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    • Abstract: the transport properties are dominated by Josephson fluxon flow (for junctions whose dimensions exceed the Josephson penetration. depth) and premature switching to the voltage state at bias cur- rents less than the critical current (for junctions whose dimen ...

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IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 15, NO. 2, JUNE 2005 237
Fabrication and Characterization of Sub-Micron Thin
Film Intrinsic Josephson Junction Arrays
P. A. Warburton, A. R. Kuzhakhmetov, G. Burnell, M. G. Blamire, Y. Koval, A. Franz, P. Müller, and H. Schneidewind
Abstract—We have fabricated intrinsic Josephson junction ar- across the barrier is spatially uniform this dependence is of the
rays in thin films of Tl-Ba-Ca-Cu-O. Such arrays are candidates form:
for applications in the sub-millimeter waveband both by virtue of
the large gap energy and due to the existence of inductive and
capacitive coupling mechanisms between junctions in the array.
(1)
Characterization of such junctions is complicated by the fact that
the transport properties are dominated by Josephson fluxon flow
(for junctions whose dimensions exceed the Josephson penetration
depth) and premature switching to the voltage state at bias cur- where is the field required to insert a flux quantum into a
rents less than the critical current (for junctions whose dimen- single junction. If, however, Josephson fluxons are present in
sions are less than the Josephson penetration depth). Here we show the junction, the phase difference is highly spatially nonuniform,
that the magnetic-field dependence of the switching current is not leading to significant deviations from the so-called Fraunhofer
Fraunhofer-like, although there is clear minimum corresponding
to the point at which a single flux quantum is inserted between the dependence of (1) [6]. In zero field such fluxons are present for
cuprate double-planes. Nevertheless a Fraunhofer-like dependence junctions with linear dimension exceeding the Josephson pen-
can be obtained if the critical current is experimentally defined by etration depth, . Small junctions, on the other hand, are sus-
specifying a low-voltage criterion. ceptible to premature switching by thermal activation. Such pre-
Index Terms—Josephson junctions, superconductivity, thermal mature switching occurs at a current, , which can be much
noise. less than , rendering direct measurements of the Fraunhofer
dependence impossible. As we will show below, for intrinsic
Josephson junctions there exists no junction size in which
I. INTRODUCTION
there is neither penetration of Josephson fluxons nor premature
S INCE the spacing of consecutive copper-oxide double
planes in many cuprate superconductors is greater than the
coherence length in the c-direction, such planes are Josephson
switching at 4.2 K. This suggests that measurements of
should never be Fraunhofer-like at 4.2 K. Nevertheless we ex-
perimentally show that by defining a critical current at an ar-
coupled. Hence a cuprate superconductor which is structured in bitrary low voltage of order , a Fraunhofer-like dependence
such a way that the current is forced to flow in the c-direction can be observed.
acts as a series array of “intrinsic” Josephson junctions [1].
Such junctions show promise for a wide variety of applications. II. ANALYSIS
For example, zero-crossing Shapiro steps at frequencies up to
2.5 THz have been measured in single crystal Bi-Sr-Ca-Cu-O Given that Josephson fluxons must be excluded, the max-
intrinsic junctions [2], suggesting that they are suitable for imum area of a junction in which one might expect to see
development as voltage standards and sub-mm-wave oscillators the Fraunhofer dependence is of order . The maximum
[3], [4]. A variety of thin-film-based device geometries has Josephson energy of such a junction is thus
also been proposed, with a view to further exploiting intrinsic
Josephson effects in device applications; for a review of such (2)
devices see [5].
The conventional way to confirm that Josephson coupling is where is the flux quantum and the critical current density.
the transport mechanism in any novel type of Josephson device For intrinsic Josephson junctions, is given by [7]
is to measure the in-plane magnetic-field dependence of the crit-
ical current, . For a junction in which the phase difference (3)
Manuscript received October 5, 2004. This work was supported in part by the
U.K. Engineering and Physical Sciences Research Council. where is the permeability of free space, is the
P. A. Warburton and A. R. Kuzhakhmetov are with University College thickness of the cuprate double-planes, and is the in-plane
London, Department of Electrical and Electronic Engineering, Torrington
Place, London, WC1E 7JE, U.K. (e-mail: [email protected]).
penetration depth. By combining (2) and (3) we find that the
G. Burnell and M. G. Blamire are with the University of Cambridge, Dept. of maximum Josephson energy for an intrinsic junction which can
Materials Science, Cambridge, CB2 3QZ, U.K. be expected to show the Fraunhofer dependence is
Y. Koval, A. Franz and P. Müller are with Universität Erlangen-Nürnberg,
Physikalisches Institut III, D-91058, Erlangen, Germany.
H. Schneidewind is with IPHT-Jena, 07745 Jena, Germany. (4)
Digital Object Identifier 10.1109/TASC.2005.849766
1051-8223/$20.00 © 2005 IEEE
238 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 15, NO. 2, JUNE 2005
Fig. 1. Schematic (not to scale) of our device geometry. The slanting lines in
H
the center of the structure indicate the orientation of the copper-oxide double
planes. shows the magnetic field vector and I the transport current. The
devices reported here are of length l = 3 m, width w = 0:5 m and film
thickness b = 240 nm.
