High temperature superconducting Josephson ...

High temperature superconducting and step sharpening

Josephson

transmission

lines for pulse

J. S. Martens, J. R. Wendt, V. M. Hietala, D. S. Ginley, C. 1. H. Ashby, T. A. Plut, G. A. Vawter, and C. P. Tigges Sandia National Laboratories, Albuquerque, New Mexico 8718.5

M. P. SiegaLa) S. Y. Hou, and Julia M. Phillips AT&T BeN Laboratories, Murray Hill, New Jersey 07974

G. K. G. Hohenwarterb) Parkview R&D, Madison, Wisconsin 53711

(Received 25 June 1992; accepted for publication 2 September 1992) An increasing number of high speed digital and other circuit applications require very narrow impulses or rapid pulse edge transitions. Shock wave transmission lines using series or shunt Josephson junctions are one way to generate these signals. Using two different high temperature superconducting Josephson junction processes (step-edge and electron beam defined nanobridges), such transmission lines have been constructed and tested at 77 K. Shock wave lines with approximately 60 YBaCuO nanobridges, have generated steps with fall times of about 10 ps. With step-edge junctions (with higher figures of merit but lower uniformity), step transition times have been reduced to an estimated 1 ps.

INTRODUCTION

Narrow pulses and/or high speed step waveforms are needed for applications such as single flux quantum’ (SFQ) and other high speed logic2 and materials characterization. Shock wave transmission lines composed of nonlinear devices embedded in a quasi-lumped structure can generate these signals. These transmission lines rely on the dependence of some reactive component of the transmission line (series inductance or shunt capacitance) on signal level to generate high slew signals. Passive networks can convert these rapid edges into a narrow pulse by, for example, taking a derivative. Significant work has been done using diodes as shunt capacitance in artificial transmission lines fabricated on semiconductors. These devices rely on the voltage dependent capacitance of diodes to form the shock wave.3 The use of Josephson elements in nonlinear transmission lines has also been considered (e.g., Ref. 4) for a variety of applications. It is possible using Josephson junctions, to form the pulse sharpening transmission line from a single film of superconducting material resulting in simpler fabrication and higher process compatibility with superconducting digital electronics. It is also anticipated that the resulting pulses will be sharper. JUNCTION

TECHNOLOGIES

The Josephson junctions used in these circuits were fabricated by two different processes that are schematically illustrated in Fig. 1. The first is a step-edge process5T6in which a step is ion milled into the LaA103 substrate prior to deposition of the high temperature superconducting (HTS) film. Because of the disruption in the substrate, a ‘kurrently with Sandia National Laboratories, Albuquerque, NM 87185. “Also with the University of Wisconsin-Madison, ECE Dept., Madison, WI 53706. 5970

J. Appl. Phys. 72 (12). 15 December 1992

weak grain boundary forms at the step which has Josephson behavior. The structure consists of a TlCaBaCuO superconducting film’ of thickness 300 nm with a step height of about 350 nm. Experimentally, it has been observed that junctions form if the step-height to film thickness ratio is between about 0.9 and 1.3. This type of junction is of reasonably high quality: I$,, products (critical currentnormal resistance product, a standard figure of merit’) of about 1 mV at 77 K and critical current densities deviating less than 20% in uniformity across the junction. The latter estimate comes from Fourier analysis of the critical current versus applied B field profile.* The other fabrication technique utilizes nanobridges formed by direct write electron beam (e-beam) lithography.9 Two mesa etches (with a degassed, pH balanced di-sodium ethylenediaminetetraacetic acid (EDTA) solution” to allow for good definition with minimal surface degradation) define narrowed and thinned active areas and direct-write e-beam exposure defines a bridge of dimensions considerably less than 20 nm by 20 nm. Since the actual bridge dimensions are on the order of a coherence length in size, the bridge functions as a Josephson weak link.* Based on the power dependence of the Shapiro steps of individual junctions,8’9 we are fairly sure that these are clean Josephson devices and not bridges in a flux flow or phase slip regime. To prevent problems with undercutting during the bridge definition stage, extremely thin ( 10-25 nm), high quality films are required. YBaCuO films made with a BaF, process” were chosen for this work. YBaCuO junctions fabricated with this technique’ have had I$, products from 10 to 250 PV at 77 K and critical current density deviations of less than 10%. The uniformity improvements are a reflection of high film uniformity and the ability to form junctions without the need for grain boundaries. Current-voltage (I-V) curves of junctions formed by both processes are shown in Fig. 2. Both 1-V curves fit very

