DC and AC quantum Hall measurements

The quantum Hall effect (QHE) is now widely used by national laboratories to establish a reference standard of DC resistance featuring low uncertainty with respect to the ohm and very high reproducibility. For high quality QHE samples, the reproducibility of the quantized Hall resistance (QHR), measured at DC or at very low frequencies (of order 1 Hz), is of order 1 part in 10/sup 9/. Accurate resistance-ratio measurement techniques have been developed to calibrate conventional resistance standards (in particular 1 /spl Omega/, 100 /spl Omega/ and 10 k/spl Omega/ standards) in terms of the QHR, with uncertainties not higher than a few parts in 10/sup 9/. The following techniques are reviewed: DC cryogenic current comparators bridges, low frequency AC cryogenic current comparator bridges and low frequency AC bridges using high permeability magnetic cores and operating at room temperature. Sources of uncertainties and limitations in the resolution of the measurements are discussed. The technique of connecting QHE samples in series or in parallel using multiple links is discussed. Another possible metrological application of QHRs would be to use them, at frequencies of order 1 kHz, as references of AC resistance for the calibration of capacitance standards, the link between the resistance and the capacitance being made using a quadrature bridge. The techniques used for these investigations are discussed, in particular the use of coaxial AC bridges for measurements of QHRs considered as four terminal-pair impedances and for the evaluation of the residual longitudinal resistivity of the samples.<>