Graphene quantum Hall effect parallel resistance arrays.

As first recognized in 2010, epitaxial graphene on SiC(0001) provides a platform for quantized Hall resistance (QHR) metrology unmatched by other two-dimensional structures and materials. Here we report graphene parallel QHR arrays, with metrologically precise quantization near 1000 Ω. These arrays have tunable carrier densities, due to uniform epitaxial growth and chemical functionalization, allowing quantization at the robust ν = 2 filling factor in array devices at relative precision better than 10-8. Broad tunability of the carrier density also enables investigation of the ν = 6 plateau. Optimized networks of QHR devices described in this work suppress Ohmic contact resistance error using branched contacts and avoid crossover leakage with interconnections that are superconducting for quantizing magnetic fields up to 13.5 T. Our work enables more direct scaling of resistance for quantized values in arrays of arbitrary network geometry.

Onsager-Casimir frustration from resistance anisotropy in graphene quantum Hall devices.

We report on nonreciprocity observations in several configurations of graphene-based quantum Hall devices. Two distinct measurement configurations were adopted to verify the universality of the observations (i.e., two-terminal arrays and four-terminal devices). Our findings determine the extent to which epitaxial graphene anisotropies contribute to the observed asymmetric Hall responses. The presence of backscattering induces a device-dependent asymmetry rendering the Onsager-Casimir relations limited in their capacity to describe the behavior of such devices, except in the low-field classical regime and the fully quantized Hall state. The improved understanding of this quantum electrical process broadly limits the applicability of the reciprocity principle in the presence of quantum phase transitions and for anisotropic two-dimensional materials.

Comparison of a 100-pF Capacitor With a 12 906-Ω Resistor Using a Digital Impedance Bridge.

We tested a digital impedance bridge in a hybrid structure for comparison of a capacitor with a resistor where the impedance ratio was measured in two separate parts. The modulus of the impedance ratio was matched arbitrarily close to the input-to-output ratio, in magnitude, of a two-stage inductive voltage divider by adjusting the operating frequency of the bridge; the residual deviation between the two together with the phase factor of the impedance ratio was measured using a custom detection system based on a four-channel 24-bit digitizer. The ratio of the inductive voltage divider was calibrated, in situ, using a conventional four-arm bridge with two known capacitors. Fluctuations of the source voltages were largely removed through postprocessing of the digitized data, and the measurement results were limited by the digitizer error. We have achieved an overall bridge resolution and stability of 0.02 µF/F in 2 h for measuring a 100-pF capacitor relative to a 12 906-Ω resistor at 1233 Hz. The relative combined standard uncertainty (k = 1) is 0.13 µF/F, dominated by the digitizer error.

Metrological Suitability of Functionalized Epitaxial Graphene.

This work presents one solution for long-term storage of epitaxial graphene (EG) in air, namely through the functionalization of millimeter-scale devices with chromium tricarbonyl - Cr(CO)3. The carrier density may be tuned reproducibly by annealing below 400 K due to the presence of Cr(CO)3. All tuning is easily reversible with exposure to air, with the idle, in-air, carrier density always being close to the Dirac point. Precision measurements in the quantum Hall regime indicate no detrimental effects from the treatment, validating the pursuit of developing air-stable EG-based QHR devices.

Superconducting Contact Geometries for Next-Generation Quantized Hall Resistance Standards.

Precision quantum Hall resistance measurements can be greatly improved when implementing new electrical contact geometries made from superconducting NbTiN. The sample designs described here minimize undesired resistances at contacts and interconnections, enabling further enhancement of device size and complexity when pursuing next-generation quantized Hall resistance devices.

Comparison between Graphene and GaAs Quantized Hall Devices with a Dual Probe.

A graphene quantized Hall resistance (QHR) device fabricated at the National Institute of Standards and Technology (NIST) was measured alongside a GaAs QHR device fabricated by the National Research Council of Canada (NRC) by comparing them to a 1 kΩ standard resistor using a cryogenic current comparator. The two devices were mounted in a custom developed dual probe that was then assessed for its viability as a suitable apparatus for precision measurements. The charge carrier density of the graphene device exhibited controllable tunability when annealed after Cr(CO)3 functionalization. These initial measurement results suggest that making resistance comparisons is possible with a single probe wired for two types of quantum standards - GaAs, the established material, and graphene, the newer material that may promote the development of more user-friendly equipment.

