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The standard deviation of the mean (the random or type A measurement uncertainty) is, as noted above, typically ±0.006 ppm for a sample-resistor comparison. The position of the sample and resistor are then interchanged in the measurement system and the values are remeasured. The Hall resistance value assigned is the unweighted mean of these two comparisons, and the random uncertainty of the 14 pooled measurements is usually ±0.004 ppm. Pooling all of the measurements is viewed as justified since usually the difference in the values obtained in the two positions is well within the scatter of the data.

In addition to the random uncertainties, there are systematic, or type B, uncertainties associated with systematic corrections and other effects. One such correction is due to a measurement system offset, or interchange, error in which the value of the Hall resistance depends on whether it is measured in the RH position or in the RR position of the measurement circuit. The largest interchange correction to date has been +0.013 ppm, but, as noted above, is usually much less (i.e., indiscernible; the correction is based on the assumption that the mean of the two values obtained is the correct value). It is not completely understood why the interchange correction is less of a problem in this measurement system than it is in the old version of the potentiometric

system [9] and in the automated bridge system [9,10]. Perhaps it is due to a higher leakage resistance and to better electrical shielding. The estimated type B uncertainty associated with the interchange correction is assumed to be the same as the random uncertainty: ±0.004 ppm.

There is an uncertainty in calibrating the gain of the electronic detector-digital voltmeter pair. The pair can appear to vary by a few tenths of a percent over the input voltage range if the DVM has a dead-band at zero volts [9]. The dead-band of our Hewlett Packard 3457A Digital Multimeter is small enough for this effect to be negligible. There remains, however, the problem of the stability of the detector-digital voltmeter gain. The day-to-day gain varies by ~0.1% when the room temperature is controlled to ±1 °C. This instability contributes an estimated ±0.003 ppm type B uncertainty to the sample-resistor measurements because our reference resistors are about 2-3 ppm smaller than the quantum Hall resistance.

The 3×1012 measurement system leakage resistance contributes an estimated ±0.002 ppm type B uncertainty.

No temperature-dependent [7] or current-dependent [8] quantized Hall resistance (QHR) corrections could be detected for the Hall-probe set used on this sample. The respective estimated type B uncertainties for the dependence of the QHR on temperature and current are ±0.002 ppm and ±0.001 ppm.

The total root-sum-square uncertainty is typically ±0.007 ppm. This uncertainty is only one third that of the old potentiometric measurement system [9] and the bridge system [9,10]. The smaller uncertainty owes to: a) the ability to directly interchange the sample and the reference resistor positions in the measurement system, rather than having to substitute another reference resistor for the sample in order to determine the interchange error; b) a smaller interchange error; c) the fact that there is only one uncorrelated uncertainty of the detector-digital voltmeter gain, rather than the three correlated uncertainties in the bridge system; and d) a larger leakage resistance.

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2.30

1985

1986

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Time

starting May 1983

Figure 3-Relative comparisons as a function of time of the resistance of the i=4 steps of three different quantum Hall devices with that of a nominal 6,453.20 wire-wound reference resistor. AR/R=(Vн-VR)/VR. The value of this resistor is increasing by (0.044+0.002) ppm/year. The last set of data points were obtained with the new measurement system.

used in the comparisons is increasing by (0.044±0.002 ppm/year). The August 1986 data shows the improved measurement accuracy of the new automated potentiometric system over that of the old, manually-operated potentiometric measurement system and the automated bridge system. This new measurement system has proved to be quite reliable, very flexible, and easy to use.

The authors acknowledge having had useful discussions with, and receiving helpful suggestions from, C. T. Van Degrift, T. E. Kiess, B. F. Field, and R. F. Dziuba of the Electricity Division of NBS. One of the authors (G. M. R.) is especially grateful to B. N. Taylor for the opportunity to work on the quantum Hall effect in the NBS Electricity Division.

References

[1] v. Klitzing, K.; G. Dorda and M. Pepper, New method for high accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45 494 (1980).

[2] Tsui, D. C., and A. C. Gossard, Resistance standard using quantization of the Hall resistance of GaAs/AlGaAs heterostructures, Appl. Phys. Lett. 38 550 (1981).

[3] Delahaye, F.; D. Dominguez, F. Alexandre, J. P. Andre, J. P. Hirtz, and M. Razeghi, Precise quantized Hall resistance measurements in GaAs/Al,Ga1-,As and In,GaAs/InP heterostructures, Metrologia 22 103 (1986).

[4] v. Klitzing, K., and G. Ebert, Application of the quantum Hall effect in metrology, Metrologia 21 11 (1985).

[5] Taylor, B. N., Impact of quantized Hall resistance on SI electrical units and fundamental constants, Metrologia 21 3 (1985).

[6] For an up-to-date collection of the measurement results from different laboratories see the Proceedings of the Conference on Precision Electromagnetic Measurements 1986, to be published in IEEE Trans. Instrum. Meas. IM-36 (June 1987).

