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Single-photon detectors based on the superconducting transition-edge sensor (TES) are used in a number of visible to near-infrared (VNIR) applications, particularly for photon-number-resolving measurements in quantum information science. To be practical for large-scale photonic quantum computing or for future spectroscopic imaging applications in astronomy, the size of VNIR TES arrays must be increased from a few pixels to many thousands. Historically, TES arrays have been read out with multiplexed superconducting quantum interference devices (SQUIDs), but the microsecond-duration pulse signals of VNIR TESs are notoriously difficult to multiplex. In this manuscript, we introduce the kinetic inductance current sensor (KICS), a more readily scalable readout technology that exploits the nonlinear kinetic inductance in a superconducting resonator to make sensitive current measurements. KICS devices can replace SQUIDs for many applications because of their ability to measure fast, high slew-rate signals, their compatibility with standard microwave frequency-division multiplexing techniques, and their relatively simple fabrication. Here, we demonstrate the readout of a VNIR TES using a KICS with $3.7$ $\text{MHz}$ of bandwidth. We measure a readout noise of $1.4$ $\text{pA}/\sqrt{\text{Hz}}$, considerably below the TES noise at frequencies of interest, and a TES energy resolution of $(0.137 \pm 0.001)$ $\text{eV}$ at $0.8$ $\text{eV}$, comparable to resolutions observed with non-multiplexed SQUID readouts., Comment: 14 pages, 8 figures

Naturally occurring background radiation is a source of correlated decoherence events in superconducting qubits that will challenge error-correction schemes. To characterize the radiation environment in an unshielded laboratory, we performed broadband, spectroscopic measurements of background events in silicon substrates located inside a millikelvin refrigerator, an environment representative of superconducting qubit systems. We measured the background spectra in silicon substrates of two thicknesses, 0.5 mm and 1.5 mm, and obtained the average event rate and the integrated power deposition. In a 25 mm^2 area and the thinner substrate, these values are 0.023 events per second and 4.9 keV/s, counting events that deposit at least 40 keV. We find the background spectrum to be nearly featureless. Its intensity decreases by a factor of 40,000 between 100 keV and 3 MeV for silicon substrates 0.5 mm thick. We find the cryogenic measurements to be in good agreement with predictions based on measurements of the terrestrial gamma-ray flux, published models of cosmic-ray fluxes, a crude model of the cryostat, and radiation-transport simulations. No free parameters are required to predict the background spectra in the silicon substrates. The good agreement between measurements and predictions allow assessment of the relative contributions of terrestrial and cosmic background sources and their dependence on substrate thickness. Our spectroscopic measurements are performed with superconducting microresonators that transduce deposited energy to a readily detectable electrical signal. We find that gamma-ray emissions from radioisotopes are responsible for the majority of events depositing E<1.5 MeV, while nucleons among the cosmic-ray secondary particles cause most events that deposit more energy. These results suggest several paths to reducing the impact of background radiation on quantum circuits.

We report on the 1,000-element transition-edge sensor (TES) x-ray spectrometer implementation of the TOMographic Circuit Analysis Tool (TOMCAT). TOMCAT combines a high spatial resolution scanning electron microscope (SEM) with a highly efficient and pixelated TES spectrometer to reconstruct three-dimensional maps of nanoscale integrated circuits (ICs). A 240-pixel prototype spectrometer was recently used to reconstruct ICs at the 130 nm technology node, but to increase imaging speed to more practical levels, the detector efficiency needs to be improved. For this reason, we are building a spectrometer that will eventually contain 3,000 TES microcalorimeters read out with microwave superconducting quantum interference device (SQUID) multiplexing, and we currently have commissioned a 1,000 TES subarray. This still represents a significant improvement from the 240-pixel system and allows us to begin characterizing the full spectrometer performance. Of the 992 maximimum available readout channels, we have yielded 818 devices, representing the largest number of TES x-ray microcalorimeters simultaneously read out to date. These microcalorimeters have been optimized for pulse speed rather than purely energy resolution, and we measure a FWHM energy resolution of 14 eV at the 8.0 keV Cu K$\alpha$ line., Comment: 5 pages, 4 figures, submitted to IEEE Transactions on Applied Superconductivity

X-ray nanotomography is a powerful tool for the characterization of nanoscale materials and structures, but is difficult to implement due to competing requirements on 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 changing 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 in a metal target held micrometers away from the sample of interest, while the TES spectrometer isolates target photons with high signal-to-noise. This combination of a focused X-ray spot, energy-resolved X-ray detection, and unique system geometry enable 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 6 layers of a Cu-SiO2 integrated circuit, and a path towards finer resolution and enhanced imaging capabilities is discussed.

