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Journal of Applied Physics

(Double) relaxation oscillation SQUIDs with high flux-to-voltage transfer: Simulations and experiments

Derk Jan Adelerhof, H. Nijstad, J. Flokstra, Horst Rogalla

Published Sep 15, 1994• 55 citations
Publisher

Abstract

Relaxation oscillation superconducting quantum interference devices (SQUIDs) (ROSs) and double relaxation oscillation SQUIDs (DROSs) have been fabricated and characterized. The SQUIDs are based on hysteretic Nb/Al,AlOx/Al/Nb Josephson tunnel junctions. The relaxation oscillations were simulated by computer. By these simulations the minimum and maximum values of the shunt inductance at which the relaxation oscillations persist have been determined for different values of the shunt resistance and of the critical current and capacitance of the junctions. The transfer from flux to dc voltage in ROSs increases linearly with the shunt resistance. The operation range of the shunt inductance, however, becomes smaller with increasing shunt resistance. In ROSs with a SQUID inductance of 20 pH, a maximum voltage modulation width of 400 μV and a flux-to-voltage transfer δV/δφ of 4 mV/φ0 have been obtained. Two ROSs have been operated in a simple flux-locked loop with direct voltage readout. The experimental white flux noise spectral density of about 3μφ0/√Hz is in good agreement with the theoretical model. The sensitivity of these SQUIDs is limited by so-called switching noise, which is noise due to the interaction between the relaxation oscillations and the Josephson frequency. In DROSs typical flux-to-voltage transfer values of 10–30 mV/φ0 and maximum values up to 80 mV/φ0 have been obtained. This transfer is determined by thermal noise on the critical currents of the SQUIDs. The effective flux noise density of DROSs in flux-locked-loop operation with direct voltage readout is in good agreement with the theoretical noise level which is mainly determined by thermal noise on the critical currents. In one of the DROSs with a SQUID inductance of 20 pH, a white flux noise of 1μφ0/√Hz has been obtained at an estimated relaxation frequency of about 80 MHz. This corresponds to an energy sensitivity of about 160 h.

