ion, Los Alamos National Laboratory,
Los Alamos, New Mexico 87544
Q. X. Jia, Y. Fan, and C. Kwon
Superconductivity Technology Center, Materials Science and Technology Division,
Los Alamos National Laboratory, Los Alamos, New Mexico 87544
L. A. Ostrovsky
Environmental Technology Laboratory, University of Colorado, Boulder, Colorado 80303
and Institute of Geophysics and Planetary Physics, Los Alamos National Laboratory, Los Alamos,
New Mexico 87545
Received 4 March 1999; accepted for publication 20 April 1999
We present a comprehensive study of broadband 02 GHz electrodynamic properties of coplanar
waveguides made from high-temperature superconducting thin-lm YBa
2
Cu
3
O
7
electrodes on
nonlinear dielectric single-crystal SrTiO
3
substrates. The waveguides exhibit strong dielectric
nonlinearities, in addition to temperature-, dc-bias-, and frequency-dependent dissipation and
refractive index. By using parameters determined from small-signal
linear
transmission
characteristics of the waveguides as a function of dc bias, we develop a model equation that
successfully predicts and describes large-signal nonlinear behavior. © 1999 American Institute
of Physics. S0021-8979 99 03615-4
I. INTRODUCTION
With changing emphasis in high-temperature supercon-
ductor
HTS
electronics research from single-layer thin
lms to multilayered thin lm structures, there has been re-
newed interest in high-frequency applications of metal-
oxide-based nonlinear dielectrics NLDs , such as SrTiO
3
STO , in combination with HTS electrodes.
13
In essence,
devices based on HTS/NLD structures promise to perform
much better than their normal-metal/NLD predecessors due
to: i reduced operational temperature leading to, in certain
cases, lower dielectric loss, larger nonlinearity, and shorter
relaxation times in the dielectric; ii lower conductor loss,
and no intrinsic dispersion up to very high frequencies
THz
in
the
superconducting
electrodes;
and
iii
cleaner electrode-dielectric interface leading to lower in-
terface loss and negligible Shottky barriers. These HTS/NLD
structures are attractive not only for immediate implementa-
tion in practical devices such as frequency-agile microwave
lters,
4
but also for the exploration of novel scientic and
technological concepts such as study of stochastic effects and
pulse shaping.
5
One of the most crucial features of this developing tech-
nology based on HTS/NLD structures is the ability to min-
iaturize substantially, i.e., to prepare compact devices. The
importance of compact size for integration with other poten-
tial circuit components is clear. But, more importantly, since
nonlinear effects in a dielectric are a function of the electric
eld applied to the dielectric, the smaller separation of elec-
trodes allows for the realization of the same effects with
smaller signal and control voltage levels. Whereas the dielec-
tric loss is mostly determined by the loss tangent of the ma-
terial irrespective of its size, the conductor loss, which is
proportional to the surface resistance R
s
of the electrodes,
increases strongly with decreasing conductor separation.
Thus, the very low R
s
of superconducting electrodes
below about 80 K at 1 GHz for YBa
2
Cu
3
O
7
YBCO
permits designs of compact devices with practically low op-
erational voltage levels
110 V .
Most potential applications would require thin lms of
both the NLD and the HTS material on an appropriate low-
loss substrate. However, at present, even the highest quality
NLD lms show much smaller dielectric constant and non-
linearity, and higher dielectric losses than their single-crystal
NLD counterparts.
6
Also, the functional dependence of di-
electric properties on external electric eld bias seems to be
quite different in thin lms for example, whereas the dielec-
tric loss decreases with bias in thin lms, it increases in
single crystals .
7
Currently, several approaches are being ex-
plored to make lms with improved properties; such as
chemical doping,
8,9
use of heteroepitaxial buffer layers,
10
and
release of lms from substrates by selective etching.
11
While
a
Electronic mail: ndik@lanl.gov
JOURNAL OF APPLIED PHYSICS
VOLUME 86, NUMBER 3
1 AUGUST 1999
1558
0021-8979/99/86(3)/1558/11/$15.00
© 1999 American Institute of Physics the effort on improving the properties of NLD lms contin-
ues, it is also important to explore, in parallel, device con-
cepts using the single crystals that possess intrinsic and more
reproducible properties.
In the following, we will summarize our work on proto-
type nonlinear devices based on YBCO coplanar waveguide
electrodes on single-crystal STO substrates. To facilitate ex-
tensive study of nonlinear and dispersive effects which will
be described later , we have adopted a time-domain measure-
ment technique,
12
which allows for separation of dc-bias ef-
fects and high-frequency effects, and uses electrically distrib-
uted transmission line concepts for analysis. The use of
distributed coplanar waveguides has enabled us to investi-
gate the high-frequency properties of STO single crystals
with high resolution because of the long interaction lengths.