Feature sizes in integrated circuits have decreased substantially over time, and it has become increasingly difficult to three-dimensionally image these complex circuits after fabrication. This can be important for process development, defect analysis, and detection of unexpected structures in externally sourced chips, among other applications. Here, we report on a non-destructive, tabletop approach that addresses this imaging problem through x-ray tomography, which we uniquely realize with an instrument that combines a scanning electron microscope (SEM) with a transition-edge sensor (TES) x-ray spectrometer. Our approach uses the highly focused SEM electron beam to generate a small x-ray generation region in a carefully designed target layer that is placed over the sample being tested. With the high collection efficiency and resolving power of a TES spectrometer, we can isolate x-rays generated in the target from background and trace their paths through regions of interest in the sample layers, providing information about the various materials along the x-ray paths through their attenuation functions. We have recently demonstrated our approach using a 240 Mo/Cu bilayer TES prototype instrument on a simplified test sample containing features with sizes of $\sim$1 $\mu$m. Currently, we are designing and building a 3000 Mo/Au bilayer TES spectrometer upgrade, which is expected to improve the imaging speed by factor of up to 60 through a combination of increased detector number and detector speed., Comment: 5 pages, 3 figures, published in IEEE Transactions on Applied Superconductivity

Superconducting transition-edge sensor (TES) microcalorimeters have great utility in x-ray applications owing to their high energy resolution, good collecting efficiency and the feasibility of being multiplexed into large arrays. In this work, we develop hard x-ray TESs to measure the absolute energies of muonic-argon ($\mu$-Ar) transition lines around 44 keV and 20 keV. TESs with sidecar absorbers of different heat capacities were fabricated and characterized for their energy resolution and calibration uncertainty. We achieved ~ 1 eV absolute energy measurement accuracy at 44 keV, and < 12 eV energy resolution at 17.5 keV.

We use an array of transition-edge sensors, cryogenic microcalorimeters with 4 eV energy resolution, to measure L x-ray emission-line profiles of four elements of the lanthanide series: praseodymium, neodymium, terbium, and holmium. The spectrometer also surveys numerous x-ray standards in order to establish an absolute-energy calibration traceable to the International System of Units for the energy range 4 keV to 10 keV. The new results include emission line profiles for 97 lines, each expressed as a sum of one or more Voigt functions; improved absolute energy uncertainty on 71 of these lines relative to existing reference data; a median uncertainty on the peak energy of 0.24 eV, four to ten times better than the median of prior work; and 6 lines that lack any measured values in existing reference tables. The 97 lines comprise nearly all of the most intense L lines from these elements under broad-band x-ray excitation. The work improves on previous measurements made with a similar cryogenic spectrometer by the use of sensors with better linearity in the absorbed energy and a gold x-ray absorbing layer that has a Gaussian energy-response function. It also employs a novel sample holder that enables rapid switching between science targets and calibration targets with excellent gain balancing. Most of the results for peak energy values shown here should be considered as replacements for the currently tabulated standard reference values, while the line shapes given here represent a significant expansion of the scope of available reference data.