DOI
10.1063/1.357392

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•Aug 26, 2001•0 citations
Relaxation oscillation superconducting quantum interference devices (SQUIDs) (ROSs) and double relaxation oscillation SQUIDs (DROSs) have been fabricated and characterized. The SQUIDs are based on hysteretic Nb/Al,AlOx/Al/Nb Josephson tunnel junctions. The relaxation oscillations were simulated by computer. By these simulations the minimum and maximum values of the shunt inductance at which the relaxation oscillations persist have been determined for different values of the shunt resistance and of the critical current and capacitance of the junctions. The transfer from flux to dc voltage in ROSs increases linearly with the shunt resistance. The operation range of the shunt inductance, however, becomes smaller with increasing shunt resistance. In ROSs with a SQUID inductance of 20 pH, a maximum voltage modulation width of 400 μV and a flux-to-voltage transfer δV/δφ of 4 mV/φ0 have been obtained. Two ROSs have been operated in a simple flux-locked loop with direct voltage readout. The experimental white flux noise spectral density of about 3μφ0/√Hz is in good agreement with the theoretical model. The sensitivity of these SQUIDs is limited by so-called switching noise, which is noise due to the interaction between the relaxation oscillations and the Josephson frequency. In DROSs typical flux-to-voltage transfer values of 10–30 mV/φ0 and maximum values up to 80 mV/φ0 have been obtained. This transfer is determined by thermal noise on the critical currents of the SQUIDs. The effective flux noise density of DROSs in flux-locked-loop operation with direct voltage readout is in good agreement with the theoretical noise level which is mainly determined by thermal noise on the critical currents. In one of the DROSs with a SQUID inductance of 20 pH, a white flux noise of 1μφ0/√Hz has been obtained at an estimated relaxation frequency of about 80 MHz. This corresponds to an energy sensitivity of about 160 h.
Double relaxation oscillation superconducting quantum interference devices (SQUIDs) (DROSs) based on Nb/AlOx tunnel junctions have been fabricated and characterized. The estimated relaxation frequencies range from 400 MHz up to 14 GHz. Transfer coefficients from flux to voltage of 2 up to 7 mV/φ0 have been obtained. Both the intrinsic flux noise and the performance in a flux-locked loop with direct-voltage readout have been determined. Special attention is paid to the effect of damping resistors on the sensitivity of DROSs. The intrinsic sensitivity improves with increasing relaxation frequency, leveling off to a value of 13h at relaxation frequencies above 2–3 GHz for SQUID inductances of about 30 pH. This sensitivity is very close to the theoretical maximum sensitivity of 6h of a comparable standard type dc SQUID. In a flux-locked loop based on direct-voltage readout, a noise level of 0.55 μφ0/√Hz corresponding to an energy sensitivity of 34h has been obtained for a DROS with a SQUID inductance of 29 pH.
Double relaxation oscillation superconducting quantum interference devices (SQUIDs) (DROSs) have been fabricated with estimated relaxation frequencies up to 14 GHz. Both the intrinsic flux noise and the performance in a flux locked loop with direct voltage readout have been studied. In flux locked loop, a noise level of 0.55 μφ0/√Hz corresponding to an energy sensitivity of 34 h has been obtained for a DROS with a SQUID inductance of 29 pH. The intrinsic sensitivity improves with increasing relaxation frequency, leveling off to a value of 13 h at relaxation frequencies higher than about 3 GHz.
Relaxation Oscillation SQUIDs (ROSs) based on 4x4 micrometers 2 Nb/AlOx Josephson tunnel junctions have been fabricated and characterized. A ROS consists of a hysteretic dc SQUID shunted by an inductor L and a resistor R in series to induce the relaxation oscillations. The values of L range from 20 nH up to about 300 nH, whereas the time constant L/R are between 8 and 45 ns. Frequency-flux characteristics have been recorded with the help of a spectrum analyzer, directly connected to the ROS. The relaxation frequencies range from 5 to 180 MHz. The experimental characteristics can be explained very well with a simple model describing the oscillation cycle. The effect of the self-induced magnetic field due to a magnetic coupling between the dc SQUID and the shunt circuit has been studied in detail. The sensitivity of ROSs and DROSs (Double Relaxation Oscillation SQUIDs) improves with increasing relaxation frequency. In (D)ROSs based on unshunted, hysteretic tunnel junction dc SQUIDs, the maximum relaxation frequency and the sensitivity are limited by LC resonances due to the SQUID capacitance and the shunt inductance. It is shown that the relaxation frequency can be increased up to frequencies of the order of 1 GHz if an extra resistor is integrated to damp these resonances. The optimum value of the damping resistor can be obtained from the ROS parameters. For stable operation of a (D)ROS, the shunt resistance should not be too large. The optimum value of this resistance can be calculated from the effective McCumber parameter and the bias current. Theoretically, the sensitivity of a ROS with a SQUID capacitance of 1 pF, a SQUID inductance of 20 pH and a relaxation frequency of 1 GHz equals about 5h, where h is Planck's constant. In a DROS with voltage readout based on similar SQUIDs, the theoretical sensitivity at a relaxation frequency of 1 GHz is 17h, with an estimated flux-to-voltage transfer coefficient of 5 mV/(phi) 0.
Relaxation Oscillation SQUIDs (ROSs) based on 4x4 {mu}m{sup 2} Nb/AlO{sub x} Josephson tunnel junctions have been fabricated and characterized. A ROS consists of a hysteretic dc SQUIID shunted by an inductor L and a resistor R in series to induce the relaxation oscillations. The values of L range from 20 nH up to about 300 nH, whereas the time constant L/R are between 8 and 45 ns. Frequency-flux characteristics have been recorded with the help of a spectrum analyzer, directly connected to the ROS. The relaxation frequencies range from 5 to 180 MHz. The experimental characteristics can be explained very well with a simple model describing the oscillation cycle. The effect of the self-induced magnetic field due to a magnetic coupling between the dc SQUID and the shunt circuit has been studied in detail. The sensitivity of ROSs and DROSs (Double Relaxation Oscillation SQUIDs) improves with increasing relaxation frequency. In (D)ROSs based on unshunted, hysteretic tunnel junction dc SQUIDS, the maximum relaxation frequency and the sensitivity are limited by LC resonances due to the SQUID capacitance and the shunt inductance. It is shown that the relaxation frequency can be increased up to frequencies of the order of 1 GHz ifmore » an extra resistor is integrated to damp these resonances. The optimum value of the damping resistor can be obtained from the ROS parameters. For stable operation of a (D)ROS, the shunt resistance should not be too large. The optimum value of this resistance can be calculated from the effective McCumber parameter and the bias current. Theoretically, the sensitivity of a ROS with a SQUID capacitance of 1 pF, a SQUID inductance of 20 pH and a relaxation frequency of 1 GHz equals about 5, where h is Planck`s constant. In a DROS with voltage readout based on similar SQUIDS, the theoretical sensitivity at a relaxation frequency of 1 GHz is 17h, with an estimated flux-to-voltage transfer coefficient of 5 mV/{phi}{sub 0}.« less
Double relaxation oscillation superconducting quantum interference devices (DROSs) with a gradiometric signal SQUID and either a reference SQUID or a reference junction will be presented in this article. The devices are user friendly, particularly those with a reference junction. Because of the large flux-to-voltage transfer of ∂V/∂Φ=0.7–1 mV/Φ0, the devices can be operated in a flux locked loop based on direct voltage readout without loss of sensitivity. The typical white flux noise of the DROSs amounts to √SΦ=5–6μΦ0/√Hz, which corresponds to an energy resolution ε=SΦ/2Lsq≃200 h. Coupled to an external planar first-order gradiometer, a white magnetic field sensitivity of √SB<2 fT/√Hz was measured inside a magnetically shielded room.
We have realized a two-stage integrated superconducting quantum interference device (SQUID) system with a closed loop bandwidth of 2.5 MHz, operated in a direct voltage readout mode. The corresponding flux slew rate was 1.3×105 Φ0/s and the measured white flux noise was 1.3 μΦ0/√Hz at 4.2 K. The system is based on a conventional dc SQUID with a double relaxation oscillation SQUID (DROS) as the second stage. Because of the large flux-to-voltage transfer, the sensitivity of the system is completely determined by the sensor SQUID and not by the DROS or the room-temperature preamplifier. Decreasing the Josephson junction area enables a further improvement of the sensitivity of the two-stage SQUID systems.