SEM-based spatial analysis of rough surfaces: Topographic edge effects and their mitigation

Nanostructured surfaces are attracting a lot of scientific interest due to their usage in a plethora of applications ranging from semiconductor industry to medical diagnostics field. A widely used technique for their inspection is the Scanning Electron Microscopy (SEM) which provides images of surfaces with both high resolution and large depth of focus. Although SEM cannot measure surface height topography, the analysis of SEM images can deliver useful information for the spatial arrangement of surface rough structures. However, this spatial advantage of SEM images is undermined in the case of rough step-like surfaces featured by stochastically distributed steep edges. The presence of the latter distorts the monotonic relationship between topography and image luminosity due to the edge effects dominating in SEM imaging. In this work, we first demonstrate that the SEM edge effect can affect widely used metrics of spatial statistics, such as the Fourier spectrum and the correlation function, potentially leading to misleading conclusions about the original topography. Then, we illustrate this phenomenon in both real SEM and artificially simulated images and highlight the impact of edge width on surface spatial statistics. Finally, we propose a method to mitigate this problem based on selectively averaging the brightness of an optimal number of neighboring-to-the-edge pixels and replacing the original edge pixels with this average. The suggested method successfully retrieved the original spatial statistics metrics when applied to both simulated and real SEM images of rough step-like surfaces.