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.     

Developments in the quantum Hall effect

The most important applications of the quantum Hall effect (QHE) are in the field of metrology. The observed quantization of the resistance is primarily used for the reproduction of the SI unit ohm, but is also important for high precision measurements of both the fine structure constant and the Planck constant. Some current QHE research areas include the analysis of new electron-electron correlation phenomena and the development of a more complete microscopic picture of this quantum effect. Recently, scanning force microscopy (SFM) of the potential distribution in QHE devices has been used to enhance the microscopic understanding of current flow in quantum Hall systems. This confirms the importance of the theoretically predicted stripes of compressible and incompressible electronic states close to the boundary of the QHE devices.     

The Material Efforts for Quantized Hall Devices Based on Topological Insulators

A topological insulator (TI) is a kind of novel material hosting a topological band structure and plenty of exotic topological quantum effects. Achieving quantized electrical transport, including the quantum Hall effect (QHE) and the quantum anomalous Hall effect (QAHE), is an important aspect of realizing quantum devices based on TI materials. Intense efforts are made in this field, in which the most essential research is based on the optimization of realistic TI materials. Herein, the TI material development process is reviewed, focusing on the realization of quantized transport. Especially, for QHE, the strategies to increase the surface transport ratio and decrease the threshold magnetic field of QHE are examined. For QAHE, the evolution history of magnetic TIs is introduced, and the recently discovered magnetic TI candidates with intrinsic magnetizations are discussed in detail. Moreover, future research perspectives on these novel topological quantum effects are also evaluated.     

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     

An electrical circuit theoretical method for time‐ and frequency‐ domain solutions of the structural mechanics problems

Shrinking device dimensions in integrated circuit technology made integrated circuits with millions of components a reality. As a result of this advance, electrical circuit simulators that can handle very large number of components have emerged. These programs use new circuit simulation techniques and can find solutions accurately and quickly. In this paper, we apply these techniques to structural mechanics problems by adopting electrical circuit equivalents. We first apply finite element formulation to the mechanical problem. The obtained sets of equations are treated as if they are sets of equations of an equivalent electrical circuit which consists of linear circuit elements such as capacitors, inductors and controlled sources. The equivalent circuit is obtained in the form of a circuit netlist and solved using a general purpose electrical circuit simulator. Several examples showing the advantages of the circuit simulation techniques are demonstrated. Asymptotic waveform evaluation technique which is widely used for simulation of large electrical circuits is also studied for the same examples and the speed‐up advantage is shown. Copyright © 1999 John Wiley & Sons, Ltd.     

Precise derivation for the equivalent circuit parameters of a crystal resonator with series capacitor

An exact formula for the equivalent circuit of a crystal resonator in series with a capacitor is derived. Network analysis is used to obtain an exact formula for the equivalent circuit parameters without applying any approximations. The result is an expansion of that obtained by those who used assumptions regarding high frequency, high quality factor, high capacitance ratio, and so on. Hence, this formula can be used for instances of low quality factor or low capacitance ratio, and even for the actual inductor-capacitor network as long as these devices have the same equivalent circuits. The enhanced accuracy of the new formula extends itself to oscillator frequency calibration, temperature compensation, and electronic frequency control.     

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.     

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     

Calculating the Effects of Longitudinal Resistance in Multi-Series-Connected Quantum Hall Effect Devices

Many ac quantized Hall resistance experiments have measured significant values of ac longitudinal resistances under temperature and magnetic field conditions in which the dc longitudinal resistance values were negligible. We investigate the effect of non-vanishing ac longitudinal resistances on measurements of the quantized Hall resistances by analyzing equivalent circuits of quantized Hall effect resistors. These circuits are based on ones reported previously for dc quantized Hall resistors, but use additional resistors to represent longitudinal resistances. For simplification, no capacitances or inductances are included in the circuits. The analysis is performed for many combinations of multi-series connections to quantum Hall effect devices. The exact algebraic solutions for the quantized Hall resistances under these conditions of finite ac longitudinal resistances provide corrections to the measured quantized Hall resistances, but these corrections do not account for the frequency dependences of the ac quantized Hall resistances reported in the literature.     

