We have measured the dispersion in phase velocity of a Nb-SiO(x)-Nb microstrip transmission line resonator over a frequency range from 50 GHz to 800 GHz. A submicron Nb/Al-AlO(x)/Nb Josephson junction was used as a voltage-controlled oscillator to excite the high order modes in the resonator. The same junction is used as a direct detector resulting in a series of step-like structures in the DC current-voltage characteristic at the position of each mode frequency. The transmission line is dispersionless up to about 500 GHz where the phase velocity begins to decrease. This is well below the gap frequency f(sub g) approx. equals 700 GHz. Results agree qualitatively with the expected theoretical behavior near f(sub g). This onset of dispersion and loss in Nb transmission lines will have a significant impact on the design of submillimeter wave RF circuits

Bumble, B.

Javadi, H. H. S.

Leduc, Henry G.

Mcgrath, William R.

English

NASA Technical Reports Server

Page 362 Third International Symposium on Space Terahertz Technology
ONSET OF DISPERSION IN Nb MICROSTRIP TRANSMISSION LINES AT
SUBMILL1METER WAVE FREQUENCIES
, x x-?r^ H. H. S. Javadi, W. R. McGrath, B. Bumble, H. G. LeDucy 60 &¥&
Center for Space Microelectronics Technology
Jet Propulsion Laboratory MAO
California Institute of Technology N 9 O
Pasadena, CA 91109
^ ABSTRACT
/'
! We have measured the dispersion in phase velocity of a Nb-SiOx-Nb
, microstrip transmission line resonator over a frequency range from 50
GHz to 800 GHz. A submicron Nb/AI-AIOx/Nb Josephson junction was used
as a voltage-controlled oscillator to excite the high order modes in the
resonator. The same junction is used as a direct detector resulting in a
series of step-like structures in the DC current-voltage characteristic at
the position of each mode frequency. The transmission line is
dispersionless up to about 500 GHz where the phase velocity begins to
decrease. This is well below the gap frequency fg = 700 GHz. Results
agree qualitatively with the expected theoretical behavior near fg. This
onset of dispersion and loss in Nb transmission lines will have a
significant impact on the design of submillimeter wave rf circuits.
https://ntrs.nasa.gov/search.jsp?R=19930018569 2020-03-17T05:44:27+00:00Z
Third International Symposium on Space Terahertz Technology Page 363
Superconducting transmission lines have many important
applications in high frequency analog circuits and high bit rate digital
systems, to name a few. These transmission lines are expected to be
nearly lossless and dispersion free up to frequencies near the
superconducting energy gap frequency fg = 2A / h, where A is the
superconductor energy gap parameter and h is Planck's constant. We are
interested in superconductive microstrip transmission lines as integrated
rf tuning elements for superconductor-insulator-superconductor (SIS)
quasiparticle mixers at frequencies near 630 GHz. These SIS mixers
provide near quantum-limited sensitivity throughout the millimeter wave
band [1-3], provided they are optimized with an appropriate rf embedding
circuit. The large geometrical capacitance Cj of the tunnel junction
provides a susceptance which shunts the rf signal away from the nonlinear
quasiparticle conductance channel. An open-circuited superconductive
microstrip transmission line (stub) can provide a parallel inductance to
resonate with the junction capacitance. This approach was first used
successfully with an SIS mixer operating near 36 GHz [4] and since has
been used at frequencies up to 360 GHz [5,6]. However, above 100 GHz,
uncertainties in material, transmission line, and junction parameters
generally lead to poor performance.
Page 364 Third International Symposium on Space Terahertz Technology
The phase velocity must be accurately known in order to correctly
design the microstrip stub for a particular application. At high
frequencies possible dispersion and loss are expected to degrade the
performance. It is thus important to know the frequency range at which
these effects become significant. Other groups [7,8] have measured short-
pulse propagation on superconductive coplanar transmission lines using
optical sampling techniques and indirectly determined loss and dispersion
from a Fourier transform analysis of the pulse distortion.
We have taken a different approach, using a Josephson junction as
both a sweep-oscillator and detector to sample the resonances of a
microstrip stub. This stub is connected in parallel across the junction as
shown in fig. 1. The ac Josephson effect provides a voltage-controlled
oscillator. The frequency is 2eVyh = 0.485 x Vb (u.V) GHz where \A> is the
junction bias voltage. This monochromatic signal sets up a standing wave
in the stub. The junction detects this standing wave and a signature is
