Equivalent Electrical Circuit Representations of AC Quantized Hall Resistance Standards

We use equivalent electrical circuits to analyze the effects of large parasitic impedances existing in all sample probes on four-terminal-pair measurements of the ac quantized Hall resistance R_H. The circuit components include the externally measurable parasitic capacitances, inductances, lead resistances, and leakage resistances of ac quantized Hall resistance standards, as well as components that represent the electrical characteristics of the quantum Hall effect device (QHE). Two kinds of electrical circuit connections to the QHE are described and considered: single-series “offset” and quadruple-series. (We eliminated other connections in earlier analyses because they did not provide the desired accuracy with all sample probe leads attached at the device.) Exact, but complicated, algebraic equations are derived for the currents and measured quantized Hall voltages for these two circuits. Only the quadruple-series connection circuit meets our desired goal of measuring R_H for both ac and dc currents with a one-standard-deviation uncertainty of 10⁻⁸ R_H or less during the same cool-down with all leads attached at the device. The single-series “offset” connection circuit meets our other desired goal of also measuring the longitudinal resistance R_x for both ac and dc currents during that same cool-down. We will use these predictions to apply small measurable corrections, and uncertainties of the corrections, to ac measurements of R_H in order to realize an intrinsic ac quantized Hall resistance standard of 10⁻⁸ R_H uncertainty or less.     

Analyzing the Effects of Capacitances-to-Shield in Sample Probes on AC Quantized Hall Resistance Measurements

We analyze the effects of the large capacitances-to-shields existing in all sample probes on measurements of the ac quantized Hall resistance R_H. The object of this analysis is to investigate how these capacitances affect the observed frequency dependence of R_H. Our goal is to see if there is some way to eliminate or minimize this significant frequency dependence, and thereby realize an intrinsic ac quantized Hall resistance standard. Equivalent electrical circuits are used in this analysis, with circuit components consisting of: capacitances and leakage resistances to the sample probe shields; inductances and resistances of the sample probe leads; quantized Hall resistances, longitudinal resistances, and voltage generators within the quantum Hall effect device; and multiple connections to the device. We derive exact algebraic equations for the measured R_H values expressed in terms of the circuit components. Only two circuits (with single-series “offset” and quadruple-series connections) appear to meet our desired goals of measuring both R_H and the longitudinal resistance R_x in the same cool-down for both ac and dc currents with a one-standard-deviation uncertainty of 10⁻⁸ R_H or less. These two circuits will be further considered in a future paper in which the effects of wire-to-wire capacitances are also included in the analysis.     

A Problem in AC Quantized Hall Resistance Measurements and a Proposed Solution

In all experiments reported to date the measured values of the ac quantized Hall resistances R_H varied with the frequency of the applied current, and differed significantly from the dc values of R_H, making it difficult to use the ac quantum Hall effect as an absolute impedance standard. We analyze the effects due to the large capacitances-to-shields existing in the sample probes on measurements of R_H to see if this is the source of the problem. Equivalent electrical circuits are utilized; they contain capacitances and leakage resistances to the sample probe shields, longitudinal resistances within the quantized Hall effect devices, and multiple connections to the devices. The algebraic solutions for the R_H values in these circuits reveal large out-of-phase contributions to the quantized Hall voltages V_H that would make it difficult to do accurate measurements with high precision ac bridges. These large out-of-phase contributions could introduce the linear frequency dependences observed in previous R_H measurements. We predict, however, that quadruple-series connections to the quantum Hall devices yield only small out-of-phase contributions to V_H which may allow accurate measurements of the quantity R_H − R_x, where R_x is the longitudinal resistance along the device.     

Intrinsic Capacitances and Inductances of Quantum Hall Effect Devices

Analytic solutions are obtained for the internal capacitances, kinetic inductances, and magnetic inductances of quantum Hall effect devices to investigate whether or not the quantized Hall resistance is the only intrinsic impedance of importance in measurements of the ac quantum Hall effect. The internal capacitances and inductances are obtained by using the results of Cage and Lavine, who determined the current and potential distributions across the widths of quantum Hall effect devices. These intrinsic capacitances and inductances produce small out-of-phase impedance corrections to the in-phase quantized Hall resistance and to the in-phase longitudinal resistance.     

Transport behavior of commercially available 100-Ω standardresistors

Several types of commercial 100-Ω resistors can be used with the cryogenic current comparator to maintain the resistance unit, derived from the quantized Hall effect (QHE), and to disseminate this unit to laboratory resistance standards. Up until now, the transport behavior of these resistors has not been investigated. Such an investigation is of importance for carrying out comparisons that are close to the level of a direct comparison of two QHE apparatuses. A set of five 100-Ω resistors from three different manufacturers has been sent to 11 participating national metrological institutes. All laboratories but one have measured the resistors based on their laboratory's quantized Hall resistance measurements. A constant drift model has been applied, and the results are evaluated in such a way that the transport properties of these resistors are treated independently for the different types of resistor. Under certain conditions, these resistors allow comparisons with uncertainties better than 1 part in 10 ⁸     

