Quantitative 3D Analysis of Porosity and Fractal Geometry in Electrochemically Etched Macroporous Silicon

Abstract

Macroporous silicon is widely employed in sensing and optoelectronic applications due to its large internal surface area and adjustable pore structure. However, quantitative correlations between morphology and functionality require accurately characterizing the three dimensional pore network. In this study, we used focused Ga+ ion beam scanning electron microscopy tomography to reconstruct representative volumes of electrochemically etched macroporous silicon layers. We extracted true three dimensional porosity and surface-to-volume ratios and compared them with two-dimensional estimates obtained from SEM images. Our results demonstrate that surface-based porosity systematically underestimates true volumetric porosity. These discrepancies arise from anisotropy, branching, and variability in pore size. Fractal analysis reveals that the pore network has moderate geometric complexity, consistent with electrochemical macropore formation mechanisms. The results highlight the importance of direct 3D characterization for reliable morphological quantification and provide a robust framework for interpreting structural trends in macroporous silicon.