Anthony Hartland

The Quantum Hall Effect and Resistance Standards

Following the discovery of the quantum Hall effect in 1980 metrologists were eager to develop the effect as a resistance standard in a similar manner to the development, a decade earlier, of the Josephson effects in superconductors as a voltage standard. This article reviews the progress made by many national laboratories to assess and compare the quality and limitations of semiconductor devices, mainly silicon MOSFETs and GaAs/AlGaAs heterostructures, as quantized Hall resistance standards with values RH (i) = RK/i = h/ie2, where RK = 25812,807 Ω is the von Klitzing constant and i is an integer. Potentiometric and cryogenic current comparator bridge techniques for the measurement of RK in terms of conventional resistance standards with 1 σ relative accuracies better than 1 part in 108 are compared, and determinations of RK in ohms with accuracies as high as 2,4 parts in 108 using calculable capacitors are described. The comparison of direct determinations of RK with alternative derivations of h/e2 leading to the CCE recommendations and subsequent international adoption, from 1 January 1990, of the value 25812,807 ± 0,005 Ω for RK are also described.

An automated cryogenic current comparator resistance ratio bridge

The method of measurement of two-terminal cryogenic and four-terminal room-temperature resistors using a DC cryogenic current comparator bridge is well established. A bridge which is based on this technique and is fully automated with a computer controlling both the measurement current and the readings of the bridge imbalance current is described. The bridge is designed to measure integer ratios of 1:1 to 1:25 of four-terminal room-temperature resistors in the range 1 Omega to 10 k Omega . An overall accuracy of 1 part in 10/sup 9/ for differences in the ratio from nominal of up to 100 p.p.m. is desired. Some initial determinations of the resolution have been made for a measurement of 10 Omega :100 Omega . These determinations were carried out without the balance servo, and the output from the null detector was measured with a digital voltmeter connected to the computer. An analysis of a set of 11 reversals gave a standard deviation for a single reversal of 1 part in 10/sup 8/ and therefore a standard error of the mean of 3 parts in 10/sup 9/. >

Measurement of the AC quantized Hall resistance

The flatness and frequency dependence of the i=2 and four quantized Hall resistance plateaus have been investigated. It was observed that for frequencies up to 6.4 kHz, a flat region exists at the center of the plateaus where the relative resistance is constant to /spl plusmn/2/spl times/10/sup -8/, and its relative value has a linear frequency dependence of (0.119/spl plusmn/0.001) (/spl mu//spl Omega///spl Omega/)/kHz and (0.107/spl plusmn/0.007) (/spl mu//spl Omega///spl Omega/)/kHz for i=2 and 4, respectively.

Comparison of capacitance with AC quantized Hall resistance

A quadrature bridge operating at a frequency of 1.233 kHz has been developed to compare 10 nF capacitances to the quantized Hall resistance on the i=2 plateau in order to realize the farad in terms of R/sub K/. Portable precision ceramic capacitance transfer standards of remarkable performance have been developed for this purpose.

Recent measurements of single electron transport in surface acoustic wave devices at the NPL

The quantized acoustoelectric current (QAC) induced by a surface acoustic wave in a one-dimensional channel, offers the possibility of a quantum current standard. We report on the accuracy and flatness of the QAC for several plateaux and demonstrate an empirical relationship between the current error and plateaux slopes. The temperature dependence of the QAC is also discussed.

The relationship between the SI Ohm, the Ohm at NPL, and the quantized Hall resistance

New measurements relating the quantized Hall resistance R<inf>H</inf>(= h/ie²), International System (SI) Ohm (Ω<inf>SI</inf>), and the National Physical Laboratory maintained ohm (Ω<inf>NPL</inf>) have now been completed at NPL in the U.K. with improvements and simplifications in the cryogenic current comparator measurements and 1000-Ω dc resistance measurements. From the measurements over the past four years the relationship between Ω<inf>NPL</inf> and Ω<inf>SI</inf> can be described by the equation Ω<inf>NPL</inf> − Ω<inf>SI</inf> = −1.049(0.020) − 0.0478(0.0074)[t − 1986.0] μΩ in which t is measured in years. For the previous two years the equivalent relationship between R<inf>H</inf> and Ω<inf>NPL</inf> is R<inf>H</inf> = 25 812.8(1 + 1.452(0.038) × 10 ⁻⁶ + 0.0694(0.0772) · [t − 1986.0] × 10⁻⁶) Ω<inf>NPL</inf> in which the uncertainties (in parentheses) are one-standard-deviation (1σ) random uncertainties of the least squares fit to the data. Combining the most recent measurements of R<inf>H</inf> and Ω<inf>SI</inf>, using a more direct method of measurement R<inf>H</inf> = 25 812.8106(17) Ω<inf>SI</inf> in which the relative combined uncertainty is 0.067 × 10⁻⁶.

Study of the limitations of the quantized acoustic current technique at PTB and NPL

We present a detailed study of surface acoustic wave devices produced at Physikalisch-Technische Bundesanstalt and Cambridge University. From the temperature dependence of the acoustic current, information on a number of critical device parameters such as the intrinsic electron temperature and Coulomb charging energy can be deduced. The results of this study indicate that the theory and experiment are in agreement and that the accuracy of the quantized acoustic current is fundamentally limited at low temperatures.

Measurements of 10 V standards using a 1 V Josephson array

A system is described which allows the measurement of 10-V electronic voltage standards using a 1-V Josephson array. A 9:1 potential divider, comprising two 3-k Omega *3-k Omega Hamon resistor networks, in effect converts 1.11 V from the array to 10 V. Following the determination of the effect of power dissipation in the Hamon networks the estimated overall uncertainty (combined 1- sigma type-A and type-B) of a measurement at 10 V is 1.5 parts in 10/sup 8/. >

An International Direct Comparison of Two Josephson-Effect Voltage Standards

A direct comparison of the Bureau International des Poids et Mesures (BIPM) and the National Physical Laboratory (NPL) Josephson-effect voltage standards has been accomplished by transporting the BIPM apparatus to the NPL during April 1978. The voltage of a saturated standard cell as measured by the BIPM system, V(BIPM), was found to differ from that measured by the NPL system, V(NPL), such that [V(BIPM) - V(NPL)]/V(BIPM) = 7 ± 2 × 10-8. This difference is 1.6 times the total expected one-standard deviation uncertainty for the combined systems. Direct comparison of the two 2e/h systems without an intermediate standard cell was also accomplished and is reported for the first time.

Low-frequency measurements of the quantized Hall resistance

Measurements of the quantised Hall resistance R/sub H/(i) for i=2 and 4 have been made over the frequency range 0.4-6.4 kHz using a modified ac bridge. The results have been corrected for cable effects and the frequency-dependence of the standard resistor R/sub s/. The measurements indicate that in addition to a linear frequency dependence f there is also a linear dependence on source-drain voltage V/sub SD/ such that: /spl Delta/R/sub H/(i)/R/sub s/=/spl alpha/[V/sub SD/+/spl nu/(i)]f where /spl alpha/(i) and /spl nu/(i) are constants.