Among several different lengths for the coplanar waveguide,
8 cm provided the best compromise between overall dissipa-
tion and cumulative nonlinear/dispersive effects.
II. DEVICE FABRICATION
A schematic of our coplanar waveguide device structure
and its pertinent dimensions are shown in Fig. 1. The elec-
trodes are 0.4- m-thick YBCO lms, patterned in the form
of 8-cm-long meandering coplanar waveguides. The YBCO
lms were pulsed-laser deposited from a stoichiometric tar-
get on 1 cm 1 cm 1 mm 100 single-crystal STO sub-
strates at a substrate temperature of 780 °C in 200 mTorr O
2
.
The pulsed laser used is a XeCl excimer laser operating at
308 nm wavelength with a repetition rate of 20 Hz and laser
energy density of 2 J/cm
2
on the target. After deposition, the
electrodes were dened by standard photolithography, and
patterned by dilute phosphoric acid 500 ppm H
3
PO
4
), fol-
lowed by rf sputtering of 0.5- m-thick Au contact pads on
both ends of the centerline and ground planes. As a last
processing step, the devices were annealed at 400 °C for 12 h
in owing O
2
.
III. MEASUREMENT SETUP
Figure 2 shows the measurement setup we used for
broadband time-domain characterization of these nonlinear
devices. The sample housing was designed specically for
this experiment: it uses a suspended-substrate geometry
without sidewalls to reduce and attenuate unwanted housing
modes; no external pressure is applied on the substrate to
reduce complications due to possible piezoelectric effects
i.e., the substrate is unclamped ; short
2 mm coplanar
waveguide segments with 50
characteristic impedance are
used as an intermediate adapter to guide broadband electro-
magnetic waves from cylindrical symmetry of the coaxial
cable to coplanar waveguide symmetry of the device; and
short
1 mm and low-inductance
2 nH Au wires are
used to bond the electrodes of the device to the intermediate
adapter.
The housing is clamped on a cold head of a cryostat in a
vacuum chamber. The input and output ports of the housing
are connected with coaxial cables to the instruments outside
the chamber via hermetically sealed connectors attached to
ports of the chamber. The bias Tees are essentially rf chokes,
which allow the dc bias to be separated from high-frequency
signals. The high-frequency channel is a bandpass lter with
3 dB cutoff frequencies of 20 kHz and 12.5 GHz.
For our high-frequency device characterization, we have
used two different measurement congurations; the standard
step-pulse time-domain-reection/time-domain-transmission
TDR/TDT conguration, and the impulse-TDT congura-
tion. The standard TDR/TDT conguration uses a 0.2 V step
pulse with a 10%90% rise time of about 30 ps as the exci-
tation signal, and monitors the reected transmitted signals
from through the device as a function of time. The impulse-
TDT conguration
connection of which is shown in a
dashed line in Fig. 2 uses a Gaussian-like pulse with about
0.4 ns full width at half maximum and with varying ampli-
tudes between 0.2 and 40 V as the excitation signal and
monitors only the transmitted signal. The step-pulse TDR/
TDT conguration has been best suited for the overall char-
acterization of the devices in the small-signal limit and as a
function of dc bias, whereas impulse-TDT conguration has
been essential for the study of nonlinear/dispersive effects in
the large-signal limit.
IV. ELECTRICAL CIRCUIT MODEL AND FORMALISM
In the analysis of broadband characteristics of our de-
vices, we will use an electrical circuit model based on
lumped circuit element equivalents of coupling inductance
L
c
and input/output impedance Z
L
for the external circuitry;
and distributed element equivalents of series resistance R,
FIG. 1. Schematic coplanar waveguide CPW device structure.
FIG. 2. Schematic measurement setup.
1559
J. Appl. Phys., Vol. 86, No. 3, 1 August 1999
Findikoglu
et al. series inductance L, shunt conductance G, and shunt capaci-
tance C per unit length of the coplanar waveguide see Fig.
3 .
In their most general form, the inductance and imped-
ance of the lumped elements are constants; and those of the
distributed circuit elements depend on angular frequency
,
temperature T, bias voltage
dc
, and signal voltage
s
. The
characteristic impedance Z
0
and propagation function
of
the coplanar waveguide are given by
13
Z
0
R
i L / G
i C
1
and
R
i L
G
i C
i c n,
2
where c is the speed of light in vacuum,
is the attenuation
constant, and n is the effective refractive index. Assuming R