Miniaturization of Josephson Junctions for Digital Superconducting Circuits

In this work, we briefly overview various options for Josephson junctions, which should be scalable down to nanometer range for utilization in nanoscale digital superconducting technology. Such junctions should possess high values of critical current, $I_c$, and normal state resistance, $R_N$. Another requirement is the high reproducibility of the junction parameters across a wafer in a fabrication process. We argue that superconductor-normal metal-superconductor ($SN$-$N$-$NS$) Josephson junction of “variable thickness bridge” geometry is a promising choice to meet these requirements. Theoretical analysis of the $SN$-$N$-$NS$ junction is performed in the case where the distance between the $S$ electrodes is comparable to the coherence length of the $N$ material. The restriction on the junction geometrical parameters providing the existence of superconductivity in the $S$ electrodes is derived for the current flowing through the junction of an order of $I_c$. The junction heating, as well as available mechanisms for the heat removal, is analyzed. The obtained results show that a $SN$-$N$-$NS$ junction with a high (submillivolt) value of $I_c{R}_N$ product can be fabricated from a broadly utilized combination of materials like Nb/Cu using well-established technological processes. The junction area can be scaled down to that of semiconductor transistors fabricated in the frame of a 40-nm process.

Figure 1

Sketch of $SN$-$N$-$NS$ Josephson junction with variable thickness bridge geometry.

Figure 2

Normalized $I_c{R}_N$ product, $v_c=e{I}_c{R}_N/2\pi k_B{T}_c$, of the $SN$-$N$-$NS$ Josephson junction in dependence on (a) normalized temperature, $t$, and (b) suppression parameter, ${\gamma }_{\mathrm{BM}}$, calculated using Eq. (7) (solid lines), (9) [dotted lines, ${\gamma }_{\mathrm{BM}}=0.001,0.01$, (a)] and Eq. (10) [dotted lines, ${\gamma }_{\mathrm{BM}}=0.3\cdots 3$, (a) and (b)]. Inset shows $v_c({\gamma }_{\mathrm{BM}})$ for ${\gamma }_{\mathrm{BM}}\le 1$. The upper solid line in (a) corresponds to the KO-1 expression [75].

Figure 3

Sketch of a $SN$-$N$-$NS$ Josephson junction with a variable thickness bridge geometry. The horizontal red, purple, and brown arrows indicate the areas where heat is transferred to the $S$ electrodes, phonon subsystems in the normal film and substrate, respectively. The vertical yellow and red arrows schematically indicate the process of heat transfer from hot electrons to the electrodes and the phonon subsystem of a normal film. Vertical green arrows indicate the process of heat transfer into the substrate.