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

Prahalad K. Rao, Omer F. Beyca, Zhenyu Kong, Satish T.S. Bukkapatnam*, Kenneth E. Case, Ranga Komanduri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1088-1111
Number of pages24
JournalIIE Transactions (Institute of Industrial Engineers)
Volume47
Issue number10
DOIs
Publication statusPublished - 3 Oct 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
Copyright © "IIE" 2015.

Funding

FundersFunder number
National Stroke Foundation1437139, IOS 1146882, CMMI 1266331, IIP 1355765, 1432914
Oklahoma State University
National Science Foundation1401511

    Keywords

    • algebraic graph theory
    • chemical mechanical planarization (CMP)
    • Fiedler number
    • graph-based image processing
    • optical metrology
    • surface morphology quantification
    • Surface quality

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