Quantification of Ultraprecision Surface Morphology using an Algebraic Graph Theoretic Approach

Assessment of progressive, nano-scale variation of surface morphology during ultraprecision manufacturing processes, such as fine-abrasive polishing of semiconductor wafers, is a challenging proposition owing to limitations with traditional surface quantifiers. We present an algebraic graph theoretic approach that uses graph topological invariants for quantification of ultraprecision surface morphology. The graph theoretic approach captures heterogeneous multi-scaled aspects of surface morphology from optical micrographs, and is therefore valuable for in situ real-time assessment of surface quality. Extensive experimental investigations with specular finished (Sa ∼ 5 nm) blanket copper wafers from a chemical mechanical planarization (CMP) process suggest that the proposed method was able to quantify and track variations in surface morphology more effectively than statistical quantifiers reported in literature.