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IEEE Transactions on Applied Superconductivity

Gain-frequency characteristics of transistors based on flux flow in hysteretic long Josephson junctions (LJJ)

M.A. Ketkar, James B. Beyer, J.E. Nordman

Published Jun 1, 1999• 2 citations
Publisher

Abstract

Transistors based on one dimensional flux flow in hysteretic long Josephson junctions (LJJ) and deriving output from the spatial average over the length can be modeled as a section of transmission line. Time domain analyses made on these transmission line sections with both the ends terminated with typical resistance values reveal a fundamental gain-frequency relationship unique to all devices whose output voltage is equal to the spatial average over the length of the junction. The maximum frequency of a transistor depends on the transit time of carriers and the parasitic elements. The analysis shows that the frequency response of a flux flow transistor is related but not equal to the inverse of the transit time of fluxons. Secondly the step response of these transmission line sections varies linearly with time, which indicates a slew rate limitation. The slew rate that affects the high frequency response of a flux flow device is shown to be a function of the critical current density of the junction and material parameters. Analysis made on niobium-lead junctions indicates that the slew rate peaks at an optimum current density level. The results of these analyses and performance comparisons are presented.

DOI
10.1109/77.783892

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IEEE Transactions on Applied Superconductivity•Jun 1, 1999•2 citations
Transistors based on one dimensional flux flow in hysteretic long Josephson junctions (LJJ) and deriving output from the spatial average over the length can be modeled as a section of transmission line. Time domain analyses made on these transmission line sections with both the ends terminated with typical resistance values reveal a fundamental gain-frequency relationship unique to all devices whose output voltage is equal to the spatial average over the length of the junction. The maximum frequency of a transistor depends on the transit time of carriers and the parasitic elements. The analysis shows that the frequency response of a flux flow transistor is related but not equal to the inverse of the transit time of fluxons. Secondly the step response of these transmission line sections varies linearly with time, which indicates a slew rate limitation. The slew rate that affects the high frequency response of a flux flow device is shown to be a function of the critical current density of the junction and material parameters. Analysis made on niobium-lead junctions indicates that the slew rate peaks at an optimum current density level. The results of these analyses and performance comparisons are presented.
Volt-ampere characteristics of the Josephson junction vortex-flow transistor were studied through comparison of experiment and numerical simulation. Fine structure in the flux flow branch, which is not predicted by a simple particle model for flux flow, is shown to be quantized in voltage. The quantization results from the interaction of the flux wave with the junction’s cavity resonances. It is shown that the separation of the voltage states is proportional to the maximum operating frequency of the device. In an amplifier circuit, quantization in the output voltage will reduce the dynamic range of the device by adding quantization noise. Hysteretic switching between states produces distortion. Possible device modifications for removing the quantization are discussed.
The first object of this work is to theoretically study the effects of tunnel junction parameters on flux-flow Josephson oscillators (FFOs) by numerical simulation and to experimentally study the rf properties of FFOs by integrating them together with an SIS (superconductor-insulator-superconductor) mixer/detector on a chip. By using a CAD modeled integrated sub-mm wave receiver, the composite linewidth of two FFOs was measured to be less than 2.1 MHz in the band 280-330 GHz. The receiver consists of two identical FFOs and an SIS mixer. The linewidth was determined by mixing the two signals in the SIS mixer and analyzing the intermediate frequency. The output power coupled to a 10 .OMEGA. microstripline was about 0.5 µW, and could be adjusted by changing the current bias of the oscillator. The FFOs are connected to the SIS mixer via interdigital capacitors. The FFOs and the SIS element are made of Nb/NbOx/PbBi junctions by the "reactive ion beam oxidation" technique with the critical current density jc controlled by the oxidation time. Lift-off stencils for defining the junction sizes and the top-electrodes were made by using electron-beam writing on PMMA/Copolymer double layer resist. The jc of a long Josephson junction (LJJ) determines the fluxon motion. For LJJs which had jc > 1 kA/cm2, velocity-matching (VM, where the phase velocity of propagating fluxons equals that of the electromagnetic wave in the LJJ) steps could be tuned linearly from about 0.2 to 1.4 mV by an applied magnetic field. Coupled radiation at around 100 GHz (about 3 nW), 261 GHz (4.6 nW), and 330 GHz (0.43 µW), from flux-flow oscillations, was observed. From the step's steepness, the junction quality factor QJ is determined. QJ is between 4 to 7 in the voltage range of 0.4 to 1 mV. Coupled radiation (> 3 nW) at around 100 GHz corresponding to resonant soliton oscillation in low jc samples (250 to 1000 A/cm2) was detected. Simulations show that, for a uniform bias feed, the height of the VM step .gammam increases almost linearly with the external magnetic field .beta.e and the quasiparticle loss .alpha., but is less dependent on the surface loss .beta.. An approximate expression .gammam = a + .alpha(1+b).beta.e agrees with simulations. The maximum ac output voltage decreases with increasing dampings .alpha. and .beta.. It is important to include the .beta.