Development of 1 $\text{M} {\Omega }$ Quantum Hall Array Resistance Standards

Abstract

We fabricated and evaluated a 1 $\text{M}{\Omega }$ quantum Hall array device with GaAs/AlGaAs substrates. This 1 $\text{M}{\Omega }$ quantized Hall resistance array device consists of 88 Hall bars, and its nominal resistance value is $10^{6} (1-0.034 \times 10^{-6}) ~\Omega $ . The ratio for this nominal value, 10150/131, was derived using the continued fraction expansion method, which adopts the triple-connection technique to minimize the influence of contact resistance and wiring resistance on the quantized resistance value. The fabricated 1 $\text{M}{\Omega }$ quantum Hall array device showed clear and flat ${i=2}$ and 4 plateaus and negligibly small longitudinal resistance. We observed the desired yield ratio of the contact resistance to 2-dimensional electron gas with sufficiently low wiring resistance and sufficiently high insulation resistance and collapse current. These results strongly support the reliability of our 1 $\text{M}{\Omega }$ quantum Hall array device. We have confirmed the desirable performance of the existing calibration system of the 1 $\text{M}{\Omega }$ wire-wound standard resistors based on the array device. We expect that this device will allow us to improve the high-resistance standard system and to convert the small current from electron pumps into easily measurable voltage without decreasing precision.