Present State of Quantized-Hall-Resistance Metrology

Abstract

The experimental techniques used by the national institutes of metrology to measure the quantized Hall resistance in terms of their representations of the ohm are described. The agreement among these measurements is examined using the results of the comparisons of national standards of electrical resistance (1 SZ) made at the BIPM.The results of measurements of the quantized Hall resistance in SI units using calculable standards of capacitance are also examined and compared with indirect evaluations based on the determination of different fundamental constants.

The ac quantum Hall effect as a primary standard of impedance

“…This effect can be calculated from the measured capacitance between the top-gate and the 2DEG but the measured top-gate effect on R xy is much larger than that. Also the connected pads inject a small current according to the multiple-series connection scheme [7,10,11]. Again, the measured effect of additional connected contacts is larger than the calculated effect.…”

“…In a regular dc QHE measurement, the potential contacts and the connected leads are used to probe the Hall potentials at the particular edge of the QHE device by means of a voltmeter. The ac QHE measurements are different: according to the multipleseries connection scheme [10,11], which has become the standard connection scheme, the high-and the low-potential of the coaxial bridge are applied to the contacts of the QHR device in such a way that the external bridge voltage equals the Hall voltage across the QHR device. This means that the external potentials from the bridge are enforced upon the potential contacts of the QHR device.…”

“…Figure1. Scheme of a QHR device in a triple-series connection scheme[10,11] with the regions whose internal and external capacitances contribute to R xxLo , R xxHi and R xy . A simplified scheme of an ac bridge for comparison with a reference resistor R Ref is also shown.…”

Compendium for precise ac measurements of the quantum Hall resistance

“…A four-terminal-pair connection scheme [23] as usually applied to conventional impedance standards would give rise to systematic and significant frequency-dependent effects and cannot be used straightforwardly in the ac QHR case. The multiple-series connection scheme [10,20,21] shown in figure 1(a) elegantly avoids these problems and is used by most NMIs, and especially in all work reviewed in this article. According to this scheme, all potential contacts of the QHE device which are at the same high or low potential are connected to one junction at high or low potential.…”

“…Securing the QHE device by glue avoids ac driven vibrations, and for the same reason the bond wires should be kept short [20]. Only a small amount of glue should be used, even if the loss factor of the glue at low temperature is very small.…”