Metallic coplanar resonators optimized for low-temperature measurements
Mojtaba Javaheri Rahim1, Thomas Lehleiter1, Daniel Bothner2, Cornelius Krellner3, Dieter
Koelle2, Reinhold Kleiner2, Martin Dressel1 and Marc Scheffler1
1
1. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
Physikalisches Institut and Center for Quantum Science in LISA+, Universität Tübingen, 72076 Tübingen, Germany
3
Institute of Physics, Goethe University Frankfurt, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
2
Abstract Metallic coplanar microwave resonators are widely employed at room temperature,
but their low-temperature performance has received little attention so far. We
characterize compact copper coplanar resonators with multiple modes from 2.5 to
20 GHz at temperatures as low as 5 K. We investigate the influence of center
conductor width (20 to 100 µm) and coupling gap size (10 to 50 µm), and we observe
a strong increase of quality factor (Q) for wider center conductors, reaching values up
to 470. The magnetic-field dependence of the resonators is weak, with a maximum
change in Q of 3.5% for an applied field of 7 T. This makes these metallic resonators
well suitable for magnetic resonance studies, as we document with electron spin
resonance (ESR) measurements at multiple resonance frequencies.
Keywords: Microwave spectroscopy, Coplanar resonators, Low temperature electron
spin resonance
liquid nitrogen temperatures [5]. We have optimized
the parameters of metallic CPW microwave
resonators for low-temperature use and present the
results in this paper.
1. Introduction Coplanar waveguides (CPWs) from superconducting
[1, 2] and metallic (non-superconducting) materials
[3-5] are widely used in microwave transmission
lines. Since conductor strip and ground planes are on
the same side of the substrate, they can be easily
adapted to active/passive components. For these
reasons CPWs are suitable for classical engineering
applications such as sensors [6] and filters [7] as well
as new modern physics experiments like cold atoms
current traps [8] and quantum information processing
[9]. The electric and magnetic energy of the carrying
signal can be efficiently coupled to the surrounding
medium, and by proper design these fields can have
the desired orientation. These characteristics are
prerequisites for, e.g. electron spin resonance (ESR)
experiments [10]. CPW resonators can support
multiple resonances, and CPW devices with
miniaturized size can be employed in the mK
temperature range experiments using dilution
refrigerators [9, 11-15]. These points become
important when the electronic and magnetic properties
of a material have to be characterized as a function of
temperature, frequency and magnetic field. There are
no reports explicitly exploring the performance of
metallic CPW resonators at temperatures lower than
2. Experimental In the functionality of a typical planar resonator, the
most decisive factors are coupling gaps [16, 17],
center conductor width [18, 19], film quality and edge
sharpness [20, 21], ground plane size and packaging
effects [22], effective permittivity (εeff) [4] and
meander line dispersion [23, 24]. Coplanar resonators
can be designed based on these theoretical
considerations, but resonator optimization for new
applications often involves additional testing and
tuning of design parameters of the actually fabricated
devices, such as presented in this work. Since we are
mainly interested in low-temperature experiments, our
CPW resonators were characterized at temperatures
down to 5 K. We designed, fabricated and measured
several sets of resonators (characteristic impedance 50
Ω) from 2.5 to 20 GHz at temperatures down to 5 K.
All resonators were designed as open-ended half wave
(λ/2) resonators for their fundamental frequency
(consequently, the “mode n” of the series of harmonic
resonance frequencies is expected when the
1 conductor (and the ground planes), and the residual
resistivity by which we can reach higher quality
factors at low temperatures. Low-loss polished
sapphire (εr≈10.5 [26], thickness 430 µm) was used as
substrate. For the sputtered resonators it was covered
with 1 µm copper film (resistivity ρ5K=0.0510 µΩcm,
residual resistance ratio RRR≈29, skin depth δ5K,2.5GHz
≈227 nm) with a 5 nm chromium buffer layer.
