Non-normal Critical Current Distributions in Josephson Junctions With Aluminum Oxide Barriers

Josephson junctions have been seen to have critical currents with probability distributions not adequately described by a normal (Gaussian) distribution. Junctions analyzed were fabricated in the MIT Lincoln laboratory SFQ5ee process with structure: substrate/Nb/Al/AlO
_x
/Nb. The AlO
_x
barrier was formed by room temperature oxidation of aluminum. Non-normal distributions are more pronounced for small junctions (diameters less than 1 μm). The observed distribution tails are higher than those for a normal distribution, which has implications for single-flux quantum circuits such as the maximum practical complexity and yield. An inverse Weibull probability distribution was found to best fit the conductance data. Methods are described to calculate the required circuit operating margins or achievable junction count, but require accurate models for the distribution tails.