Optimization of QHE-devices for metrological applications

In the framework of an European project aiming at the realization of a system for the calibration of capacitance standards based on the quantum Hall effect (QHE), optimized QHE devices for the metrological application as dc as well as ac standards of resistance are developed. The present paper describes the dc characterization of a large number of devices with different layouts, contact configurations, carrier concentrations, and mobilities. The results demonstrate the influence of the device parameters on the critical current, the width of the quantized plateaus, the longitudinal voltages along the device and the quantized Hall resistance. Recommendations are given for the layout and mobility of QHE devices in view of their use as dc standards of resistance     

Precision Tests of a Quantum Hall Effect Device DC Equivalent Circuit Using Double-Series and Triple-Series Connections

Precision tests verify the dc equivalent circuit used by Ricketts and Kemeny to describe a quantum Hall effect device in terms of electrical circuit elements. The tests employ the use of cryogenic current comparators and the double-series and triple-series connection techniques of Delahaye. Verification of the dc equivalent circuit in double-series and triple-series connections is a necessary step in developing the ac quantum Hall effect as an intrinsic standard of resistance.     

Evaluation of the frequency dependence of the resistance and capacitance standards in the BIPM quadrature bridge

The Bureau International des Poids et Mesures (BIPM) has established a measurement chain allowing calibration of capacitance standards in terms of the quantized Hall resistance (QHR). An important element in the chain is a quadrature bridge linking a pair of ac resistors of values 2R/sub K/ /spl ap/ 51.6 k/spl Omega/ to a pair of capacitance standards. The quadrature bridge can be operated at five different frequencies: 513, 1027, 1541, 3082, and 6164 Hz. For such measurements, we use different ratios (1/1, 4/1 and 1/4) for the main inductive voltage divider in the quadrature bridge and three different pairs of capacitors of values 3000, 2000, and 1000 pF. A calculable coaxial resistance of 1290.6 /spl Omega/ (R/sub K//20) is used as a reference to evaluate the frequency dependence of the 51.6-k/spl Omega/ resistances. This allows the calibration of capacitance standards at the five different frequencies. The measured frequency dependences of 10 and 100 pF capacitance standards are reported.     

Temperature Dependence of the Hall and Longitudinal Resistances in a Quantum Hall Resistance Standard

We present detailed measurements of the temperature dependence of the Hall and longitudinal resistances on a quantum Hall device [(GaAs(7)] which has been used as a resistance standard at NIST. We find a simple power law relationship between the change in Hall resistance and the longitudinal resistance as the temperature is varied between 1.4 K and 36 K. This power law holds over seven orders of magnitude change in the Hall resistance. We fit the temperature dependence above about 4 K to thermal activation, and extract the energy gap and the effective g-factor.     

A simple resistance network for calibrating resistance bridges

This paper describes a simple, passive, low-cost resistance network, closely related to Hamon build-up resistors, that enables the calibration of dc and low-frequency ac resistance and conductance bridges. The network is configured so that the four component resistors can be connected to realize 35 distinct four-terminal resistances, all interrelated by the usual formulas for the series and parallel connections of resistors. Theoretical analysis and experimental results show that with due care in the design, the network can be readily constructed to achieve an accuracy of better than 1 μΩ for resistances of the order of 100 Ω (1:10⁸) for angular frequencies from dc to 10⁴ rad/s     

Domain configuration under rotational flux and applied stress conditions in silicon-iron

Measurements of power loss have been made on individual grains in polycrystalline specimens of commercial 3% grain-oriented silicon-iron under longitudinal and transverse ac magnetization and rotational flux conditions. The domain configurations have also been observed using a stroboscopic Kerr magnetic-optic apparatus. The effect of longitudinal stress and dc bias fields on the domain patterns and power loss under these ac magnetization conditions has also been investigated. It can be concluded that the highest power loss occurs under pure rotational flux conditions and that the application of longitudinal compressive stress increases the power loss, but to a lesser extent when a transverse ac flux is present. The application of a longitudinal dc field increases the power loss for all ac magnetizing conditions, and it has been observed that a longitudinal tensile stress has the opposite effect on the domain configuration to the application of a transverse dc field.     

Derivation of an electronic equivalent of QHE devices

Models of quantum Hall effect (QHE) devices described by an equivalent circuit are used both to analyze measurement systems and to study QHE physics. Although the most widely used equivalent is the one proposed by Ricketts and Kemeny, various other circuits have been published to suit to different needs in QHE analysis, including a network with only resistors and unity-gain amplifiers. In the following we discuss a general approach to the analysis of the electrical behavior of QHE devices, and show that they can be classified as gyrators. Gyrators are nonreciprocal network elements whose properties are well known from the theory of electrical network. They can be regarded as generalized equivalents of Hall effect devices, thus setting a general framework for the study of the electrical behavior of QHE and the derivation of equivalent circuits. Through the application of this technique, an electronic circuit capable of simulating a QHE device with nonnull longitudinal resistance is derived     

Strain-gauge differential circuits with current transformers

Conclusions Differential strain-gauge circuits with current transformers have several advantages as compared with ordinary bridges or bridges with voltage transformers, since the former circuits eliminate the effect on the measurement precision of the conductor resistances and the contact resistances of the current collectors and switching devices. Moreover, two strain gauges are sufficient for the operation of these circuits. The above differential circuits are more sensitive than bridge circuits,and they have a linear characteristic, with the output voltage being proportional to the transducer resistance. Less stringent requirements can be specified for the stability and value of the switching devices when these circuits are used for multipoint measurements. The circuits operate with alternating currents and, therefore, they possess all the advantages of ac strain-gauge circuits.     

