Josephson Junctions

General Form:
bname 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 level=2.

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 $\pi$ 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$\pi$ . 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.