Implementation of a graphene quantum Hall Kelvin bridge-on-a-chip for resistance calibrations.

The unique properties of the quantum Hall effect allow one to revisit traditional measurement circuits with a new flavour. In this paper we present the first realization of a quantum Hall Kelvin bridge for the calibration of standard resistors directly against the quantum Hall resistance. The bridge design is particularly simple and requires a minimal number of instruments. The implementation here proposed is based on the bridge-on-a-chip, an integrated circuit composed of three graphene quantum Hall elements and superconducting wiring. The accuracy achieved in the calibration of a 12 906Ω standard resistor is of a few parts in 108, at present mainly limited by the prototype device and the interferences in the current implementation, with the potential to achieve few parts in 109, which is the level of the systematic uncertainty of the quantum Hall Kelvin bridge itself.

Advanced Temperature-Control Chamber for Resistance Standards.

Calibration services for resistance metrology have continued to advance their capabilities and establish new and improved methods for maintaining standard resistors. Despite the high quality of these methods, there still exist inherent limitations to the number of simultaneous, measurable resistors and the temperature stability of their air environment. In that context, we report progress on the design, development, and initial testing of a precise temperature-control chamber for standard resistors that can provide a constant-temperature environment with a stability of ± 6 m°C. Achieving this stability involved customizing the chamber design based on air-flow simulations. Moreover, microprocessor programming allowed the air flow to be optimized within an unsealed chamber configuration to reduce chamber temperature recovery times. Further tests were conducted to improve the stability of the control system and the efficiency of the chamber.

Two-Terminal and Multi-Terminal Designs for Next-Generation Quantized Hall Resistance Standards: Contact Material and Geometry.

In this paper, we show that quantum Hall resistance measurements using two terminals may be as precise as four-terminal measurements when applying superconducting split contacts. The described sample designs eliminate resistance contributions of terminals and contacts such that the size and complexity of next-generation quantized Hall resistance devices can be significantly improved.

Next-generation crossover-free quantum Hall arrays with superconducting interconnections.

This work presents precision measurements of quantized Hall array resistance devices using superconducting, crossover-free, multiple interconnections as well as graphene split contacts. These new techniques successfully eliminate the accumulation of internal resistances and leakage currents that typically occur at interconnections and crossing leads between interconnected devices. As a result, a scalable quantized Hall resistance array is obtained with a nominal value that is as precise and stable as that from single-element quantized Hall resistance standards.

Towards epitaxial graphene p-n junctions as electrically programmable quantum resistance standards.

We report the fabrication and measurement of top gated epitaxial graphene p-n junctions where exfoliated hexagonal boron nitride (h-BN) is used as the gate dielectric. The four-terminal longitudinal resistance across a single junction is well quantized at the von Klitzing constant [Formula: see text] with a relative uncertainty of 10-7. After the exploration of numerous parameter spaces, we summarize the conditions upon which these devices could function as potential resistance standards. Furthermore, we offer designs of programmable electrical resistance standards over six orders of magnitude by using external gating.

Nano-printed miniature compound refractive lens for desktop hard x-ray microscopy.

Hard x-ray lenses are useful elements in x-ray microscopy and in creating focused illumination for analytical applications such as x-ray fluorescence imaging. Recently, polymer compound refractive lenses for focused illumination in the soft x-ray regime (< 10 keV) have been created with nano-printing. However, there are no such lenses yet for hard x-rays, particularly of short focal lengths for benchtop microscopy. We report the first instance of a nano-printed lens for hard x-ray microscopy, and evaluate its imaging performance. The lens consists of a spherically focusing compound refractive lens designed for 22 keV photon energy, with a tightly packed structure to provide a short total length of 1.8 mm and a focal length of 21.5 mm. The resulting lens technology was found to enable benchtop microscopy at 74x magnification and 1.1 µm de-magnified image pixel size at the object plane. It was used to image and evaluate the focal spots of tungsten-anode micro-focus x-ray sources. The overall system resolution with broadband illumination from a tungsten-anode x-ray tube at 30 kV and 10 mm focal distance was measured to be 2.30±0.22 µm.

