Semi-Supervised Deep Kernel Active Learning for Material Removal Rate Prediction in Chemical Mechanical Planarization

Chunpu Lv, Jingwei Huang, Ming Zhang, Huangang Wang, Tao Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The material removal rate (MRR) is an important variable but difficult to measure in the chemical–mechanical planarization (CMP) process. Most data-based virtual metrology (VM) methods ignore the large number of unlabeled samples, resulting in a waste of information. In this paper, the semi-supervised deep kernel active learning (SSDKAL) model is proposed. Clustering-based phase partition and phase-matching algorithms are used for the initial feature extraction, and a deep network is used to replace the kernel of Gaussian process regression so as to extract hidden deep features. Semi-supervised regression and active learning sample selection strategies are applied to make full use of information on the unlabeled samples. The experimental results of the CMP process dataset validate the effectiveness of the proposed method. Compared with supervised regression and co-training-based semi-supervised regression algorithms, the proposed model has a lower mean square error with different labeled sample proportions. Compared with other frameworks proposed in the literature, such as physics-based VM models, Gaussian-process-based regression models, and stacking models, the proposed method achieves better prediction results without using all the labeled samples.
Original languageEnglish
Article number4392
Number of pages21
Issue number9
Early online date29 Apr 2023
Publication statusPublished - May 2023

Bibliographical note

Copyright © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (


  • Article
  • semi-supervised regression
  • active learning
  • deep kernel learning
  • virtual metrology
  • phase partition
  • phase match


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