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From the quantum Hall effect to capacitance

The realisation of the unit of capacitance by means of the quantum Hall effect (QHE) has made considerable progress. Already since 1990, the QHE has served as the quantum standard for electrical resistance with direct current (DC). At PTB, a significant development has now been achieved in the measuring technique which also allows the precise measurement of the quantum Hall resistance with alternating current (AC) and provides a quantum standard for the capacitance.

Quanten-Hall-Element mit typischen Messkurven

A new system of physical units is planned which will consistently exploit the advantages of quantum standards and will be based solely on fundamental constants. The capacitance is thereby an important electrical quantity, not only to provide for the continuity of the old system but also for a consistency test within the new system. The link of a capacitance C with fundamental constants is based on the fact that, at a frequency ω, the AC resistance 1/(ωC) can be compared with the quantum Hall resistance. The quantum Hall resistance, which only depends on fundamental constants, thus also provides a quantum standard for the capacitance.

However, precision measurements in the kHz range reveal parasitic effects in the quantum Hall element which lead to frequency- and current-dependent deviations from the DC value. By means of control gates which generate an AC electrical field, these deviations can be adjusted at will or compensated completely, but this adjustment is characterised by an inadmissible arbitrariness.

A further development of the complex AC measuring technique makes it now possible to measure with alternating current all those quantities which have to be checked also in the case of direct current. For the first time, the measurement of the AC longitudinal resistance provides a metrologically well-defined and sensible criterion for the adjustment of the outer alternating field: If the AC longitudinal resistance of a QHE element is balanced to zero, the AC quantum Hall resistance within an extended measurement uncertainty of 2 · 10–8 (k = 2) becomes equal to the DC quantum Hall resistance, independent of outer influence quantities such as frequency, current and temperature.

This criterion is analogous to the internationally determined guidelines for reliable DC resistance calibrations by means of the QHE. The details for the realisation of an AC quantum standard of the capacitance shall be discussed at an international expert's meeting this year and lead to corresponding guidelines for AC.

Contact at PTB:

Phone: +49-531-592-0