AC measurements of the quantized Hall resistance

• Published in: IEEE transactions on instrumentation and measurement Vol. 44; no. 2; pp. 245 - 248
• Main Authors: Hartland, A., Kibble, B.P., Rodgers, P.J., Bohacek, J.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: New York, NY IEEE 01.04.1995; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Bridge circuits; Coaxial components; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Conductors; Detectors; Electrical resistance measurement; Electronic structure and electrical properties of surfaces, interfaces, thin films and low-dimensional structures; Electronic transport in interface structures; Electronics; Equivalent circuits; Exact sciences and technology; Frequency measurement; Impedance measurement; Measurement standards; Metrology; Metrology, measurements and laboratory procedures; Physics; Quantum hall effect (including fractional); Resistors; Testing, measurement, noise and reliability; Units and standards; Resistors; Magnetic flux; Hall effect device; Flux density; Electric bridges; Measuring system; Quantum Hall effect; Equivalent circuits
• ISSN: 0018-9456; 1557-9662
• DOI: 10.1109/19.377822

The quantized Hall resistance R/sub H/(i), for i=2, 4 and 6 has been measured over the frequency range from dc to 3 kHz using a standard four terminal-pair impedance bridge. For the ith plateau we found that R/sub H/(i) depended linearly on the magnetic flux density B and quadratically on the frequency f. That is, the relative difference /spl Delta/R/sub H/(i,f)/R/sub H/(i) between the ac and dc values is consistent with the empirical relationship k(i)Bf/sup 2/, where k(i) is constant. Below 3 kHz k(i) decreases by approximately a factor of six as i increases from 2 to 6. These results are consistent with inductances /spl ap/100 /spl mu/H, which depend on B, in series with each terminal of the quantum Hall device. From dc to 3 kHz we can derive the ac value of a standard resistor in terms of R/sub H/(2) with a type A relative uncertainty (1/spl sigma/) of 0.05/spl times/10/sup -6/ f/sup 2/ when f is expressed in kHz.< >