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###

TJM Model Temperature Dependence

When the junction is not operating at the nominal temperature as
specified with the `tnom` parameter, a correction factor is
applied to the critical current to account for the temperature
difference. The superconducting energy gap and therefor the junction
gap voltage will also change as a function of temperature.

In the TJM model, the energy gaps are always computed from the BCS
integral equation involving superconducting transition temperature,
Debye temperature, and operating temperature. The materials may be
different on the two sides of the barrier. The junction gap voltage
is the sum of the gap potentials of the two materials.

The critical current temperature variation again follows BCS theory.
The temperature correction factor *tcf* multiplies the instance
critical current to account for the temperature difference between
operating and nominal temperatures.

*tcf* = (*Vg*/*Vg*_{nom})(*tanh*(*eVg*/4*KT*)/*tanh*(*eVg*_{nom}/4*KT*_{nom}))

Here, *Vg*
is the computed gap voltage, *e*
is the electron charge,
*K*
is Boltzmann's constant, *T*
is temperature in Kelvin,

** Next:** The WRspice User Interface
** Up:** Josephson Junction Model
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Stephen R. Whiteley
2022-09-18