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Human Interpretable Virtual Metrology in the Semiconductor Manufacturing
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Doctoral consortium paper proposing a multi-output virtual metrology system for PVD metal layers with a model-agnostic explanation method based on projective operators (ProjSe) and a stability index.
Problem
Virtual metrology in semiconductor manufacturing needs accurate, explainable multi-output prediction of metal-layer physical properties (thickness, resistance at 17 points) from equipment sensor process parameters, which current methods lack.
Approach
Extends the projective selection (ProjSe) variable-selection theory to a model-agnostic explanation method for vector-valued (multi-output) predictions, plus a stability index for explanations, and compares it to SHAP and TreeInterpreter.
Key results
- The proposed projective-operator explanation method outperforms SHAP and TreeInterpreter in computation time.
- The introduced stability index and correlation of the explanations are comparable to SHAP and TreeInterpreter.
- ProjSe-based feature selection results aligned with industry experts' experience and the underlying physics of the process.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the projective-operator explanatory method instead of SHAP or TreeInterpreter | Projective-operator explanatory method · Real-world datasets | computation time | Helped |
| Use the projective-operator explanatory method instead of SHAP or TreeInterpreter | Projective-operator explanatory method · Real-world datasets | stability index | No clear effect |
| Use the projective-operator explanatory method instead of SHAP or TreeInterpreter | Projective-operator explanatory method · Real-world datasets | correlation | No clear effect |
| Select and rank process parameters with ProjSe | Virtual metrology system for PVD metal-layer properties · Semiconductor manufacturer dataset | feature-selection alignment with expert knowledge | Helped |
Surprising findings
- ProjSe performs well for around 20 outputs but struggles with fewer outputs.
Limitations
- Explanation method is preliminary; user studies and public-dataset tests are planned but not done.
- ProjSe struggles with feature selection when the number of outputs is small.
- Data is proprietary industrial data from a single manufacturer.
Experimental setup
Datasets: industrial PVD process data from a semiconductor manufacturer (Infineon)
Benchmarks: industrial PVD virtual metrology dataset
Metrics: computation time stability index correlation
Baselines: SHAP TreeInterpreter tree-model-based feature selection
Builds on: ProjSe SHAP LIME
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