An improved levelized incomplete Lu method and its application to 2d semiconductor device simulation

Abstract

Numerical simulation of semiconductor devices plays a very important role in the design and development of integrated circuits. We will present a new circuit simulator with an improved Levelized Incomplete LU method to perform such simulations. To have an environment for evaluating the interaction between a semiconductor device and a circuit, we use the equivalent circuit approach. This approach allows for simple representation carrier transport models of devices through equivalent circuit elements such as voltage controlled current sources and capacitors. Therefore, we can perform mixed‐level simulation in general circuit simulators. We will take a PN diode switching circuit and MOSFET as examples to test our equivalent circuit model and the improved circuit simulator. The comparison between improved matrix solution method and the conventional method will be demonstrated too. We will also show our method yields better matrix solutions than conventional methods     

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.     

Computer-Aided Optimum Design of Magnetic Circuits with Permanent Magnets

A computer oriented method is developed for optimum design of magnetic circuits with permanent magnets. It consists of finding an electrical equivalent for the magnetic circuit and writing a computer program that evaluates the various circuit elements, solves the resulting network equations, computes the leakage and reluctance factors, and solves the design equations iteratively. The design can be carried out to satisfy criteria such as minimum magnet volume or minimum material cost. The program can also be used to obtain the expected performance of specified designs thus allowing the designer to evaluate his design ideas without excessive prototype building. The execution time is of the order of a few seconds, and the designer can use the program in interactive mode thus saving substantial engineering time.     

Practical and Fundamental Impact of Epitaxial Graphene on Quantum Metrology

The discovery 8 years ago of the quantum Hall effect (QHE) in graphene sparked an immediate interest in the metrological community. Here was a material which was completely different from commonly used semiconductor systems and which seemed to have some uniques properties which could make it ideally suited for high-precision resistance metrology. However, measuring the QHE in graphene turned out to be not so simple as first thought. In particular the small size of exfoliated graphene samples made precision measurements difficult. This dramatically changed with the development of large-area graphene grown on SiC and in this short review paper we discuss the journey from first observation to the highest-ever precision comparison of the QHE.     

The spectrum study of blood pressure during the disturbance of organic vascular beds

Abstract

Like electrical circuit components, the vascular beds in organs present impedance to waves in systemic circulation. In this study, the authors design an animal experiment to study the effect of the impedance to the pressure waves. We view the systemic circulation as an electrical circuit network, and interpret the vascular beds in organs as lumped components in the electrical circuit. Nature's designing of the systemic circulation minimizes the pressure wave reflection, and maximizes blood distribution. This is very similar to the concept adopted by electrical engineers in designing electrical circuits.     

A comparison among different setups for measuring on-waferintegrated inductors in RF applications

This paper presents a comparison to study the most suitable setup for measuring an integrated inductor using a vector network analyzer. It assumes that the inductor will be modeled with the Π model, the lumped equivalent circuit most often used by designers. We have demonstrated that measuring an inductor with a one-port analyzer is not suitable for an accurate characterization of this type of device. Instead, we propose that the best method is measuring the inductor placed in series between the two ports of the analyzer. The method presented can be extrapolated to the study of how to measure other two-port devices in which the lumped equivalent circuit used to characterize its performance is previously known     

Spin Hall effect devices

The spin Hall effect is a relativistic spin-orbit coupling phenomenon that can be used to electrically generate or detect spin currents in non-magnetic systems. Here we review the experimental results that, since the first experimental observation of the spin Hall effect less than 10 years ago, have established the basic physical understanding of the phenomenon, and the role that several of the spin Hall devices have had in the demonstration of spintronic functionalities and physical phenomena. We have attempted to organize the experiments in a chronological order, while simultaneously dividing the Review into sections on semiconductor or metal spin Hall devices, and on optical or electrical spin Hall experiments. The spin Hall device studies are placed in a broader context of the field of spin injection, manipulation, and detection in non-magnetic conductors.     

Effect of top-down nanomachining on electrical conduction properties of TiO2 nanostructure-based chemical sensors

