Josephson Junctions

- General Form:
`b`*name**n*+*n*- [*np*] [*modname*] [*parameters*...]

The default Josephson junction model is an extended version of the RSJ
model as used by Jewett[11]. There are actually three
Josephson junction models available, through the `level` model
parameter, which can take values 1 through 3. The default `level=1` model is the RSJ model mentioned. This model has a
simplified Verilog-A version which can be found among the Verilog-A
examples. This can be compiled with the `adms` utility into a
run-time loadable module which can be loaded with the **devload**
command. A pre-compiled module is provided with the example. Once
loaded into * WRspice*, the model can be accessed with

For `level=3`, a microscopic tunnel junction "Werthamer" model,
also known as a Tunnel Junction Model (TJM) is provided. The model is
more physics-based than the empirical RSJ model.

Unless stated otherwise, information presented here applies to
instances of the standard RSJ model (`level=1`) and the Verilog-A
Josephson junction model (`level=2`) provided with * WRspice* in
the Verilog-A examples.

The instance parameters for the microscopic model are described in the 2.17.1.2.

Josephson Junction Instance parameters, Levels 1 and 2

Parameter Name |
Description |
---|---|

pijj=1|0 |
Whether the device is a ``pi'' junction. |

area=val |
Scale factor that multiplies all currents and other values, effectively modifying the junction area. |

ics=val |
Instantiated critical current, used as scale factor for capacitance, conductances. |

temp_k=val |
Device temperature, Kelvin. |

lser=val |
Junction series parasitic inductance. |

lsh=val |
Shunt resistor series parasitic inductance. |

ic=vj,phi |
The initial junction voltage and phase (initial condition) for transient analysis. |

vj=vj |
The initial junction voltage (initial condition) for
transient analysis, alias ic_v. |

phi=phi |
The initial junction phase (initial condition) for
transient analysis, alias ic_phase. |

control=name |
Controlling voltage source or inductor name. |

vshunt=val |
Voltage to specify external shunt resistance. |

n (read only) |
SFQ emission count. |

phsf (read only) |
True if SFQ count change at current time point. |

phst (read only) |
Time of last SFQ emission. |

v (read only) |
Terminal voltage. |

phase (read only) |
Junction phase, alias phs. |

tcf (read only) |
Temperature compensation factor. |

vg or vgap (read only) |
Gap voltage. |

vless (read only) |
Gap threshold voltage. |

vmore (read only) |
Gap knee voltage. |

icrit (read only) |
Maximum critical current. |

cc (read only) |
Capacitance current. |

cj (read only) |
Josephson current. |

cq (read only) |
Quasiparticle current. |

c (read only) |
Total device current. |

cap (read only) |
Capacitance. |

g0 (read only) |
Subgap conductance. |

gn (read only) |
Normal conductance. |

gs (read only) |
Quasiparticle onset conductance. |

gshunt (read only) |
External shunt conductance from vshunt. |

rshunt (read only) |
External shunt resistance from vshunt. |

lshval (read only) |
External shunt resistor parasitic inductance. |

g1 (read only) |
NbN quasiparticle parameter. |

g2 (read only) |
NbN quasiparticle parameter. |

node1 (read only) |
Node 1 number. |

node2 (read only) |
Node 2 number. |

pnode (read only) |
Phase node number. |

lsernode (read only) |
Internal lser node number. |

lserbrn (read only) |
Internal lser branch number. |

lshnode (read only) |
Internal lsh node number. |

lshbrn (read only) |
Internal lsh branch number. |

- Examples:
`b1 1 0 10 jj1 ics=200uA`

b1 1 0 10 jj1 ics=200uA

bxx 2 0 type1 control=l3

b2 4 5 ybco phi=1.57

The *n+* and *n-* are the positive and negative element nodes,
respectively. These are followed by an optional phase node. The
phase node, if specified, generally should have no other connections
in the circuit, but the voltage of this node gives the phase of the
junction in radians. The *modname* is the name of the Josephson
junction model. If no model is specified, then a default model is
used (see the description of the Josephson model for the default
values). Other (optional) parameters follow in any order.

`pijj`

If the`pijj`parameter is given and set to a nonzero integer value, the device instance will behave as a ``pi'' junction. This type of junction has a ground state with phase rather than 0. The value given on the device line (if any) overrides the value given in the model.`area`**range:**0.05 - 20.0**Deprecated, do not use in new files.**

Histrorically, this parameter has been used to set the actual critical current of a Josephson junction instance. It is not a physical area, but rather a scale factor, representing the ratio of the instance critical current to the reference critical current. The parameter is retained for backwards compatibility, but should not be used in new circuit descrfiptions. The`ics`parameter (below) should be used instead. By using`ics`, one can change the critical current of the reference junction without changing the instance critical currents, which is not the case for`area`. In the new paradigm, the reference junction critical current corresponds to a ``typical'' mid-sized junction, with a not necessarily convenient critical current value. Use of`area`assumes that the reference critical current is something nice, like the historical 1mA, and unchanging. If not specified and`ics`is not given, the effective value is 1.0.`ics`**range:**0.02*`icrit`- 50.0*`icrit`

This gives the actual critical current of the instantiated junction, and in addition scales all conductance and capacitance values from the reference junction appropriately. This is equivalent to giving the`area`parameter with a value of`ics`/`icrit`. The default is`icrit`, the reference junction critical current.`temp_k`**range:**0.0 - 0.95*`tc`

This is the assumed operating temperature of the device, in Kelvin. The default is the model`deftemp`value. See the model description for more information about temperature modeling.`lser`**range:**0.0 - 10.0pH

