Josephson effect
In 1962,Early Josephson standards
Although the AC Josephson effect provides a much more stable voltage reference than Weston cells, the first single-junction Josephson standards were difficult to use because they generated very small voltages (1–10 mV). Several attempts were made to raise the voltage by connecting two or more junctions in series. The most ambitious of these used 20 junctions in series to realize a voltage of 100 mV with an uncertainty of a few parts in 109. Ensuring that every junction was on a constant voltage step required individually adjusting the bias current to each of the 20 junctions. The difficulty of this procedure makes arrays of significantly more than 20 junctions impractical. In 1977, Levinson et al. made a suggestion that would ultimately lead to a solution to the multiple-bias problem. Levinson pointed out the importance of the parameter in determining the characteristics of RF-induced Josephson steps. is a measure of the damping of Josephson oscillations by the junction shunting resistance . In particular, he showed that junctions with a large capacitance and a large () could generate an I–V curve with hysteretic constant-voltage steps like those shown in Fig. 1b. These steps have become known as zero-crossing steps because they cross the zero-current axis of the I–V curve. The lack of stable regions between the first few steps means that for small DC bias currents, the junction voltage must be quantized. With a common bias current at or near zero, the voltage across a large array of these junctions must also be quantized. The possibility of obtaining constant-voltage steps at zero current over a wide range of junction and operating parameters suggested the possibility of building a voltage standard using large arrays of junctions. After several preliminary experiments, a joint effort in 1984 between the National Bureau of Standards in the U. S. and the Physikalisch-Technische Bundes-Anstalt in Germany resolved the problems of junction stability and microwave distribution and created the first large Josephson array based on Levinson's idea. Further design improvements and system development produced the first practical 1 V Josephson standards in 1985. Advances in superconductive integrated circuit technology, largely driven by the quest for a Josephson junction computer, soon made possible much larger arrays. In 1987, the design was extended to a chip with 14484 junctions that generated about quantized voltages spanning the range from to . Numerous further refinements were made as 10 V Josephson standards were implemented in many national standards laboratories. By 1989, all of the hardware and software for a complete voltage metrology system was commercially available. Today, there are Josephson array voltage standards in more than 70 national, industrial, and military standards laboratories around the world. A program of international comparisons carried out by the Bureau International des Poids et Mesures (BIPM) has measured differences between a traveling Josephson standard and those of NMIs that are typically less than 1 part in 109.Junction design details
Figure 3 illustrates the basic structure of one junction in a large series array. The junction is an overlap between two superconductive thin films that are separated by a thin oxide barrier. The junction sits above a ground plane and is separated from it by a few micrometers of insulation. A dc current and a microwave current are driven through the junction. The design parameters for the junction are its length , width , critical current density (critical current per unit area), and the microwave drive frequency . The practical realization of an array voltage standard requires a thorough understanding of how these parameters affect the stability of the quantized voltage levels shown in Fig. 1b. Stable operation requires that four conditions be satisfied: # must be small enough that the flux induced through the junction area by the microwave magnetic field is much less than the flux quantum # Both and must be small enough that the lowest resonant cavity mode of the junction is greater than # To avoid chaotic behavior, the junction plasma frequency , which is proportional to , must be less than about one third . # The junction's critical current should be as large as possible to prevent noise-induced quantum step transitions. If any of these conditions is violated, the junction voltage is likely to switch randomly among several steps, making measurements impossible. A rigorous derivation of these conditions is the subject of several papers by Kautz. Figure 4 illustrates the region of stable behavior in the three-dimensional space of , , and . The margin of stable operation, represented by the shaded volume in Fig. 4, increases with and is ultimately set by a trade-off between stability and the economics of providing a very high frequency microwave source. While stable arrays have been demonstrated at frequencies as low as 24 GHz, most practical standards operate in the range 70–96 GHz. Table 1 lists a typical set of junction parameters for a commonly used design.Array design