The present research was motivated by the growing interest of the scientific community towards the understanding of basic gas-surface interaction mechanisms in 1D nanostructured metal oxide semiconductors, whose significantly enhanced chemical detection sensitivity is known. In this work, impedance spectroscopy (IS) was used to evaluate how a top-down patterning of the sensitive layer can modulate the electrical properties of a gas sensor based on a fully integrated nanometric array of TiO(2) polycrystalline strips. The aim of the study was supported by comparative experimental activity carried out on different thin film gas sensors based on identical TiO(2) polycrystalline sensitive thin films. The impedance responses of the investigated devices under dry air (as the reference environment) and ethanol vapors (as the target gas) were fitted by a complex nonlinear least-squares method using LEVM software, in order to find an appropriate equivalent circuit describing the main conduction processes involved in the gas/semiconductor interactions. Two different equivalent circuit models were identified as completely representative of the TiO(2) thin film and the TiO(2) nanostructure-based gas sensors, respectively. All the circuit parameters were quantified and the related standard deviations were evaluated. The simulated results well approximated the experimental data as indicated by the small mean errors of the fits (in the range of 10(-4)) and the small standard deviations of the circuit parameters. In addition to the substrate capacitance, three different contributions to the overall conduction mechanism were identified for both equivalent circuits: bulk conductivity, intergrain contact and semiconductor-electrode contact, electrically represented by an ideal resistor R(g), a parallel R(gb)C(gb) block and a parallel R(c)-CPE(c) combination, respectively. In terms of equivalent circuit modeling, the sensitive layer patterning introduced an additional parameter in parallel connection with the whole circuit block. Such a circuit element (an ideal inductor, L) has an average value of about 125 μH and exhibits no direct dependence on the analyte gas concentration. Its presence could be due to complex mutual inductance effects occurring both between all the adjacent nanostrips (10 μm spaced) and between the nanostrips and the n-type-doped silicon substrate underneath the thermal oxide (wire/plate effect), where a two order of magnitude higher magnetic permeability of silicon can give L values comparable with those estimated by the fitting procedure. Slightly modified experimental models confirmed that the theoretical background, regulating thin film devices based on metal oxide semiconductors, is also valid for nanopatterned devices.     

Noise-tolerant quantum MOS circuits using resonant tunneling devices

Resonant tunneling devices are promising candidates for comingling with traditional CMOS circuits, yielding better performance in terms of reduced silicon area, faster circuit speeds, lower power consumption, and improved circuit noise margin. These resonant tunneling devices have several intrinsic merits that include: high current density, low intrinsic capacitance, the negative differential resistance effect, and relative ease of fabrication. In this paper, we briefly describe some circuit configurations of Silicon quantum MOS logic family, with a special emphasis on noise-tolerant design that is now becoming an important constraint for robust and reliable operation of very deep submicron VLSI chips. More specifically, we discuss a novel strategy to incorporate quantum-tunneling devices into mainstream dynamic CMOS circuits with a view to improving the noise immunity of the latter. Dynamic CMOS circuits are rampantly used in modern high-performance VLSI chips achieving the best tradeoff between circuit speed, silicon area, and power consumption. However, they are inherently less noise-tolerant than their static CMOS counterparts. With the continuously deteriorating noise margins due to aggressive down scaling of the CMOS fabrication technologies, the performance overhead due to existing remedial noise-tolerant circuit techniques becomes prohibitively high. In this paper, we propose a novel method that utilizes the negative differential resistance property of quantum tunneling devices. The performance and noise immunity of the proposed circuits are evaluated through both analytical studies and SPICE simulations. We demonstrate that the noise tolerance of dynamic CMOS circuits can be greatly improved with very little degradation in circuit speed. The benefit of the proposed technique is evident even for currently available Silicon-based resonant tunneling devices with a relatively small peak-to-valley current ratio.     

CMOS circuit testing via time-resolved luminescence measurements and simulations

The continuous trend in modern CMOS technology toward smaller devices and faster clock frequency is challenging the picosecond imaging circuit analysis technique. In this paper we discuss the role of the single-photon avalanche diode with very sharp time resolution in testing CMOS circuits. Thanks to the 30 ps-time resolution, innovative measurements regarding delays and jitter are presented, along with a case study. A compact model of the luminescence is also proposed and used to compare on-chip electrical signals with optical waveforms.     

Noise analysis in air-coupled PVDF ultrasonic sensors

In this paper we analyze the noise generated in a piezo-polymer based sensor for low frequency ultrasound in air. The sensor includes two curved PVDF transducers for medium and short range applications. A lumped RLC equivalent circuit was derived from the measurement of the transducer's electrical admittance, in air, by taking into account both mechanical and dielectric losses, which we suppose are the major sources of noise in similar devices. The electrical model was used to study and optimize the noise performance of a 61 kHz transducer and to simulate the electrical behavior of the complete transmitter-receiver system. The validity of the overall electrical model with low noise was confirmed after verifying, with Pspice, agreement of the practical and theoretical results.