Analysis of topography of silicon wafers and wafer-based structures by geomorphometric modeling

Analysis of topography of silicon wafers and wafer-based structures is an important stage of microelectronic manufacturing. In particular, such an analysis allows one to measure deformation of these objects, as well as to estimate their mechanical stresses. In such works, one can use digital elevation models (DEMs) of wafers and structures with a nano- and micrometer-range elevation difference and resolution. Such DEMs can be produced by optical profilometry. In this study, we evaluate geomorphometric modeling to analyze topography of silicon wafers and structures. We used two types of samples: (1) a silicon–quartz structure with a diameter of 150 mm and a deflection of about 20 μm; and (2) a mechanically polished silicon wafer including an analysis area with a size of 0.23 mm x 0.17 mm and an elevation range of about 20 μm. We obtained raw data for these samples with resolutions of 57 μm and 0.4 μm using an optical profilometer Veeco WYKO NT9300. After processing and smoothing raw data, we produced DEMs of two samples with resolutions of 570 μm and 0.4 μm, respectively. Digital models of 12 curvatures and 8 other morphometric variables were derived from the DEMs. The morphometric models were much more informative than the DEMs: they allowed us to reveal hidden topographic patterns of the wafer and structure surfaces.