotated to the orthogonality space by PCA to summarize the extracted variables responding to the primary independent hyperspace. As the result of the PCA-LASSO combination, the scale of machine variables extracted was improved by 83%, besides the accuracy of the linear-SVM is 98%. It is also effective as the pre-process of Partial Least Square (PLS).

Optimizing lithography and plasma etching is the key for manufacturing nanoelectronics and Micro-Electromechanical Systems (MEMS). We propose a Deep Learning (DL) based virtual metrology algorithm for CD-SEM images that addresses the background noise, the low contrast edges, and the discrepancies between design and wafer that occur in such images and achieves automatic and accurate segmentation that is robust to changes in structure and process recipe. Accurate segmentation of CD-SEM images of the nanostructures provides the flexibility to make a very diverse set of measurements. The results show that the DL applied to CD-SEM images significantly improves the accuracy and robustness of virtual metrology.

The prediction of total anthocyanin concentration in red-grape homogenates using visible-near-infrared spectroscopy and artificial neural networks

Crop yields are important for food security and people’s living standards, and it is therefore very important to predict the yield in a timely manner. This study used different vegetation indices and red-edge parameters calculated based on the canopy reflectance obtained from near-surface hyperspectral data and UAV hyperspectral data and used the partial least squares regression (PLSR) and artificial neural network (ANN) methods to estimate the yield of winter wheat at different growth stages. Verification was performed based on these two types of hyperspectral remote sensing data and the yield was estimated using vegetation indices and a combination of vegetation indices and red-edge parameters as the modeling independent variables, respectively, using PLSR and ANN regression, respectively. The results showed that, for the same data source, the optimal vegetation index for estimating the yield was the same in all of the studied growth stages; however, the optimal red-edge parameters were different for different growth stages. Compared with using only the vegetation indices as the modeling factor to estimate yield, the combination of the vegetation indices and red-edge parameters obtained superior estimation results. Additionally, the accuracy of yield estimation was shown to be improved by using the PLSR and ANN methods, with the yield estimation model constructed using the PLSR method having a better prediction effect. Moreover, the yield prediction model obtained using the near-surface hyperspectral sensors had a higher fitting and accuracy than the model obtained using the UAV hyperspectral remote sensing data (the results were based on the specific growth stressors, N and water supply). This study shows that the use of a combination of vegetation indices and red-edge parameters achieved an improved yield estimation compared to the use of vegetation indices alone. In the future, the selection of suitable sensors and methods needs to be considered when constructing models to estimate crop yield.