QUADRATIC FREQUENCY DEPENDENCE OF AN AC QHR DEVICE M. E. Cage National Institute of Standardsand Technology Gaithersburg,MD 20899-8172 Abstract An equivalent electrical circuit model of an ac quantized Hall resistance device externally connected in quadruple series predicts a quadratic fre~uency dependence no more than -4 x 10-9 /kHz. This agrees with experiment when indirectly comparing that device with a calculable quadrifilar resistor in interchanged 1:1 ratios using a four-terminal-pair bridge. I III II I t I ! I Introduction AC quantized Hall resistance (ac QHR) standards have linear and quadratic frequency dependences, as do the reference resistors with which they are compared, and the ac measurement bridges themselves [1]. This paper deals only with the quadratic dependences. The bridge quadratic dependence is dominant [1] and must be removed. Then either a reference resistor with a calculable quadratic dependence is required to extract its ac-dc difference [2] and thereby determine the quadratic dependence of the ac QHR standard, or the quadratic dependence of the ac QHR standard itself must be determined [3]. This experiment does all of the above. Quadrifilar (Gibbings) resistors [2] are often employed as calculable reference resistors to extract the ac-dc differences. Uniform transmission line models can calculate quadratic frequency effects due to parasitic inductances and capacitances, and other models calculate quadratic dependences due to skin effects and eddy currents in the resistor wires and surrounding shield. Quadrifilar resistance values change because of instabilities in the thin wires. So rather than directly compare an ac QHR device with a quadrifilar resistor,. we found it easier to compare a quadrifilar resistor with a stable wire- wound resistor without having to bother with a superconducting magnet and cyrogens, and then compare that stable wire-wound resistor with an ac QHR device using the magnet. Reference [1] describes those comparisons in detail, demonstrates that all dc QHR guideline properties and all dc and ac QHR values can be measured in a single cooldown without changing 1"1 I'" ! If. sample probe leads at the device, and shows that quadruple-series-connected ac QHR values measured in the four-terminal-pair mode converge to the dc QHR value. The next section summarizes that experiment. EXDeriment The only ac QHR device available was a GaAs/AIGaAs heterostructure we labeled acl. It was mounted on a custom-built header using 100 J.1m diameter platinum wires to avoid vibrational effects of ac currents in a magnetic field. The header had a ground plane over most of its back surface to minimize wire-to-wire capacitances at the device (which is critical to reduce quadratic frequency dependences when using quadruple-series connections [3D. The device was homogeneous, but had potential pad contact resistances as large as 7,644 n. That 7,644 n contact exhibited Corbino-like behavior: its resistance increased with decreasing current at small currents due to isolated spikes diffused into the two-dimensional electron fluid. This behavior created problems: static voltages induced when changing connections during balances sometimes required minutes or hours to decay, causing the QHR values to fluctuate. That limited the tyP.e A 1cr relative uncertainties to II parts in 107, which was frustrating with 5 parts in 109 measurement resolutions at 20 J.1A. A 12,906.4 n wire-wound resistor labeled 12.9WWl was assembled from resistor components made of wire wound on mica cards and placed in a shielded container. It was designed for minimum capacitances-to-shield and placed in an oil bath. A quadrifilar resistor, also of nominal 12,906.4 n value and labeled 12.9QF1, had a self-contained air bath and was thermally-lagged with additional insulation. Its resistance could unpredictably change a few parts in 107 over several hours, necessitating computational adjustment to a reference frequency that we chose as 1,592 Hz. The three dc single-series 12,906.4 n i =2 quantized Hall resistances of QHR device acl, and its externally-connected dc quadruple-series resistance, were compared with the 12,906.4 n wire-wound reference resistor 12.9WWl at 29 J.1A and 1.6 K using an automated U.S. Government work not protected by U.S. copyright. :11 I 554 I