Download Strip-shaped samples in a microwave Corbino spectrometer

REVIEW OF SCIENTIFIC INSTRUMENTS 78, 086106 共2007兲
Strip-shaped samples in a microwave Corbino spectrometer
Marc Scheffler,a兲 Serife Kilic, and Martin Dressel
1. Physikalisches Institut, Universität Stuttgart, 70550 Stuttgart, Germany
共Received 3 June 2007; accepted 18 July 2007; published online 15 August 2007兲
The Corbino geometry, where a flat sample is pressed against an open end of a coaxial cable, is an
established probe layout for broadband microwave spectroscopy. Here we show that besides the
conventional case of the sample covering the complete Corbino probe, also strip-shaped samples can
be studied with a Corbino spectrometer. This increases the sensitivity for highly conductive samples
and furthermore opens the route for the study of anisotropic materials. © 2007 American Institute
of Physics. 关DOI: 10.1063/1.2771088兴
In the study of metals and superconductors, two different
approaches are established for broadband microwave spectroscopy: the bolometric technique1 is well suited for superconductors due to its good sensitivity at low temperatures,
but it does not reveal phase information. On the other hand
there is the Corbino approach, where one measures the reflection coefficient of a planar sample pressed flat against the
open end of a coaxial line 共compare left part of Fig. 1兲. This
technique is established for more than ten years2 and has
been applied at cryogenic temperatures for the study of
superconductors,3 heavy-fermion metals,4 colossal magnetoresistive 共CMR兲 manganites,5 quantum-Hall systems,6 and
doped semiconductors.7 Furthermore, there are numerous experiments on dielectric samples using this geometry. The
Corbino approach is phase sensitive, i.e., can reveal the full
complex response. Since the sample properties are averaged
over all directions within the Corbino plane, crystallographic
directions cannot be distinguished. The absolute sensitivity is
typically limited because it is difficult to probe extremely
small losses. For this reason Corbino studies on conducting
materials have so far been limited to “poor” conductors5,7,8
when bulk samples are concerned, whereas good metals and
superconductors could only be studied as thin films.3,4
In a detailed study of our cryogenic Corbino spectrometer, we have shown recently that at this stage the sensitivity
for the measured reflection coefficient 共at low temperature兲
cannot be improved beyond 0.001.8 The only way to increase
the sensitivity in terms of the conductivity of metallic
samples is therefore to adjust the sample geometry toward a
sample impedance close to 50 ⍀, the characteristic impedance of the coaxial cable.8 For this reason, thin films are
preferred to bulk samples in the study of metals and superconductors. However, there are typical limits for the minimal
film thickness due to the film growth procedures.
Nevertheless there remain two sample dimensions that
can be tuned to optimize the sensitivity: radial 共i.e., inner and
outer diameters of the Corbino ring兲 and azimuthal 共with a
sample that does not cover the full 360° of the Corbino disk兲.
In the following we describe how changing these two dimensions can improve the sensitivity.
a兲
Present address: Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands; electronic mail:
[email protected]
0034-6748/2007/78共8兲/086106/3/$23.00
All samples studied here consist of 25 nm thick NiCr
thin films deposited onto sapphire substrates; these films
exhibit constant, purely real resistivity in the frequency range
discussed here, as seen in the inset of Fig. 2. For strip-shaped
samples, evaporation through metal shadow masks was
employed. Gold contact pads in Corbino geometry 共thickness
of 200 nm兲 were deposited on top of all samples. Microwave
measurements were performed at room temperature using
the spectrometer and calibration procedures described
previously.8
The properties of a Corbino disk are determined by its
inner and outer diameters. For thin films, the sample impedance ZCorb is given by
ZCorb =
ln共a2/a1兲
,
2␲t␴
共1兲
where t is the thickness of the film, ␴ the conductivity, and
a2 and a1 the outer and inner radii of the Corbino ring, respectively. While the impedance can be decreased dramatically for the study of insulators by making a1 and a2 almost
equal,6 an impedance increase with respect to conventional
dimensions is possible only in a limited range: a2 cannot be
larger than the outer diameter of the Corbino probe, and a1
has to be at least big enough to ensure good electrical contact
between the sample and the inner conductor of the Corbino
probe.
