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Journal of Applied Physics

Dynamic behavior of Josephson tunnel junctions in the subnanosecond range

H. H. Zappe, K. R. Grebe

Published Feb 1, 1973• 39 citations
Publisher

Abstract

Transitions from the zero-voltage to the voltage state have been directly measured on large (≃104 μm2) Josephson junctions. By adjusting the current load, the switching times (10–90%) were varied from 60 to 400 psec. Good agreement was found between theoretical and experimental results. The times required to transfer current from junctions into superconductive inductances (10−11−10−10 H) were also investigated. The switching times ranged from 300 to 550 psec and agreed basically with our simple theoretical model. To explain the details of the voltage developed during current transfer, self-pumped junction resonances had to be invoked. Although these times are expected to be smaller in miniaturized devices, they represent to our knowledge the shortest times ever reported for circuits with a dissipation of less than 10−5 W in continuous operation.

DOI
10.1063/1.1662274

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Physical Review•Jan 7, 1966•19 citations
Transitions from the zero-voltage to the voltage state have been directly measured on large (≃104 μm2) Josephson junctions. By adjusting the current load, the switching times (10–90%) were varied from 60 to 400 psec. Good agreement was found between theoretical and experimental results. The times required to transfer current from junctions into superconductive inductances (10−11−10−10 H) were also investigated. The switching times ranged from 300 to 550 psec and agreed basically with our simple theoretical model. To explain the details of the voltage developed during current transfer, self-pumped junction resonances had to be invoked. Although these times are expected to be smaller in miniaturized devices, they represent to our knowledge the shortest times ever reported for circuits with a dissipation of less than 10−5 W in continuous operation.
We have studied the current-voltage characteristics of small area tunnel junctions at temperatures below 1 K. The junctions were made in an edge geometry with a Nb base electrode and had areas less than .05 μm2and critical currents in the nA range. Although the measured I-V characteristics resemble those of ordinary hysteretic junctions, the supposed zero-voltage portion of the curve proved to have a finite slope and to deviate from zero voltage. For these junctions it is apparently possible for occasional 2π phase slips to occur without switching to the usual voltage state. This behavior can be explained either by macroscopic quantum tunneling or by a model in which the effective shunt conductance of the junction is frequency dependent.
We fabricated high quality Josephson tunneling junctions by self-aligned lift-off process. Parameters including its critical current, normal resistance and capacitance which determine the dynamic energy consumption and speed of the superconducting electronics had been measured. The critical current of a 22 × 22 μm2Junction is 1796 ± 52 μA calculated from the dependent curve between the lifetime of zero-voltage and switching current. The junction capacitance is 24.7 ± 3.9 pF obtained by observing Fiske self-resonant step when applied several Gauss magnetic field.
We have constructed tunneling cryotron flip-flops, have observed current transfer from one leg to the other, and have measured the time required for current transfer to be 2 nsec. The results are in agreement with the model previously proposed.1 The tunneling cryotron flip-flop consists of two devices in parallel, linked by a wholly superconducting path. A current is fed to the parallel devices; the current is steered from one device to the other by application of a control pulse. The measurements have been made on a loop of 1.16 in. in length (L=1.08×10−10H), containing two 10 mil diam junctions, having zero-field critical currents of 21 mA and 29 mA, respectively (in operation these are biased to near maxima on the gain curves, at 33 mA and 42 mA). The measuring apparatus is similar to that previously described.1 In operation, a current of 20 mA is transferred from one device to the other by the application of a 2 mA control pulse, a gain of 10. The time required for this current to transfer, Δttransfer, is 1.4 nesc≤Δttransfer≤2.0 nsec, with an uncertainty of at most 0.4 nsec. According to the previously proposed model of a constant gap voltage driving the loop inductance and which does not include the junction transition times (Ref. 1), the transfer time for 20 mA of current should be 2 nsec. One implication of this excellent agreement is that the junction transition time is appreciably smaller than the previously measured upper bound of 800 psec.2 Additional operating details will be discussed.
We have studied the temperature dependence of escape phenomena in various underdamped Josephson junctions (JJs). The junctions had different Josephson coupling energies E J which were relatively small, but larger than the charging energy E C . Upon increasing the temperature T , we first observe the usual cross-over between macroscopic quantum tunnelling and thermally activated (TA) behaviour at temperatures k B T ∼ ℏω p , where ω p is the plasma frequency of the junction. Increasing T further, the width of the switching current distribution has, counterintuitively, a non-monotonic temperature dependence. This can be explained by the novel cross-over from TA behaviour to underdamped phase diffusion. We show that this cross-over is expected to occur at temperatures such that k B T ∼ E J (1 − 4/π Q ) 3 /2, where Q is the quality factor of the junction at the plasma frequency, in agreement with experiment. Our findings can be compared with detailed model calculations which take into account dissipation and level quantization in a metastable well. Particular attention is paid to the sample with the smallest E J , which shows extensive phase diffusion even at the lowest temperatures. This sample consists of a dc-SQUID and a single JJ close to each other, such that the SQUID acts as a tunable inductive protection for the single junction from fluctuations of a dissipative environment. By varying the flux through the dc-SQUID, we present, for the first time, experimental evidence of the escape of a JJ from the phase diffusion regime to the free running state in a tunable environment. We also show that in the zero voltage state the losses mainly occur at frequencies near the plasma resonance.
When a Josephson junction in the zero-voltage state is current-biased below its critical current, the rate that it escapes to the finite-voltage state depends on the quantum state of the junction. By employing a slow current sweep, it is possible to observe experimentally the emptying of the thermally populated first excited level as a well-defined feature in the escape rate. This feature provides a simple method of determining the junction's energy relaxation time T1{T}_{1}T1​, a key parameter for evaluating its utility for quantum computation. We discuss the temperature regime where this effect is readily observable and describe how the emptying depends directly on the relaxation time. Our model of the junction dynamics agrees well with the measured escape rate of a $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}\ifmmode\times\else\texttimes\fi{}10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ $\mathrm{Nb}\text{\ensuremath{-}}\mathrm{AlOx}\text{\ensuremath{-}}\mathrm{Nb}$ device in the 25 to 300mK300\phantom{\rule{0.3em}{0ex}}\mathrm{mK}300mK temperature range, yielding ${T}_{1}\ensuremath{\approx}4\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$.
We have performed a quantitative electrodynamic experiment on a Josephson oxide tunneling junction. Using a current source at 30 Mc/sec, we have verified the time dependence of the Josephson equation, j=j0j={j}_{0}j=j0​ $sin [{\ensuremath{\gamma}}_{l}\ensuremath{-}{\ensuremath{\gamma}}_{r}\ensuremath{-}(\frac{2e}{\ensuremath{\hbar}})\ensuremath{\int}\mathrm{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{dl}]$, where $(\frac{\ensuremath{\partial}}{\ensuremath{\partial}t})[{\ensuremath{\gamma}}_{l}\ensuremath{-}{\ensuremath{\gamma}}_{r}\ensuremath{-}(\frac{2e}{\ensuremath{\hbar}})\ensuremath{\int}{l}^{r}\mathrm{A}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{dl}]=\ensuremath{-}(\frac{2eV}{\ensuremath{\hbar}})$. Thus the limiting voltage is shown to obey the quantum relationship relationship, $2eV=\ensuremath{\hbar}\ensuremath{\omega}$. Measurements were made completely in the coherent state showing the diffraction nature of the junction as a function of applied magnetic field. The Josephson (parametric) inductance of the junction was directly observed and is in good agreement with the theory.