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well to those of the resistively shunted junction (RSJ)* model. The critical currents of the nanobridge junctions are about l-2 orders smaller than for the step-edge junctions and normal state resistances are about 0.5-l orders larger. This is consistent with the geometrical and material ditTerences.5P6P12 For the purposes of pulse former circuit design and fabrication, the key parameters are 1, (lower with nanobridges), I$, products (higher with step-edge), yield, and uniformity (both higher with nanobridges). All of these circuits were fabricated on LaA103 substrates that were initially 300-500 pm thick. In this case of the step-edge circuits where higher speeds were expected, the substrates were thinned (after processing) to approximately 75 pm to reduce the effects of surface waves and dispersion in the transmission structure. All of the structures were defined with conventional (400 nm optical) and/or e-beam lithography and etches based on degassed, pH balanced EDTA solutions. All circuits have annealed Ag contacts, are incorporated into coplanar waveguide structures, and were measured with either Cascade probes or a monolithic Josephson spectral technique described in the next section.

(4

Not to scale

length

03

FIG. 1. The structures of the two HTS junctions used in this work. (a) shows a step-edge structure where a step is milled in the LaA103 substrate prior to growth. The TlCaBaCuO film grown forms a grain boundary and, hence, a junction at the step. (b) shows a YBaCuO nanobridge in which a small bridge is defined by direct write e-beam lithography.

o

.

I

1

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8

12

16

20

V WJ)

(A)

PULSE

FORMER

CIRCUIT

AND THEORY

The reactive nonlinearity being used in some of these circuits is the Josephson inductance that increases with current level8 (until the critical current). Hence if an artificial transmission line is composed of many series junctions with some quasi-lumped shunt capacitance, the velocity of the shock wave will be less than the phase velocity resulting in a falling edge with increased slope.13 The structure and equivalent circuit of such a line are shown in Fig. 3. Since nanobridge junctions exclusively are used in these results, the very small junction capacitance has been omitted. Because the spacing between the junctions is small (of order 10 pm) and the line impedance low, the transmission line inductance can be neglected relative to that of the junctions. Assuming that the shock wave exists over a sufficiently large electrical length, an important conclusion is that the fall time is limited to something on the order of 6~~ where ~~ is the fundamental junction time constant given by ( a0 is the flux quantum) I3 @PO

%= 23TI3,

(1)

*

The amplitude squared of the shock wave will behave as13 1 Vj2czA[ l-tanh

03 FIG. 2. Representative Z-Y curves of the two types of junctions step-edge and (b) nanobridge. 5971

J. Appl. Phys., Vol. 72, No. 12, 15 December 1992

(a)

( (x~~of)B)],

where ZJis the velocity of the shock wave, x is the position along the line, 7. is defined in Eq. ( 1 ), and B is a parameter describing the nonlinearity.13 Most importantly, B is negative for serial Josephson systems (inductance nonlinearity) and is positive for capacitive nonlinearities. This causes the rising edge to be steepened for capacitive systems and the falling edge steepened for inductive systems. As I$,, increases, the prefactor B/( ~7~) in the tanh argument will increase making the transition steeper. Martens et al.

