Abstract
Manufacturing of integrated circuits involves many sequential processes executed to nanoscale tolerances, and the yield depends on the often-unmeasured quality of intermediate steps. Taking physical quality measurements in this high-throughput industry can be expensive and time-consuming. Instead, we seek to predict product quality characteristics using readily available sensor readings of the tool environment during processing of each wafer and employ Gaussian Process Regression (GPR) paradigm to realize this Virtual Metrology (VM) concept. Convergence of the GPR based VM estimation of product quality is hastened through an active sampling scheme, whereby the predictive uncertainty of the GPR model informs which wafer’s quality to measure next in order to obtain maximal additional information for the VM model. We evaluate these methods using a large dataset collected from a plasma-enhanced chemical vapor deposition (PECVD) process, with relevant tool sensor readings and the corresponding physical measurements of mean film thicknesses for 32,000 wafers. By selecting which wafers to physically measure for VM model updates, the GPR based VM method achieves ~10% greater accuracy on average than the partial least squares based method.
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Notes
- 1.
In deriving a GP, the underlying parametric model’s weights are integrated out, so the tunable parameters of the GP prior are referred to as hyperparameters to emphasize the non-parametric nature of this approach.
- 2.
Since the dependence of the latent function, f on the parameters, θ tends to be well-concentrated, approximating this dependence as a line through the MLE, \( \widehat{\theta } \) seems reasonable.
- 3.
The invariance of mutual information to homeomorphic transformations make this learning process robust to scaling or rotating of the current embedding, or to centering and scaling of the inputs and outputs.
- 4.
RMSE more heavily penalizes large predictive errors than mean absolute error (MAE), and typically yields clearer outliers.
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Darwin, T., Garnett, R., Djurdjanovic, D. (2018). Gaussian Process Regression for Virtual Metrology of Microchip Quality and the Resulting Selective Sampling Scheme. In: Ni, J., Majstorovic, V., Djurdjanovic, D. (eds) Proceedings of 3rd International Conference on the Industry 4.0 Model for Advanced Manufacturing. AMP 2018. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-89563-5_19
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