A Josephson junction switches to the voltage state by escape
out of a potential well of height
(5)
where is the normalized bias current [8]. Our model is
based upon the simplifying assumption that thermal activation
from this potential well occurs when , where is a
phenomenological factor of order 1 and is Boltzmann’s con-
stant. (This approximation is only applicable in the limit
. A full and more precise model applicable for has
been published in [9].) Under this assumption the normalized
current at which switching to the voltage state occurs is given
by
(6)
Fig. 2. (a) Part of the current-voltage characteristics of an intrinsic Josephson
By combining (4) and (6) we can now obtain the maximum junction array in zero magnetic field at T = 4:2 K. Only ten of the quasiparticle
value of the normalized switching current for a Josephson junc- branches are shown here. (b) Enlargement of the low-voltage region of (a).
tion in which fluxons are excluded. By putting
and we find that at —i.e. in using argon-ion milling and sub-micron features using a 30
junctions in which we can expect the critical current to follow keV gallium focussed ion-beam.
the Fraunhofer dependence, the apparent critical current, , is Transport measurements in zero magnetic field are performed
at most 68% of the actual critical current, , at the usual mea- by immersing the sample into a liquid helium storage vessel.
surement temperature. Conversely, if we pose the question “at Measurements in a magnetic field of up to 3 T are performed in
what temperature should measurements be made so that the ap- an Oxford Instruments helium cryostat. The sample may be ro-
parent critical current is within 5% is the actual critical current?” tated with respect to the field with angular resolution better than
we find an upper limit for this temperature to be 260 mK. 0.1 . This high precision allows us to avoid inserting pancake
vortices, for which it is essential that the misalignment between
III. EXPERIMENTAL the applied field vector and the copper-oxide planes be less than
, where is the lower critical field of
Our device geometry which makes use of mis-aligned in the c-direction. For our maximum applied
films is shown in Fig. 1. The substrate is field of 3 T this implies that the misalignment must be smaller
vicinal lanthanum aluminate with its surface cut at an angle than . Details of the alignment procedure can be found
of 20 to the (0 0 1) axis. The films, of thickness 240 nm are elsewhere [12].
grown by sputtering an amorphous Ba-Ca-Cu-O precursor and
ex situ annealing in a thallous atmosphere at around 800 IV. RESULTS
[10]. During the annealing process the TBCCO film recrys-
tallizes epitaxially on the vicinal substrate with the result that A. Current-Voltage Characteristics
the copper-oxide double planes are mis-aligned by 20 with The current-voltage characteristics of a device of width
respect to the substrate surface. This epitaxy is confirmed both are shown in Fig. 2. The characteristics are
by four-circle x-ray diffraction and cross-sectional transmission multi-branched (in common with all intrinsic Josephson de-
electron micrography [11]. Micron-scale features are patterned vices), each branch corresponding to an additional junction
WARBURTON et al.: FABRICATION AND CHARACTERIZATION OF INTRINSIC JOSEPHSON JUNCTION ARRAYS 239
Fig. 3. Temperature dependence of the switching current in zero field. The Fig. 4. Dependence of the switching current (circles) and critical current
points are the experimental data and the line is a fit using the thermal activation (diamonds) upon an in-plane aligned magnetic field at T = 4:2 K, in both
model of equation (6). The fitting parameter is  = 0:8 (see text for details). cases normalized to their respective zero-field values. The critical current
is defined at a voltage criterion of 5 V . The line shows the Fraunhofer
dependence (equation (1)) with H = 2:37 T as the fitting parameter.
entering the voltage state. The reason for higher order branches
switching at lower apparent critical current values is not
understood. The supercurrent branch is not at zero voltage, that the Josephson phenomena we observe are indeed intrinsic
the dissipation here being due to thermally-activated phase to the cuprate double-planes.
diffusion [12], [13]. The current at which the jump from the Nevertheless it is clear that the switching current dependence
supercurrent branch occurs (equal to 5.5 here) is therefore does not follow the Fraunhofer dependence, which is to be ex-
not the Josephson critical current. We have previously shown pected given that thermal fluctuations play a strong role in the
by studying the temperature dependence of the supercurrent switching process. We therefore also plot in Fig. 4 the mag-
branch in this device that the zero-field low-temperature critical netic-field dependence of the critical current defined at an ar-
current is 7.2 [13], corresponding to a Josephson energy of bitrary voltage criterion of 5 . Here the data are normalized
K. This critical current, in common with BCS supercon- to the zero-field value which is 190 nA. The fit to the Fraunhofer
ductors, is approximately constant for temperatures less than dependence (1) suggests that this low-voltage definition of the
half the superconducting transition temperature. critical current is a more accurate measure of the true critical
current than is the switching current. Care must therefore be
B. Temperature Dependence of the Switching Current taken in interpreting the critical-current field-dependence data
for all small intrinsic Josephson junctions at 4.2 K.
The temperature dependence of the switching current is
shown in Fig. 3, where we restrict ourselves to , in
which regime the critical current is essentially constant. We now V. CONCLUSIONS
use our simplified thermal activation model (6) to account for We have shown that due to premature switching it is not pos-
the temperature dependence of . This dependence is shown sible to directly measure the Fraunhofer dependence of the crit-
in Fig. 3, with as described in the previous ical current in intrinsic Josephson junctions at 4.2 K. We esti-
section. The only fitting parameter is the phenomenological mate an upper bound on the temperature for such measurements
term , which is 0.8 here. We conclude that, although the model to be successful to be 260 mK. We have further developed a
is clearly oversimplified, it is adequate for giving order of simplified model of thermally-activated premature switching of
magnitude estimates for the degree to which measurements of Josephson junctions with . This model allows us to es-
the switching current underestimate the critical current in small timate the magnitude by which measurements of the switching
intrinsic Josephson junctions with . current underestimate the critical current.
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