We investigated current-voltage characteristics of unshunted and externally shunted Josephson junctions (JJs) with high critical current densities, Jc, in order to extract their basic parameters and statistical characteristics for JJ modeling in superconducting integrated circuits and to assess their potential for future technology nodes. Nb/AlOx-Al/Nb JJs with diameters from 0.5 {mu}m to 6 {mu}m were fabricated using a fully planarized process with Mo or MoNx thin-film shunt resistors with sheet resistance Rsq = 2 {Omega}/sq and Rsq = 6 {Omega}/sq, respectively. We used our standard MIT LL process SFQ5ee to fabricate JJs with Jc = 0.1 mA/{mu}m^2 and our new process SFQ5hs to make JJs with Jc = 0.2 mA/{mu}m^2 and higher current densities up to about 1 mA/{mu}m^2. Using LRC resonance features on the I-V characteristics of shunted JJs, we extract the inductance associated with molybdenum shunt resistors of 1.4 pH/sq. The main part this inductance, about 1.1 pH/sq, is the inductance of the 40-nm Mo resistor film, while the geometrical inductance of superconducting Nb wiring contributes the rest. We attribute this large inductance to kinetic inductance arising from the complex conductivity of a thin normal-metal film in an electromagnetic field with angular frequency {omega}, {sigma}({omega})={sigma}0/(1+i{omega}{tau}), where {sigma}0 is the static conductivity and {tau} the electron scattering time. Using a resonance in a large-area unshunted high-Jc junction excited by a resistively coupled small-area shunted JJ, we extract the Josephson plasma frequency and specific capacitance of high-Jc junctions in 0.1 to 1 mA/{mu}m^2 Jc range. We also present data on Jc targeting and JJ critical current spreads. We discuss using 0.2-mA/{mu}m^2 JJs in VLSI Single Flux Quantum circuits and 0.5-mA/{mu}m^2 JJs in high-density integrated circuits without shunt resistors.
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