Study of $\hbox{MgB}_{2}$ Josephson Junction Arrays and Sub- $\mu\hbox{m}$ Junctions

Sandwich-type MgB 2 /MgO/MgB 2 Josephson junctions with sizes ranging from 0.5 μm × 0.5 μm to 10 μm × 10 μm were fabricated using electron beam lithography. The junctions show critical current densities as high as 130 kA/cm 2 . The smallest of the junctions operated free of hysteresis below 4.2 K. They may be ideal for use in rapid single flux quantum circuits with no requirement for external shunt resistors. The 10-μm junctions show good agreement with the expected Fraunhofer-like modulation of critical current with magnetic field; however, the smaller junctions show a sinusoidal modulation, indicating an anomalous current distribution that needs to be further investigated. Series arrays of Josephson junctions were made to quantitatively study the uniformity of junction parameters, which shows a 54% spread in critical current of a 100 junction array of 4-μm junctions.