Standard UV photolithography and Ar-ion beam
etching processes were used to form the resonators. In
the case of the electroplated resonators, the photolithography was first performed on a 50 nm
evaporated copper film with 5 nm chromium buffer
layer. Afterwards the structure was placed in an
electroplating bath to grow a 1 µm copper film
(ρ5K=0.0415 µΩcm, RRR≈50, δ5K,2.5GHz≈205 nm).
After removing the resist, Ar-ion beam etching
removed the 50 nm copper film and the buffer layer
between the center conductor and the ground planes.
relationship L = nλ/2 is fulfilled where L is the center
conductor length), and they are capacitively coupled
to input and output CPWs via two identical gaps.
Figure 1(a)-(c) show schematically the structure and
the geometrical parameters of the chips. The
miniaturization of the resonator size is necessary with
regard to the small volumes of the samples which are
supposed to be investigated via the resonators. In
order to reach high filling fraction of the sample
volume with respect to the resonator mode volume,
the center conductors of the resonators were meanderlike folded as depicted in figure 1(a); with the length
of L=2.55 cm, expecting a fundamental mode (first
mode) of 2.5 GHz. In addition, the small size
facilitates implementation in superconducting
magnets and/or dilution refrigerators.
Table 1. The geometrical parameters of the fabricated
resonators according to figures 1(a)-(c): W is the width of
the center conductor, S denotes the distance between the
center conductor and the ground planes, G indicates the gap
size, D is the inner diameter of a turn. “10:50” means 10,
20, 30, 40 and 50 µm.
W
(µm)
20
40
60
80
100
Figure 1. (a) The meandered structure of the fabricated
CPW resonators. The orange parts show the metallization
(copper). The geometrical parameters are shown in the
enlarged sketches of (a), (b) and (c). G stands for the
coupling gaps, W is the center conductor width, S shows the
distance between the center conductor and the ground
planes, and D is the width of the ground plane between two
adjacent lines of the meander structure. The photograph (d)
shows the brass box in which a CPW resonator chip is
placed. The SMA connectors guide the microwave signal
into and out of the resonator. (e) Temperature dependence
of the fundamental mode of an electroplated resonator with
W=60 µm and G=40 µm. (Inset) Resonance frequency vs.
temperature.
G
(µm)
10:50
10:50
10:50
10:50
10:50
D
(µm)
264
226
190
240
300
D
W+2S
≈7.33
≈3.14
≈1.76
≈1.67
≈1.67
Chip Size
(mm2)
3×4
3×4
3×4
6×10.5
6×10.5
Resonators of W=20 to 60 µm were fabricated all
together on a single piece of sapphire; the same was
done for the resonators of W=80 and 100 µm. The
processed chips were placed in especially designed
brass boxes shown in figure 1(d). Standard SMA
connectors were connected to the chips in the box by
H20E-FC EPO-TEK® conductive adhesive. The chip
sizes (box sizes) were kept small to shift parasitic
modes to higher frequencies (4×7 mm2 for W=20 to
60 µm and 6×10.5 mm2 for W=80 and 100 µm).
Table I shows the indicated dimensions and distances
in figures 1(a)-(c) for each set. The ⁄
2 ratio
is bigger than 1 for all the sets which is enough to
neglect the ground plane width effect on the
characteristic impedance [25]. The resonators were
fabricated either from a sputtered copper film
(“sputtered resonators”) or by a copper electroplating
process (“electroplated resonators”). The comparison
between the sputtered and electroplated resonators
provides information about the influence of the
surface roughness, the edge quality of the center
3. Results and Discussion
The microwave measurements were performed by
utilizing an Agilent® microwave source and power
meter. With a Janis® helium flow cryostat we reach
temperatures down to 5 K. The loaded quality factors
⁄Δ where fr is the
were calculated by
resonance frequency and Δf is the half power
2 S
(µm)
8
16
24
32
40
bandwidth of the resonance signal. All the Q values
quoted throughout this article are loaded quality
factors, which approximately equal the internal
quality factors of our resonators.1
The fundamental frequency of the resonators slightly
shifts up by increasing W+2S (from ~2.60 GHz for
W=20 µm and S=8 µm to ~3.15 GHz for W=60 µm
and S=24 µm). This is due to the decrease of effective
permittivity (Ԑeff) by increasing W+2S [3, 4, 22, 25].
