We present the first steps taken towards a graphene quantum Hall effect ac resistance standard at RISE. A new measurement setup has been developed including a graphene quantum Hall effect device suitable for the kilohertz range and a coaxial cryoprobe to be used together with a coaxial impedance bridge based on inductive voltage dividers. 1:1 ratio resistance measurements of the graphene device against a 12.9 kΩ ac resistance standard resulted in a linear frequency dependent (≈ 0.2(μΩ/Ω)/kHz) deviation from the quantized dc value.

In this work we investigate the long-term stability of epitaxial graphene (epigraphene) quantum Hall resistance standards, including single devices and an array device composed of 236 elements providing (R K/236 ≈ 109 Ω) , with R K the von Klitzing constant. All devices utilize the established technique of chemical doping via molecular dopants to achieve homogenous doping and control over carrier density. However, optimal storage conditions and the long-term stability of molecular dopants for metrological applications have not been widely studied. In this work we aim to identify simple storage techniques that use readily available and cost-effective materials which provide long-term stability for devices without the need for advanced laboratory equipment. The devices are stored in glass bottles with four different environments: ambient, oxygen absorber, silica gel desiccant, and oxygen absorber/desiccant mixture. We have tracked the carrier densities, mobilities, and quantization accuracies of eight different epigraphene quantum Hall chips for over two years. We observe the highest stability (i.e. lowest change in carrier density) for samples stored in oxygen absorber/desiccant mixture, with a relative change in carrier density below 0.01% per day and no discernable degradation of quantization accuracy at the part-per-billion level. This storage technique yields a comparable stability to the currently established best storage method of inert nitrogen atmosphere, but it is much easier to realize in practice. It is possible to further optimize the mixture of oxygen absorber/desiccant for even greater stability performance in the future. We foresee that this technique can allow for simple and stable long-term storage of polymer-encapsulated molecular doped epigraphene quantum Hall standards, removing another barrier for their wide-spread use in practical metrology. 

Graphene quantum Hall effect (QHE) resistance standards have the potential to provide superior realizations of three key units in the new International System of Units (SI): the ohm, the ampere, and the kilogram (Kibble Balance). However, these prospects require different resistance values than practically achievable in single graphene devices (~12.9 kΩ), and they need bias currents two orders of magnitude higher than typical breakdown currents IC ~ 100 μA. Here we present experiments on quantization accuracy of a 236-element quantum Hall array (QHA), demonstrating RK/236 ≈ 109 Ω with 0.2 part-per-billion (nΩ/Ω) accuracy with IC ≥ 5 mA (~1 nΩ/Ω accuracy for IC = 8.5 mA), using epitaxial graphene on silicon carbide (epigraphene). The array accuracy, comparable to the most precise universality tests of QHE, together with the scalability and reliability of this approach, pave the road for wider use of graphene in the new SI and beyond. © 2022, The Author(s).

One of the aspirations of quantum metrology is to deliver primary standards directly to end-users thereby significantly shortening the traceability chains and enabling more accurate products. Epitaxial graphene grown on silicon carbide (epigraphene) is known to be a viable candidate for a primary realisation of a quantum Hall resistance standard, surpassing conventional semiconductor two-dimensional electron gases, such as those based on GaAs, in terms of performance at higher temperatures and lower magnetic fields. The bottleneck in the realisation of a turn-key quantum resistance standard requiring minimum user intervention has so far been the need to fine-tune the carrier density in this material to fit the constraints imposed by a simple cryo-magnetic system. Previously demonstrated methods, such as via photo-chemistry or corona discharge, require application prior to every cool-down as well as specialist knowledge and equipment. To this end we perform metrological evaluation of epigraphene with carrier density tuned by a recently reported permanent molecular doping technique. Measurements at two National Metrology Institutes confirm accurate resistance quantisation below 5n-1. Furthermore, samples show no significant drift in carrier concentration and performance on multiple thermal cycles over three years. This development paves the way for dissemination of primary resistance standards based on epigraphene

This paper describes a method for realisation of inductance and quality factor to high frequencies by determining the frequency response of gain-and phase-error of an inductance meter using two coils made of a single copper wire. As a starting point a traceable calibration of inductance at 1 kHz is used

The Reference Step Method for calibrators can be modified for calibration also of the gain ratios on a meter. The method has earlier been evaluated in the range 100 mV-1000 V on DMM HP 3458A1 and shows that an accuracy of typically < ± 0.2 μ V/V could be obtained. We have investigated the performance of the method when calibrating ratios in the range 1 mV-100 mV on two common nV-meters. In our comparisons with the Josephson Voltage Standard the differences are within ± ± 12μ V/V at the ratio 10m V:1mV and within ± ± 1.3μ V/V at 100mV:10mV.

Here we demonstrate a stable and tunable method to alter the carrier concentration of epitaxial graphene grown on silicon carbide. This technique relies on chemical doping by an acceptor molecule. Through careful tuning one can produce chemically doped graphene quantum resistance devices which show long-term stability in ambient conditions and have performance comparable to that of GaAs quantum resistance standards. This development paves the way for controlled device fabrication of graphene quantum hall resistance standards, which can be reliably tailored to operate below 5 T and above 4 K out-of-the-box, without further adjustments from the end-user.

Josephson impedance comparison bridges have been developed at PTB and SP. The bridges are based on programmable Josephson voltage standards. We report the first ever comparison of Josephson impedance bridges performed with 1:1 and 1:10 capacitance ratio measurements up to 2 kHz.

We describe a low frequency Josephson impedance bridge and the measurement methods. The bridge is useable below 400 Hz and is based on two programmable Josephson voltage standards. Measurements of 1:1, 1:2 and 1:10 capacitance ratio have been performed and compared with ratio measurements of an inductive voltage divider bridge. © 2016 IEEE.