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,

1 ,

\ ciio

300 nm pit etched into Substrate

of order nm Equivalent Circuit:

Equivalent

Circuit:

FIG. 3. Structure of the serial junction shock line. This line uses the current-dependent inductance of the junctions to form the shock wave and has been built with both nanobtidge junctions (YBaCuO) and those formed with the step-edge process (TlCaBaCuO). In the case of the step-edge junctions, the equivalent circuit will have each junction element, a current limiting element in series with a variable inductance, replaced by two in series (since two steps are used).

The serial system is a classical shock wave structure that has a number of advantages including being able to keep the junctions below their critical current and hence dissipating essentially no power. The output signal level is limited by the critical current since in this structure the current level in any junction is not intended to rise above the critical current. Hence, in a 50 R system, the output voltage is limited to about 501, A less conventional structure uses junctions as shunt elements to the transmission line as shown in Fig. 4. As the input pulse propagates, sequential junctions are switched out of the critical current branch. This relies on the fast switching of the junction (which is on the scale of re) but embeds the junctions in a transmission line structure to allow shock wave formation and more reasonable impedance levels. The main difference from the previous structure is that this line can be represented by a capacitive nonlinearity and it is the rising edge that will be steepened. Such a structure can generate much larger signal levels and, although no theoretical analysis has been done, it seems able to generate even sharper steps based on simulations. Since the junctions enter the voltage branch, this circuit consumes considerably more power (order PW per junction) and does introduce circuit design complexities since often several feeds are necessary to uniformly bias the junctions in the transmission line. As is obvious from Fig. 4, junctions with high R, are particularly useful to limit attenuation and broadening of the shock wave. PULSE

FORMER

RESULTS

Serial Josephson lines (Fig. 3) have been made with e-beam defined nanobridge junctions. In the nanobridge 5972

J. Appl. Phys., Vol. 72, No. 12, 15 December 1992

FIG. 4. Structure of the shunt junction shock line. So far, this structure has only been built with step-edge junctions (TlCaBaCuO). This structure allows the input signal to switch the junctions into the voltage state altering the effective capacitance. While consuming more power, this line seems able to form sharper pulses. Since two steps are used in the shunt section, each shunt elements consists of two series junctions.

case, about 60 junctions were used which created some granularity problems, probably increasing the fall time and causing ripples in the output response. The average I$,, product was about 200 ,uV at 77 K. For this experiment, a pulse with rise and fall times approximately equal to 20 ps and amplitude 50 ,uA (just below critical currents) was applied to the line. One would expect a time constant on the order of 10 ps based on ELq. ( 1). Measured results are shown in Fig. 5 and the fall time was approximately 12 ps. This wave form was measured with a 50 GHz digitizing

0

20

40

60

80

Time (ps) FIG. 5. Data for a nanobridge serial line. Measured with a sampling oscilloscope, the result is near the bandwidth limit. The fall time agrees reasonably well with the theoretically expected 10 ps. A pulse of rise/fall time 20 ps and amplitude 50 P A was applied to the input of the line. A buffer output amplifier was used to obtain the signal shown, the actual step height is approximately 500 pV. Martens et al.