The I–V curve shown in Fig. 1b shows steps covering the range from about to and is for a junction driven by a nearly optimum level of microwave current. At lower microwave current the steps cover a smaller range of voltage and at higher microwave current the steps become smaller and begin to move off the zero current axis. In a large array, every junction must generate a large zero crossing step and thus the microwave power must be adjusted to a value low enough to accommodate the one junction receiving the largest microwave drive. Thus, in order to obtain the largest voltage from the smallest number of junctions, an array standard requires a circuit design that can deliver nearly uniform microwave power to many thousands of junctions, all of which are connected in series. The solution to this problem is a simple extension of Fig. 3 to a series of junctions in a line over a ground plane as shown in Fig. 5a. This results in a microwave stripline that can propagate microwave power with relatively low loss. The capacitive impedance of the junctions is so small (approximately 1 mΩ ) relative to the strip line impedance (approx. 3 Ω) that each junction has a very minor effect on the propagation of microwave power in the strip line. Typically, each junction will absorb about 0.02% to 0.04% of the power propagating through it. It is thus possible to connect several thousand junctions in series and still achieve a power uniformity of about ±1.5 dB. With careful design, striplines with as many as 4800 junctions have been used. Because Josephson standards require about junctions, it is necessary to adopt a series/parallel circuit similar to that shown in Fig. 5b. 9/sup> Here, a network of low- and high-pass filters allow the microwave power to be split into four parallel paths while maintaining a dc path in which all junctions are connected in series. A typical integrated circuit layout for an array of junctions is shown in Fig. 6. The microwave drive power is collected from aFabrication
Voltage standard chips are typically fabricated on silicon or glass substrates. The integrated circuit has eight levels: (1) a 300 nm thick Nb ground plane, (2) a 2 μm layer of SiO that forms the microstripline dielectric, (3) a 200 nm Nb film that forms the lower electrode of the Josephson junctions, (4) a 3 nm metal oxide layer that forms the Josephson tunneling barrier, (5) a 100 nm Nb junction counter electrode (6) a 300 nm SiO2 film with windows for contacts to the counter electrode, (7) a 400 nm film of Nb that connects the junction counter electrodes, and (8) a 100 nm resistive film that forms the stripline terminations.Measurement systems
A block diagram of a modern Josephson voltage standard system is shown in Fig. 7. The Josephson array chip is mounted inside a high-permeability magnetic shield at the end of a cryoprobe that makes the transition between a liquid helium Dewar and the room temperature environment. Some systems use a cryocooler to cool the chip and eliminate the need for liquid helium. Three pairs of copper wires are connected to the array. One pair supplies bias current, a second monitors the array voltage with an oscilloscope, and the third pair delivers the array voltage to the calibration system. All of the wires pass through multiple levels of RFI filtering in a box at the top of the Dewar. The box, the filters, and the Dewar itself form a shield that protects the Josephson array from electromagnetic interference that could cause step transitions. Microwave power is delivered through a waveguide consisting of a 12 mm diameter tube with WR-12 launching horns on each end. Tubes of solidExample measurement algorithm
The voltage of an unknown reference relative to the Josephson array voltage is determined using the circuit shown in Fig. 9 (a subset of Fig. 7) in which the unknown and the Josephson array are connected in series opposition across a null meter. A reversing switch is used to eliminate the effect of thermal and other offset voltages. The step number and sometimes the frequency are adjusted to make the null voltage as small as possible. The circuit equation can then be written: : Here, is the Josephson array voltage, ''V''0 is a combination of thermal offset voltages and any offset voltage in the nullmeter, mt represents a linear drift component of the offset voltage, is the polarity of the reversing switch, is the differential null voltage, and represents noise in the unknown, the null meter, and any other sources of random noise. Now define a parameter , where is a measurement at time and is determined from using : where is an initial direct measurement of by the system voltmeter and the "Round" function means rounded to the nearest integer. The direct measurement of is obtained by setting the array to the step, which can be seen from Fig. 7 to connect the voltmeter directly to the Zener reference. Based on measurements of and , a set of values and is acquired for . Three successive values of are examined for consistency within 2 μV before the data are accepted. This eliminates data that may be