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IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 17, NO. 2, JUNE 2007
Superconducting Quantum Interference Filters as
RF Amplifiers
Oleg V. Snigirev, Maxim L. Chukharkin, Alexey S. Kalabukhov, Michael A. Tarasov, Anatoly A. Deleniv,
Oleg A. Mukhanov, and Dag Winkler
Abstract—The superconducting Quantum Interference Filter
(SQIF) is a new type of superconducting device which has been
recently proposed for highly sensitive magnetometers for absolute
magnetic field measurements. It benefits of very high voltage-tofield response, which is, in contrast conventional dc SQUIDs,
not periodical. The SQIF can also be used as a radiofrequency
amplifier in a similar way as the dc SQUID that can operate in
a gigahertz frequency range. We designed a series type of SQIF
amplifier that is compatible to conventional YBa2 Cu3 O7 (YBCO)
technology on bicrystal substrates. We present analytical, numerical and scale modeling as well as first electrical measurements
results at frequencies up to 10 GHz. The SQIF array consists of
50 loops with randomly distributed areas from 0.5 to 1.5 times of
30 m2 . We also compared it to the regular array of con3
ventional SQUIDs with the same loop areas. We have additional
dc contacts to each 5-th SQUIDs and the SQIFs for control and
comparison. Devices are fabricated using Josephson junctions
with 3 m width formed in YBCO over 24/24 and 12/12 degrees
grain boundaries in yttrium-stabilized zirconia (YSZ) bicrystal
substrates.
Index Terms—High-temperature superconductors, microwave
amplifiers, SQUIDs.
results have been obtained for SQUID with microstrip input
coil at frequencies up to 1 GHz. At a temperature of about 0.1 K
was found close to 50 10 mK at
the noise temperature
frequency 0.5 GHz [6]. This noise temperature is about 40 times
lower than that achievable by cooled semiconductor amplifier.
Typical values of gain are close to 20 dB for frequencies
below 1 GHz and drop to 10–12 dB for frequencies 1–4 GHz [5],
is approximately equal to
, where is the de[7], and
vice physical temperature. However, at higher frequencies about
8 GHz the measured gain of the microstrip SQUID decreases
to 6 dB [7]. The main reasons for decreasing of gain the most
, of used
probably can be low characteristic voltages,
Josephson junctions (between 100 and 200
)
and the decreasing coupling of the signal to interferometer.
A rough estimation of the maximum power gain for the
SQUID as a parametric amplifier is given by the ratio between
and signal
Josephson characteristic frequency
:
frequency
(1)
I. INTRODUCTION
S
UPERCONDUCTING quantum interference filters
(SQIFs) have been proposed to significantly improve
the voltage-to-magnetic-field transfer factor in comparison to
conventional superconducting quantum interference devices
(SQUIDs) [1], [2]. It has also been suggested that the performance of the SQIF is weakly dependent on the parameter spread
of Josephson junctions [3]. This all makes SQIFs attractive for
applications of high-temperature superconductors. Recently,
radiofrequency amplifiers based on both low- and high-Tc dc
SQUIDs have been proposed and realized [4], [5]. Remarkable
Manuscript received August 29, 2006; revised August 29, 2006. This work
was supported by the CRDF RUE1-1610-MO-05. This work relates to Department of Navy Grant N00014-06-1-4056 issued by the Office of Naval Research
Global. The United States Government has a royalty-free license throughout the
world in all copyrightable material contained herein.
O. V. Snigirev is with the Department of Physics, Moscow State University,
199899 Moscow, Russia (e-mail: Oleg.Snigirev@phys.msu.ru).
M. L. Chukharkin is with the Department of Physics, Moscow State University, 199899 Moscow, Russia.
A. S. Kalabukhov, A. A. Deleniv, and D. Winkler are with the Department of
Microelectronics and Nanoscience, Chalmers University of Technology, S412
96 Goteborg, Sweden.
M. A. Tarasov is with the Institute of Radio Engineering and Electronics,
RAS, Mokhovaja 11-7, 101999 Moscow, Russia.
O. A. Mukhanov is with the HYPRES, Inc., 175 Clearbrook Road, Elmsford,
NY 10523 USA.
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TASC.2007.898032
is the flux quantum. If one applies Equation (1) to exhere
perimental data in papers [5] and [7], a remarkable agreement
can be found.
