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 language | English |
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Pages (from-to) | 1088-1111 |
Number of pages | 24 |
Journal | IIE Transactions (Institute of Industrial Engineers) |
Volume | 47 |
Issue number | 10 |
DOIs | |
Publication status | Published - 3 Oct 2015 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:Copyright © "IIE" 2015.
Funding
Funders | Funder number |
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National Stroke Foundation | 1437139, IOS 1146882, CMMI 1266331, IIP 1355765, 1432914 |
Oklahoma State University | |
National Science Foundation | 1401511 |
Keywords
- algebraic graph theory
- chemical mechanical planarization (CMP)
- Fiedler number
- graph-based image processing
- optical metrology
- surface morphology quantification
- Surface quality