developed in the DC current-voltage (I-V) curve of the junction by a
frequency downconversion process. As the bias voltage, and thus frequency
is swept, small current steps will appear in the DC I-V curve of the
junction at frequencies corresponding to the modes of the stub. The
Third International Symposium on Space Terahertz Technology Page 365
frequency spacing of the modes is given by Af = v^/21 where v$ is the
phase velocity and / is the physical length of the stub. Thus by measuring
the voltage interval between steps, the phase velocity can readily be
obtained if it is constant over this interval. In general, this technique can
be used at high frequencies well above the energy gap frequency fg. A
similar approach using microstrip resonators with a single resonance
below fg has recently been reported [9]. Values of surface resistance and
phase velocity were determined up to about 400 GHz. We have used long
microstrip resonators with many high order modes to determine the phase
velocity as a function of frequency up to 800 GHz, which is above the gap
frequency of niobium (Nb). The onset of dispersion has clearly been
observed.
High quality Nb / AI-AlOx / Nb tunnel junctions are fabricated using
a trilayer process [10]. The junction area, defined by electron-beam
lithography, is between 0.3u.2 and 1u,2. The DC sputtered Nb films are 2000 -
3300 A thick. The current density is as high as 104 A/cm2 and the normal
state resistance is 50Q. - 70Q. SiOx serves as both a planarization layer
for the junction trilayer and the dielectric layer for the microstrip stub.
Page 366 Third International Symposium on Space Terahertz Technology
The thickness is td » 1500A and the dielectric constant is taken to be er =
5.5 [11]. The dielectric thickness is comparable to the magnetic
penetration depth. In this case, the phase velocity is « c and hence is
strongly affected by the field penetration into the Nb. This makes v$ a
sensitive probe of the superconductive properties of Nb.
Junctions fabricated for use as SIS mixers have stubs 2ji wide by
60u, - 70u, long to provide a fundamental broad band resonance near 630
GHz. However, to study the phase velocity, junctions were fabricated with
stubs 2ji wide by 518u, or 1064u. long. A longer stub gives a smaller
spacing between resonant modes, thus providing a better indication of the
phase velocity in a given frequency range. Careful examination of these
stubs however, indicated jagged edges and undercutting of the SiOx.
Additional junctions were fabricated with stubs 6u, and 12u, wide to
reduce uncertainties due to these edge effects. These stubs were either
500u,, 750{i, or 1000|i long.
The fundamental resonance frequency of a 1000u, long stub is
estimated to be about 50 GHz [4]. This leads to steps in the I-V curve
which are =0.1 mV apart. The inset of fig. 2 shows one example. The
Third International Symposium on Space Terahertz Technology Page 367
subgap conductance of this junction is very large with an almost point-
contact type of appearance. While junctions with much lower subgap
conductance also showed resonant peaks, the step structure was seen
mostly in junctions similar to that shown in fig. 2. An external magnetic
field was used to enhance the steps in different voltage ranges [12]. In
order to accurately locate these small steps in current, a small amplitude,
low frequency ( ~ 200 Hz ) ac voltage was superimposed on Vt,. The
resulting ac signal was detected with a lock-in amplifier. The interval
between two adjacent peaks is then measured to determine v$ which is
plotted as a function of the frequency of the higher step. Due to the
discreteness of the data, the resolution for changes in velocity is the
frequency spacing of the modes. Figure 2 shows the results for 4 different
microstrip stubs. About 10 to 14 resonances were observed between 50
GHz and ~ 750 GHz. A smooth curve was drawn through the resulting
velocity vs frequency data. The scatter in velocity values about this curve
is typically 5%, with only a few points deviating by ~ 10%.
Curve 1 is an example of a junction with a 2|i wide stub. Resonances
of these narrow stubs were usually not observable above about 500 GHz.
This may be due to increased scattering or losses from the edge effects
Page 368 Third International Symposium on Space Terahertz Technology
mentioned earlier. Curves 2, 3, and 4 represent stubs 1000p. long with
widths of 6u. or 12u,. At low frequencies, a slight curvature can been seen
in the data as expected from the mode spacing (see discussion below).
Otherwise the curves are horizontal up to about 500 GHz where they begin
to bend down indicating the onset of dispersion. The gap frequency of a
pristine Nb film is fg ~ 740 GHz at OK. Thus the dispersion begins at