II. AMPLIFIER DESIGN
A. Coupling at Microwaves
A desired high gain of an amplifier requires a considerable
circular current flowing in the SQUID loop at the signal frequency, which in turn will provide a high parametric conversion
in the SQUID junctions and, thus, a signal amplification. While
for the high-Tc SQUIDs it is cumbersome to couple the high frequency signal using multi-turn microstrip coil, another approach
with resonant coupling has been suggested recently [8]. In this
work, high-Tc dc SQUID was coupled to a slot-line input circuit. In this case input coil is a part of the SQUID loop and thus
mutual inductance is less than SQUID inductance. In the frame
of classical approach one can find that power gain for single interferometer is given by the following equation:
(2)
is the SQUID dynamic resistance and
represents
where
the dissipation in the input circuit and can be determined from
the input circuit quality factor, . When the mutual inductance
is low, the amplification of the single SQUID also decreases,
identical
but it is possible to recover it by using an array of
SQUIDs or randomly scattered-area interferometers (SQIF).
1051-8223/$25.00 © 2007 IEEE
SNIGIREV et al.: SUPERCONDUCTING QUANTUM INTERFERENCE FILTERS AS RF AMPLIFIERS
719
Fig. 2. Calculated S-parameters of the SQIF amplifier with N = 50 and gold
input coil.
Fig. 1. The layout of the series array of 50 randomly scattered interferometers.
Slot line is patterned in normal metal (200 nm-thick gold layer) deposited over
the 400 nm thick SiO isolation layer.
B. SQIF Design
At a frequency of 5 GHz, the free space wavelength is 6 cm,
and for SiO as the insulator with
, wavelength is close
to 3 cm. In order to avoid complex microwave electrodynamics,
, which means less
the length of array should not exceed
than 3.5 mm. In general, the SQUID amplifier gain, noise figure
and saturation temperature are improved with the increase of the
number of SQUIDs in the array, . But with increasing number
of elements in the array, the length of the entire structure also
limit. For
,
increases and can easily exceed the
the total array length is 1.5 mm and appears to be a reasonable compromise between technological and electrodynamical
requirements.
The SQUID amplifier should also be matched with input and
output 50 transmission lines. Hence, the dynamic resistance
of the SQUID should also be close to 50 . Because of this
we used the series array of SQUIDs. However, the series array
may be more sensitive to the parameter spread of the Josephson
junctions than the parallel SQIF [3].
The layout of the series array of 50 randomly scattered interferometers is shown in Fig. 1. Signal coupling in simplest test
case was done using a slot line patterned in normal metal (200
nm-thick gold layer) deposited over the 400 nm thick SiO isolation layer. The slot line is closed at the end of the SQIF structure, thus acting as a closed coil at low frequencies.
C. Microwave Simulations
The Agilent RF Design Environment 2003C (RFDE Momentum) [9] was used to simulate the SQIF structure at
microwave frequencies. We assume that at frequencies of interest (1–10 GHz) the SQUID input impedance is real and close
, where is the Josephson junction normal resistance. A
to
50 load was connected to the array output. In the simulations,
was set to 10 .
The results of -parameters numerical calculations in the
range 1–8 GHz are shown on Fig. 2. The reflections are negli-
gible
dB , so the input power is dissipated in the
slot line matched to the array.
In order to estimate the power gain of the SQIF amplifier, it
, between the
is first necessary to find the mutual inductance,
slot line and partial interferometer. To do this, we inserted two
current probes in one of the interferometers and excited the slot
dBm source.
line input with the 1 mW
The variation of external flux in the single interferometer loop
, where
is the current flowing in the input coil.
is
is more
If the single interferometer normalized inductance
than one, the external flux is almost completely compensated
produced
by the interferometer self-inductance flux
by circulating current
. After that the estimation of
is
straightforward:
(3)
Using this estimation, it is possible to define now the maximum power gain. It turns out, that in the case of the slot line
coupling, the minimum voltage-to-flux transfer function of the
in order to provide power gain
SQIF should be at least 1
more than 1.
In our initial experiments we tuned input circuit for lower frequency of about 1–2 GHz to simplify the experimental setup and
to have the length of the input coil far away from the limitations
described in the previous section.
III. FABRICATION
Three test SQIF chips and one SQUID-array chip were fabricated on Y ZrO (YSZ) bicrystal substrates with 24 (12/12) degrees misorientation angle. Standard UV-photolithography and
dry etching were used. The junction width was 3 m on all
samples. The YBa Cu O (YBCO) thin films (200–250 nm)
were deposited on (100) YSZ mono and bicrystal substrates
with 12/12 degrees misorientation angles. Prior to the YBCO
film deposition a buffer layer of CeO was deposited at 790 C
in an 0.2 mBar oxygen atmosphere. The YBCO film was deposited in the same vacuum cycle at 780 C and at 0.7 mBar
oxygen pressure.
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IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 17, NO. 2, JUNE 2007
Fig. 3. Expanded dependence of SQIF output voltage vs. applied magnetic field
(T = 40 K).
Fig. 4. Comparison between responses of identical and scattered-area SQUID
arrays at T = 40 K.
