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

作者：Rao Prahalad K; Beyca Omer F; Kong Zhenyu; Bukkapatnam Satish T S^*; Case Kenneth E; Komanduri Ranga

来源：IIE Transactions, 2015, 47(10): 1088-1111.

DOI：10.1080/0740817X.2014.1001927

• Surface quality
• surface morphology quantification
• optical metrology
• chemical mechanical planarization (CMP)
• algebraic graph theory
• Fiedler number
• graph-based image processing

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.

• 出版日期2015-10-3