We have investigated photoinduced intramolecular electron transfer dynamics following metal-to-ligand charge-transfer (MLCT) excitation of [Fe(CN)$_4$(2,2'-bipyridine)]$^{2-}$ (1), [Fe(CN)$_4$(2,3-bis(2-pyridyl)pyrazine)]$^{2-}$ (2) and [Fe(CN)$_4$(2,2'-bipyrimidine)]$^{2-}$ (3) complexes in various solvents with static and time-resolved UV-visible absorption spectroscopy and Fe 2p3d resonant inelastic X-ray scattering. We observe $^3$MLCT lifetimes from 180 fs to 67 ps over a wide range of MLCT energies in different solvents by utilizing the strong solvatochromism of the complexes. Intramolecular electron transfer lifetimes governing $^3$MLCT relaxation increase monotonically and (super)exponentially as the $^3$MLCT energy is decreased in 1 and 2 by changing the solvent. This behavior can be described with non-adiabatic classical Marcus electron transfer dynamics along the indirect $^3$MLCT->$^3$MC pathway, where the $^3$MC is the lowest energy metal-centered (MC) excited state. In contrast, the $^3$MLCT lifetime in 3 changes non-monotonically and exhibits a maximum. This qualitatively different behaviour results from direct electron transfer from the $^3$MLCT to the electronic ground state (GS). This pathway involves nuclear tunnelling for the high-frequency polypyridyl skeleton mode ($\hbar\omega$ = 1530 cm$^{-1}$), which is more displaced for 3 than for either 1 or 2, therefore making the direct pathway significantly more efficient in 3. To our knowledge, this is the first observation of an efficient $^3$MLCT->GS relaxation pathway in an Fe polypyridyl complex. Our study suggests that further extending the MLCT state lifetime requires (1) lowering the $^3$MLCT state energy with respect to the $^3$MC state and (2) suppressing the intramolecular distortion of the electron-accepting ligand in the $^3$MLCT excited state to suppress the rate of direct $^3$MLCT->GS electron transfer.

We present X-ray absorption spectroscopy and resonant inelastic X-ray scattering (RIXS) measurements on the iron L-edge of 0.5 mM aqueous ferricyanide. These measurements demonstrate the ability of high-throughput transition-edge-sensor (TES) spectrometers to access the rich soft X-ray (100-2000eV) spectroscopy regime for dilute and radiation-sensitive samples. Our low-concentration data are in agreement with high-concentration measurements recorded by conventional grating-based spectrometers. These results show that soft X-ray RIXS spectroscopy acquired by high-throughput TES spectrometers can be used to study the local electronic structure of dilute metal-centered complexes relevant to biology, chemistry and catalysis. In particular, TES spectrometers have a unique ability to characterize frozen solutions of radiation- and temperature-sensitive samples., Comment: 19 pages, 4 figures

We have examined the role of the substrate on electron-phonon coupling in normal metal films of Mn-doped Al at temperatures below 1 K. Normal metal-insulator-superconductor junctions were used to measure the electron temperature in the films as a function of Joule heating power and phonon temperature. Theory suggests that the distribution of phonons available for interaction with electrons in metal films may depend on the acoustic properties of the substrate, namely, that the electron-phonon coupling constant Sigma would be larger on the substrate with smaller sound speed. In contrast, our results indicate that within experimental error (typically +/- 10%), Sigma is unchanged among the two acoustically distinct substrates used in our investigation., Comment: 4 pages, 2 figures. Version 2 contains changes reflected in the final published article

Understanding the subgap behavior of Normal-Insulator-Superconductor (NIS) tunnel junctions is important in order to be able to accurately model the thermal properties of the junctions. Hekking and Nazarov developed a theory in which NIS subgap current in thin-film structures can be modeled by multiple Andreev reflections. In their theory, the current due to Andreev reflections depends on the junction area and the junction resistance area product. We have measured the current due to Andreev reflections in NIS tunnel junctions for various junction sizes and junction resistance area products and found that the multiple reflection theory is in agreement with our data.

In a normal-metal/insulator/superconductor (NIS) tunnel junction refrigerator, the normal-metal electrons are cooled and the dissipated power heats the superconducting electrode. This paper presents a review of the mechanisms by which heat leaves the superconductor and introduces overlayer quasiparticle traps for more effective heatsinking. A comprehensive thermal model is presented that accounts for the described physics, including the behavior of athermal phonons generated by both quasiparticle recombination and trapped quasiparticles. We compare the model to measurements of a large area (>400 um^2) NIS refrigerator with overlayer quasiparticle traps, and demonstrate that the model is in good agreement experiment. The refrigerator IV curve at a bath temperature of 300 mK is consistent with an electron temperature of 82 mK. However, evidence from independent thermometer junctions suggests that the refrigerator junction is creating an athermal electron distribution whose total excitation energy corresponds to a higher temperature than is indicated by the refrigerator IV curve.