frequencies well below fg. This agrees with previously reported results [8]
using an optical sampling technique. While SIS mixers are predicted to
operate well up to fg [13], the resonant embedding circuit utilizing
superconductive microstrip transmission lines is limited to lower
frequencies.
Figure 3 shows the data for a SOOji long x 12ji wide stub. In this
case, resonances, and hence the phase velocity, were obtained up to =
SOOGHz which is above the gap frequency of Nb. At low frequencies, the
velocity is dispersionless. Around 500 GHz, the velocity begins to
decrease and reaches its lowest value near 730 GHz. For this data point,
the frequency resolution for velocity change is about 50 GHz. This
minimum is expected theoretically to occur near 770 GHz (see fig. 3) using
a gap frequency of 660 GHz as determined from the I-V curve of this
Third International Symposium on Space Terahertz Technology page 359
junction at zero magnetic field (a more complete discussion of the theory,
will be given in the future [14]). In addition, we have observed a small
suppression of the energy gap with external magnetic field in these
junctions which may describe the lower frequency of the observed phase
velocity minimum. Other loss mechanisms may also play a role. The
velocity begins to increase above 730 GHz as is expected theoretically,
since the superconductor begins to behave as a normal metal for
frequencies well above fg. The solid line in fig. 3 is the theoretical
prediction for the velocity. We have used the approach followed by Kautz
[15] which employs the Mattis-Bardeen [16] theory for the electrical
conductivity. The magnetic penetration depth was adjusted to X = 900A to
fit the theory to the low frequency asymptote of the velocity. As seen
from fig. 3, theory and experiment show the same general trend. However,
based on the Mattis-Bardeen conductivity, the theory predicts a 9%
decrease in velocity at the dip whereas the experiment shows a 35% dip.
Errors in velocity resulting from uncertainties in the mode spacings can
result from end effects on the microstrip line and the possibility of a
negative resistance loop in the I-V curve at the position of the resonance
[17]. However for our geometry, the end-effect correction to the length is
« 1%, and the worst-case negative resistance, predicted for a lightly-
Page 370 Third International Symposium on Space Terahertz Technology
damped resonance, could only cause a 5% shift in the apparant position of
the resonance. Thus neither effect can account for the large change we
observe. At low frequencies, superconductive microstrip is a slow-wave
transmission line due to the penetration of the electromagnetic field into
the superconductor over a length comparable to the thickness of the
dielectric. For frequencies well above fg> the phase velocity increases
towards the value for a normal line. The onset of dispersion just below
the gap frequency is due to the departure of the imaginary part of the pair
conductivity from a 1/f frequency dependence [15].
Some additional insight may be gained by first considering a
Josephson junction directly coupled to a lossless microstrip stub. Using
the notation in reference [18], the resonant frequencies of the stub are
solutions to the transcendental equation
-L -ten(-=£-) ' (1)
s fs TS
where Cs = e reo/w/td is the total capacitance of the stub and fs is the
fundamental mode of the stub. This mode occurs when the length of the
Third International Symposium on Space Terahertz Technology Page 371
stub,/, equals one wavelength and is given by fs = v^ / 21.
In fig. 4 both sides of eqn. (1) are plotted vs (f/fs) for an arbitrary
value of Cj/Cs- At low frequencies, intersections between the straight
line ( left hand side of eqn. 1) and the tangent curves are between (m-
1/2)fs and mfs where m is an integer. These solutions move progressively
toward (m-1/2)fs for m » 1. Thus at high frequencies, the solutions of
eqn. (1) (i.e.: the modes of the stub) are equidistant. If plotted in the spirit
of fig. 2, they represent a horizontal line.
We have extended eqn. (1) to the case of a lossy transmission line,
yielding
s
 i -o/ cos(
's
where a is the attenuation constant. In fig. 4, the right hand side of eqn.
Page 372 Third International Symposium on Space Terahertz Technology
(2) is plotted for three arbitrary cases of loss: a/ = 0.05, 0.10, and 0.15.
As can be seen, the distance between the solutions first decreases and
then increases as losses in the microstrip line increase. In light of this,
our experimental observations can be interpreted as evidence for
increased loss in either the superconductor or the dielectric layer. Losses
due to radiation will be negligible given the cross sectional dimensions of
the stub, 0.15ji x 12ji, compared to relevent free space wavelengths, X0 ~