Degradation of GaAs/AlGaAs Quantized Hall Resistors With Alloyed AuGe/Ni Contacts

Careful testing over a period of 6 years of a number of GaAs/AlGaAs quantized Hall resistors (QHR) made with alloyed AuGe/Ni contacts, both with and without passivating silicon nitride coatings, has resulted in the identification of important mechanisms responsible for degradation in the performance of the devices as resistance standards. Covering the contacts with a film, such as a low-temperature silicon nitride, that is impervious to humidity and other contaminants in the atmosphere prevents the contacts from degrading. The devices coated with silicon nitride used in this study, however, showed the effects of a conducting path in parallel with the 2-dimensional electron gas (2-DEG) at temperatures above 1.1 K which interferes with their use as resistance standards. Several possible causes of this parallel conduction are evaluated. On the basis of this work, two methods are proposed for protecting QHR devices with alloyed AuGe/Ni contacts from degradation: the heterostructure can be left unpassivated, but the alloyed contacts can be completely covered with a very thick (> 3 μm) coating of gold; or the GaAs cap layer can be carefully etched away after alloying the contacts and prior to depositing a passivating silicon nitride coating over the entire sample. Of the two, the latter is more challenging to effect, but preferable because both the contacts and the heterostructure are protected from corrosion and oxidation.     

Comparison of quantized Hall resistances RH(2) andRH(4) of a GaAs/AlGaAs heterostructure device

Quantized Hall resistances R_H(4) and R_H(2) of a GaAs/AlGaAs heterostructure were compared with reference resistors whose values are close to h/4e² or h/2e². The values of the reference resistors were compared with a 100 ohm standard resistor via a cryogenic current comparator (CCC) resistance bridge. Results showed that (4×R_H(4)-2×R_H(2))/2×R_H (2)=(0.037±0.019)×10^-6     

Direct resistance comparisons from the QHR to100 M/spl Omega/ using a cryogenic current comparator

Measurements of room-temperature 100 M/spl Omega/ standard resistors and cryogenic thin-film resistors based directly on a quantized Hall resistance standard have been made with a cryogenic current comparator (CCC) bridge. This 15 496:2 ratio CCC attains a current sensitivity of 10.7 fA/Hz/sup 1/2/ in measurements of cryogenic thin-film resistors, without extensive shielding or filtering. A resistive primary winding helps the CCC maintain stability in the presence of external noise. The resistive-winding technique may be useful for the absolute measurement of small currents delivered by single-electron tunneling devices.     

Comparison of Quantized Hall Resistance with a 1-? Standard

A major step in the precise determination of the quantized Hall resistance is the comparison of a resistor of value nominally 6453.2 ? with a 1-? standard. For this purpose the National Measurement Laboratory will use a build-up resistor comprising 83 resistors each of 80? ?, giving a ratio of 64534/9. An accuracy of better than 1 in 108 is expected.     

Contact resistance characteristics of the low cost CuNiCr thin film resistor system

In this paper an investigation of the use of copper as a contact and interconnecting material for thin film resistors and hybrid circuits is reported. The current-voltage characteristics of Nichrome thin film resistors with copper contacts and the contact resistance of $\text{Cu}\text{NiCr}$ metallizations were measured. The effect of thermal annealing on the contact characteristics was also studied.     

Automatic Self-Certification of a Computer-Controlled Calibration System

The theory, techniques, and apparatus that are used to perform an automatic self-certification of a computer-controlled calibration system are described. This process determines the linearity and bias deviations of the instrumentation of the system. These deviations are stored in the digital computer for subsequent use as corrections to the nominal instrument values when the system is applied to external devices. Dc measurements and stimuli, the uncertainties of which are of the order of 0.001 percent, have been achieved using this technique, exceeding the specifications normally associated with the uncorrected instrumentation. A similar reduction in uncertainty results from the self-certification process in ac voltage and resistance measurements. Using a 1-volt dc source, 1000-ohm resistor, and ac-dc thermal transfer as references, the scales of measure are automatically reestablished over a wide dynamic range in less than five minutes. Laboratory applications of this computer-controlled system have been made to classical metrology problems that include measurements of standard resistors, saturated standard cells, and resistance thermometers. Semi-automatic calibrations of test and measuring instruments have been performed to demonstrate potential productivity and accuracy.