Graphene Devices for Tabletop and High-Current Quantized Hall Resistance Standards.

We report the performance of a quantum Hall resistance standard based on epitaxial graphene maintained in a 5-T tabletop cryocooler system. This quantum resistance standard requires no liquid helium and can operate continuously, allowing year-round accessibility to quantized Hall resistance measurements. The ν = 2 plateau, with a value of R K/2, also seen as R H, is used to scale to 1 kΩ using a binary cryogenic current comparator (BCCC) bridge and a direct current comparator (DCC) bridge. The uncertainties achieved with the BCCC are such as those obtained in the state-of-the-art measurements using GaAs-based devices. BCCC scaling methods can achieve large resistance ratios of 100 or more, and while room temperature DCC bridges have smaller ratios and lower current sensitivity, they can still provide alternate resistance scaling paths without the need for cryogens and superconducting electronics. Estimates of the relative uncertainties of the possible scaling methods are provided in this report, along with a discussion of the advantages of several scaling paths. The tabletop system limits are addressed as are potential solutions for using graphene standards at higher currents.

Geometric calibration and correction for a lens-coupled detector in x-ray phase-contrast imaging.

A lens-coupled x-ray camera with a tilted phosphor collects light emission from the x-ray illuminated (front) side of phosphor. Experimentally, it has been shown to double x-ray photon capture efficiency and triple the spatial resolution along the phosphor tilt direction relative to the same detector at normal phosphor incidence. These characteristics benefit grating-based phase-contrast methods, where linear interference fringes need to be clearly resolved. However, both the shallow incident angle on the phosphor and lens aberrations of the camera cause geometric distortions. When tiling multiple images of limited vertical view into a full-field image, geometric distortion causes blurring due to image misregistration. Here, we report a procedure of geometric correction based on global polynomial transformation of image coordinates. The corrected image is equivalent to one obtained with a single full-field flat panel detector placed at the sample plane. In a separate evaluation scan, the position deviations in the horizontal and vertical directions were reduced from 0.76 and 0.028 mm, respectively, to 0.006 and 0.009 mm, respectively, by the correction procedure, which were below the 0.028-mm pixel size of the imaging system. In a demonstration of a phase-contrast imaging experiment, the correction reduced blurring of small structures.

A Universal Moiré Effect and Application in X-Ray Phase-Contrast Imaging.

A moiré pattern is created by superimposing two black-and-white or gray-scale patterns of regular geometry, such as two sets of evenly spaced lines. We observed an analogous effect between two transparent phase masks in a light beam which occurs at a distance. This phase moiré effect and the classic moiré effect are shown to be the two ends of a continuous spectrum. The phase moiré effect allows the detection of sub-resolution intensity or phase patterns with a transparent screen. When applied to x-ray imaging, it enables a polychromatic far-field interferometer (PFI) without absorption gratings. X-ray interferometry can non-invasively detect refractive index variations inside an object1-10. Current bench-top interferometers operate in the near field with limitations in sensitivity and x-ray dose efficiency2, 5, 7-10. The universal moiré effect helps overcome these limitations and obviates the need to make hard x-ray absorption gratings of sub-micron periods.

Enhancing Tabletop X-Ray Phase Contrast Imaging with Nano-Fabrication.

X-ray phase-contrast imaging is a promising approach for improving soft-tissue contrast and lowering radiation dose in biomedical applications. While current tabletop imaging systems adapt to common x-ray tubes and large-area detectors by employing absorptive elements such as absorption gratings or monolithic crystals to filter the beam, we developed nanometric phase gratings which enable tabletop x-ray far-field interferometry with only phase-shifting elements, leading to a substantial enhancement in the performance of phase contrast imaging. In a general sense the method transfers the demands on the spatial coherence of the x-ray source and the detector resolution to the feature size of x-ray phase masks. We demonstrate its capabilities in hard x-ray imaging experiments at a fraction of clinical dose levels and present comparisons with the existing Talbot-Lau interferometer and with conventional digital radiography.