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Draft 17 July 2002

Revised Technical Guidelines for Reliable DC Measurements of the Quantized Hall Resistance

F. Delahaye and B. Jeckelmann


This paper describes the main tests and precautions necessary for both reproducible and accurate results in the use of the quantum Hall effect as a means to establish a reference standard of dc resistance having a relative uncertainty of a few parts in 109.

1. Introduction

This document is a revised version of the Technical Guidelines for Reliable Measurements of the Quantized Hall Resistance established in 1988 [1]. The 1988 text was based on the suggestions of a Working Group on the Quantum Hall Effect* established by the Comité Consultatif d' électricité (CCE). At its 22nd meeting (September 2000), the Comité Consultatif d' électricité et Magnétisme (CCEM, new denomination of the CCE) asked the authors of the present paper to prepare a revised version of the Guidelines taking into account comments and suggestions received from the National Metrology Institutes (NMIs).

Indeed, since 1988 considerable progress was made in the NMIs on the subject of accurate comparisons of quantized Hall resistances (QHR) as realized using different types of QHE devices [2,3,4,5]. Also it was possible to confirm, in particular through on-site comparisons of resistance standards based on the quantum Hall effect (QHE) [6], that the reproducibility of the QHR, as realized by the different NMIs, is as good as a few parts in 109. A generally admitted conclusion is that the 1988 Guidelines were found adequate to ensure accurate QHR measurements, in the sense that every QHE device that gave a discrepant result was also found to fail at least one of the tests suggested in the Guidelines. In particular, it was confirmed that an important criterion is the absence of longitudinal voltage drop along both sides of the QHE device.

The aim of the present text is not to recommend strict rules but rather to propose guidelines to serve as a reminder of the main tests and precautions necessary to assure reliable measurements of the QHR at a relative uncertainty of a few parts in 109. Also, this text is not intended to be a review paper on the subject of the metrological application of the QHE. The interested reader is referred to recently published reviews [7,8,9].

2. Device choice

Metal-oxide-semiconductor field-effect transistors (MOSFETs) or GaAs/AlGaAs devices (and possible alternative heterostructures) can be used for accurate measurements of the QHR. An important feature is the value of the measuring current which can be used without producing significant longitudinal dissipation in the device. It has been shown that, from this point of view, specially designed MOSFETs can compete with GaAs-based heterostructures and accept measuring currents as high as 50 µA [3]. It was demonstrated that QHRs measured on both types of devices are in agreement to better than 1 part in 109 [3,4]. However, GaAs devices are usually preferred for routine QHR measurements, and this for a number of reasons: GaAs devices can be used at a relatively high temperature (of the order of 1.5 K instead of 0.5 K for MOSFETs) and at a relatively low magnetic flux density B (as low as 6 T); they are simpler to operate as no gate electrode is needed; moreover, it is reasonably easy to obtain suitable GaAs devices as there are several fabrication sources.

In the case of GaAs/AlGaAs devices, a mobility µ higher than 10 T-1 and a carrier concentration n in the range 3  1015 m-2 to 5.5  1015 m-2 are suitable in order to obtain wide and well-quantized = 2 plateaux for the values of temperature mentioned above and with B in the range 6 T to 11 T. If n is increased to values above 6  1015 m-2, the second electrical sub-band in the potential well at the interface between GaAs and AlGaAs is populated as well. As a consequence, a second current path develops in the device producing interference with the usual quantum Hall picture. If good quantization conditions for the i = 4 plateau are important, a mobility of 10 T-1 is not sufficient. As shown in [10], the minimum longitudinal resistivity for i = 4 rapidly increases when the mobility decreases below 30 T-1, occurring for current levels required for high-accuracy QHR measurements. Other parameters to be considered are the critical current and the plateau width. At the critical current, the quantum Hall effect breaks down and the longitudinal resistivity abruptly increases by several orders of magnitude. It was shown [10] that the critical current is independent of the mobility when µ is between 15 T-1 and 130 T-1 for i = 2, and between 30 T-1 to 130 T-1 for the case of i = 4. On the other hand, the plateau width decreases with increasing mobility although not as dramatically as predicted previously. Considering the different aspects, a mobility of 40 T-1 to 80 T-1 seems to be an optimal choice for GaAs devices, especially for high-accuracy measurements on plateaux other than the i = 2 plateau.

In the case of silicon MOSFETs a mobility of about 0.8 T and a carrier concentration of 13  1015 m-2 were found adequate to obtain a well-quantized = 4 plateau at a temperature of 0.4 K and for B of the order of 13 T [3].

The devices should be fitted with source (S) and drain (D) contacts (gate and substrate for MOSFETs) and with at least two, preferably three, pairs of Hall-voltage contacts (Fig. 1). As the critical current scales linearly with the sample width, for width w at least up to 1.5 mm [10], the width should be chosen as large as possible. The current contacts (S and D), where the electrons are injected into the two-dimensional electron gas (2DEG), should extend over the whole width of the device to reach the desired critical current. Deviations from the nominal QHR can be caused if the populations of the electronic edge states are not equilibrated (see Sect. 4). In order to prevent the formation and detection of non-equilibrium distributions, narrow side arms (wp < 100 m) along the edge of the device should be avoided and the distances between the contacts should be as large as possible.

Fig. 1. Device with three pairs of Hall-voltage contacts. For the magnetic field pointing out of the sample in z direction, the drain contact D and the Hall potential contacts 1 to 3 are on the same potential.
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