New Design of Quantized Hall Resistance Array Device

Abstract

We propose a new design for a 10- $\hbox{k}\Omega$ quantized Hall resistance (QHR) array device. This design realizes quantized resistance values that approach decade values with fewer Hall bars. In this design, the 10- $\hbox{k}\Omega$ QHR array device consists of only 16 Hall bars, and this number is about 16 times lower than that in the previous design, although the nominal value is identical to the previous one. The nominal value of this device shows a relative difference of only 0.034 $\mu\Omega/\Omega$ , based on $R_{K - 90} (=25\,812.807 \Omega)$ , from the exact value of 10 $\hbox{k}\Omega$ . This fact might allow us to evaluate each Hall bar in the array device. The parameters of this 10- $\hbox{k}\Omega$ QHR array device were measured by a conventional QHR and cryogenic current comparator using the 100- $\Omega$ standard resistor. According to the measurement, the value of the 10- $\hbox{k}\Omega$ QHR array device agrees with its nominal value within around one part in $10^{8}$ . In the same manner, new combinations of Hall bars were designed for the 100- $\Omega$ –1- $\hbox{M}\Omega$ range.