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arXiv:0809.3272 · Applied Physics Letters

Temperature dependence of critical current fluctuations in Nb/AlOx/Nb Josephson junctions

Shawn Pottorf, Vijay Patel, James E. Lukens

Published Jan 26, 2009• 14 citations
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Abstract

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.

DOI
10.1063/1.3074446

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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.
We have measured the low-frequency noise in the critical current Ic of six dc superconducting quantum interference devices (SQUIDs) with resistively shunted Nb–NbOx–PbIn Josephson junctions in the temperature range T=0.09–4.2K. Each device is voltage biased, the applied flux is an integer number of flux quanta, and the current fluctuations are measured with a second dc SQUID. At low frequencies f, there is a component of the power spectrum of the critical current fluctuations given approximately by SIc(f)=CIc2T2∕Af, where A is the area of both junctions, and C≈(3.9±0.4)×10−23m2∕K2. For quantum bits based on Josephson junctions, the scaling of SIc(f) with T2 implies that the dephasing time limited by critical current l∕f noise should scale as 1∕T for temperatures down to at least 0.09K.
Experimental measurements on critical current noise in underdamped niobium based Josephson devices by a technique based on the switching current measurements is reported. By sweeping the junction with a current ramp we measure the critical current switching as a function of the time using the standard time of flight technique. In such a way it is possible to obtain the critical current fluctuations ΔIc=Ic(t)-<Ic(t)> and the relative standard deviations which corresponds to the root square of the current fluctuation power. Pointing at the white noise fluctuations (above few Hz) and taking into account the physical frequency of the device, it is possible to evaluate the power spectral density of the critical current. The analysis has involved high quality underdamped Josephson junctions having an area ranging from (4x4) μm2 to (40x40) μm2 in the temperature range from 4.2 K to few tenth of mK. These measurement provide very useful information about the intrinsic noise of Josephson devices involving SQUIDs and qubits.
Superconducting qubit circuits require high quality low critical current density Josephson tunnel junctions. We have developed high quality epitaxial NbN/AlN/NbN tunnel junctions with critical current density, Jc, ranging from as low as a few A/cm2to a few tens of kA/cm2. In this work, we measured current-voltage characteristics for junctions with a Jc~ 32 A/cm2in the temperature range from 17 mK to above 6.7 K. All the junctions are in good quality and have a high gap voltage (>; 5.5 mV). We found that the junctions' sub-gap resistances were temperature dependent above 2.5 K and saturated at temperatures below 2.5 K. A junction sub-gap leakage current Irof about 23 pA was measured. The voltage noise power spectral density for 3 junctions with different sizes has been measured at the base temperature of 17 mK with the junctions biased above the gap voltage. The spectral densities clearly show 1/fbehavior at low frequency and are proportional to the junction's linear dimension.
For a study of the supercurrent–phase relationship, we have fabricated Nb/Al/AlOx/Al/AlOx/Al/Nb-based Josephson junctions of low critical current density. At 4.2 K, junctions of a nominal area of 10×10 μm2 showed a nonhysteretic dc current–voltage characteristic with a critical current of about 10 μA. Similar junctions were part of washer-type rf superconductor quantum interference devices. These samples were inductively coupled to high-quality tank circuits for measurements at 4.2 K or at higher temperatures up to values close to the critical temperature of niobium. In this range, the current–phase relation, as deduced from impedance measurements of the phase-biased junction, did not deviate significantly from the sinusoidal shape.
Measurements have been made of the low-frequency spectral density of the voltage noise in current-biased resistively shunted Josephson tunnel junctions under conditions in which the noise mixed-down from frequencies near the Josephson frequency (${\ensuremath{\nu}}_{J}$) to the measurement frequency ($\ensuremath{\ll}{\ensuremath{\nu}}_{J}$) is in the regime $h{\ensuremath{\nu}}_{J}>{k}_{B}T$. In this limit, quantum corrections to the mixed-down noise are important. The spectral densities measured on junctions with current-voltage characteristics close to the Stewart-McCumber model were in excellent agreement with the predicted values, with no fitted parameters. The mixed-down noise for a wide range of bias voltages was used to infer the spectral density of the current noise in the shunt resistor at frequency $\ensuremath{\nu}$. With no fitted parameters, this spectral density at frequencies up to 500 GHz was in excellent agreement with the prediction $(\frac{2h\ensuremath{\nu}}{R})coth(\frac{h\ensuremath{\nu}}{2{k}_{B}T})$. The presence of the zero-point term, $\frac{2h\ensuremath{\nu}}{R}$, at frequencies $h\ensuremath{\nu}>{k}_{B}T$ was clearly demonstrated. The current-voltage characteristics of a junction with ${\ensuremath{\beta}}_{L}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{L}_{s}{I}_{0}}{{\ensuremath{\Phi}}_{0}}\ensuremath{\sim}1$ and ${\ensuremath{\beta}}_{C}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{I}_{0}{R}^{2}C}{{\ensuremath{\Phi}}_{0}}\ensuremath{\ll}1$, where I0{I}_{0}I0​ is the critical current, CCC is the junction capacitance, and Ls{L}_{s}Ls​ is the shunt inductance, showed structure at voltages where the Josephson frequency was near a subharmonic of the LsC{L}_{s}CLs​C resonant frequency. The additional nonlinearity of the $I\ensuremath{-}V$ characteristic caused mixing down of noise near higher harmonics of the Josephson frequency, thereby greatly enhancing the voltage noise. The measured noise was in good agreement with that predicted by computer simulations.
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.