Quantum Hall Array Resistance Standards Research Articles

Update: On the synthesis of quantum Hall array resistance standards (2015 Metrologia 52 31)

Update: On the synthesis of quantum Hall array resistance standards (2015 Metrologia 52 31)

Error modelling of quantum Hall array resistance standards

Quantum Hall array resistance standards (QHARSs) are integrated circuits composed of interconnected quantum Hall effect elements that allow the realization of virtually arbitrary resistance values. In recent years, techniques were presented to efficiently design QHARS networks. An open problem is that of the evaluation of the accuracy of a QHARS, which is affected by contact and wire resistances. In this work, we present a general and systematic procedure for the error modelling of QHARSs, which is based on modern circuit analysis techniques and Monte Carlo evaluation of the uncertainty. As a practical example, this method of analysis is applied to the characterization of a 1 MΩ QHARS developed by the National Metrology Institute of Japan. Software tools are provided to apply the procedure to other arrays.

A 1 k standardresistor device based on quantum Hall array

Quantum metrological standards based on the fundamental physical constants are the trend of modern metrology because of their attributes such as high accuracy, high stability, and good reproducibility. The quantum Hall effect (QHE), which refers to the electronic charge e and the Planck constant h, is used to define the quantum resistance standard. The quantum Hall resistance (RH) of h/2e2 at the filling factori=2 is used as the standard. It is obvious that the RH is non-integral. However the resistors that need to be calibrated each have a decimal value, such as 1 k, 10 k, 100 k, etc. The calibration chain from the non-integral RH to the real resistor is long. The quantum Hall array resistance standards (QHARSs) are invented to solve this problem. The QHARS which are based on the decimal resistance values can shorten the calibration chain, improve the resistance transfer accuracy, and finally realize the quantization of the whole resistance calibration chain. The QHARS can also replace the traditional physical transfer standard resistor and realize the quantization of the transfer standard resistor. The decimal QHARS devices can be realized by connecting single QHE devices in series or parallel with the multiple link technology. In this paper we report the design, fabrication and characterization of a 1 k QHARS device based on the GaAs/AlxGa1-xAs heterostructures. In our design, the 1 k array device consists of only 29 Hall bars. The nominal value of the device is 999.9999658 with a relative deviation of -3.4210-8 from 1 k. The ratio between the maximum and minimum current flowing through the Hall bars is as small as 14.5. The 1 k QHARS devices are measured in the national resistance standard system at a temperature of 1.5 K. The measurement is taken at the central magnetic field of the 2nd quantum Hall plateau. We compare our 1 k QHARS resistor with a 1 k transfer standard resistor using the direct current comparator. The 1 k transfer standard resistor has already been calibrated in advance with our single QHR standard by cryogenic current comparator. Therefore the resistance of our 1 k QHARS resistor can be obtained. The relative deviation between the measured resistance value and the designed value is -1.9610-7with a standard uncertainty of 2.0710-7. The results show that we have realized the 1 k quantum Hall resistance standard device which can be used for the resistance calibration.

On the synthesis of quantum Hall array resistance standards

Quantum Hall effect (QHE) is the basis of modern resistance metrology. In quantum Hall array resistance standards (QHARS), several individual QHE elements, each one with the same QHE resistance (typically half of the von Klitzing constant), are arranged in networks that realize resistance values close to decadic values (such as 1 kΩ or 100 kΩ), of direct interest for dissemination. The same decadic value can be approximated with different grades of precision, and even for the same approximation several networks of QHE elements can be conceived. This paper investigates the design of QHARS networks by giving methods to find a proper approximation of the resistance of interest, and to design the corresponding network with a small number of elements; results for several decadic case examples are given. The realization of these networks with multiterminal QHE elements requires a new multiple bridge connection, here described.

Development of Quantum Hall Array Resistance Standards at NMIJ

A quantum Hall array resistance standard (QHARS) device with a nominal value close to 10 kΩ on the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> = 2 plateau has been developed on a GaAs/AlGaAs heterosubstrate. This QHARS device consists of 266 Hall bar elements, and its nominal value has only 0.0342 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> difference based on <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K-90</sub> ( = 25 812.807 Ω) from an integer value of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> . As a result of comparison measurements with the conventional Quantized Hall Resistance Standard via the 100- Ω standard resistor, the value of the QHARS device agrees with its nominal value within 3.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-8</sup> .

Application of the quantum Hall effect to resistance metrology

Abstract The quantum Hall effect (QHE) discovery has revolutionized metrology by providing with a representation of the unit of resistance, R K , that can be reproduced within a relative uncertainty of one part in 109 and is theoretically only linked to Planckʼs constant h and the electron charge e. This breakthrough also results from the development of resistance comparison bridges using cryogenic current comparator (CCC). The QHE experimental know-how now allows the realization of perfectly quantized Quantum Hall Array Resistance Standards (QHARS) by combining a large number of single Hall bars. In the context of an evolution of the Systeme International (SI) of units by fixing some fundamental constants of physics, the determination of the von Klitzing constant R K through the use of the so-called Thompson–Lampard calculable capacitor and the realization of refined universality tests of the QHE are of prime importance. Finally, the fascinating graphene material might be a new turning point in resistance metrology.

