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.