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, cilt.47, sa.10, ss.1088-1111, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Konu: 10
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1080/0740817x.2014.1001927
  • Sayfa Sayıları: ss.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.