Quantification of Ultraprecision Surface Morphology using an Algebraic Graph Theoretic Approach

Prahalad Rao, Satish Bukkapatnam, Zhenyu Kong*, Omer Beyca, Kenneth Case, Ranga Komanduri

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

7 Citations (Scopus)


Assessment of progressive, nano-scale variation of surface morphology during ultraprecision manufacturing processes, such as fine-abrasive polishing of semiconductor wafers, is a challenging proposition owing to limitations with traditional surface quantifiers. We present an algebraic graph theoretic approach that uses graph topological invariants for quantification of ultraprecision surface morphology. The graph theoretic approach captures heterogeneous multi-scaled aspects of surface morphology from optical micrographs, and is therefore valuable for in situ real-time assessment of surface quality. Extensive experimental investigations with specular finished (Sa ∼ 5 nm) blanket copper wafers from a chemical mechanical planarization (CMP) process suggest that the proposed method was able to quantify and track variations in surface morphology more effectively than statistical quantifiers reported in literature.

Original languageEnglish
Pages (from-to)12-26
Number of pages15
JournalProcedia Manufacturing
Publication statusPublished - 2015
Externally publishedYes
Event43rd North American Manufacturing Research Conference, NAMRC 2015 - Charlotte, United States
Duration: 8 Jun 201512 Jun 2015

Bibliographical note

Publisher Copyright:
© 2015 Published by Elsevier B.V.


The authors acknowledge the generous support of the NSF via the following grants: CMMI 1266331, 1437139, 1432914, 1401511, IIP 1355765, IOS 1146882. One of the authors (SB) also wishes to acknowledge AT&T Professorship (Oklahom a State University) and Rockwell International professorship (Texas A&M University) for additional support. The authors dedicate this article to the fond memory of Dr. Ranga Komanduri (1942-2011), a scholar and a mentor, whose presence would be deeply missed.

FundersFunder number
National Science Foundation1437139, IOS 1146882, CMMI 1266331, IIP 1355765, 1401511, 1432914


    • Fiedler number
    • Surface morphology quantification
    • chemical mechanical polishing (CMP)
    • copper CMP
    • graph theory
    • semiconductor wafer metrology


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