Direct comparison of 1 MΩ quantized Hall array resistance and quantum Hall resistance standard

Abstract

We report precision measurements of a 1 MΩ quantum Hall resistance array made of GaAs/ AlGaAs heterostructure. The quantized Hall array resistance at filling factor 2 is directly compared with the quantum Hall resistance standard with a cryogenic current comparator resistance bridge with a relative measurement uncertainty of 17 × 10 −9 at the 95% confidence level. The robustness of quantization in the array is systematically investigated with respect to the temperature, magnetic field, and excitation current. We observe through repeated thermal cycles that the quantized Hall array resistance is almost unchanged within the relative measurement uncertainty, reflecting the invariant nature of high resistance close to 1 MΩ. This demonstrates a stable quantum mechanical resistance of 1 MΩ as well as the potential for a genuine current-to-voltage converter for precision measurements of small current. The observed relative deviation of the quantized Hall array resistance from a designed value, verified by a double consistency check through a 10 kΩ resistance standard and the Hall array resistance plateau at filling factor 4, respectively, is comparable to the relative measurement uncertainty. Finally, the associated uncertainty budget and the origin of the measured deviation are discussed.

Thermal and Electrical Performance Study of Cold-Finger ³He Cryostat in Precision Measurement of Quantum Hall Resistance and Single-Electron Current

“…Figure 3(a) shows an Allan deviation of the bridge voltage difference. It follows the inverse-square-root time dependence of white noise (red dotted line) up to the sampling time of 10 3 s. For longer sampling times, the flicker noise regime, as indicated by flattening of the Allan deviation plot (blue dashed line) is started at about 10 3 s. This result is similar to that for the KRISS QHR standard [5].…”

Accurate graphene quantum Hall arrays for the new International System of Units

“…(K) Magnetic Flux Dens. (T) GaAs 23 100 1/200 ~0.129 0.1 2 2 1.3 8.4–9 GaAs 25 88 5075/131 ~1000 20 8.5 0.001 1.5 9–10 GaAs 29 10 5 ~129 2.5 12.7 0.005 0.3–1 8–9 Graphene 20 100 1/200 ~0.129 10 7 10 5 0.1 2 7–9 Graphene 21 6 2/6 ~8.60 1.9 0.75 0.15 1.7 9 Graphene 24 10 5 ~129 10 20 0.5 4 6 Graphene 22 13 1/26 ~0.993 0.45 3 0.3 1.6 7.5–9 Graphene (this work) 236 1/236 ~0.109 0.03 0.2 5 2.1 5 Graphene (this work) 236 1/236 ~0.109 0.5 0.5 8.5 2.1 4.25 The table includes previous reports on quantum Hall arrays, including both traditional GaAs and modern graphene approaches. The table columns show the material, number of indi...…”

“…Arrays provide an elegant way to achieve quantized resistances at arbitrary levels via series and parallel connections of individual HBs 19 – 25 , while effectively increasing I C via parallel connections. These benefits have been recognized for decades, starting as early as 1993 with arrays for improved Wheatstone bridges 26 – 28 .…”

The Elementary Charge for the Definition and Realization of the Ampere

“…Based on this technique, various quantum Hall array resistance standards have been realized since 1999 (see refs. [] and references therein). Using p‐type and n‐type QHE devices in graphene, the fabrication of series arrays could even be simplified.…”