edfas.org 9 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 25 NO. 4 We have found it essential for the reconstruction to model the x-ray source accurately. During the research, we improved the CT spatial resolution by a factor of two simply by starting from a better estimate of the mean transmission through the sample. Detailed radiationtransport modeling of the 3D shape of the x-ray source (and its changes as the source was tilted through various angles) improved the resolution by another factor of two. Both analytical steps were needed to produce the highquality reconstruction results we obtained with a mere 100 photons detected per voxel. In addition to the shape of the source, the x-ray energy spectrum is also incorporated into the analysis. Again, we use radiation-transport modeling to learn the form of the spectrum. Our TES detectors report the energy of each transmitted photon, allowing our reconstruction algorithm to weight each photon according to its measured energy. This weighting eliminates “beam-hardening artifacts,” a class of bias often present when imaging with energy-integrating detectors. Maximum-likelihood and Bayesian methods have an additional advantage: users can obtain confidence intervals for the reconstruction. It is possible in principle to give a probability that two adjacent pieces of metal are connected or not, or a confidence interval for the width of a given metal line. The first full IC measurement with Tomcat was made in early 2022 over the course of 300 hours. X-ray transmission scanning at a single angle was repeated for twelve to sixteen hours in a day, then the sample was rotated about the vertical axis to a new angle for the next day, until the sample was imaged many times each over a full range of ±45° in 12 steps. This sample IC was designed and fabricated by colleagues who shared the GDS circuit-design files. The data were used to reconstruct some 100 μm2 of the sample IC, an IC known to have wiring features as narrow as 160 nm. Comparison of the reconstructed data to the GDS file shows that Tomcat successfully identified and resolved all features in field of view (Fig. 6). We are not aware of any similar, published, structure-by-structure verification of a laboratory CT reconstruction based on the circuit’s design file. FUTURE DIRECTIONS We are now pursuing improvements to the existing Tomcat instrument. The first is to install TES arrays with smaller supporting electronics, which allows us to operate many more cryogenic detectors. This change will improve the system’s imaging speed, which has been limited so far by the small x-ray detection area. Figure 7 shows one of the “microsnouts” now being installed in Tomcat. These small structures will allow us to pack 3000 TESs in 12 arrays close to the IC sample.[18] Coupled with higher-transmission x-ray vacuum windows, the new design should measure x-ray photons at twenty times the rate possible with the single array of 240 TESs used in the first design (Fig. 2). Tomcat uses the energy resolution of the TES to distinguish signal photons from background. Many electrons from the SEM beam penetrate the platinum target layer, and the bremsstrahlung they create beyond the target could come from practically anywhere, smearing the images badly. The Pt fluorescence photons, on the other hand, are guaranteed to be emitted in the target and thus confined to a 100 nm spot. This was the initial reason to use high-resolution spectroscopy in the instrument. With our experience and modeling to date, and with the platinum target film roughly 100 nm thick, we have found that even the bremsstrahlung can be mostly confined to a small region—small enough to be a useful signal for tomography at the desired spatial resolution. In this limit, the energy-resolving power of a TES is less critical. Recent Fig. 7 The “microsnout” now replacing its much larger predecessor.
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