[7] Cage, M. E.; B. F. Field, R. F. Dziuba, S. M. Girvin, A. C. Gossard, and D. C. Tsui, Temperature dependence of the quantum Hall resistance, Phys. Rev. B 30 2286 (1984).

[8] Cage, M. E.; R. F. Dziuba, B. F. Field, E. R. Williams, S. M. Girvin, A. C. Gossard, D. C. Tsui, and R. J. Wagner, Dissipation and dynamic nonlinear behavior in the quantum Hall regime, Phys. Rev. Lett. 51 1374 (1983). [9] Cage, M. E.; R. F. Dziuba, B. F. Field, T. E. Kiess, and C. T. Van Degrift, Monitoring the U.S. legal unit of resistance via the quantum Hall effect, IEEE Trans. Instrum. Meas. IM-36 (June 1987, to be published).

[10] Field, B. F., A high-accuracy automated resistance bridge for measuring quantum Hall devices, IEEE Trans. Instrum. Meas. IM-34 2286 (1984).

Volume 92

The NBS Large-Area Alpha-Particle Counting Systems

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Recently the National Bureau of Standards (NBS) has developed two alpha-particle counting systems for the calibration of large area sources. These internal-source and an external-source gasproportional counting systems were requested by the United States Air Force (USAF) to calibrate large-area sources to serve as transfer standards between the USAF and NBS. The sources are rectangular, 8-in×5-in, with 238 Pu deposited on an aluminum substrate. The active area is an array of 1-mm diameter dots spaced a minimum of 4 mm apart. The four sources used range in total activity from 102 to 105 Bq.

Measurements described here have characterized the potential errors when calibrations are performed with the two systems, and when the calibrated sources are used to calibrate field monitoring equipment.

About the Authors: J. M. R. Hutchinson and S. J. Bright are with the Center for Radiation Research in NBS' National Measurement Laboratory.

2. Counting Systems

2.1 Internal Gas-Proportional Counter

The counter is pictured in figure 1 and shown schematically in figures 2a and 2b. A 13-in × 9-in Herfurth large-area flow proportional counter HGZ 730-C is mounted on four aluminum pedestals. The various grills, safety grids, and aluminized-mylar-foil window are removed and replaced with a vertically movable baseplate which supports the source and seals the counting volume by means of an "O" ring. Pressure for the seal is applied by five clamps. A clamp was not mounted on one of the sides, thereby permitting easy insertion of the source on this side. The baseplate is moved up and down with a lab-jack which is driven by a small motor. The vertical excursions both at the top and bottom of the baseplate movement are limited by microswitches which cut off the motor when the baseplate presses on them. The baseplate is not attached to the lab-jack so that if the motorized downward motion of the jack were accidently activated while the clamps were closed, the baseplate would remain clamped to the rest of

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Figure 1-Internal 2π-alpha-particle gas-proportional counter with a large-area source in counting position. When counting, the baseplate is raised and the clamps are tightened.

the counter, the jack would move down alone, and no damage would result to the motor.

The normal counting gas is P-10 at atmospheric pressure. Typically it takes 2-3 minutes after the gas flow is turned on before the alpha-particle pulses reach full height. After that, the counting space is flushed at a rate of about a bubble through the bubbler per one or two seconds. The procedure for counting a source in this counter is given in the Appendix.

A schematic drawing of the electronics for this and the external counting system is given in figure 3. Pulses originating in the counting volume as a result of energetic alpha particles producing ions within the counter, with subsequent gas multiplication, are passed into a charge-sensitive preamplifier, then into an amplifier, and are recorded in a multichannel analyzer which is read out on tape for subsequent evaluation. The pulse-height spectrum can be monitored on the MCA screen.

The high voltage is applied through a circuit which cuts off whenever the upper limiting microswitch is not under pressure from the baseplate. This is a safety feature which makes it impossible

for an operator to introduce a source into the counter while the counter wires are at high voltage.

2.2 'External' Gas Proportional Counter

The counter is pictured in figure 4 and shown schematically in figure 5. It is used to compare sources with activities too high for the internal counter with previously calibrated standards. This counter is of identical original design to the internal counter. However, the movable "baseplate" is replaced by an aluminized mylar window which is supported by a mounting plate, permanently attached. Baffles can be inserted to reduce count rates to acceptable levels for very active sources.

The large-area source is inverted and placed onto the mounting plate and this represents the counting position. In order to make accurate comparisons with standards in this counting geometry, it was necessary that the source-to-detector configurations be reproducible and also that the active layer be "thin" to the emitted alpha particles so that variations in distance from the counter would not affect the count rate significantly.

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Figures 2a and 2b-Schematics of the internal gas-proportional counter. The detector has 19 anode wires with 1 cm separation (fig. 2b).

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