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.

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.

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.

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.

Calculating the Effects of Longitudinal Resistance in Multi-Series-Connected Quantum Hall Effect Devices.

Many ac quantized Hall resistance experiments have measured significant values of ac longitudinal resistances under temperature and magnetic field conditions in which the dc longitudinal resistance values were negligible. We investigate the effect of non-vanishing ac longitudinal resistances on measurements of the quantized Hall resistances by analyzing equivalent circuits of quantized Hall effect resistors. These circuits are based on ones reported previously for dc quantized Hall resistors, but use additional resistors to represent longitudinal resistances. For simplification, no capacitances or inductances are included in the circuits. The analysis is performed for many combinations of multi-series connections to quantum Hall effect devices. The exact algebraic solutions for the quantized Hall resistances under these conditions of finite ac longitudinal resistances provide corrections to the measured quantized Hall resistances, but these corrections do not account for the frequency dependences of the ac quantized Hall resistances reported in the literature.

Precision Tests of a Quantum Hall Effect Device DC Equivalent Circuit Using Double-Series and Triple-Series Connections.

Precision tests verify the dc equivalent circuit used by Ricketts and Kemeny to describe a quantum Hall effect device in terms of electrical circuit elements. The tests employ the use of cryogenic current comparators and the double-series and triple-series connection techniques of Delahaye. Verification of the dc equivalent circuit in double-series and triple-series connections is a necessary step in developing the ac quantum Hall effect as an intrinsic standard of resistance.

Sources of Uncertainty in a DVM-Based Measurement System for a Quantized Hall Resistance Standard.

Transportable 10 kΩ standard resistors have become fairly widespread in industrial, university, and government standards laboratories because of their low temperature coefficient of resistance, case of transportation, and convenient value. The values of these resistors, however, tend to drift with time, requiring periodic recalibration against an invariant standard such as the quantized Hall resistance. The availability of a simple, inexpensive measurement system for calibrating 10 kΩ resistors against such an invariant standard would be of great benefit to primary standards laboratories. This paper describes a simple automated measurement system that uses a single, high accuracy, commercially available digital voltmeter (DVM) to compare the voltages developed across a 10 kΩ standard resistor and a quantized Hall resistor when the same current is passed through the two devices. From these measurements, the value of the 10 kΩ standard resistor is determined. The sources of uncertainty in this system are analyzed in detail and it is shown that it is possible to perform calibrations with relative combined standard uncertainties less than 1×10-7 (0.1 ppm).

A Problem in AC Quantized Hall Resistance Measurements and a Proposed Solution.

In all experiments reported to date the measured values of the ac quantized Hall resistances RH varied with the frequency of the applied current, and differed significantly from the dc values of RH, making it difficult to use the ac quantum Hall effect as an absolute impedance standard. We analyze the effects due to the large capacitances-to-shields existing in the sample probes on measurements of RH to see if this is the source of the problem. Equivalent electrical circuits are utilized; they contain capacitances and leakage resistances to the sample probe shields, longitudinal resistances within the quantized Hall effect devices, and multiple connections to the devices. The algebraic solutions for the RH values in these circuits reveal large out-of-phase contributions to the quantized Hall voltages VH that would make it difficult to do accurate measurements with high precision ac bridges. These large out-of-phase contributions could introduce the linear frequency dependences observed in previous RH measurements. We predict, however, that quadruple-series connections to the quantum Hall devices yield only small out-of-phase contributions to VH which may allow accurate measurements of the quantity RH - Rx , where Rx is the longitudinal resistance along the device.

Special Report on Electrical Standards: New Internationally Adopted Reference Standards of Voltage and Resistance.

This report provides the background for and summarizes the main results of the 18th meeting of the Consultative Committee on Electricity (CCE) of the International Committee of Weights and Measures (CIPM) held in September 1988. Also included are the most important implications of these results. The principal recommendations originating from the meeting, which were subsequently adopted by the CIPM, establish new international reference standards of voltage and resistance based on the Josephson effect and the quantum Hall effect, respectively. The new standards, which are to come into effect starting January 1, 1990, will result in improved uniformity of electrical measurements worldwide and their consistency with the International System of Units or SI. To implement the CIPM recommendations in the U.S. requires that, on January 1, 1990, the value of the U.S. representation of the volt be increased by about 9.26 parts per million (ppm) and the value of the U.S. representation of the ohm be increased by about 1.69 ppm. The resulting increases in the U.S. representations of the ampere and watt will be about 7.57 ppm and 16.84 ppm, respectively. The CCE also recommended a particular method, affirmed by the CIPM, of reporting calibration results obtained with the new reference standards that is to be used by all national standards laboratories.

New Results From Previously Reported NBS Fundamental Constant Determinations.

A new treatment of previously reported results of three electric-unit-dependent fundamental constant experiments carried out at NBS over the last decade or so yields accurate, indirect values in SI units for a number of important quantities. These include the fine-structure constant α, the Avogadro constant N A, the Josephson frequency-voltage ratio 2e/h, and the quantized Hall resistance R H≡h/e 2.