This paper describes the main tests and precautions necessary for both reproducible and accurate results in the use of the quantum Hall effect as a means to establish a reference standard of dc resistance having a relative uncertainty of a few parts in 10 9 .

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.

When measured with ac at kilohertz frequencies the quantized Hall resistance (QHR) of a quantum Hall effect (QHE) device is usually found to be current- and frequency-dependent. This is a limitation on its use as a quantum impedance standard. We develop a model for the principal ac losses arising in the QHE device and show how they are responsible for the observed QHR current and frequency coefficients. We believe that losses are mainly caused by dissipative ac charging of the device along its edges. Charging is induced by the passage of the Hall current and by capacitive coupling between an edge and any nearby conductor maintained at an ac potential different to that of the edge, as for example at shield potential. The loss power is proportional to frequency and increases more rapidly than the square of the applied voltage or current. We model losses in terms of in-phase loss currents, which are a function of the amplitude of the ac charge reaching or leaving edges. The QHR frequency coefficient is zero only when the loss current for one portion of the high-potential edge and that for a corresponding portion of the low-potential edge are equal and of opposite sign. We propose a simple method for approaching that balance condition: gates are located under the device edges and their ac potentials adjusted so that the QHR current coefficient, evaluated at a constant frequency, is zero. We report measurements of the residual QHR frequency coefficients obtained after adjustment for GaAs/GaAlAs devices of two different types. For five different devices of the most favourable type, the QHR frequency coefficients do not exceed ±2 parts in 108 per kilohertz.

Accurate measurements have been made of the quantized Hall resistance (QHR) corresponding to the quantum number i = 2, RH (2), of two GaAs-based heterostructures using alternating current in the frequency range from 1 Hz to 1,6 kHz. The QHR is compared with a conventional ac reference resistance standard (Vishay type) of the same nominal value. The measurements are made with an alternating current comparator bridge at 1 Hz and with a coaxial ac bridge from 400 Hz to 1,6 kHz. The quantum Hall effect (QHE) sample is connected to the coaxial bridge using a double series connection. An analysis of the circuit properties of the sample shows that this technique of connection is sufficient to define the QHR as a four terminal-pair impedance. It also avoids perturbing effects from small capacitances between the terminals of the sample and from inductive reactances in series with the terminals. At frequencies up to at least 1,6 kHz a central region on the Hall resistance plateau has been observed for which the Hall resistance RH (2) is independent of the magnetic flux density to within 1 part in 108. The ratio of RH (2) to the reference resistance varies by less than 2 parts in 107 from 1 Hz to 1,6 kHz. A significant part of this variation is probably due to the frequency dependence of the reference resistance itself.

This paper describes the main tests and precautions that guarantee both reproducible and accurate results in the use of the quantum Hall effect as a means to establish a reference standard of resistance having a relative uncertainty of a few parts in 108.