Using a 4-megapixel hybrid photon counting detector for fast, lab-based nanoscale x-ray tomography

TL;DR

This work demonstrates that a large-area hybrid photon counting detector can be integrated into a tabletop SEM-based nano-xCT tool to achieve fast, high-resolution, nondestructive imaging of semiconductor integrated circuits at the 130-nm node. By leveraging the HPCD’s high quantum efficiency and fast photon counting, the authors achieve a ~800× increase in overall imaging speed and collect ~40× more photons than prior work, enabling 3D reconstructions with a voxel size of $40\times40\times80~\text{nm}$ and resolving 160-nm wiring features. They implement geometry corrections for a large flat-panel detector and a physics-based TomoScatt reconstruction with a two-stage ML+MAP workflow on limited-angle data across 7 angles, yielding quantitative image quality metrics: $MTF_{50} \approx 82~\text{nm}$, $FSC_{50} \approx 77~\text{nm}$, and $CNR \approx 69$ for critical features. The results establish the state-of-the-art in lab-based nano-xCT metrology, enabling rapid, in-house failure analysis and nondestructive characterization, with clear pathways for further improvements via hardware upgrades and higher SEM spot quality.

Abstract

Hybrid photon counting detectors (HPCDs) have unlocked new capabilities for x-ray-based measurements at synchrotrons around the world in the last 30 years. By leveraging independently optimized sensor and readout layers, they offer high quantum efficiency ($> 80 \%$), ultra-low dark counts, sub-pixel point-spread function, and high count rates ($> 10^{6}$ counts per pixel per second). Furthermore, their small pixel size and large active area endow them with excellent coverage and resolution for both real-space and reciprocal space imaging. Here, we demonstrate that HPCDs are also well-suited for laboratory-based nanoscale x-ray tomography (nano-xCT). We perform nano-xCT on an integrated circuit fabricated at the 130-nm node and produce a 3D reconstruction with 40 times more photons collected 20 times faster than in this group's previous work, for an overall speedup of 800$\times$. We review the technical considerations of using an HPCD for tabletop tomography. We quantify our reconstruction image quality using well-established metrics, including the modulation transfer function (MTF), Fourier shell correlation (FSC), and contrast-to-noise (CNR), to validate our choice of experimental parameters that provide sufficient resolution and imaging speed. Using these metrics, we determine that even under current experimental conditions, 160 nm wiring features are reconstructed at 75-80 nm spatial resolution.

Figures (4)

• Figure 1: Experimental schematic. (A) Computer assisted design (CAD) drawing of our SEM chamber showing the electron column, the stage and sample holder, the energy dispersive spectrometer (EDS), and the HPCD (placed outside the SEM vacuum chamber). (B) Cartoon side-view of the sample highlighting the interaction between the electron beam and the Pt target, the propagation of the generated x-ray spectrum through the IC sample, and the collection of the attenuated x-ray radiation by an HPCD. In cone-beam xCT, the source-detector-distance ($S_D$) and the source-feature-distance ($S_F$) determine the geometric magnification $M_G = S_D/S_F$.
• Figure 2: Geometric considerations of a large flat-panel detector. (A) Plot of how pixel sensitivity changes as a function of distance on the detector surface from the pixel closest to the source. A purely geometric component $(z/r)^3$ is shown in red, while geometry- and energy-dependent change to the pixel absorption statistics for 10 keV and 20 keV are shown in green and light blue, respectively. Since the detector is rectangular, the plot shows the effect for pixels from the center all the way to a corner, with the edges of the detector marked by black and gray dashed lines. The green shaded area denotes a $\pm 1 \%$ window that we consider to represent a negligible effect. This plot highlights the necessity of implementing a $(z/r)^3$ correction on our data while confirming that energy-dependent effects at 10 keV are negligible. Normal-incidence radiograph stitched together without (B) and with (C) this geometric correction implemented, highlighting the imaging artifacts that would be written onto the reconstructed dataset if the correction were omitted.
• Figure 3: Reconstruction results from a 7-angle dataset covering a $78.5\degree$ arc collected with an HPCD. Two wiring layers (A,B), a digital logic layer (C), and a via layer (D) are all clearly distinguishable and well-resolved. Reconstruction voxels are 40 $\times$ 40 $\times$ 80 nm, so slices are 80 nm thick. From top to bottom, the slices depicted are separated by 640 nm, 560 nm, and 320 nm. The via layer contacts the Si wafer. Scale bar is 1µm in all images. Supplementary Material Fig. 4 shows a slice-by-slice comparison between the HPCD reconstruction and the spectrometer reconstruction (nakamura_nanoscale_2024) for the four slices shown here.
• Figure 4: Implementation of image quality metrics. (A) Cropped region of wiring layer 2 (Fig. \ref{['results']}B) showing a wire misaligned with the image pixel axis along which 20 lines have been drawn that will be used for MTF and CNR analysis. Scale bar is 1µm. (B) Example linecut from (A), showing change in reconstructed density between the wiring feature and the empty space adjacent to it. Pink and green vertical dashed lines denote two distinct regions on the linecut that are used for calculating CNR according to Equation \ref{['eq_cnr']}. (C) Plot of MTF contrast versus feature size in the sample. MTF curves are calculated for each of the 20 lines shown in (A), and the mean MTF curve is shown in dark blue, with the shaded region indicating a $\pm 2\sigma$ confidence interval around the mean. MTF50 and MTF10 vertical lines highlight where the mean MTF contrast drops below 50 % and 10 %, respectively. We take the MTF50 threshold of 82 nm to be a conservative estimate of our system resolution to distinguish wiring from the background. (D) FSC curve of correlation versus spatial frequency (see Equation \ref{['eq_fsc']}), calculated from two completely independently reconstructed halves of a single dataset. The 1 bit per voxel and FSC50 thresholds are indicated by the orange and red dashed lines, respectively, with values 3$\sigma$ above the noise floor indicated by the green dashed line. The FSC50/1 bit thresholds give a reconstruction-wide 3D resolution of 77 nm (the inverse of the spatial frequency threshold), consistent with our voxel size of 40 nm $\times$ 40 nm $\times$ 80 nm.