We have optimized deposition conditions for both CeO
buffer layer and the YBCO film to obtain high critical parameters of the films. Investigation of crystalline structure of
films using X-ray diffraction (XRD) in – and -scan modes
showed absence of peaks due to other orientations of YBCO in
a-b plane. The CeO film has the expected 45 degrees in-plane
rotation. The surface of the films was examined by atomic force
microscopy. The typical roughness of the YBCO films does not
exceed 5 nm. The critical temperatures of the YBCO films are
K.
in the range 87–89 K with
IV. MEASUREMENTS
A. DC Characterization
DC electrical measurements were performed in the temperature range 4–77 K. The
, , and
of all structures were
measured. The magnetic response was measured using an external normal metal coil, and it shows a number of sharp maxima
instead of a single SQIF peak. This may be caused by the large
spread of the junction parameters. The critical current spread
and normal resistance scatter have been measured for selected
SQUIDs for two SQIF chips. It turns out that the ratio of mean
square variance of measured critical currents to its minimum
value was close to 30%.
Three reasons for the large spread in data have been suggested. At first, a spread of the width of junctions in arrays. The
critical current versus magnetic field dependence was measured
(see Fig. 3 for a set of junctions and indicated no spread in the
width spread).
Then the spread of the transport properties of barrier was examined. No square-root law correlation [10] was found between
the values of characteristic voltage of junctions and the critical
current density.
The last reason, which remains, is the spread of “working”
thicknesses of the junctions at the bicrystal boundary. This could
be caused by, e.g., an initial non-superconducting “dead” layer
in the vicinity of grain boundary on top of which a film with
good superconducting properties emerges.
In the course of our research an interesting observation has
been made. It turns out that developed technology keeps the
Fig. 5. SQIF pattern measured at T = 60 K.
in-plane dimensions of the structures to well defined values. In
this case, for an array of identical SQUIDs (SQIF-4), the period of voltage-to flux curve is single-valued, with a maximum
voltage swing comparable to an SQIF array, see Fig. 4. We note
that the flux-to-voltage transfer factor is the most important parameter for the amplifier performance. It does not matter how it
is obtained—whether in array of specially scattered SQUIDs, or
in an array of identical SQUIDs. However, the presence of periodic response can be a very useful feature in a practical amplifier. With the aim to verify this assumption, we deposited YBCO
films on high-quality SrTiO bicrystal substrate with 30 degrees
misorientation angle. We have seen that an array of SQUIDs fabricated on SrTiO bicrystal substrate has a much lower spread in
parameters of the partial junctions in the array (of about 20%).
As a result, a SQIF pattern appeared in critical current versus
magnetic field (see Fig. 5).
B. Microwave Measurements
The detailed description of our microwave measurement
setup has been done previously [11]. Briefly, to measure the
signal coupling at microwave frequencies, the SQIF amplifier
was bonded onto a teflon printed circuit board together with a
thermometer and a flux biasing coil. The board is placed inside
a metal box with SMA connectors. DC bias current was fed
SNIGIREV et al.: SUPERCONDUCTING QUANTUM INTERFERENCE FILTERS AS RF AMPLIFIERS
721
V. CONCLUSION
The main goal of this work was to implement and study
first time a YBCO Josephson junctions technology in SQIF
microwave amplifiers in order to enhance the power gain due
to the improved voltage-to-flux response of these Josephson
junctions. The main problems encountered were large spread
in the Josephson junctions parameters (much more than minimum modulation depth over partial SQIF elements) and the
complicated coupling to a microwave transmission line.
While the first problem solely lies in the bicrystal substrates
quality and is common to conventional SQUIDs, in which a
metal input coil fabricated on the top of high-Tc films introduces additional resistive losses. These losses can be reduced
by making the gold layer thicker.
We plan to address all these issues in our future work.
Fig. 6. Preliminary measured power gain for the SQIF amplifier at 40 K. This
data does not take into account the effects of additional circuit losses.
through an isolated bias tee, and the output signal was read out
by a cold low-noise amplifier with a noise temperature about
6 K. A calibration of the signal lines was done prior to the SQIF
installation. The -parameters were measured using a vector
network analyser.
Here we present very preliminary data on the frequency response of the SQIF amplifier. The maximum of the output on the
first sample signal turned out to be at somewhat lower frequency
than expected, about 100 MHz. The maximum difference between output power of the SQIF amplifier at optimum current
and flux biases, and at zero bias current, was 30 dB, as shown
on Fig. 6. After taking into account all additional circuit losses,
the actual power gain was not above 5 dB. We could not directly
measure reflection coefficient (S11) at the SQIF input because
of very large attenuation factor in the input line ( 80 dB). However, we believe that these losses are most probably located in
the input coil made of a thin gold film (about 200 nm). Currently
we are looking into this issue in order to improve coupling at
microwave frequencies.
ACKNOWLEDGMENT
The authors would like to thank Dr. Michael Mueck for
fruitful discussions and help in paper preparation.
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