Graphene-Based Star–Mesh Resistance Networks

Advances in the development of graphene-based technology have enabled improvements in dc resistance metrology. Devices made from epitaxially grown graphene (EG) have replaced the GaAs-based counterparts, leading to an easier and more accessible realization of the ohm. By optimizing the scale of the growth, it has become possible to fabricate quantized Hall array resistance standards (QHARS) with nominal values between 1 $\text{k}\Omega $ and 1.29 $\text{M}\Omega $ . One of these QHARS device designs accommodates a value of about 1.01 $\text{M}\Omega $ , which made it an ideal candidate to pursue a proof-of-concept that graphene-based QHARS devices are suitable for forming wye–delta ( $Y$ – $\Delta$ ) resistance networks. In this work, the 1.01- $\text{M}\Omega $ array output is nearly 20.6 $\text{M}\Omega $ due to the $Y$ – $\Delta $ transformation, which itself is a special case of star–mesh transformations. These mathematical equivalence principles allow one to extend the quantized Hall resistance (QHR) to the 100- $\text{M}\Omega $ and 10- $\text{G}\Omega $ resistance levels with fewer array elements than would be necessary for a single array with many more elements in series. The 1.01- $\text{M}\Omega $ device shows promise that the $Y$ – $\Delta $ transformation can shorten the calibration chain, and, more importantly, provide a chain with a more direct line to the quantum international system of units (SI).