SOOu. [19]. It is expected that absorption of water in evaporated SiOx
films could contribute losses at microwave and millimeter wave
frequencies. Losses due to absorbed water molecules constitute broad
peaks in the frequency domain. The attenuation of a microstrip line is
linearly proportional to frequency provided the loss in the dielectric is
frequency independent. A linear dependence is much weaker than the sharp
increase in attenuation expected near the gap frequency. Moreover, since
we observe a strong dispersion near the Nb gap frequency, the
superconductors are the most probable source for the losses. The
superconducting electrodes of the microstrip line are not perfect, defect
free, bulk crystalline materials, but are polycrystalline thin films with
fine grains and possibly surface layers and interface defects. These
Third International Symposium on Space Terahertz Technology Page 373
microstructural features of real films may be responsible, in part, for the
large dispersion we observe.
In summary, we have presented evidence for the onset of dispersion
and loss at submillimeter wave frequencies in Nb-SiOx-Nb microstrip
transmission lines. This behavior is expected at frequencies approaching
the gap frequency, but the range over which Nb microstrip lines are
dispersionless was previously not well known. These results will have a
direct impact on the application of Nb microstrip lines in millimeter wave
and submillimeter wave circuits. For operation near 1 THz, higher
temperature superconductors such as NbN or NbCN will have to be
investigated.
This work was supported in part by the Jet Propulsion Laboratory,
California Institute Of Technology, under contract to the National
Aeronautics and Space Administration and the Innovative Science and
Technology Office of the Strategic Defense Initiative Organization.
Page 374 Third International Symposium on Space Terahertz Technology
REFERENCES
1. C.A. Mears, Q. Hu, P.L. Richards, A. H. Worsham, D.E. Prober, and A.V.
Raisanen, Appl. Phys. Lett. 57, 2487 (1990).
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LeDuc, Digest, 15th. Int. Conf. on IR and Millimeter Waves, p.245, Orlando,
FL (1990).
3. B.N. Ellison, P.L Schaffer, W. Schaal, D. Vail, and R.E. Miller, Int. J. IR and
mm Waves 10, 937 (1989).
4. A.V. Raisanen, W.R. McGrath, P.L. Richards, F.L. Lloyd, IEEE Trans. Microwave
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5. Q. Hu, C.A. Mears, P.L. Richards, and F.L. Lloyd, IEEE Trans. Magn. 25, 1380
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IEEE Trans. Magn. 27, 2650 (1991).
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8. C.C. Chi, W.J. Gallagher, I.N. Duling III, D. Grischkowsky, N.J. Halas, M.B.
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Superconductivity 1, 145 (1991).
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0. H.G. LeDuc, B. Bumble, S.R. Cypher, and J.A. Stern, submitted to 3rd.
International Symposium on Space Terahertz Technology, University of
Michigan, Ann Arbor, March 1992.
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Page 376 Third International Symposium on Space Terahertz Technology
FIGURE CAPTIONS
Figure 1. (a) Geometry of open-circuited microstrip stub and Josephson
junction, (b) Cross sectional view of stub and junction.
Figure 2. Phase velocity vs. frequency for four different Nb microstrip stubs
at 4.2K. The stub dimensions are 1: 2u, x 1064u.; 2: 12u. X 1000u,; 3: 6u. X
1000|i; 4: 6u, X 1000^. Inset shows current steps in DC IV curve
associated with high order modes in the stub.
Figure 3. Phase velocity vs. frequency for a Nb stub 12ji wide X SOOu, long. The
different symbols refer to data taken with different applied external
magnetic fields. The solid line is the theoretical prediction. The arrow
indicates the gap frequency as determined for the Nb junction (at zero
magnetic field) which is used in the calculation.
Figure 4. Graphical representation of both sides of the transcendental eqns (1)
and (2). X-axis is frequency normalized to fs (fundamental resonance of
the stub). Straight line is a plot of the left hand side of eqns (1) and (2)
with arbitrary slope. Right hand side of eqn (1) is represented by tangent
Third International Symposium on Space Terahertz Technology Page 377
curves while right hand side of eqn (2) is plotted for values of a/ = 0.05,
0.10, 0.15. Intersections of the straight line and the tangent curves
represent the modes of the stub. When losses are significant ( a/ > 0 ), the
mode frequencies are determined by the closest approach of the two
curves as indicated by the arrows.
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Onset of dispersion in Nb microstrip transmission lines at submillimeter wave frequencies

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