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This paper reports on progress in the analysis of time-domain optical coherence tomography (OCT) applied to the dimensional metrology of through-silicon vias (TSVs), which are vertical interconnect accesses in silicon, enabling three-dimensional (3D) integration in microelectronics, and estimates the deviations from earlier, simpler models. The considered TSV structures are 1D trenches and circular holes etched into silicon with a large aspect ratio. As a prerequisite for a realistic modeling, we work with spectra obtained from reference interferograms measured at a planar substrate, which fully includes the dispersion of the OCT apparatus. Applying a rigorous modal approach, we estimate the differences to a pure ray tracing technique. Accelerating our computations, we focus on the relevant fundamental modes and apply a Fabry-Perot model as an efficient approximation. Exploiting our results, we construct and present an iterative procedure based on the minimization of a merit function, which concludes TSV heights reliably, accurately, and rapidly from measured interferograms.

Electromagnetic analysis for optical coherence tomography based through silicon vias metrology