Within these ranges, the sample impedance can be tuned
by changing the diameters. Figure 2 shows the real part of
the impedance at an exemplary frequency of 5 GHz for
samples with Corbino contacts of different dimensions:
while the outer diameter is fixed at 1.75 mm, the inner diameter varies between 0.25 and 1.2 mm. The fit in Fig. 2
共dashed line兲 follows Eq. 共1兲 with the conductivity as the
only free parameter. The excellent agreement proves the
logarithmic dependence of the film impedance on the ring
dimensions. By going to rather small diameters of the inner
conductor, the sample impedance can be enhanced by a
factor of 2 with respect to the conventional geometry 共with
a1 = 0.8 mm兲.
In the azimuthal direction, a considerable increase of the
impedance is possible before reaching technological limits.
Here we switch from the traditional Corbino geometry,
where the sample covers the full 360° of the coaxial probe,
to a linear geometry, where a rectangular strip connects the
78, 086106-1
© 2007 American Institute of Physics
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086106-2
Rev. Sci. Instrum. 78, 086106 共2007兲
Scheffler, Kilic, and Dressel
FIG. 1. 共Left兲 Scheme of conventional Corbino geometry. 共Right兲 Stripshaped sample with Corbino contacts. The effective sample area is the dark
gray region.
inner and outer conductors of the probe only in two narrow
sections of the full Corbino disk, as indicated in the right part
of Fig. 1. Then the impedance Zstrip of the strip-shaped
sample is given by
Zstrip =
共a2 − a1兲
,
4tw␴
FIG. 3. 共Color online兲 Complex impedance Z = Re共Z兲 + i Im共Z兲 of 25 nm
thick NiCr strip samples with different strip widths, as stated in legend. The
full lines show experimental data; the dashed lines are fits. 共a2 = 1.75 mm;
a1 = 0.8 mm.兲
共2兲
where w is the width of the strip. The sample impedance can
thus be increased considerably by reducing its width.
A set of impedance spectra of strip-shaped samples with
varying width is displayed in Fig. 3. At very low frequencies,
where the impedance is basically the dc resistance, one can
clearly see how the impedance is tuned by changing the
sample width. With increasing frequency, however, the spectra strongly deviate from the constant behavior expected for
a metallic film 共and demonstrated in the inset of Fig. 2 for
full Corbino samples兲. The reason is the capacitive influence
of the dielectric substrate. While this can typically be neglected for low-impedance films, the substrate becomes more
important with increasing film impedance.
Thin film strip and substrate act as parallel contributions
to the total impedance Z, which therefore can be modeled as
1 / Z = 1 / Zstrip + i␻C, where ␻ = 2␲ f is the angular microwave
frequency and C the capacitance of the substrate. For our
FIG. 2. 共Color online兲 Real part of impedance at 5 GHz of 25 nm thick
NiCr films with different inner diameters a1 and constant outer diameter
a2 = 1.75 mm; the fit follows Eq. 共1兲. The inset shows the impedance spectra
for two exemplary samples 共a1 = 0.9 mm and a1 = 1.1 mm兲.
materials and frequencies, Zstrip = Rstrip as well C are real, and
we can easily fit the complex impedance data, as shown in
Fig. 3.
The left panel of Fig. 4 shows the resulting fit parameters Rstrip and C with the expected behavior. The resistance
Rstrip depends inversely on the strip width w and can be tuned
over large ranges: between 42 and 404 ⍀ for the data shown
here; the resistance of the corresponding full-area Corbino
sample is 7.6 ⍀. The substrate capacitance C on the other
hand decreases slightly with increasing strip width: the effective cross section of the capacitor between inner and outer
Corbino contacts as electrodes is reduced as the area covered
by the metal gets larger.