-term in the mathematical model. The second part of this work is devoted to rf properties of long YBa2Cu3O7-.delta. (YBCO) grain boundary junctions made on 0- 32 °. [001]-tilt YSZ bicrystals. Josephson flux-flow resonances and Fiske resonances were observed. The first resonances could be tuned from about 0.5 to 2.0 mV in a 30 µm long junction at 16 K, and we determined the ratio between barrier thickness and relative dielectric constant td/.epsilon.r=2.9 Å and the loss .alpha.= 1.3 at 16 K. Simulations support the experimental observation that Josephson vortices can propagate unidirectionally in an overdamped, homogeneous junction up to .alpha.Ã? 2. From the Fiske resonances at 256-638 GHz, their Q-values, and the Steward-McCumber parameter, we find td/.epsilon.r=4 Å, the London penetration depth .gamma.L=145±5 nm and the surface resistance RS ~20 m.OMEGA. at 280 GHz. We conclude that the boundary is dielectric and the YBCO grains are well superconducting within 5-20 nm from the boundary. The dielectric between the grains could be part of a tunnel barrier and/or a matrix for filamentary conduction. Josephson flux-flow transitors based on long bicrystal junctions were made with an Au loop used as the control line. The line modulated the critical current Ic. Current gain larger than unity was obtained below 70 K. The gain increased with the junction length and varied roughly like the square root Ic when adjusting the temperature. A transresistance larger than 5 .OMEGA. was obtained at 15 K. Better performance is expected from junctions with high current densities.
The dynamics of fluxons in the vortex flow transistor (VFT) has been much studied. The fluxon transit time determines the fundamental speed limit of operation. Since fluxons can travel at the velocity of electromagnetic waves in the junction, the VFT has the potential for operating in high frequency systems ( ≈ 100 GHz). However, owing to the low input and output impedance of the VFT, use of the device in a conventional circuit would be quite limited. A distributed amplifier configuration consisting of many VFTs has been proposed to remedy the problems of low impedance levels. However, the realization of such an amplifier circuit at microwave or millimetre wave frequencies depends on obtaining a circuit model. In this paper, microwave superconducting VFT distributed amplifiers using the balanced control technique is reviewed. This kind of amplifier has the advantage that the capacitive feedthrough effect is decreased to a negligible extent. This is the major limiting factor for high frequency applications. The self-field effect which makes the current step inclined is reduced by injecting bias current only around the region of one end of the junction thus obtaining steeper I- V characteristics. With the asymmetric geometry, the slope of the current step is about one hundred times steeper than those obtained with the conventional overlap geometry. Owing to the diamagnetic behaviour of the Josephson junction, a little of the magnetic field induced by the current in the control line is allowed to penetrate the junction. Thus, the transresistance rm of a VFT is very small. Some methods for maximizing rm and minimizing the output impedance r0 also appear in this review. The feasibility of fabricating VFT distributed amplifiers using low-Tc superconducting material has been demonstrated. The power gain of the amplifier can be as high as 15 dB with a flat frequency response.
A Josephson fluxon-antifluxon transistor (JFAT) can be constructed utilizing high-T/sub c/ bicrystal or SNS long junctions with a control line on top of the junction, This device can be modeled numerically by solving the perturbed sine-Gordon equation. A JFAT has a higher current gain and a faster transient response compared to a conventional Josephson flux-flow transistor which has a U-shaped control line on top of the long junction. Dependences of the control characteristics on the width and the location of the control line, as well as on the junction length are calculated. The influence of a superconducting ground plane on device characteristics are also discussed. These results are important to the design of high-T/sub c/ digital circuits based on JFATs.
Josephson fluxonic bipolar junction transistor (JFBJT) has been proposed as a superconducting amplifying element. The results on a simple realization of this device are provided to demonstrate its working principle. These experiments demonstrate that JFBJT provides current gain without suffering from the problems associated with the regular long junction vortex flow transistors. In particular, no resonance structure is present in its I-V characteristics and its impedance can be matched to any load without degradation of its characteristics. Suggestion is made on how a practical device can be fabricated.
By combining a long Josephson junction (LJJ) with single-flux-quantum (SFQ) circuits, new digital applications for long junctions can be explored. To fully investigate the dynamics of the hybrid LJJ/SFQ circuits, a numerical model was developed for an unshunted long junction coupled to shunted SFQ Josephson transmission line (JTL) through superconducting strips. The model is based on a one-dimensional array of Josephson junctions that is described by a set of discrete sine-Gordon equations. Simulations support our experimental observation that the first zero-field step can exist when the LJJ is terminated by SFQ elements. The influences on the first zero-field step by the self-inductance, the critical current, and the shunt resistance of JTL cells are studied in detail. Simulation also confirms that each 4/spl pi/ phase leap at the end of the long junction creates two separated SFQ pulses after several overdamped JTL cells.