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

A $1\,{\text G}\Omega $ star-mesh quantized Hall array resistance standard (QHARS) assembled from 37 individual elements, each exhibiting the quantum Hall effect (QHE), was fabricated and tested. The $1\,{\text G}\Omega $ QHARS has three orders of magnitude fewer elements than a largely series $1\,{\text G}\Omega $ QHARS, which would require approximately 77480 elements. A dual source bridge (DSB), 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 $1\,{\text G}\Omega $ star-mesh QHARS was used as a standard to calibrate 100 M $\Omega $ , $1\,{\text G}\Omega $ , and 10 G $\Omega $ 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 $i=2$ quantized Hall resistance value of $12906.4037...\Omega $ , where guarded Hamon transfer standards and DSBs are used to build-up to high resistance ranges from 1 M $\Omega $ standard resistors.