Methodology and implementation of a tunable deep-ultraviolet laser source for photoemission electron microscopy.

Photoemission electron microscopy (PEEM) is a unique and powerful tool for studying the electronic properties of materials and surfaces. However, it requires intense and well-controlled light sources with photon energies ranging from the UV to soft X-rays for achieving high spatial resolution and image contrast. Traditionally, many PEEMs were installed at synchrotron light sources to access intense and tunable soft X-rays. More recently, the maturation of solid-state lasers has opened a new avenue for laboratory-based PEEMs using laser-based UV light at lower photon energies. Here, we report on the characteristics of a laser-based UV light source that was recently integrated with a PEEM instrument. The system consists of a high repetition rate, tunable wavelength laser coupled to a harmonics generation module, which generates deep-UV radiation from 192 nm to 210 nm. We comment on the spectral characteristics and overall laser system stability, as well as on the effects of space charge within the PEEM microscope at high UV laser fluxes. Further, we show an example of imaging on gallium nitride, where the higher UV photon energy and flux of the laser provides considerably improved image quality, compared to a conventional light source. These results demonstrate the capabilities of laser-based UV light sources for advancing laboratory-based PEEMs.

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.

Magnetotransport in hybrid InSe/monolayer graphene on SiC.

The magnetotransport properties of a hybrid InSe/monolayer graphene in a SiC system are systematically studied. Compared to those of its bare graphene counterpart, in InSe/graphene, we can effectively modify the carrier density, mobility, effective mass, and electron-electron (e-e) interactions enhanced by weak disorder. We show that in bare graphene and hybrid InSe/graphene systems, the logarithmic temperature (lnT) dependence of the Hall slope R H = Î´R xy /δB = Î´ρ xy /δB can be used to probe e-e interaction effects at various temperatures even when the measured resistivity does not show a lnT dependence due to strong electron-phonon scattering. Nevertheless, one needs to be certain that the change of R H is not caused by an increase of the carrier density by checking the magnetic field position of the longitudinal resistivity minimum at different temperatures. Given the current challenges in gating graphene on SiC with a suitable dielectric layer, our results suggest that capping a van der Waals material on graphene is an effective way to modify the electronic properties of monolayer graphene on SiC.

Graphene Quantum Hall Effect Devices for AC and DC Electrical Metrology.

A new type of graphene-based quantum Hall standards is tested for electrical quantum metrology applications at alternating current (ac) and direct current (dc). The devices are functionalized with Cr(CO)3 to control the charge carrier density and have branched Hall contacts based on NbTiN superconducting material. The work is an in-depth study about the characteristic capacitances and related losses in the ac regime of the devices and about their performance during precision resistance measurements at dc and ac.

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.

Highly sensitive broadband binary photoresponse in gateless epitaxial graphene on 4H-SiC.

Due to weak light-matter interaction, standard chemical vapor deposition (CVD)/exfoliated single-layer graphene-based photodetectors show low photoresponsivity (on the order of mA/W). However, epitaxial graphene (EG) offers a more viable approach for obtaining devices with good photoresponsivity. EG on 4H-SiC also hosts an interfacial buffer layer (IBL), which is the source of electron carriers applicable to quantum optoelectronic devices. We utilize these properties to demonstrate a gate-free, planar EG/4H-SiC-based device that enables us to observe the positive photoresponse for (405-532) nm and negative photoresponse for (632-980) nm laser excitation. The broadband binary photoresponse mainly originates from the energy band alignment of the IBL/EG interface and the highly sensitive work function of the EG. We find that the photoresponsivity of the device is > 10 A/W under 405 nm of power density 7.96 mW/cm2 at 1 V applied bias, which is three orders of magnitude greater than the obtained values of CVD/exfoliated graphene and higher than the required value for practical applications. These results path the way for selective light-triggered logic devices based on EG and can open a new window for broadband photodetection.

Abrikosov vortex corrections to effective magnetic field enhancement in epitaxial graphene.

Here, we report the effects of enhanced magnetic fields resulting from type-II superconducting NbTiN slabs adjacent to narrow Hall bar devices fabricated from epitaxial graphene. Observed changes in the magnetoresistances were found to have minimal contributions from device inhomogeneities, magnet hysteresis, electron density variations along the devices, and transient phenomena. We hypothesize that Abrikosov vortices, present in type-II superconductors, contribute to these observations. By determining the London penetration depth, coupled with elements of Ginzburg-Landau theory, one can approximate an upper bound on the effect that vortex densities at low fields (< 1T) have on the reported observations. These analyses offer insights into device fabrication and how to utilize the Meissner effect for any low-field and low-temperature applications using superconductors.

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.

Development of gateless quantum Hall checkerboard p-n junction devices.

Measurements of fractional multiples of the ν = 2 plateau quantized Hall resistance (R H ≈ 12906 Ω) were enabled by the utilization of multiple current terminals on millimetre-scale graphene p-n junction devices fabricated with interfaces along both lateral directions. These quantum Hall resistance checkerboard devices have been demonstrated to match quantized resistance outputs numerically calculated with the LTspice circuit simulator. From the devices' functionality, more complex embodiments of the quantum Hall resistance checkerboard were simulated to highlight the parameter space within which these devices could operate. Moreover, these measurements suggest that the scalability of p-n junction fabrication on millimetre or centimetre scales is feasible with regards to graphene device manufacturing by using the far more efficient process of standard ultraviolet lithography.