Resistance metrology based on the quantum Hall effect

The Quantum Hall effect (QHE), a macroscopic effect of solid state physics, provides a universal representation of the unit of resistance which depends on the elementary charge e and the Planck constant h only. If implemented according to specific technical guidelines, the quantum resistance standard can be reproduced with a relative uncertainty below one part in 109. Calibrations of wire resistors in terms of the QHE can be carried out with similarly low uncertainties by using resistance bridges equipped with cryogenic current comparators, the performance of which relies on the magnetic flux sensitivity of superconducting quantum interference devices (SQUID). Using a special connection technique, the fundamental properties of the QHE allow the fabrication of arrays combining a large number of single Hall bars connected in series or in parallel and which demonstrate quantum accuracy. Similar to the case of voltage metrology with Josephson array voltage standards, an improvement of resistance metrology is expected from the availability of quantum Hall array resistance standards (QHARS). The QHE Wheatstone bridge, which is another application of the same connection technique, opens the way to new universality tests of the QHE with a relative uncertainty below one part in 1011. At frequencies in the kilohertz range, the recent progress in the application of coaxial bridges to the QHE allows metrologists to operate a quantum resistance standard with alternating current reaching an accuracy of some parts in 108. Finally, the discovery of the QHE in graphene opens new horizons for the resistance metrology.

QUANTUM HALL EFFECT AND OHM METROLOGY

The quantum Hall effect (QHE) discovery has revolutionized the ohm metrology: the representation of the unit of resistance is now universal and the ohm can be maintained in each national metrology institute with a relative uncertainty of one part in 109. This breakthrough also results from the development of resistance comparison bridges using cryogenic current comparator (CCC). The fundamental properties of the QHE allow the realization of Quantum Hall Array Resistance Standards (QHARS) by combining a large number of single Hall bars connected in series and/or in parallel. These standards can be as accurate as a single Hall bar. More generally, the multiple connection technique allows metrologists to design useful circuits based on quantum Hall resistors like voltage dividers or Wheatstone bridges. The QHE Wheatstone bridge is particularly suitable for comparing quantum standards. By detecting the unbalance current of this bridge with a CCC, new universality tests of the QHE with a target uncertainty less than 1011 can be realized.

A new generation of QHARS: discussion about the technical criteria for quantization

New quantum Hall array resistance standards (QHARS) with nominal values in the range from RK/200 to 50RK (i = 2 plateau) have been developed (RK is the von Klitzing constant). The design of the QHARS based on the connection in parallel of Hall bars is made suitable for use in both magnetic field directions. Measurements performed with currents up to 4 mA at 1.3 K show that RK/200 (∼129 Ω) and 16RK/4130 (∼100 Ω) resistance standards have Hall resistances which agree with their nominal values within 5 parts in 109 (1σ). While increasing the temperature, the Hall resistance varies linearly with the longitudinal resistance. Because the sign of this deviation depends on the magnetic field direction, the average of the Hall resistance values measured for both magnetic field directions remains constant within 5 parts in 109 up to 4.2 K. Owing to their large working current, these QHARS have allowed an accurate calibration of a 100 Ω wire resistor using a commercial resistance bridge. An RK/20 (∼1290 Ω) resistance standard made of ten Hall bars placed in parallel by quadruple connections has also been studied. It is found that the resistances measured by using three different voltage terminal pairs agree within 5 parts in 109 in relative value.

Quantum resistance standards with double 2deg

We have developed a new generation of quantum Hall array resistance standards (QHARS) obtained from GaAs/AlGaAs heterostructures with double two-dimensional electron gases (2DEGs) grown by the metal-organic vapor phase epitaxy process. We have achieved the fabrication of such a multilayer system with well matched carrier density and mobility of the two 2DEGs and characteristics required for metrological use. This technological achievement allowed calibrations in terms of a quantized Hall resistance (R/sub K//2 on i=2 plateau) of a single Hall bar (R/sub K//4) and 50 Hall bars placed in parallel by triple connections QHARS129 (R/sub K//200). In both cases relative deviations of their Hall resistance from their expected nominal value are found lower than eight parts in 10/sup 9/, corresponding to the measurement uncertainty (1/spl sigma/). These measurements were performed on QHARS129 samples supplied by higher measuring currents up to 2 mA at 1.3 K.

R K /100 and RK/200 quantum Hall array resistance standards

It is theoretically possible to combine several Hall bars in arrays to define quantum standards with perfectly quantized resistance values. We have thus developed and fabricated quantum Hall array resistance standards (QHARS) made of a large number N (N=100, 50) of Hall bars placed in parallel using a triple connections technique. The Hall resistance of these quantum standards is found to be very well quantized. On the i=2 Hall plateau, the resistance of specific good arrays stays equal to RK/2N within 5 parts in 109 for supplying currents up to 2 mA at a temperature of 1.3 K. The mean longitudinal resistance of the Hall bars which constitute the arrays has been determined through the analysis of the array equivalent electrical circuit. This measurement shows that the carrier transport in the Hall bars is dissipationless. This work, therefore, demonstrates the efficiency of the multiple connections technique and consequently that QHARS are likely to extend the quantum Hall effect metrological applications.