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A graph-theoretic approach for quantification of surface morphology variation and its application to chemical mechanical planarization process

Author

Listed:
  • Prahalad K. Rao
  • Omer F. Beyca
  • Zhenyu (James) Kong
  • Satish T. S. Bukkapatnam
  • Kenneth E. Case
  • Ranga Komanduri

Abstract

We present an algebraic graph-theoretic approach for quantification of surface morphology. Using this approach, heterogeneous, multi-scaled aspects of surfaces; e.g., semiconductor wafers, are tracked from optical micrographs as opposed to reticent profile mapping techniques. Therefore, this approach can facilitate in situ real-time assessment of surface quality. We report two complementary methods for realizing graph-theoretic representation and subsequent quantification of surface morphology variations from optical micrograph images. Experimental investigations with specular finished copper wafers (surface roughness (Sa) ∼ 6 nm) obtained using a semiconductor chemical mechanical planarization process suggest that the graph-based topological invariant Fiedler number (λ2) was able to quantify and track variations in surface morphology more effectively compared to other quantifiers reported in literature.

Suggested Citation

  • Prahalad K. Rao & Omer F. Beyca & Zhenyu (James) Kong & Satish T. S. Bukkapatnam & Kenneth E. Case & Ranga Komanduri, 2015. "A graph-theoretic approach for quantification of surface morphology variation and its application to chemical mechanical planarization process," IISE Transactions, Taylor & Francis Journals, vol. 47(10), pages 1088-1111, October.
    • Handle: RePEc:taf:uiiexx:v:47:y:2015:i:10:p:1088-1111
    DOI: 10.1080/0740817X.2014.1001927
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    Cited by:

    1. Jaeseung Baek & Myong K. Jeong & Elsayed A. Elsayed, 2024. "Spatial randomness-based anomaly detection approach for monitoring local variations in multimode surface topography," Annals of Operations Research, Springer, vol. 341(1), pages 173-195, October.
    2. Chenang Liu & Rongxuan Raphael Wang & Ian Ho & Zhenyu James Kong & Christopher Williams & Suresh Babu & Chase Joslin, 2023. "Toward online layer-wise surface morphology measurement in additive manufacturing using a deep learning-based approach," Journal of Intelligent Manufacturing, Springer, vol. 34(6), pages 2673-2689, August.

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