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The ac quantum Hall resistance as a quantum standard of capacitance


The ac quantum Hall resistance show a frequency- and current-dependence which is known for a long time but nevertheless was not understood. Now, three different loss mechanisms have been identified and eliminated. The main mechanism is dissipation of capacitive currents in the two-dimensional electron gas, and these currents can be eliminated by means of voltage-controlled gates. Another contribution has been attributed to relaxation losses of an adsorbate layer on the surface of the quantum Hall device. It can be eliminated by sufficient vacuum preparation before the quantum Hall device is installed into the cryo-magnetic system. The remaining ac losses have been attributed to polarization losses of the GaAs substrate and are eliminated by a novel shielding technique. This makes the ac quantum Hall resistance independent of frequency and current and equal to the quantized dc value, each within an uncertainty of at most 1x10-8.
The ac quantum Hall resistance has now been applied as an impedance standard and a set of capacitance standards ranging from 10 pF to 10 nF has been calibrated traceable to the von-Klitzing constant. For this purpose, a quadrature bridge with two quantum Hall devices in a new double-device holder has been applied for the first time. The relative uncertainty of the whole capacitance chain has not yet reached the ultimate limit but approaches the target of 1x10-8. Then one will have realized a quantum standard of capacitance whose uncertainty beats the conventional artefacts.

Figure 1: Measuring chain from the ac quantum Hall resistance to a 10 pF capacitance standard.