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arXiv:1008.4513 · Journal of Applied Physics

Universal resistance capacitance crossover in current-voltage characteristics for unshunted array of overdamped Nb–AlOx–Nb Josephson junctions

S. Sergeenkov, V.A.G. Rivera, Euclydes Marega Jr., Fernando Manuel Araújo-Moreira

Published May 1, 2010• 6 citations
arXivHTMLPDF

Abstract

We report on some unusual behavior of the measured current-voltage characteristics (CVC) in artificially prepared two-dimensional unshunted array of overdamped Nb–AlOx–Nb Josephson junctions. The obtained nonlinear CVC are found to exhibit a pronounced (and practically temperature independent) crossover at some current Icr=(1/2βC−1)IC from a resistance R dominated state with VR=RI2−IC2 below Icr to a capacitance C dominated state with VC=ℏ/4eCI−IC above Icr. The origin of the observed behavior is discussed within a single-plaquette approximation assuming the conventional resistively shunted junction model with a finite capacitance and the Ambegaokar–Baratoff relation for the critical current of the single junction.

DOI
10.1063/1.3407566

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We report on some unusual behavior of the measured current-voltage characteristics (CVC) in artificially prepared two-dimensional unshunted array of overdamped Nb–AlOx–Nb Josephson junctions. The obtained nonlinear CVC are found to exhibit a pronounced (and practically temperature independent) crossover at some current Icr=(1/2βC−1)IC from a resistance R dominated state with VR=RI2−IC2 below Icr to a capacitance C dominated state with VC=ℏ/4eCI−IC above Icr. The origin of the observed behavior is discussed within a single-plaquette approximation assuming the conventional resistively shunted junction model with a finite capacitance and the Ambegaokar–Baratoff relation for the critical current of the single junction.
We present characteristics of overdamped Josephson junctions consisting of Nb/AlOx/Al/ AlOx/Nb structures. The junctions were fabricated using a well-developed Nb/AlOx/Nb-junction technology and showed well-defined Josephson characteristics at 4.2 K. The characteristic voltage Vc [the product of the critical current Ic and the effective normal resistance Rn(eff)] of junctions, which determines high-frequency performance of the junction, was in the range of 0.1–0.5 mV, and the critical current density Jc in the range of 102–104 A/cm2. Maximum-to-minimum variations in Ic over a wafer were ±4% for junctions with Vc=0.15 mV and ±13% for junctions with Vc=0.5 mV.
We have measured Nb–AlOx–Nb Josephson tunnel junctions which have resistive shunts with different parasitic inductances. Numerical simulations reveal that specific features in the experimental current–voltage (I–V) characteristics of these devices are dc signatures of complex ac behavior. Depending on the inductance of the shunt loop and the capacitance of the junction, these features may either appear or disappear as the temperature of the device is increased. Examination of the simulated voltage waveforms allows us to map regions of the parameter space which exhibit complicated behavior. These regions should be avoided when a nearly sinusoidal voltage waveform is desired, as is the case for Josephson junction-based oscillators. The agreement of the experimental and simulated I–V curves also enables us to accurately determine the inductance of the shunts and the capacitance of the junctions.
Nb/Al-AlOx/Nb Josephson junctions of few micrometers size, derived by the basic hysteretic SIS process, have shown stable overdamped current voltage, I-V, characteristic with Ic of 1–10 mA and Vc of 100–600 μV at 4.2 K. The moderate dependence on temperature of these parameters has allowed to use them at temperatures above 4.2 K, near the Nb transition temperature, measuring quantized voltage steps several hundreds μA wide on single and 10 junctions arrays at T ≫ 8 K. This paves the way to their use in cryocooler setup of reduced cost and power consumption for a future generation of programmable and AC voltage standard.
We investigated current-voltage characteristics of unshunted and externally shunted Josephson junctions (JJs) with high critical current densities Jcin order to extract their basic parameters and statistical characteristics for JJ modeling in superconducting integrated circuits as well as to assess their potential for future technology nodes. Nb/AlOx-Al/Nb junctions with diameters from 0.5 to 6 μm were fabricated using a fully planarized process with Mo or MoNxthin-film shunt resistors with sheet resistance Rsq= 2 Ω/sq and Rsq= 6 Ω/sq, respectively. We used our current standard MIT Lincoln Laboratory process node SFQ5ee to fabricate JJs with Jc= 0.1 mA/μm2and our new process node SFQ5hs (where “hs” stands for high speed) to make JJs with Jc= 0.2 mA/μm2and higher current densities up to about 1 mA/μm2. Using LRC resonance features on the I-V characteristics of shunted JJs, we extract the inductance associated with Mo shunt resistors of 1.4 pH/sq. The main part of 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 ω, σ(ω) = σ0/(1 + iωτ), where σ0is the static conductivity and r the electron scattering time. Using a resonance in a large-area unshunted high-Jcjunction excited by a resistively coupled small-area shunted JJ, we extract the Josephson plasma frequency and specific capacitance of high-Jcjunctions in 0.1-1 mA/μm2Jcrange. We also present data on Jctargeting and JJ critical current spreads. We discuss the potential of using 0.2-mA/μm2JJs in very large scale integration single flux quantum circuits and 0.5-mA/μm2JJs in high-density integrated circuits without shunt resistors.
We measured the low frequency critical current noise in Nb/AlOx/Nb Josephson junctions. Unshunted junctions biased above the gap voltage and resistively shunted junctions biased near the critical current Ic have been measured. For both, the spectral density of δIc/Ic, Sic(f), is proportional to 1/f, scales inversely as the area A and is independent of Jc≡Ic/A over a factor of nearly 20 in Jc. For all devices measured at 4.2 K, Sic(1 Hz)=2.0±0.4×10−12/Hz when scaled to A=1 μm2. We find that, from 4.2 to 0.46 K, Sic(f) decreases linearly with temperature.
Overdamped Nb/Al-AlOx/Nb Josephson junctions are an intermediate state between the SIS and SNS Josephson junctions. With a proper choice of fabrication parameters, stable and reproducible nonhysteretic curent-voltage characteristics have been obtained Featuring critical current densities up to 70 kA/cm2and characteristic voltages up to 450 μV at 4.2 K, overdamped junctions are suitable for many aplications ranging from RSFQ electronic circuits to programmable and ac voltage standards. Tests on single junctions arrays of series-connected junctions have shown a suitable behaviour when driven by a microwave with frequencies around 75 GHz. The quantized steps have proven to be stable and flat at nV level. These junctions also shown an improved temperature dependence, which can be interesting in view of the development instrumentation with an integrated quantum voltage reference operated in a closed cycle refrigerator.