Virtual Metrology for Semiconductor Manufacturing Processes

Virtual metrology (VM) refers to the estimation of critical wafer characteristics through computational models, rather than direct physical measurement. In advanced semiconductor fabs, where each physical measurement can add cost, time and risk of contamination, VM offers a non-intrusive alternative by exploiting vast process and sensor datasets. By integrating information from in-situ sensors, such as optical emission spectroscopy and chamber monitoring, with historical equipment and recipe data, VM models predict outputs like film thickness, etch depth or overlay errors with high accuracy. This approach supports real-time process control, run-to-run compensation and fault detection, thereby improving yield, reducing cycle time and optimising tool utilisation. Machine learning techniques—including regression, deep neural networks and ensemble learning—form the backbone of modern VM systems. These models learn complex, non-linear relationships between process inputs and metrology outputs, enabling predictive monitoring across etching, deposition and lithography steps. VM thus underpins the shift towards Industry 4.0 in semiconductor manufacturing, ensuring tighter process control, enhanced throughput and more sustainable production.

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One study introduced a plasma-information virtual metrology (PI-VM) framework for real-time prediction of etch profile parameters using optical emission spectroscopy data. Statistical regression methods were trained on features extracted from emission spectra to estimate etch depth, critical dimension bowing and complex etch-area metrics, achieving R² values above 0.8 for key outputs. This work demonstrated how plasma physics insights can guide feature selection and model design, yielding robust monitoring of plasma etching processes.

In another development, deep learning architectures were applied to virtual metrology in a high-volume fabrication environment. A convolutional neural network (CNN) model was trained on historical process logs and sensor readings to predict overlay errors in photolithography, extending earlier successes in plasma-based etch and deposition. The CNN outperformed traditional machine-learning baselines, reducing mean prediction error and showing promise for wider deployment across multiple tool platforms without extensive feature engineering.

More recently, a multi-source ensemble method was proposed to address data heterogeneity in VM applications. By employing a random-source selection strategy within a bagging framework, tree-based learners were constructed on diverse sensor streams, reducing inter-model correlation and mitigating overfitting. Applied to plasma etch data, this ensemble approach delivered improved predictive stability and generalisation compared with single-model and naive data-fusion techniques, highlighting the value of advanced data-fusion strategies in VM systems.

Virtual Metrology for Semiconductor Manufacturing Processes publication trend

The graph below shows the total number of articles in virtual metrology for semiconductor manufacturing processes across all publications each year (not limited to Nature Index journals).

Technical terms

Virtual metrology (VM): A predictive modelling approach that estimates wafer metrology outputs using process and sensor data instead of physical measurement.

Optical emission spectroscopy (OES): An in-situ sensor technique that captures the light emitted by plasma species to infer process conditions.

Convolutional neural network (CNN): A deep learning architecture, originally designed for image analysis, here adapted to learn complex patterns in sequential sensor and process data.

Run-to-run control: A feedback strategy in which VM predictions are used to adjust tool settings between successive wafer runs to compensate for drift and disturbances.

Ensemble learning: A machine-learning approach that combines multiple models to improve predictive accuracy and robustness, often through methods like bagging or boosting.

References

1. Development of Virtual Metrology Using Plasma Information Variables to Predict Si Etch Profile Processed by SF6/O2/Ar Capacitively Coupled Plasma. Materials (2021).
2. Virtual Metrology in Semiconductor Fabrication Foundry Using Deep Learning Neural Networks. IEEE Access (2022).
3. Multi-source ensemble method with random source selection for virtual metrology. Annals of Operations Research (2024).