Controlling ac losses in quantum Hall effect devices

Abstract

When measured with ac at kilohertz frequencies the quantized Hall resistance (QHR) of a quantum Hall effect (QHE) device is usually found to be current- and frequency-dependent. This is a limitation on its use as a quantum impedance standard. We develop a model for the principal ac losses arising in the QHE device and show how they are responsible for the observed QHR current and frequency coefficients. We believe that losses are mainly caused by dissipative ac charging of the device along its edges. Charging is induced by the passage of the Hall current and by capacitive coupling between an edge and any nearby conductor maintained at an ac potential different to that of the edge, as for example at shield potential. The loss power is proportional to frequency and increases more rapidly than the square of the applied voltage or current. We model losses in terms of in-phase loss currents, which are a function of the amplitude of the ac charge reaching or leaving edges. The QHR frequency coefficient is zero only when the loss current for one portion of the high-potential edge and that for a corresponding portion of the low-potential edge are equal and of opposite sign. We propose a simple method for approaching that balance condition: gates are located under the device edges and their ac potentials adjusted so that the QHR current coefficient, evaluated at a constant frequency, is zero. We report measurements of the residual QHR frequency coefficients obtained after adjustment for GaAs/GaAlAs devices of two different types. For five different devices of the most favourable type, the QHR frequency coefficients do not exceed ±2 parts in 108 per kilohertz.

Towards Accurate Measurement of the Frequency Dependence of Capacitance and Resistance Standards up to 10 MHz

“…2. Two 1 kfQ and one 100 Q resistance standards have been developed which will enable 10 comparisons. There are several differences between the HF-CRS and the calculable Gibbings [6] and Haddad [7] resistance standards already in use in several National Metrology Institutes.…”

Effects of metallic gates on ac measurements of the quantum hall resistance

“…Although various controversial results have been obtained, a few common features were observed [1] : the plateaus in the quantum Hall resistance R H are no longer as flat and broad as they are at dc. In addition, the QHR has a linear frequency dependence caused by losses along the sample edges due to the presence of metallic gates in the vicinity of the 2DEG [3,4]. In this paper, we show that, by removing metallic gates from the vicinity of the sample, the frequency dependence of the QHR can be strongly reduced without any external potential adjustment.…”

The ac quantum Hall effect: About gates and image charges

“…Split gates are known to be capable of eliminating the capacitive effects of a QHR device [1,2]. It has been shown here, firstly, that a back-gate is necessary to define the current-and potential-distribution in the device.…”

“…Only under this condition, the capacitances of the 2DEG are well-defined and can be controlled by means of the electric in-plane field of the side-gates. Looking back on the results obtained for a QHR device with a split back-gate (and without side-gates) [1,2], it becomes clear that a split back-gate combines two functions in one: Firstly, it defines the current distribution in the device and causes the Hall voltage to drop mainly along the device edges while the bulk behaves like a dielectric at an almost constant potential [1,4]. This gate effect does not depend on the gate voltage.…”

“…Providing an ac QHR device with a split back-gate and applying adjustable ac voltages to both half-gates controls the capacitive ac losses [1,2]. A capacitance always implies induced image charges.…”