Basics

Josephson JunctionRSFQ-BasicCircuit fabricationInductance measurement

Josephson Junction

The Josepshon Junction as key element of RSFQ

The resistively and capacitively shunted junction (RCSJ) model is using an easy equivalent network to qualify the behaviour of a Josephson Junction (JJ). It is composed by a resistor and a capacitance parallel connected to an ideal JJ with a critical current. The quantum mechanical nature of is unconsidered but for theoretical estimation working it's sufficiently.

All parameters can be determined by the main technology parameter η for low temperature superconductor (LTS) shunted JJs and the McCumber parameterβc.

βc=2πΦ0- ·Ic- ·RN2- ·CJ

Capacitance per areaCF and current density J yields by parameterη1.

η1=CFJ

The second parameter can be determined by using the magnetic flux quantumΦ0.

η2=Φ0- ·βc2π- ·η1

These both parameters describe generally the behaviour of a specific technology. To characterize a particular JJ the critical currentI0, the junction resistanceRN and the junction capacitanceCJ. The specific junction parameter for a given critical current are defined by using

RN=η2Ic

and

CJ=η1- ·Ic

In this documentation all junctions have a characteristic v

We use a spice like simulation software with a RCSJ-model for JJs. Based on this model differential equation system can developed which describe the dynamic behaviour of a real JJ.

φ˙=2πΦ0ν

ν˙=1CJ(Ib-Icsin(φ)-νRN)

By using the McCumber parameterβc and the standardised time τ this system can transformed to a second order nonlinear differential equation.

τ=2πΦ0- ·Ic- ·RN- ·t

i=βc- ·∂2φ∂τ2+∂φ∂τ+sin(φ)

In the design of RSFQ electronic applications the characteristic voltage,IcRN, and the McCumber parameter,βc, are important.

However, the external shunted junction is only completely described with a parasitic inductanceLp, defined by the interconnection between the junction area and the shunt resistor.

Rapid Single Flux Quantum-Basics

The rapid single flux quantum circuit family

RSFQ logic is a superconductive digital circuit technique, in which the data are represented by the presence or absence of a flux quantumΦ0=h/2e(Planck constant h and elementary charge e) in a cell, which is generated of JJ and inductances. The introduction of an external shunt resistor for Jospehon tunnel junction, was the origin for a new generation of digital electronics The JJ is operating as a gate for data pulses, represented as single flux quanta (SFQ). The RSFQ is composed by three functional elements: inductance L, the critical current of a Josephson junctionIc and the bias currentIb. A RSFQ circuit consists of three building blocks:

  1. The first brick is responsible for the active transfer of SFQ pulses. It is marked by a small inductance.
  2. If we use a larger loop inductance between two junctions, the circulating current is to small to flip the second junction and the information is stored. This idea is used for building bistable cells.
  3. Two read an arbitrary information in such a loop, we need a decision element, namely the two junction comparator.

Manufacturing circuit

Jena Superconductive Electronics Foundry

All cells of the presented library are designed in accordance with the characteristic parameters of the tri-layer niobium technology of Jena superconducting electronics foundry (JeSEF).

This is a 1 kANb/AL2O3-Al/Nb low Tc process. It was certified in accordance with DIN ISO 9001:2000. This is the process: RSFQ1.

Functional Elements

Bias current

The bias current is build with a constant voltage source of U=2,5 mV and a resistor.

Inductances

The functional inductances are provided by superconducting microstripline's. The ground via of the JJ has a small inductance as well. This parasitic inductance is labeled withLp in the schematics. Its value should be as small as possible. In the circuit diagram three different inductances are used depending on the electronic feature.

Josephson junction

We use mostly overdamped junctions with a McCumber parameterβc=1. The design kit contains 13 different JJs. The layout of them is linked together with the electronic and geometric properties on the right.

Inductance measurement

Using the superconducting quantum interference device-modulation for accurate inductance measurement

As already mentioned before the inductance of a superconducting loop is one of three degrees of freedom adjusting the behaviour of a RSFQ circuit. For creating a functional circuit it is important to have well defined and reproducible inductance values. In RSFQ usually microstrip lines are utilized to perform this task. Being aware of the sheet inductance value, which is a characteristic parameter of a fabrication process, is essential for the design process. Therefore this parameter has to be experimentally evaluated. Analyzing the inductances is also a common first step when examining a new chip.

To acquire these fundamental data the method of SQUID-modulation is typically used. This procedure is based on the flux quantization in superconducting loops and is today the most accurate method for measuring inductances. By using this high precision method values far below L=1pH can be detected.

Measuring setup

The measuring setup contains a SQUID loop, which is composed ofL1,L2,J1,J2 and the parasitic inductancesLp1 andLp2. Furthermore two current sources and a voltmeter are needed. Depending on the performance of the voltmeter an appropriate amplifier is required to boost the output signal amplitude, which is in order of several micro volt.

Implementing this setup provides the exact value of the inductanceLg=L1+L2. In the process the value of the critical current of the JJs is of no importance, also equality or inequality of both junctions or both inductances have no influence on the solution. Fortunately the parasitic inductancesLp and the inductances of the current supply lineLwire have no effect on the experimental results as well.

Current-voltage characteristic of a SQUID

The maximum bias current above which the SQUID is entering the voltage state is called critical current. The current-voltage characteristic of a symmetric SQUID without an external magnetic field is the same as the one of a single JJ. But in contrast to a single JJ the critical current of a SQUID is a function of the external magnetic fieldIc(Φext). This is a harmonic function with a periodicity of a flux quantum (Φ0) as can be recognized in the following picture. As the image shows, the critical current could beIc=0 in theory if the loop inductanceLloop=0. But in practice this inductance will beLloop>0 at every time, so the critical current of the SQUID will beIc>0 as well. The difference betweenIc,MAX andIc,MIN depends on the inductance and decreases with increasing loop inductance values.

Thus the current-voltage characteristic of a SQUID can be manipulated by an external magnetic fieldΦext as illustrated in this figure:

Measuring procedure

The operation point, marked in the picture above, is set by the bias current sourceIB1. The external magnetic field is modified by the magnetic field caused by the currentIcontrol flowing through the inductanceL1+L2=Lg. The following picture shows schematically the result of such a measurement. Therein the exactly detectable curve depends on many different parameter. For example the initial external magnetic field which act like a current offset in the V(Icontrol) function or the selected bias currentIB1 as can be recognized in the image.

Fortunately the periodicity of the function depend only from the inductanceLg and the stored magnetic flux inside of the SQUID. Because of the flux quantization inside a superconducting ring the relation is given by:

I=Lg- ·Φ0

To enhance the accuracy of the results one can use a higher number of periods n. So the inductance value can be obtained by:

Lg=Φ0(n- ·ΔI)

Experimental results

 

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