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

Rao P. K., Beyca O. F., KONG Z. (., BUKKAPATNAM S. T. S., CASE K. E., KOMANDURI R.

IIE TRANSACTIONS, vol.47, no.10, pp.1088-1111, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 10
  • Publication Date: 2015
  • Doi Number: 10.1080/0740817x.2014.1001927
  • Journal Name: IIE TRANSACTIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1088-1111
  • Istanbul Technical University Affiliated: No


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) approximate to 6nm) obtained using a semiconductor chemical mechanical planarization process suggest that the graph-based topological invariant Fiedler number ((2)) was able to quantify and track variations in surface morphology more effectively compared to other quantifiers reported in literature.