Series and parallel connection of multiterminal quantum Hall-effect devices

Abstract

The circuit properties of networks which include multiterminal quantum Hall-effect (QHE) devices are discussed. It is shown that QHE devices can be placed in a series or in parallel using multiple links to give equivalent four-terminal quantized resistances which are in practice, to a high degree of accuracy, independent of contact resistances to the two-dimensional electron gas in the samples and of series resistances in the links. The same technique of multiple links can also be used to incorporate QHE devices in resistance or impedance bridges, resulting in a balance condition which is practically unaffected by contact or series resistances. These properties are established using calculations based on equivalent circuits of QHE devices. Metrological applications include the obtainment of accurate reference standards of resistance with values which are multiples or submultiples of individual quantized Hall resistances (QHRs) and, using a resistance bridge, the precise comparison of QHRs. An experimental verification is reported, demonstrating that the effective equivalent resistance of two QHE devices connected in parallel does not differ from nominal by more than a few parts in 109.