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Fig. 5 Dc characteristic of a 12 000junction series array. The inset shows how the centre part of the dc characteristic splits into 2 branches under micro-wave radiation because due to the low resolution the dc bias only follows the envelope of the constant voltage steps. For these curves the vertical resolution is 2.5 V/div and the horizontal current resolution is 10 ¡xA/div. With the help of a multi-exposure three constant voltage steps (10 V, 0.6 V, -10 V) with the same current resolution but with a voltage resolution of500 aV/div are inserted.

The principle accuracy of the standard is restricted by the precision of the determination of the microwave frequency apart from basic quantum deviations like macroscopic quantum tunneling [Tsai et al., 1983; Gallop, 1991], which are practically negligible. The main source of uncertainty is the uncompensated drift of the thermal emfs in the dc leads. In practice, a reproducibility better than 5 x 10"10 V can be achieved [Niemeyer et al., 1986],

The use of overlapping zero-current constant voltage steps guarantees on the one hand the possibility of adjusting reference voltages from zero to the maximum value in steps of the fundamental distance. The range between two adjacent fundamental values may be covered by tuning the external drive frequency. But on the other hand, there is a delicate stability problem related to the zero current steps: the voltage output is multivalued if the system is biased to a fixed current, e.g. 7=0. There is no stable voltage state between two fundamental values. This means that if the system loses the step, it might not find back to the voltage step originally adjusted and has to be readjusted again. This can be avoided to a certain degree by the use of a special bias voltage source. In particular, it is difficult to bring about fast changes of the polarity of the voltage but such changes are desirable for

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determining the thermal emf drift. A way out of this dilemma has been suggested in [Benz, 1995; Hamilton et al., 1995]. A series array of highly damped, non-hysteretic Josephson junctions provides single-valued standard voltage steps at a certain current bias. The complete array is composed of a binary sequence of sections each of which is biased by a current source. A programmable multiplexer chooses the sections whose voltage output sums up to the reference voltage requested. Moreover, ac voltages with frequencies up to the MHz range can be synthesized with the fundamental accuracy of the dc standard. First versions have reached an output reference voltage of 250 mV. A sophisticated technology is required to realize this standard type: Depending on the drive frequency, a 1 V circuit is composed of 7 000 to 50 000 junctions and a 10 V series array even needs 10 times this number with a parameter spread of less than 20% to 30%. No junction failure is allowed, even a superconductively shorted junction is prohibited in the programmable version, whereas the traditional standard is not sensitive to shorts and tolerates a significantly larger junction parameter spread.

In spite of the difficulties described, the traditional series array standard is well established now in most of the standard laboratories all over the world and commercially available [Niemeyer; 1992; Popel, 1992]. Compact versions with an integrated cold semiconductor local oscillator are under development [Hebrank et al, 1995].

4 The SET current standard

In analogy to the Josephson effect, constant current steps might be expected at I = ef or / = 2ef in the I-U characteristic if the SET or Bloch oscillations of small current-biased tunnel junctions - normal or superconducting - are phase-locked to an external rf source with the frequency f. Unfortunately, the experimental situation is much more complex because the current-biased junction is extremely difficult to realize. As a large charging energy is required - and by this, ultrasmall capacitances - it is forbidden to simply connect the small junction to the external world via leads. The lead capacitance and, at higher frequencies, the impedance of the free space

o ' o o would simply shunt a single current-biased junction. Only at relatively low frequencies is it possible to find a high-impedance lead configuration with Z(co) » Rq, which allows charging effects to be obtained at a single junction. For a review and more references, see [Devoret and Grabert, 1992].

Therefore, a configuration which is easier to handle in experiments is a very small metallic (or semiconducting) island separated by two or more small tunnel junctions with a tunneling resistance Ry » Rq to the electromagnetic environment ( Fig. 6). When appropriate rf voltages are applied to the gates, one single charge is transferred across the central island per rf cycle in the case of the turnstile and the pump.

Fig. 6 Circuit diagrams of several single charge devices, a) SET transistor; b) Turnstile device; c) Single electron pump U : applied voltage, I : current across the tunnel junction, Cg, Cgv : gate capacitances, Cv : junction capacitances, Rv : tunnel resistances, Ugg : dc or rf gate voltages.

The simplest circuit, the SET transistor, which was first realized by [Kuzmin and Likharev, 1987; Fulton and Dolan, 1987], forms the elementary building block of the more complex devices. The determination of its properties is therefore of importance for the operation of SET circuits. Fig. 7 shows a SET transistor of aluminium and aluminium oxide.

For preparing small tunnel junctions, a special two-layer e-beam resist mask forms small suspended bridges in the tunnel region. Two successive non-vertical evaporations, together with an oxidation process of the first layer, form small overlapping areas in the shadow of the resist bridges [Niemeyer, 1974; Dolan, 1977; Dolan and Dunsmuir, 1988]. Besides the possibility of manufacturing ultra-small tunnel junctions, the main advantage of the method is that the complete circuit can be produced without the vacuum cycle being interrupted.

Fig. 7 SET transistor, made of AllAl¿OjAl. The circles denote the position of the tunnel junctions. A typical dc characteristic of a voltage-biased transistor which clearly shows the Coulomb blockade and the modulation of the voltage with the gate voltage applied is shown in Fig. 8.
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