This explanation of the substrate acting as a capacitor is
confirmed by additional measurements shown in Fig. 5,
where we have changed the diameter of the inner Corbino
contact. Again the data can be fitted with the simple RC
model. The resulting fit parameters are shown in the right
panel of Fig. 4. As expected, Rstrip decreases with increasing
a1 共decreasing strip length兲, whereas C increases with larger
a1 共decreasing electrode distance兲.
FIG. 4. 共Color online兲 Strip resistance Rstrip 共squares, left axis兲 and substrate
capacitance C 共open circle, right axis兲 as obtained from the fits in Figs. 3
共left plot兲 and 5 共right plot兲.
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086106-3
Rev. Sci. Instrum. 78, 086106 共2007兲
Notes
FIG. 5. 共Color online兲 Complex impedance of 25 nm thick NiCr strip
samples with different diameters of inner Corbino contact a1, as stated in
legend. The full lines show experimental data; the dashed lines are fits.
共w = 0.2 mm; a2 = 1.75 mm兲
These experiments demonstrate that the dimensions of a
metallic strip can be used to drastically change the impedance of thin-film samples to be studied in a Corbino spectrometer, and even larger changes are possible by reducing
the strip width further than the 0.06 mm width presented
here. Thus it is possible to adjust the impedance of highly
conductive samples considerably toward the optimum impedance of 50 ⍀. However, with increasing film impedance,
the capacitive effects of the substrate become more important
and can make the data analysis more complicated. Here a
simple RC model can be used to extract the film impedance.
This requires knowledge of the value of C, which can either
be obtained from reference measurements on the same substrate and the same electrode geometry but without the thin
film or—in cases where the lowest-frequency impedance of
the film is known to be constant—it can be deduced from RC
fits to the low-frequency end of the spectra. Furthermore, our
results make it possible to estimate the influence of the substrate capacitor quantitatively: assuming a capacitance of
200 fF for our case and a frequency of 5 GHz, the influence
is less than 1% if the film impedance is lower than 16 ⍀.
Since most materials of current interest are much more conductive than our test material NiCr, the influence of the substrate will therefore often be negligible if the dimensions of
the strip are chosen properly.9
The strip-shaped geometry not only increases the impedance but also breaks the radial symmetry of the Corbino
probes and leads to a current distribution within the metallic
sample with current only in one direction. For singlecrystalline samples, this approach can therefore be used to
study anisotropic microwave conductivity without averaging
over several crystallographic directions.
The authors thank Gabriele Untereiner for the preparation of the samples and Elvira Ritz for help with the measurements. They acknowledge financial support by the DFG.
P. J. Turner et al., Rev. Sci. Instrum. 75, 124 共2004兲.
J. C. Booth, D. H. Wu, and S. M. Anlage, Rev. Sci. Instrum. 65, 2082
共1994兲.
3
D. H. Wu, J. C. Booth, and S. M. Anlage, Phys. Rev. Lett. 75, 525 共1995兲;
J. C. Booth, D. H. Wu, S. B. Qadri, E. F. Skelton, M. S. Osofsky, A.
Piqué, and S. M. Anlage, ibid. 77, 4438 共1996兲.
4
M. Scheffler, M. Dressel, M. Jourdan, and H. Adrian, Nature 共London兲
438, 1135 共2005兲; Physica B 378–380, 993 共2006兲.
5
A. Schwartz, M. Scheffler, and S. M. Anlage, Phys. Rev. B 61, R870
共2000兲; e-print arXiv:cond-mat/0010172.
6
F. Hohls, U. Zeitler, and R. J. Haug, Phys. Rev. Lett. 86, 5124 共2001兲.
7
M. Lee and M. L. Stutzmann, Phys. Rev. Lett. 87, 056402 共2001兲.
8
M. Scheffler and M. Dressel, Rev. Sci. Instrum. 76, 074702 共2005兲.
9
In addition to the experiments with varying strip width and length, we
have also studied the variation of film thickness and have obtained equivalent results.
1
2
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