Current-waveform dependence of punchthrough probability in a Josephson tunnel junction

The so-called punchthrough phenomenon occurring in a logic gate using a Josephson tunnel junction is studied theoretically. An analytical solution of the Josephson equation describing the dynamic behavior of the Josephson gate in its resetting process is obtained with the modified averaged Lagrangian method. The solution leads to an expression for the punchthrough probability, which is capable of quantitative discussion and is applicable to arbitrary waveforms of the gate current. From the obtained expression, a study is made of the waveform dependence of the punchthrough probability, as well as its dependence on junction parameters. It is shown that the present analytical results agree well with those of computer simulations.