(587d) Robust Virtual Metrology of Plasma Etch Tools Using Growing Structure Multiple Models Systems with Dynamic Partial Least Squares Models

Bo Lu^a, John Stuber^b, Thomas F. Edgar^a
a McKetta Department of Chemical Engineering, ^b Texas Instruments Inc.
The University of Texas at Austin, 1 University Station C0400, Austin, TX 78712
Email: edgar@che.utexas.edu

Traditional semiconductor manufacturing factories have relied on run-to-run process control with external metrology. Only the most critical processes have metrology on every wafer; even in these cases, excursions in product quality are not detected until many more wafers have been processed. Virtual metrology aims to predict end-of-batch outputs using fault diagnostic trace data and other end-point readings. Based on predictions made by virtual metrology, control engineers can then make the decision on whether to perform additional metrology sampling or apply feed-forward adjustment in subsequent processing steps. However, semiconductor processes experience shifts and drifts in their operation, making it difficult to develop data-driven models with high fidelity predictions. To increase the robustness of these models, model updates such as recursive model update or moving-window updates can be used (Khan et al. 2007, Lu et al. 2014). However, adaptive models do not predict well across discontinuity or major events (such as preventive maintenance) and are sensitive to disturbances in update data. On the other hand, Mixture modeling by combining the predictions of more accurate local models has also been proposed; but this approach requires large amount of training data to initialize and introduces additional complexity in both the modeling and the interpretation of results. Consequently, there exists a need to develop a robust virtual metrology framework capable of maintaining prediction accuracy across event boundaries and over longer periods of process drifts and disturbances.

In this study, a novel divide-and-conquer approach combining growing structure multiple model systems (GSMMS) with Dynamic Partial Least Squares (DPLS) has been proposed. GSMMS models based on simple least squares models have been shown to be effective in approximating nonlinearity in dynamic systems with two or three input variables (Liu et al. 2009). The GSMMS utilizes a growing self-organizing map (GSOM) to adaptively allocate future incoming data to the appropriate node. In cases of process discontinuities or disturbances that are previously unseen, the GSOM “grows” a new node to accommodate the new behavior. This flexible partitioning scheme reduces the need for large amount of initial training data. Efficient dynamic partial least squares (DPLS) models provide estimates of local model parameters for each GSOM node for much larger space of input variables (Galicia et al. 2011). The proposed method is applied to an industrial dataset of a metal etch process from Texas Instruments. Comparisons against the moving-window adaptive PLS model and the mixture modeling with K-means clustering demonstrates the robustness of the GSMMS-DPLS model over current state-of-art alternatives.

References

Galicia, H.J., He, Q.P. & Wang, J., 2011. A reduced order soft sensor approach and its application to a continuous digester. Journal of Process Control, 21(4), pp.489–500.

Khan, A., Moyne, J. & Tilbury, D., 2007. An approach for factory-wide control utilizing virtual metrology. … , IEEE Transactions on Semiconductor Manufacturing, 20(4), pp.364–375.

Liu, J. et al., 2009. Growing Structure Multiple Model Systems for Anomaly Detection and Fault Diagnosis. Journal of Dynamic Systems, Measurement, and Control, 131(5), p.051001.

Lu, B., Stuber, J. & Edgar, T.F., 2014. Integrated Online Virtual Metrology and Fault Detection in Plasma Etch Tools. Industrial & Engineering Chemistry Research, 53(13), pp.5172–5181.