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oscilloscope (rise time ~7 ps) hence the resolution on this measurement is on the margin but the measured result is qualitatively close to that expected. The degree of resolution obtained did require a careful, temperature-stabilized calibration of the entire signal path. In the case of the step-edge circuits, the expected transition times from simulations were considerably shorter than the oscilloscope rise time. To provide a better estimate of the response, on-chip Josephson spectroscopy was used. As is well known, Shapiro steps occur in the I-V curve upon application of a rf signal. These steps occur at voltages of hv/2e (v is the applied frequency) and integer multiples thereof (depending on the power level).’ For sufficiently high quality junctions, the step height can be fairly precisely related to the rf current levels present.‘4’15 The process is more complicated than it sounds for a number of reasons: ( 1) nonlinearities in the junction cause mixing between signal components, (2) the step-height-power relation is multivalued meaning it is wise to attenuate signal levels before sensing (in our case the signal is sampled by weak coupling and hence is small), (3) the rf signal that is coupled to the sense junction may differ from the actual rf signal because of the frequency dependent admittance of the measurement junction assembly, and (4) phase information is difficult to recover since it is the power spectrum that is immediately derived from the Shapiro step heights. The first problem is simplified if power levels are kept low enough (but not so low that one is outside the dynamic range of about 5 orders of magnitude15). If power levels are below a saturation level (of order - 30 dBm), the Shapiro step generation process (ac Josephson effect) is additive15 in that two spectral components will produce two independent voltage steps. To calibrate the measurements and to provide information on the levels of nonlinearity, a series of multitone tests were performed in which multiple signals were sent down a coplanar waveguide on which a measurement junction was flip-chipped (with several small dipoles for power coupling). For the power levels involved ( < - 30 dBm generally), inter-tone mixing was found to be negligible. Some harmonics were generated but all of the step heights agreed well with those predicted by the RSJ model. In the case of incident tones that were harmonically related, it was found that subtracting the expected internally generated harmonic components allowed for accurate spectroscopy. These multitone tests were run for frequencies to 100 GHz and for power levels from -70 to -30 dBm. Even using a constant coupling factor, the step heights were close enough (within about 10%) to that predicted by the RSJ model that we believe the model will correctly produce spectra to much higher frequencies. In part, the calibration method also answers the third problem. For intermediate and higher frequencies, the coupled power to incident power ratio was not observed to vary significantly with frequency and hence it was assumed to be flat for frequencies above 20 GHz. The second problem seems to be minor for this particular weakly coupled test structure: for the expected signal levels, excursions were limited to the first two multivalued sections of the step height-t-f power curve. For the fourth concern, we can 5973

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1992

-Input

Iti0

waveform

I

200 360 460 560 600 700 800 Time (ps)

FIG. 6. Test of the Josephson spectroscopic technique of pulse measurement. The sum of a 10 and 12 GHz sinusoid was applied to the test line with the Josephson detectors present and the spectral components retrieved from the Shapiro steps. The reconstructed wave form ‘is shown with the original signal.

make some assumptions about the time signal by forcing the input signals to be odd-symmetric have forms. In doing the reverse transform, we can assume that the wave form is odd-symmetrized to fix the phase information. As a verification test, a pair of sinusoids, frequencies 10 and 12 GHz, were applied to the test line and sampled by the measurement junctions. Three different junction assemblies (a single step-edge or nanobridge junction connected to a series of small dipoles and a current bias) on a separate substrate were used and flip-chipped onto the test sample. The step heights from the three assemblies matched within 10%. The reconstructed and original wave forms are shown in Fig. 6 and illustrate at least the basic functionality of the technique. The shunt line arrangement was made with step-edge junctions, approximately 100 in this case and the simulations, shown in Fig. 7, suggest a rise time on the order of 1 ps. The simulations were performed using a modified version of JSPICE16 (a circuit simulation program including

0

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10

Time (ps) FIG. 7. Shunt step-edge results along with JSPICE (Josephson SPICE) simulation results. Note that the rise time is on the order of 1 ps. A 10 GHz sinusoid of amplitude 20 mV was applied to the input. A buffer amplifier was used to obtain the signal shown, the actual step height was about 5 mV. Martens et al.

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Josephson elements) and using nonhysteretic junction models with parameters typical of the TlCaBaCuO devices resulting from the step-edge process. The simulation model also included transmission line discontinuities (tapers at contact pads and width changes at the semi-lumped capacitance) and launch parasitics. On-chip Josephson spectroscopy was used and the results are shown in Fig. 7 as well. Again to maintain the odd symmetry, a full sinusoid was used as the input signal ( 10 GHz, 20 mA peak). As suggested by the transform data, the rise time is on the order of 1 ps. The difference from simulation results can probably be explained by neglected parasitics (particularly in coupling to the Josephson detectors). ANALYSIS