This models series inductance of the physical Josephson junction structure, caused by constriction of current through the junction orifice. This inductance might typically be in the range of 0.1 to 0.3 picohenries. If nonzero, an internal node is added to the model, providing the connection point of the inductance and the Josephson junction. The default value is 0.0, meaning that no parasitic inductance is assumed. Nonzero given values less than 0.01pH revert to zero.`lsh`**range:**0.0 - 100.0pH

This parameter specifies the series inductance of the external shunt resistance. The`vshunt`instance or model parameter must be specified such that a positive external shunt conductance is applied, otherwise this parameter is ignored. Ordinarily, the`lsh0`/`lsh1`model parameters would be used to specify the inductance, this parameter can be used to override these values on a per-instance basis if desired.`ic`**Levels 1 and 3 only.**

The keyword is expected to be followed by two numbers, giving the initial junction voltage and phase in radians. These apply in transient analysis when the ```uic`'' option is included in the transient analysis specification. The initial junction voltage and phase both default to 0.0.`vj`or`ic_v`

This provides the initial voltage of the junction when the ```uic`'' option is included in the transient analysis specification. The initial junction voltage defaults to 0.0.`phi`or`ic_phase`

This provides the initial junction phase in radians when the ```uic`'' option is included in the transient analysis specification.`control`**level 1 only.**

The`control`parameter is only needed if critical current modulation is part of the circuit operation, and is only relevant to Josephson junction model types that support critical current modulation, that is, the model parameter`cct`is given a value larger than 1. The*name*in the`control`specification is the name of either a voltage source or inductor which appears somewhere in the circuit. The current flowing through the indicated device is taken as the junction control current.`vshunt`**range:**0.0 - nominal gap voltage

See the description of the`vshunt`model parameter. The model parameter, if given, will provide the default used in all instances. However this can be overridden on a per-instance basis with the`vshunt`instance parameter.

The remaining parameters are ``read only'' and can be accessed with
the `@`*device*[*param*] special vector notation
during the simulation (in callbacks) or after the simulation if the
vector is saved with the **save** command or equivalent.

`n`(read only)

This integer value is incremented whenever the junction phase changes by plus or minus 2 . It is intended for pass/fail testing of single flux quantum (SFQ) circuit operation.`phsf`(read only)

This flag is set true at the time point when the SFQ emission count changes. This is intended to facilitate pass/fail testing of SFQ circuits.`phst`(read only)

This read-only parameter contains the last time that the SFQ emission count changed, intended for use in SFQ pass/fail testing.`v`(read only)

The voltage across the junction.`phase`(read only)

The junction phase. Reading this is an alternative to using a third node to obtain the phase.- tcf (read only)

The temperature correction factor that modifies the critical current at operating temperatures other than nominal. See the description of the temperature dependence of the RSJ model in 2.17.2.2. `vg`or`vgap`(read only)

The gap voltage of the junction.`vless`(read only)

The voltage where the quasiparticle step current begins to rise. it is the lower bounding point used to indicate the`delv`gap spread, i.e., it is equal to`vg - delv/2`.`vmore`(read only)

The voltage where the quasiparticle step ends and the normal resistive part begins. It is the upper point used to indicate the`delv`gap spread, equal to`vg + delv/2`.`icrit`(read only)

The critical current of the junction instance.`cc`(read only)

The current flowing through the geometric capacitance of the junction.`cj`(read only)

The pair current (supercurrent) flowing through the junction.`cq`(read only)

The quasiparticle (normal) current flowing through the device.`c`(read only)

The total current flowing through the device, the sum of`cc`,`cj`and`cq`.`cap`(read only)

The geometric capacitance of the device instance.`g0`(read only)

The subgap conductance of the device instance.`gn`(read only)

The normal state conductance of the device instance.`gs`(read only)

The conductance of the quasiparticle branch at the gap voltage.`gshunt`(read only)

If the`vshunt`instance or model parameter is given and nonzero,`gshunt`will return the external conductance added to the intrinsic conductance so that the total conductance multiplied by the critical current will equal`vshunt`.`rshunt`(read only)

If`gshunt`is nonzero,`rshunt`will be the reciprocal, otherwise it will be 0.`lshval`(read only)

If the`vshunt`instance or model parameter is given and nonzero, this will be the parasitic inductance assumed in the external shunt resistance. This will depend on the settings of the`lsh0`and`lsh1`model parameters, and the`lsh`instance parameter which overrides the model parameters if given.`g1`(read only)

This applies if the`rtype`model parameter is set to 3, which indicates use of the NbN polynomial model for subgap conductance. This is the third-order amplitude in the polynomial.`g2`(read only)

This applies if the`rtype`model parameter is set to 3, which indicates use of the NbN polynomial model for subgap conductance. This is the fifth-order amplitude in the polynomial.`node1`(read only)

The internal node number of the first node.`node2`(read only)

The internal node number of the second node.`pnode`(read only)

The internal node number of the third (phase) node, 0 or -1 if not used.`lsernode`(read only)

The internal node number of the device internal node added for series parasitic inductance. This will be 0 or -1 if not used (no series parasitic inductance assumed).`lserbrn`(read only)

If series parasitic inductance is nonzero (`lser`given) this will be the internal number of the branch node of the inductor.`lshnode`(read only)

If the`vshunt`instance or model parameter is given and nonzero, and series parasitic inductance is nonzero, this will be the internal node number of the internal device node that incorporates the series inductance.`lshbrn`(read only)

If the`vshunt`instance or model parameter is given and nonzero, and series parasitic inductance is nonzero, this will be the internal branch number of the inductor's branch.