Implementation of a 1 GΩ Star-Mesh Graphene Quantized Hall Array Resistance Standard Network for High Resistance Calibration

A 1GΩ star-mesh quantized Hall array resistance standard (QHARS) assembled from thirty-seven individual elements, each exhibiting the quantum Hall effect (QHE), was fabricated and tested. The 1GΩ QHARS has three orders of magnitude fewer elements than a largely series 1GΩ QHARS, which would require approximately 77 480 elements. A dual source bridge, using a nanovolt detector and a modified algorithm using least-squares analysis was used to interpolate a bridge null from five measurement points taken near the null of the linear measurement system. The 1GΩ star-mesh QHARS was used as a standard to calibrate 100MΩ, 1GΩ, and 10GΩ high resistance standards. The star-mesh measurements agreed within the combined standard uncertainties of the values of these standards based on traditional high resistance scaling from the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> = 2 quantized Hall resistance value of 12 906.403 7 . . . Ω, where guarded Hamon transfer standards and dual source bridges are used to build-up to high resistance ranges from 1MΩ standard resistors.