Electronic applications of large-area graphene films require rapid and accurate methods to map their electrical properties. Here we present the first electrical resistance tomography (ERT) measurements on large-area graphene samples, obtained with a dedicated measurement setup and reconstruction software. The outcome of an ERT measurement is a map of the graphene electrical conductivity. The same setup allows to perform van der Pauw (vdP) measurements of the average conductivity. We characterised the electrical conductivity of chemical-vapour deposited graphene samples by performing ERT, vdP and scanning terahertz time-domain spectroscopy (TDS), the last one by means of a commercial instrument. The measurement results are compared and discussed, showing the potential of ERT as an accurate and reliable technique for the electrical characterization of graphene samples.
The modelling of electrical connections of single, or several, multiterminal quantum Hall effect (QHE) devices is relevant for electrical metrology: it is known, in fact, that certain particular connections allow i) the realization of multiples or fractions of the quantised resistance, or ii) the rejection of stray impedances, so that the configuration maintains the status of quantum standard. Ricketts-Kemeny and Delahaye equivalent circuits are known to be accurate models of the QHE: however, the numerical or analytical solution of electrical networks including these equivalent circuits can be difficult. In this paper, we introduce a method of analysis based on the representation of a QHE device by means of the indefinite admittance matrix : external connections are then represented with another matrix, easily written by inspection. Some examples, including the solution of double-and triple-series connections, are shown.
Fully-digital impedance bridges are emerging as measuring instruments for primary electrical impedance metrology and the realization of impedance units and scales. This paper presents a comprehensive analysis of electronic fully-digital impedance bridges, for both generating (based on digital-toanalog converters) and digitizing (based on analog-to-digital converters) bridges. The sources of measurement error are analyzed in detail and expressed by explicit mathematical formulae ready to be applied to the specific bridge and measurement case of interest. The same can be employed also as a basis to optimize the design and the operating parameters of digital bridges, and to evaluate the measurement uncertainty. A practical application of the analysis to the digital bridges developed and measurements performed in the framework of an international research project is presented.
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