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 (Peer-Reviewed Journal) 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, Scopus
  • Page Numbers: pp.1088-1111


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.