corrupted by the transient that occurs when there is a spontaneous transition between quantum voltage steps. Since and change by equal amounts during a step transition, remains constant thus making the data collection process relatively immune to step transitions. Data are collected efficiently even for a Josephson array chip that may be making as many as five transitions per minute. The scatter in the data that results from noise in the unknown and in the null meter can generally be modeled by a Gaussian process with one standard deviation on the order of 20 to 100 nV. There are, however, occasional noise spikes that do not fit this process and generate glitches in the data that may lie 1 μV to 10 μV away from the well behaved data. An outlier test is used to detect and eliminate such data. After the collection of the first data set, the polarity of the unknown is reversed (), the bias is readjusted to select a step that minimizes , and a second set of data is acquired. Two more reversals generate third and fourth data sets. Best estimates for , and are obtained from a least-squares recursion analysis that minimizes the root-sum-square (RSS) error of the set for all in the four data sets. In typical measurements of Zener standards, the noise of the standard often dominates the computed value of . The type A uncertainty for is the standard deviation of the mean for the set of . Typically, this entire calibration algorithm is controlled by a computer and is completed in a few minutes. Except in the case of data with nonuniform delays between the reversals, a simple average of the absolute values of the full set of is an equally good estimate of . Systems like that shown in Fig. 7 are used to calibrate secondary standards, such as Weston cells, Zener references, and precise digital voltmeters. These calibrations are greatly simplified by the fact that the Josephson array voltage can be set to any value , where the integer can have any value in the range of about to . The typical uncertainty in measurements of 10 V Zener standards is limited by noise in the Zener to about 0.01 ppm. The ability to set the Josephson array to a wide range of discrete voltages also makes it the most accurate tool for measuring the linearity of high-accuracy digital voltmeters.Uncertainty
While the voltage appearing across the terminals of a Josephson device is, in principle, given exactly by , in any real measurement there are a variety of potential sources of error and uncertainty as listed in Table 2. In the case of a known error, such as a reference frequency offset or a known leakage resistance, a correction can be made. It is then the metrologist's task to assign realistic numbers to all uncertainties including the uncertainty in the corrections. One method of doing this notes that only items 1 and 2 in Table 2 depend on the voltage across the Josephson array. All of the other components are about the same regardless of the array voltage. Therefore, the combined effect of items 3–8 can be quantitatively evaluated by making a set of measurements of a short circuit using exactly the same algorithm that is used for any other measurement. The standard error resulting from items 3–8 is just the root mean square (RMS) value of the set of short circuit measurements. Additional experiments must be performed to estimate frequency and leakage uncertainty. Internationally accepted procedures for combining uncertainty and establishing confidence intervals is the subject of the BIPM's Guide to the Evaluation of Uncertainty in Measurement.Guide to the Expression of Uncertainty in Measurement, Geneva, International Organization for Standardization (1995) Typically, the total uncertainty contribution of a Josephson system in a measurement averaging time of a few minutes is a few nanovolts. Since the most common use of these systems is the calibration of Zener standards with a noise level of 50–100 nV, the contribution of the Josephson system is negligible. Table 2. Potential sources of error and uncertainty for a Josephson standardTraceability and equivalence
A Congressional act in 1904 established the U.S. Legal Volt to be a quantity defined by the National Bureau of Standards, now the National Institute of Standards and Technology (NIST). With the 1990 international agreement on the Josephson representation of the volt, NIST defined the U.S. Legal Volt to be the same as the international volt representation. Since the success of the first Josephson array voltage standards in 1984, their use has proliferated to more than 70 national measurement institutes (NMIs), military, and commercial laboratories around the world. This has resulted in some confusion about the traceability of non-NMIs that are in possession of a JVS that is, in principle, as good as the national standard. Some guidance on this question is provided in International Standards Organization (ISO) documents that state the general principle that intrinsic standards like the JVS, that have participated in a comparison with an NMI, can claim traceability.References
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