The fundamental for both W=80 and 100 µm are ~3
GHz. The thickness in these cases is about 100 nm
lower (compared to those with W=20 to 60 µm) which
causes Ԑeff to increase and thus the fundamental mode
is below ~3.15 GHz (of W=60 µm) [3, 4]. The
temperature dependence of the resonance frequency is
plotted in figure 1(e); the rightward shift of the
resonance frequency upon cooling has several
reasons: (i) thermal contraction, (ii) Ԑeff of CPW
decreases in absolute value as the conductivity of the
metallic conductor increases [3] and (iii) the relative
permittivity of sapphire substrate decreases with
lowering the temperature [26]. When the resonator is
cooled down, the quality factor increases
significantly: at liquid nitrogen temperatures Q is
more than 2.5 times the room temperature value and it
can reach an enhancement of almost a factor of 4
upon further cooling as shown in figures 2(a) and (b).
This increase of the quality factor comes to a halt
around 20 K because the residual-resistance regime,
in which the resistivity of the copper film is governed
by defects and does not decrease by further lowering
the temperature [27], is reached.
Figure 2. Temperature (a, b) and frequency (c, d)
dependence of the quality factor Q for different resonator
modes and structures. The first three modes of an
electroplated resonator with W=40 µm and G=40 µm (a),
and W=60 µm and G=40 µm (b) exhibit increasing Q upon
cooling with saturation in the residual-resistance regime.
The quality factor for different modes of (c) electroplated,
and (d) sputtered resonators with W=60 at 5 K. The legend
refers to the G values.
metallic CPWs, where the losses should
monotonously increase with increasing frequency,
leading to a monotonous decrease of Q. The reason
behind the observed non-monotonic behavior might
be found in the details of the meander structure, but a
thorough understanding might require additional
studies. Similar observations have been reported
previously on aluminum CPW resonators of much
larger dimensions and at room temperature [30].
Figure 3 displays the quality factor values for the
modes 2 and 3 of all the resonators. The values of
between ~300 (W=60 µm and G=10 and 30 µm) and
470 (W=100 µm and G=20 and 40 µm) are the highest
values observed for a metallic CPW resonator with
narrow center conductor widths of 60 to 100 µm. We
reach Q=120 at room temperature for a resonator with
W=100 µm and G=20 and 50 µm. As far as the design
parameters of the resonator are concerned, the center
conductor width W clearly is the most relevant in
obtaining high Q values; we did not observe a
pronounced dependence on G or ⁄
2 .
Microwave losses in metals are supposed to grow
with frequency; thus for the higher modes a lower
quality factor is expected. However, for example for
the resonators of W=60 µm, independent of the G
values and fabrication method, the highest Q values
are observed at the 3rd mode (~8.4 GHz); see figures
2(c) and (d). Such behavior is found in all five sets of
resonators, i.e. mode 2 (~5 GHz; for W ≤ 40 µm) or
mode 3 (~8 GHz; for W ≥ 60 µm) have the highest Q
values. This is in contrast to basic considerations of
1
The measured, loaded quality factor QL is a combination
of internal and external quality factors, Qint and Qext,
respectively [28]:
. Considering the coupling
The sputtered resonators have slightly higher Q compared to the electroplated resonators, although the
sputtered films have a higher residual resistivity. The
higher Q values of the sputtered resonators can be
explained by the lower surface roughness of the
capacitance of our resonators (which amounts to
approximately 10 fF for the extremal case of G=10 µm for
W=100 µm) [29], we expect Qext well above 20000 for all
studied resonances, which is much higher than the measured
QL, and therefore we can neglected Qext with respect to Qint. 3 have already been employed for ESR experiments
[15, 36-46]. Although microstrip and stripline
resonators have also been successfully applied in ESR
measurements [36-38, 41, 45, 47], coplanar
configurations might be more appropriate candidates
since they carry the signal non-dispersively in contrast
to a microstrip configuration [45, 48].
