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Josephson Junction Model

Type Name: jj

The Josephson junction model is an extended version of the RSJ model as used by Jewett[11].

The parameters marked with an asterisk in the area column scale with the area parameter given in the device line.

JJ Model Parameters
name area parameter units default example
pijj   pi junction - 0 1
icrit * Junction critical current A 1.0e-3 1.5e-3
cap * Junction capacitance F 1.0e-12 5.0e-13
rn or rnorm * Normal state resistance $ \Omega$ 1.7 2.0
r0 or rsub * Subgap resistance $ \Omega$ 30 50
vg or vgap   Gap voltage V 3.0e-3 2.8e-3
delv   Gap voltage spread V 1.0e-4 8.0e-5
rtype   Quasiparticle branch model - 1 2
cct   Critical current model - 1 3
icon   Critical current first zero A 1.0e-2 2.5e-2
icfact   Ratio of critical to gap currents - $ \pi$/4 0.7
vshunt   Voltage to specify fixed shunt resistance - 0 200uV

If pijj is set to a nonzero integer value, instances will be ``pi'' junctions by default, though this can be overridden per instance by giving pijj=0 on the device line.

The rtype parameter determines the type of quasiparticle branch modeling employed. Legal values are as follows:

0 The junction is completely unshunted (effectively sets rn and r0 to infinity).
1 Standard piecewise-linear model.
2 Analytic exponentially-derived approximation.
3 Fifth order polynomial expansion model.
4 ``Temperature'' variation, allow modulation of the gap parameter.

The default is rtype=1. Setting rtype=0 will disable modeling of the quasiparticle current, effectively setting the RSJ shunt resistance to infinity. Conditions with rtype=1 and 2 are as described by Jewett, however it is not assumed that the normal resistance projects through the origin. The icfact parameter can be set to a value lower than the default BCS theoretical value to reflect the behavior of most real junctions. The quasiparticle resistance is approximated with a fifth order polynomial if rtype=3, which seems to give good results for the modeling of some NbN junctions (which tend to have gently sloping quasiparticle curves).

Rtype=4 uses a piecewise-linear quasiparticle characteristic identical to rtype=1, however the gap voltage and critical current are now proportional to the absolute value of the control current set with a control=src_name entry in the device line. This is to facilitate modeling of temperature changes or nonequilibrium effects. For control current of 1 (Amp) or greater, the full gap and critical current are used, otherwise they decrease linearly to zero. If no device control source is specified, the algorithm reverts to rtype=1. It is expected that a nonlinear transfer function will be implemented with a controlled source, which will in turn provide the controlling current to the junction in this mode. For example, the controlling current can be translated from a circuit voltage representing temperature with an external nonlinear source. The functional dependence is in general a complicated function, but a reasonable approximation is 1 - (T/Tc)4 . See the examples for an example input file (ex8.cir) which illustrates rtype=4.

It is currently not possible to use other than the piecewise linear model with temperature variation. If rtype=4, then legal values for the critical current parameter are cct=0 (no critical current) and cct=1 (fixed critical current). If another value is specified for cct, cct reverts to 0. Thus, magnetic coupling and quasiparticle injection are not simultaneously available.

In general, the cct variable can take on the following values:

0 No critical current.
1 Fixed critical current.
2 Sin(x)/x modulated supercurrent.
3 Symmetric linear reduction modulation.
4 Asymmetric linear reduction modulation.

The control parameter should be used with devices using cct 2,3, or 4. With cct=2, the first zero is equal to the value of the model parameter icon. For cct=3, the maximum critical current is at control current zero, and it reduces linearly to zero at control current = $ \pm$icon . Junctions with cct=4 have maximum critical current at control current = - icon, and linear reduction to zero at control current = + icon. If cct is specified as 2, 3, or 4, the area parameter, if given, is set to unity. Otherwise, the model parameters are scaled appropriately by the area before use.

If the vshunt parameter is given, every device instance will be shunted by a linear resistor. This is in addition to the resistance of the quasiparticle branch. The value of this resistance is

Rshunt = Vshunt/Ic
where Vshunt is the value given for the model parameter, and Ic is the (maximum) critical current of the Josephson junction device. This parameter is useful for simulating SFQ circuits, as it can automatically provide the appropriate shunt resistance, which would otherwise be a separate resistor.

next up previous contents index
Next: The WRspice User Interface Up: Superconductor Devices Previous: Josephson Junctions   Contents   Index
Stephen R. Whiteley 2017-11-08