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Applied Physics Letters

Josephson behavior in granular NbN weak links

J. H. Claassen

Published May 1, 1980• 29 citations
Publisher

Abstract

A substrate step technique has been used to fabricate superconducting NbN weak links of length ∼750 Å, width ∼1.5 μm. The film in the weak-link region is less than 100 Å thick, and shows evidence of being granular. These devices have very high resistance (as much as 30 Ω), are quite rugged, and show almost ideal Josephson response to microwave radiation at 70 GHz. A vortex flow model is expected to apply because of the small coherence length in the weak-link material. However, the well-known resistively shunted junction model is found to be a significantly better predictor of device behavior.

DOI
10.1063/1.91652

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We report here numerical calculations on the properties of superconducting weak links as mixers with external local oscillators (LO). Our calculations are based on the resistively shunted-junction model. We assume that the LO and the signal are ideal current sources of amplitudes ILO and IS and of frequencies ωLO and ωs, respectively. We calculate the IF voltage across the weak link as a function of the bias current, the LO current amplitude ILO, and the normalized signal frequency Ωs = ħωs/(2 e Ic R), where Ic is the critical current and R is the shunt resistance. If ωIF/ωLO and Is/Ic are small, we find a linear IF response. Using this method we find the frequency dependence of the IF response, estimate the conversion efficiency for the matched case in both the absence and the presence of noise, and calculate the required LO power. We have fabricated thin-film constrictions by using electron lithography. We have made constrictions of indium films with thicknesses of ~ 1 200 A with widths as narrow as 2 000 A and lengths as short as 1 000 A and have studied their I-V characteristics in the presence of RF radiation and measured their X-band mixing properties. We have measured an NEP of 10-13 W/Hz1/2 and a dynamic range of 23 dB (3 dB deviation from linearity) and estimate that, with optimum matching, these would become 3 × 10-18 W/Hz1/2 and 74 dB, respectively.

Revue de Physique Appliquée•Jan 1, 1974•23 citations
A substrate step technique has been used to fabricate superconducting NbN weak links of length ∼750 Å, width ∼1.5 μm. The film in the weak-link region is less than 100 Å thick, and shows evidence of being granular. These devices have very high resistance (as much as 30 Ω), are quite rugged, and show almost ideal Josephson response to microwave radiation at 70 GHz. A vortex flow model is expected to apply because of the small coherence length in the weak-link material. However, the well-known resistively shunted junction model is found to be a significantly better predictor of device behavior.
A series of NbN thin film SQUIDs with transition temperatures ranging from 5 K to ∼14 K are being characterized by microwave measurements at 9.6 GHz. The data are being used to determine the critical current, resistance, and energy sensitivity of each device, to identify features that may be related particularly to the granular nature of the weak links, and to study systematically the variations of the SQUID response with temperature. The devices are nominally 1 μm long, 10 nm thick and from 1 μm to ∼50 μm wide and are fabricated on 1 mm-diameter quartz rods. All have previously been well characterized as SQUIDs at 23 MHz. Detailed results are presented for the first five devices studied.
A study of the magnetic flux noise in thin film NbN SQUIDS with variable thickness weak links has been initiated using the fractional step rise parameter, a , to characterize the noise. A series of devices have been fabricated and measured which exhibit Kurkijarvi magnetic flux noise, each over a restricted temperature range below their T . The T ' s for the devices ranged from below 5K to as (high as 15.7K. The variable thickness weak links are nominally 1 micrometer in length, between 50 microaeters to submicrometer in width and less than 10 MI. in thickness. For these thicknesses, the weak link region is granular ("inhomogeneous") in nature and the temperature dependence of the critical current obeys either the Josephson or the mean field theories depending on the strength of the intergranular coupling. The deduced magnetic flux noise obeys Kurki-jarvi theory for critical current values greater than 2@ /L but lessthanapproximately 61p /L for most deGices tested. The dependence of the 'measured magnetic flux noise on the degree of granularity of the weak link and the temperature dependence of the critical current is discussed.
Thin-film SQUID’s fabricated from the high Tc refractory material NbN have been studied at 9.4 GHz. Devices with granular weak links display a Josephson critical current dependence over a wide range of temperatures below Tc. We have observed open loop signal-to-noise ratios as high as 20 000 corresponding to a minimum detectable energy of 1×10−30 J in a 1 Hz bandwidth over a temperature range of several °K. In two samples, the response time was found to be limited by the intrinsic gap response time, τg∼h//2Δ (T). These devices are rugged, stable, cycle well, and have good SQUID properties at both 9.4 GHz and 20 MHz.
High resistance granular NbN microbridges with submicron dimensions have been fabricated and investigated. Devices with critical currents less than 5 microamps and bridge resistances of the order of 50 ohms have been studied as a function of temperature at both zero and finite voltages. The current‐voltage characteristics were measured with various levels of applied radiation in the frequency range 11–40 GHz. For these frequencies, constant voltage‐current steps were observed at the Josephson frequency, 2eV/h for low applied voltages, at higher voltages the radiation induced step spacing deviated from that of ideal Josephson behavior. Additional current steps were also observed at temperatures just above the bridge Tc where no finite critical current could be dected. These effects and other characteristics observed on the I‐V curves will be reported and discussed.
We report here numerical calculations on the properties of superconducting weak links as mixers with external local oscillators (LO). Our calculations are based on the resistively shunted-junction model. We assume that the LO and the signal are ideal current sources of amplitudes ILO and IS and of frequencies ωLO and ωs, respectively. We calculate the IF voltage across the weak link as a function of the bias current, the LO current amplitude ILO, and the normalized signal frequency Ωs = ħωs/(2 e Ic R), where Ic is the critical current and R is the shunt resistance. If ωIF/ωLO and Is/Ic are small, we find a linear IF response. Using this method we find the frequency dependence of the IF response, estimate the conversion efficiency for the matched case in both the absence and the presence of noise, and calculate the required LO power. We have fabricated thin-film constrictions by using electron lithography. We have made constrictions of indium films with thicknesses of ~ 1 200 A with widths as narrow as 2 000 A and lengths as short as 1 000 A and have studied their I-V characteristics in the presence of RF radiation and measured their X-band mixing properties. We have measured an NEP of 10-13 W/Hz1/2 and a dynamic range of 23 dB (3 dB deviation from linearity) and estimate that, with optimum matching, these would become 3 × 10-18 W/Hz1/2 and 74 dB, respectively.