Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Prognostics and Health Management of Wafer Chemical-Mechanical Polishing System using Autoencoder

Kart-Leong Lim, Rahul Dutta

TL;DR

This work addresses predicting wafer material removal rate ($MRR$) in CMP manufacturing using the PHM 2016 dataset, where ground-truth labels for supervised learning are scarce. It introduces an autoencoder trained with an autoencoder-based clustering (ABC) loss to produce a latent space aligned with cluster structure, enhancing linear regression performance in the latent space. The study compares two clustering strategies—Kmeans and infinite Gaussian mixture models (iGMM)—against baselines based on statistical moments, raw/concatenated time-series, and PCA, reporting that the ABC approach improves RMSE, with the best configuration achieving competitive results (e.g., RMSE around 4.77). The findings indicate that deep clustering for regression can yield practical benefits in industrial PHM tasks, potentially reducing production costs through better wear prediction and forecasting.

Abstract

The Prognostics and Health Management Data Challenge (PHM) 2016 tracks the health state of components of a semiconductor wafer polishing process. The ultimate goal is to develop an ability to predict the measurement on the wafer surface wear through monitoring the components health state. This translates to cost saving in large scale production. The PHM dataset contains many time series measurements not utilized by traditional physics based approach. On the other hand task, applying a data driven approach such as deep learning to the PHM dataset is non-trivial. The main issue with supervised deep learning is that class label is not available to the PHM dataset. Second, the feature space trained by an unsupervised deep learner is not specifically targeted at the predictive ability or regression. In this work, we propose using the autoencoder based clustering whereby the feature space trained is found to be more suitable for performing regression. This is due to having a more compact distribution of samples respective to their nearest cluster means. We justify our claims by comparing the performance of our proposed method on the PHM dataset with several baselines such as the autoencoder as well as state-of-the-art approaches.

Prognostics and Health Management of Wafer Chemical-Mechanical Polishing System using Autoencoder

TL;DR

This work addresses predicting wafer material removal rate () in CMP manufacturing using the PHM 2016 dataset, where ground-truth labels for supervised learning are scarce. It introduces an autoencoder trained with an autoencoder-based clustering (ABC) loss to produce a latent space aligned with cluster structure, enhancing linear regression performance in the latent space. The study compares two clustering strategies—Kmeans and infinite Gaussian mixture models (iGMM)—against baselines based on statistical moments, raw/concatenated time-series, and PCA, reporting that the ABC approach improves RMSE, with the best configuration achieving competitive results (e.g., RMSE around 4.77). The findings indicate that deep clustering for regression can yield practical benefits in industrial PHM tasks, potentially reducing production costs through better wear prediction and forecasting.

Abstract

The Prognostics and Health Management Data Challenge (PHM) 2016 tracks the health state of components of a semiconductor wafer polishing process. The ultimate goal is to develop an ability to predict the measurement on the wafer surface wear through monitoring the components health state. This translates to cost saving in large scale production. The PHM dataset contains many time series measurements not utilized by traditional physics based approach. On the other hand task, applying a data driven approach such as deep learning to the PHM dataset is non-trivial. The main issue with supervised deep learning is that class label is not available to the PHM dataset. Second, the feature space trained by an unsupervised deep learner is not specifically targeted at the predictive ability or regression. In this work, we propose using the autoencoder based clustering whereby the feature space trained is found to be more suitable for performing regression. This is due to having a more compact distribution of samples respective to their nearest cluster means. We justify our claims by comparing the performance of our proposed method on the PHM dataset with several baselines such as the autoencoder as well as state-of-the-art approaches.

Paper Structure

This paper contains 17 sections, 5 equations, 4 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Autoencoder based clustering loss
  4. Clustering approach
  5. Kmeans
  6. Infinite Gaussian mixture model
  7. Experiment: Deep clustering for predictive modeling
  8. Feature extraction
  9. Statistical moments on time series
  10. Concatenated time series
  11. Autoencoder setup
  12. Baselines results
  13. Reconstruction loss vs Clustering loss
  14. Clustering loss: Infinite GMM vs Kmeans
  15. Reconstruction loss + Clustering loss with Kmeans
  16. ...and 2 more sections

Figures (4)

  • Figure 1: Left: Reconstruction loss based autoencoder latent space is not optimized for regression. Right: Clustering in the latent space can improve regression due to the samples being more sparsely distributed (with respect to their cluster mean, as depicted in red).
  • Figure 2: Backpropagation training (dashed arrows) of the raw latent space $z$ using reconstruction loss and ABC loss. The ABC loss exploits GMM hidden variables $B,\sigma$ and $\pi$ for the encoder weight training. Finally, MRR regression modeling and prediction are performed in the latent space of the trained encoder.
  • Figure 3: The MRR histograms of wafers. We observed two distributions which refer to samples with low wear ($50\leq MRR\leq100$) and high wear ($140\leq MRR\leq200$) respectively for each dataset partitioning (i.e. training, validation and test)
  • Figure 4: Variables of usages, pressure, slurry and rotation of a CMP process for a wafer sample.