We present detailed measurements of the temperature dependence of the Hall and longitudinal resistances on a quantum Hall device [(GaAs(7)] which has been used as a resistance standard at NIST. We find a simple power law relationship between the change in Hall resistance and the longitudinal resistance as the temperature is varied between 1.4 K and 36 K. This power law holds over seven orders of magnitude change in the Hall resistance. We fit the temperature dependence above about 4 K to thermal activation, and extract the energy gap and the effective g-factor.
We use equivalent electrical circuits to analyze the effects of large parasitic impedances existing in all sample probes on four-terminal-pair measurements of the ac quantized Hall resistance RH. The circuit components include the externally measurable parasitic capacitances, inductances, lead resistances, and leakage resistances of ac quantized Hall resistance standards, as well as components that represent the electrical characteristics of the quantum Hall effect device (QHE). Two kinds of electrical circuit connections to the QHE are described and considered: single-series “offset” and quadruple-series. (We eliminated other connections in earlier analyses because they did not provide the desired accuracy with all sample probe leads attached at the device.) Exact, but complicated, algebraic equations are derived for the currents and measured quantized Hall voltages for these two circuits. Only the quadruple-series connection circuit meets our desired goal of measuring RH for both ac and dc currents with a one-standard-deviation uncertainty of 10−8
RH or less during the same cool-down with all leads attached at the device. The single-series “offset” connection circuit meets our other desired goal of also measuring the longitudinal resistance Rx for both ac and dc currents during that same cool-down. We will use these predictions to apply small measurable corrections, and uncertainties of the corrections, to ac measurements of RH in order to realize an intrinsic ac quantized Hall resistance standard of 10−8
RH uncertainty or less.
Experimentally obtained magnetic field images contain not only magnetic field noise, but also uncertainty in the position at which the data points are recorded. Such position noise degrades the images where the magnetic field gradients are strongest. Our high-Tc scanning superconducting quantum interference device (SQUID) microscope was found to be limited by a position noise of about 0.145 μm. For a straight wire carrying 500 μA with a rms magnetic noise of 0.185 nT, and source–sample separation 150 μm, we find that the rms position noise must be less than 62 nm for it to have less impact on the image quality than intrinsic magnetic SQUID noise.
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