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Electrical metrologists have been seeking ways to directly link the impedance of a 10 pF capacitor at frequencies near 1.5 kHz to the quantum Hall resistance (QHR). The uncertainty of such measurements has been limited by deformation of the QHR plateaus and the observation of a frequency dependence of the QHR amounting to no less than 1 or 2 parts in 107 per kilohertz.
Research at the BIPM has led to a simple solution to this problem. It consists of adding back-gate electrodes to the header into which the QHR device is mounted, and applying variable ac voltages to them. The gate voltages are adjusted while observing the current coefficient of the QHR at constant frequency. For those gate voltages for which the current coefficient vanishes the QHR frequency coefficient is significantly reduced. The figure below illustrates how the proper combination of voltages applied to gates placed below the high- and low-potential edges of a conventional "dc" QHR device removes the rather severe deformation of the plateau observed in the upper plots (no applied gate voltages). When the gate voltages are set to null out the current dependence of the QHR, the frequency coefficient of RH falls from 1 x 10–7 per kHz to about 2 x 10–8 per kHz.
Details of this work can be found in the following paper:
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Figure. High-resolution plots showing the influences of applied gate voltages on the real and imaginary components of the quantized Hall impedance at 1.5 kHz.
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Summary
