Abstract

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.

© 2019 Optical Society of America

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Supplementary Material (4)

NameDescription
» Data File 1       Effective index n_eff(Delta_x) for propagation of the fundamental mode of an 1D trench at the center wavelength lambda_c = 1.329 µm of the applied light source spectrum; pure TE- and pure TM-polarization are considered.
» Data File 2       Effective index n_eff(D) for propagation of the fundamental mode in radial direction (+/- 1st harmonic in azimuthal direction) at a circular hole of diameter D in silicon at the center wavelength lambda_c = 1.329 µm of the applied light source.
» Visualization 1       Simulation of the OCT interferogram (intensity pattern I(z)−I_0) when varying the height H of a circular TSV (Through Silicon Via) of diameter D = 5 µm when illuminated by a Gaussian beam of the waist w = 2.7 µm. Dispersion is present.
» Visualization 2       Simulation of the OCT interferogram (intensity pattern I(z)—I_0) when varying the height H of a circular TSV (Through Silicon Via) of diameter D = 5 µm when illuminated by a Gaussian beam of the waist w = 2.7 µm. Dispersion is absent.

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