Analytical determination of atypical quantized resistances in graphene p-n junctions.

A mathematical approach is introduced for predicting quantized resistances in graphene p-n junction devices that utilize more than a single entry and exit point for electron flow. Depending on the configuration of an arbitrary number of terminals, electrical measurements yield nonconventional, fractional multiples of the typical quantized Hall resistance at the v = 2 plateau (R H ≈ 12906 Ω) and take the form: a b R H . This theoretical formulation is independent of material, and applications to other material systems that exhibit quantum Hall behaviors are to be expected. Furthermore, this formulation is supported with experimental data from graphene devices with multiple source and drain terminals.

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.

Elucidating Charge Transport Mechanisms in Cellulose-Stabilized Graphene Inks.

Solution-processed graphene inks that use ethyl cellulose as a polymer stabilizer are blade-coated into large-area thin films. Following blade-coating, the graphene thin films are cured to pyrolyze the cellulosic polymer, leaving behind an sp2-rich amorphous carbon residue that serves as a binder in addition to facilitating charge transport between graphene flakes. Systematic charge transport measurements, including temperature-dependent Hall effect and non-contact microwave resonant cavity characterization, reveal that the resulting electrically percolating graphene thin films possess high mobility (≈ 160 cm2 V-1 s-1), low energy gap, and thermally activated charge transport, which develop weak localization behavior at cryogenic temperatures.

Manetoresistance of Ultralow-Hole-Density Monolayer Epitaxial Graphene Grown on SiC.

Silicon carbide (SiC) has already found useful applications in high-power electronic devices and light-emitting diodes (LEDs). Interestingly, SiC is a suitable substrate for growing monolayer epitaxial graphene and GaN-based devices. Therefore, it provides the opportunity for integration of high-power devices, LEDs, atomically thin electronics, and high-frequency devices, all of which can be prepared on the same SiC substrate. In this paper, we concentrate on detailed measurements on ultralow-density p-type monolayer epitaxial graphene, which has yet to be extensively studied. The measured resistivity ρxx shows insulating behavior in the sense that ρxx decreases with increasing temperature T over a wide range of T (1.5 K ≤ T ≤ 300 K). The crossover from negative magnetoresistivity (MR) to positive magnetoresistivity at T = 40 K in the low-field regime is ascribed to a transition from low-T quantum transport to high-T classical transport. For T ≥ 120 K, the measured positive MR ratio [ρxx(B) - ρxx(B = 0)]/ρxx(B = 0) at B = 2 T decreases with increasing T, but the positive MR persists up to room temperature. Our experimental results suggest that the large MR ratio (~100% at B = 9 T) is an intrinsic property of ultralow-charge-density graphene, regardless of the carrier type. This effect may find applications in magnetic sensors and magnetoresistance devices.

Gateless and reversible carrier density tunability in epitaxial graphene devices functionalized with chromium tricarbonyl.

Monolayer epitaxial graphene (EG) has been shown to have clearly superior properties for the development of quantized Hall resistance (QHR) standards. One major difficulty with QHR devices based on EG is that their electrical properties drift slowly over time if the device is stored in air due to adsorption of atmospheric molecular dopants. The crucial parameter for device stability is the charge carrier density, which helps determine the magnetic flux density required for precise QHR measurements. This work presents one solution to this problem of instability in air by functionalizing the surface of EG devices with chromium tricarbonyl -Cr(CO)3. Observations of carrier density stability in air over the course of one year are reported, as well as the ability to tune the carrier density by annealing the devices. For low temperature annealing, the presence of Cr(CO)3 stabilizes the electrical properties and allows for the reversible tuning of the carrier density in millimeter-scale graphene devices close to the Dirac point. Precision measurements in the quantum Hall regime show no detrimental effect on the carrier mobility.

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.

Comparison between NIST Graphene and AIST GaAs Quantized Hall Devices.

Several graphene quantized Hall resistance (QHR) devices manufactured at the National Institute of Standards and Technology (NIST) were compared to GaAs QHR devices and a 100 Ω standard resistor at the National Institute for Advanced Industrial Science and Technology (AIST). Measurements of the 100 Ω resistor with the graphene QHR devices agreed within 5 nΩ/Ω of the values for the 100 Ω resistor obtained through GaAs measurements. The electron density of the graphene devices was adjusted at AIST to restore device properties such that operation was possible at low magnetic flux densities of 4 T to 6 T. This adjustment was accomplished with a functionalization method utilized at NIST, allowing for consistent tunability of the graphene QHR devices with simple annealing. Such a method replaces older and less predictable methods for adjusting graphene for metrological suitability. The milestone results demonstrate the ease with which graphene can be used to make resistance comparison measurements among many National Metrology Institutes.

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.

The Quantum Hall Effect in the Era of the New SI.

The quantum Hall effect (QHE), and devices reliant on it, will continue to serve as the foundation of the ohm while also expanding its territory into other SI derived units. The foundation, evolution, and significance of all of these devices exhibiting some form of the QHE will be described in the context of optimizing future electrical resistance standards. As the world adapts to using the quantum SI, it remains essential that the global metrology community pushes forth and continues to innovate and produce new technologies for disseminating the ohm and other electrical units.