Nanoscale Three-Dimensional Imaging of Integrated Circuits Using a Scanning Electron Microscope and Transition-Edge Sensor Spectrometer.

X-ray nanotomography is a powerful tool for the characterization of nanoscale materials and structures, but it is difficult to implement due to the competing requirements of X-ray flux and spot size. Due to this constraint, state-of-the-art nanotomography is predominantly performed at large synchrotron facilities. We present a laboratory-scale nanotomography instrument that achieves nanoscale spatial resolution while addressing the limitations of conventional tomography tools. The instrument combines the electron beam of a scanning electron microscope (SEM) with the precise, broadband X-ray detection of a superconducting transition-edge sensor (TES) microcalorimeter. The electron beam generates a highly focused X-ray spot on a metal target held micrometers away from the sample of interest, while the TES spectrometer isolates target photons with a high signal-to-noise ratio. This combination of a focused X-ray spot, energy-resolved X-ray detection, and unique system geometry enables nanoscale, element-specific X-ray imaging in a compact footprint. The proof of concept for this approach to X-ray nanotomography is demonstrated by imaging 160 nm features in three dimensions in six layers of a Cu-SiO2 integrated circuit, and a path toward finer resolution and enhanced imaging capabilities is discussed.

Noise-resilient deep learning for integrated circuit tomography.

X-ray tomography is a non-destructive imaging technique that reveals the interior of an object from its projections at different angles. Under sparse-view and low-photon sampling, regularization priors are required to retrieve a high-fidelity reconstruction. Recently, deep learning has been used in X-ray tomography. The prior learned from training data replaces the general-purpose priors in iterative algorithms, achieving high-quality reconstructions with a neural network. Previous studies typically assume the noise statistics of test data are acquired a priori from training data, leaving the network susceptible to a change in the noise characteristics under practical imaging conditions. In this work, we propose a noise-resilient deep-reconstruction algorithm and apply it to integrated circuit tomography. By training the network with regularized reconstructions from a conventional algorithm, the learned prior shows strong noise resilience without the need for additional training with noisy examples, and allows us to obtain acceptable reconstructions with fewer photons in test data. The advantages of our framework may further enable low-photon tomographic imaging where long acquisition times limit the ability to acquire a large training set.

Physics-assisted generative adversarial network for X-ray tomography.

X-ray tomography is capable of imaging the interior of objects in three dimensions non-invasively, with applications in biomedical imaging, materials science, electronic inspection, and other fields. The reconstruction process can be an ill-conditioned inverse problem, requiring regularization to obtain satisfactory results. Recently, deep learning has been adopted for tomographic reconstruction. Unlike iterative algorithms which require a distribution that is known a priori, deep reconstruction networks can learn a prior distribution through sampling the training distributions. In this work, we develop a Physics-assisted Generative Adversarial Network (PGAN), a two-step algorithm for tomographic reconstruction. In contrast to previous efforts, our PGAN utilizes maximum-likelihood estimates derived from the measurements to regularize the reconstruction with both known physics and the learned prior. Compared with methods with less physics assisting in training, PGAN can reduce the photon requirement with limited projection angles to achieve a given error rate. The advantages of using a physics-assisted learned prior in X-ray tomography may further enable low-photon nanoscale imaging.

Toward a New Primary Standardization of Radionuclide Massic Activity Using Microcalorimetry and Quantitative Milligram-Scale Samples.

We present a new paradigm for the primary standardization of radionuclide activity per mass of solution (Bq/g). Two key enabling capabilities are 4π decay-energy spectrometry using chip-scale sub-Kelvin microcalorimeters and direct realization of mass by gravimetric inkjet dispensing using an electrostatic force balance. In contrast to traditional traceability, which typically relies on chemical separation of single-radionuclide samples, 4π integral counting, and additional spectrometry methods to verify purity, the system described here has both 4π counting efficiency and spectroscopic resolution sufficient to identify multiple radionuclides in the same sample at once. This enables primary standardization of activity concentrations of mixed-radionuclide samples. A major benefit of this capability, beyond metrology, is in assay of environmental and forensics samples, for which the quantification of multiplenuclide samples can be achieved where presently inhibited by interferences. This can be achieved without the need for chemical separations or efficiency tracers, thereby vastly reducing time, radioactive waste, and resulting measurement uncertainty.

A tabletop X-ray tomography instrument for nanometer-scale imaging: reconstructions.

We show three-dimensional reconstructions of a region of an integrated circuit from a 130 nm copper process. The reconstructions employ x-ray computed tomography, measured with a new and innovative high-magnification x-ray microscope. The instrument uses a focused electron beam to generate x-rays in a 100 nm spot and energy-resolving x-ray detectors that minimize backgrounds and hold promise for the identification of materials within the sample. The x-ray generation target, a layer of platinum, is fabricated on the circuit wafer itself. A region of interest is imaged from a limited range of angles and without physically removing the region from the larger circuit. The reconstruction is consistent with the circuit's design file.

FAST UPDATING MULTIPOLE COULOMBIC POTENTIAL CALCULATION.

We present a numerical method to efficiently and accurately re-compute the Coulomb potential of a large ensemble of charged particles after a subset of the particles undergoes a change of position. Errors are bounded even after a large number of such shifts, making it practical for use in Monte Carlo Markov chain methods in molecular dynamics, computational astrophysics, computational chemistry, and other applications. The method uses truncated multipole expansions of the potential energy functional and a tree decomposition of the computational domain to reduce the computational complexity. Computational costs scale logarithmically in the size of the problem. Scaling, accuracy, and efficiency are confirmed with numerical experiments. The new method outperforms a direct calculation for moderate problem sizes.

Ultrafast Time-Resolved X-ray Absorption Spectroscopy of Ferrioxalate Photolysis with a Laser Plasma X-ray Source and Microcalorimeter Array.

The detailed pathways of photoactivity on ultrafast time scales are a topic of contemporary interest. Using a tabletop apparatus based on a laser plasma X-ray source and an array of cryogenic microcalorimeter X-ray detectors, we measured a transient X-ray absorption spectrum during the ferrioxalate photoreduction reaction. With these high-efficiency detectors, we observe the Fe K edge move to lower energies and the amplitude of the extended X-ray absorption fine structure reduce, consistent with a photoreduction mechanism in which electron transfer precedes disassociation. These results are compared to previously published transient X-ray absorption measurements on the same reaction and found to be consistent with the results from Ogi et al. and inconsistent with the results of Chen et al. ( Ogi , Y. ; et al. Struct. Dyn. 2015 , 2 , 034901 ; Chen , J. ; Zhang , H. ; Tomov , I. V. ; Ding , X. ; Rentzepis , P. M. Chem. Phys. Lett. 2007 , 437 , 50 - 55 ). We provide quantitative limits on the Fe-O bond length change. Finally, we review potential improvements to our measurement technique, highlighting the future potential of tabletop X-ray science using microcalorimeter sensors.