Superconducting planar resonators can be
substantially limited by their critical fields [26, 35],
and broadband transmission line structures [15, 44]
have limitations in sensitivity. In order to test whether
our metallic CPW resonators can be employed for
ESR experiments, a 2,2-diphenyl-1-picrylhydrazyl
(DPPH) sample (200×100 µm2) was placed on the
middle of the resonator meander line and fixed by a
small amount of vacuum grease. The obtained ESR
lines are plotted in figure 5(b); here we plot the
change in Q (i.e. QB-QB=0) vs. relative magnetic field
(B-BResonance) for various resonance fields (depending
on frequency). We measured the resonator
transmission at each magnetic field while keeping the
temperature constant at 5 K in a cryostat equipped
with a superconducting magnet. As expected, the
higher intensity of the ESR signal is observed at the
higher field/frequency. The extra peaks on the sides of
the ESR signals are due to the narrower ESR line
width than the resonator line width.
Figure 3. The enhancement of Q by widening the center
conductor plotted for mode 2 (a), and mode 3 (b) at T=5 K.
The different symbols refer to different G values and films
as indicated.
sputtered films compared to the electroplated films
(13 nm vs. 60 nm from AFM) and could also be due
to the better edge definition [21]. The sharper and
straighter line edges in the sputtered resonators are
displayed in the SEM images of figure 4. The
redeposited thin raised walls (non-removable by
ultrasonic vibration) during the ion milling process on
the edges of the sputtered lines [31] makes it difficult
to discuss the edge definition role in the achieved
higher Q.
Many physical experiments for which CPW structures
are utilized, e.g. ESR studies, have to be performed in
the presence of an external magnetic field. Therefore,
we studied the influence of an external static magnetic
field on our resonators.
We have performed another series of the ESR
experiment on the heavy fermion compound,
YbRh2Si2 (3 × 4 mm2); a rare example where an ESR
investigation of the Kondo ions’ spin dynamics is
feasible [49]. ESR studies have already been done on
this material using conventional and superconducting
planar resonators [45, 49]. In figure 5(c) we plot the
ESR lines obtained at 1.7 K for two different
resonance fields. The lines exhibit a Dysonian shape
typical for metals. The deeper lines at higher
resonance fields/frequencies demonstrate the higher
intensity of the ESR signals as already anticipated.
Figure 4. SEM images of (a) an electroplated line edge, and
(b) sputtered line edge. Panel (c) shows the upraised edges
on both the center conductor and the ground plane of a
sputtered resonator.
4. Conclusion Figure 5(a) shows the relative change of Q in a
magnetic field applied in the plane of the resonator,
parallel to the meander lines [see the inset of figure
5(a)]. Even at fields as high as 7 T, the reduction in Q
is less than 3.5% for all the modes, in contrast to the
massive suppression of Q in magnetic fields typically
found in superconducting resonators [28, 32-34]. The
observation
can
be
explained
by
the
magnetoresistance of copper at higher fields [35].
Planar structures (microstrip, stripline and coplanar)
In conclusion, we have characterized, improved, and
utilized miniaturized metallic CPW resonators for
cryogenic measurements. Significant improvement of
the quality factors is realized by cooling down the
resonators to liquid helium temperatures; we reached
Q values as high as 470 whereas the miniaturized size
of the resonators limited the center conductor width
not to be wider than 100 µm. Compared to the
electroplated resonators, lower surface roughness and
4 physics of exotic behavior of materials such as
YbRh2Si2 [45, 50, 51].
Acknowledgements This work was supported by the Deutsche
Forschungsgemeinschaft (DFG), including SFB/TRR
21, and by the EU-FP6-COST Action MP1201. The
authors thank Gabriele Untereiner for technical
support, Ali Tavassolizadeh for providing the
sputtered films, Rainer Stöhr and Roman Kolesov for
support with the electroplating, and Harald Giessen
for access to the cleanroom facilities.
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Figure 5. (a) Normalized Q values decay at external
magnetic field. The data are taken at T=5 K with the
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