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the trace along the V-axis, gives clues about the quality of the insulating barrier
of the junction.
The geometry of the junction causes it to also behave like a classical parallel
plate capacitor, which can be understood as simply shunting the junction in parallel
as shown in Figure 2.2c. The junction’s capacitance C J depends only on its
geometrical parameters according to the usual formula:
C J = ε A d
(2.10)
Here, ε is the dielectric constant of the insulator, A is the junction’s area, and
d the insulator’s thickness. Since the junction’s capacitance scales linearly with
the barrier thickness while its critical current scales exponentially, it is possible
to control C J and I c independently of each other.
2.2.3 Circuit Potential
As the junction’s capacitance behaves exactly like a conventional capacitor, the
most straightforward way to integrate the junction into the standard LC-oscillator
circuit is by putting it in the place of the oscillator’s capacitor and designing it such
that C J = C. The resulting circuit can be analyzed in a variety of different ways.
The easiest approach is to simply use the Josephson relations and Kirchhoff’s
current law. For this, the current I(t) flowing through the oscillator’s inductor
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