
The cells with a "_jj" name suffix, and have "noL" as a label in the
schematic symbol, are a variation that use no inductors.  These gates
may be freely mixed with conventional RSFQ gates.

1. Theory

It can be seen that the two roles that inductors play in SFQ circuits
can be assumed by arrays of Josephson junctions.  These arrays
establish a phase difference in response to current flow, like
inductors.  If the phase change is "small", then the array will tend
to propagate an SFQ pulse, as in a JTL.  It the phase change is
"large", a junction loop can trap a persistent current (corresponding
to a "flux" quantum) but it is not magnetic flux!  For example,
consider a loop of six identical junctions.  Suppose that each
junction has a phase of 60 degrees.  The total phase around the loop
is 360 degrees, satisfying the boundary conditions, while a persistent
current of Ic*sin(60) is flowing.  Clearly, all phase angles and
corresponding persistent current of 0 is also a valid solution.

2. Local Assumption

There are probably many possible ways to exploit this comcept.  Here,
the following is assumed:

The fab process provides individual junctions, and junction "stacks"
containing  four barriers (junctions).  All junctions have the same
critical current density, and the same damping coefficient.

Practically, parasitic inductance, which will be present in any circuit,
will affect circuit behavior and should be minimized.  The use of
junction stacks minimizes the parsitic series inductance.

Can such a fab process be developed?

The ideal process would provide repeatable and robust planar SNS
junctions, self damped.  One possible approach would be an in-situ
full-wafer four-barrier formation process, similar conceptually to the
trilayer process in present use.  The challenge would be to incorporate
etch-stopping at points within this structure, to enable

a) Etching through the entire structure, for isolation.
b) Contact to the lowest metal layer, removing all material above.
c) Contact to the top metal of the lowest junction, removing all material
above, providing the single junctions.
d) (Trivially) contact to the top level, providing the second contact
to the stack junctions.

2. Potential Advantages

Why use junctions rather than inductors?

a) Inductors tend to take a large fraction of total area in SFQ
circuits, and replacement by junction stacks would potentially greatly
increase circuit density.  While inductors require a certain area to
provide the required inductance, junctions can in principle be
arbitrarily small.

b) Junction/inductor loops are sensitive to external magnetic fields,
which can potehtially cause failure due to cross-talk with other
circuits, or from fields produced by power busses, ambient magnetic
fields including power lines and the earth's field, and fields from
flux trapped in superconducting metalization.  Magnetic shielding is a
major requirement for operating and testing SFQ circuits, and magnetic
coupling and trapped-flux reduction fundamentally impact SFQ circuit
layout.

Elimination of inductors would potentially greatly reduce magnetic
effects.  This should further improve circuit density, and may allow
operation with less-stringent or no magnetic shielding.

c) This may require further analysis, but it is likely that
junction-only circuits will be less sensitive to junction
critical-current variation, if it can be assumed that all junctions
have the same spatial and run-to-run variation.