AND CONCLUSIONS

Both varieties of Josephson shock-wave transmission lines clearly sharpened their respective edges of the input wave forms. This was all done at 77 IS with fairly simple circuitry. As has been theoretically reasoned, the amount of sharpening increased with the quality of the junction as measured by the I$, products. For this reason, the nanobridge YBaCuO junctions suffered a disadvantage with respect to the TlCa&CuO step-edge structures although the yield and uniformity with that structure are superior. The measured transition times of the shaped pulses are consistent with both conventional JSPICE simulations and with theoretical analysis within the limits of granularity and coupling parasitics. This suggests that a significant fraction of the junctions are functioning in each line (estimated > 80%) and that their uniformity is quite high. In the case of the serial lines at least, the Josephson inductance is following the expected bias dependencies fairly closely (probably within 10% based on the JSPICE simulations). The signals generated by these circuits are useful for applications. With a simple passive network, the steepedge can be converted into a narrow impulse. Thus an on-chip pulse generator for SFQ circuits is available. This

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may help to some degree with the difficult problem of testing these ultrafast circuits. ACKNOWLEDGMENTS

This work was performed at Sandia National Laboratories and was supported in part by the U. S. Department of Energy (division of Basic Energy Science) under contract No. DE-ACXM-76POO789. ‘K. K. Likharev and V. K. Semenov, IEEE Trans. Appl. Supercond. 1, 3 (1991). *S. Hasuo, S. Kotani, A. Inoue, and N. Fujimaki, IEEE Trans. Magn. MAG27, 2602 (1991). ‘D. Jager and F. J. Tegude, Appl. Phys. 15, 393 (1978); C. J. Madden, R. A. Marsland, M. J. W. Rodwell, D. M. Bloom and Y. C. Pao, Appl. Phys. Lett. 54, 1019 (1989). ‘A. Davidson, IEEE Trans Magn. MAG17, 103 (1981). sK. P. Daly, W. D. Dozier, J. F. Burch, S. B. Coons, R. Hu, C. E. Platt, and R. W. Simon, Appl. Phys. Lett. 58, 543 (1991). 6J. S. Martens, T. E. Zipperian, G. A. Vawter, D. S. Ginley, V. M. Hietala, and C. P. Tigges, Appl. Phys. Lett. 60, 2401 (1992). ‘D. S. Ginley, J. F. Kwak, E. L. Ventmini, B. Morosin, and R. J. Baughman, Physica C 160, 42 (1989). *T. Van Duzer and C. W. Turner, Principles of Superconductive Devices and Circuits (Elsevier, New York, 1981), Chaps. 4-5. 9J. R. Wendt, J. S. Martens, C. I. H. Ashby, T. A. Plut, V. M. Hietala, C. P. Tigges, D. S. Ginley, M. P. Siegal, J. M. Phillips, and G. K. G. Hohenwatter, Appl. Phys. Lett. 60, 1597 (1992). “C. I. H. Ashby, J. S. Martens, T. A. Plut, D. S. Ginley, and J. M. Phillips, Appl. Phys. Lett. 60, 2147 (1992). “M. P. Siegal, J. M. Phillips, Y. F. Hsieh, and J. H. Marshall, Physica C 172, 282 ( 1990). “J. Marmhart and P. Martinoh, Appl. Phys. Lett. 58, 643 ( 1991). 13G. J. Chen and M. R. Beasely, IEEE Trans. Appl. Supercond. 1, 140 (1991). “D. G. McDonald, V. E. Kose, K. M. Evenson, J. S. Wells, and J. D. Cupp, Appl. Phys. Lett. 15, 121 (1969). 15Y. Y. Divin, 0. Y. Polyanski, and A. Y. Shulman, IEEE Trans. Magn. MAG19, 613 (1983). 16R. E. Jewett, “Josephson junctions in SPICE2G5,” Electronics Research Lab internal memoranda, Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, Dec. 1982, p. 94720.

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