PHYSICAL REVIEW B
VOLUME 58, NUMBER 17
1 NOVEMBER 1998-I
Coexistence of the hot-spot effect and flux-flow instability in high-T c superconducting films
Z. L. Xiao and E. Y. Andrei
Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08855
P. Ziemann
Abteilung für Festkörperphysik, Universität Ulm, D-89069 Ulm, Germany
~Received 20 February 1998!
Voltage jumps were observed in current-voltage (I-V) characteristics of YBa2Cu3O72d superconducting
film. The measurements demonstrate that the observed voltage instability originates from two different mechanisms, depending on the temperature and the magnetic field. This is inferred from the shape of the I-V
characteristics, the temperature and magnetic-field dependencies of the critical current, and the critical voltage
associated to the voltage jumps. Relevant models indicate that the voltage jumps at low temperatures are due
to the hot-spot effect, whereas those at temperatures near T c are due to flux-flow instabilities.
@S0163-1829~98!01741-X#
Voltage jumps in current-voltage (I-V) characteristics at
high current densities have been observed both in low-T c
~Refs. 1–5! and high-T c superconducting films.6–8 Theoretically such voltage jumps can be induced by many
mechanisms.7,8 Two of them are the flux-flow instability9
and the hot-spot effect,1,10 which are related to the nonlinear
viscosity of the moving vortices and the localized normal
hot spot maintained by Joule heating, respectively. In low-T c
superconductors the voltage jumps in I-V characteristics caused by both the flux-flow instability and the
hot-spot effect have been studied.1–5 In high-T c superconductors, the voltage jump phenomenon previously
observed in YBa2Cu3O72d ~YBCO! ~Refs. 6 and 7! and
Bi2Sr2CaCu2O81d ~Ref. 8! superconducting films was successfully interpreted as due to flux-flow instabilities. There
are, however, no previous reports of evidence for hot spots as
alternative sources of discontinuities in I-V characteristics of
high-T c superconducting films. In this paper we present the
observation on the coexistence of the hot-spot effect and the
flux-flow instability in YBa2Cu3O72d superconducting film.
Voltage jumps were observed in the current-voltage (I-V)
characteristics at high current densities. Near the transition
temperature T c , our experiments show voltage jumps, which
are characteristic of flux-flow instabilities as reported in the
previous work of Refs. 7 and 8. At low temperatures, however, the I-V characteristics showed the typical behavior of
the hot-spot effect. The temperature and magnetic-field dependence of the critical current and the critical voltage, associated to the voltage jump, is also quite different from that
observed near T c . Based on the model of the hot-spot effect,
we have extracted the heat-transfer coefficient from the film
to bath and the length of the hot spot through analysis of the
experimental data at low temperatures. The cause of the appearance of the hot-spot effect in this film is presumed to be
the existence of weak spots in the sample.
The 200-nm-thick film was prepared by hollow cathode
magnetron sputtering onto ~100! SrTiO3 substrate. As revealed by x-ray texture analysis, the resulting film is purely
c-axis oriented. First the film was patterned into a microbridge ~500 mm long, 9 mm wide! by photolithography and
0163-1829/98/58~17!/11185~4!/$15.00
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wet chemical etching. Silver contact pads were evaporated
allowing the measurement of I-V curves using the standard
four-point method. After attachment on a copper sample
holder, in which the thermometer was mounted, the sample
was placed in a magnet cryostat that supplies external magnetic fields up to 5 T. In this study the magnetic field was
always kept parallel to the c axis of the film and perpendicular to the current direction. The measurements were conducted with rectangular current pulses of 1.5 s in length and
an interval time of 3 s between pulses. More experimental
details are given in Ref. 7. The film has a zero-resistance
temperature ~measured in the low-current limit without external magnetic field! of T c 587.60 K with a superconducting transition width ~between 0.1 R N and 0.9 R N ) of about
2.0 K.
Figure 1 presents some of the I-V isotherms obtained in a
magnetic field of 0.5 T and at different temperatures as assigned to each curve. At temperature-dependent critical currents I * (T), voltage jumps to a value of higher than 2 V can
be clearly resolved ~experimentally the maximum voltage is
restricted to 2 V to avoid the destruction of the microbridge!.
As reported in our previous works,7 these voltage jumps
were observed in magnetic fields up to 5.0 T and at temperatures not too close to the critical temperature T c . The shape
of I-V isotherms at low temperatures for this film, however,
is quite different from that at high temperatures (T.79 K in
a magnetic field of 0.5 T!. For example, at the temperature of
65 K and in a magnetic field of 0.5 T, a voltage discontinuity
appears in the I-V characteristic at a current I m , which is
smaller than the critical current I * where the main voltage
jump occurs. The critical voltage V * , at which the voltage
jump occurs, decreased slightly with increasing temperature,
in contrast to V * observed in other films as reported in Refs.
6 and 7 and to the V * in this film at high temperatures, where
the critical voltage V * increases strongly with increasing
temperature. The I-V characteristics near I m become
smeared when the temperature rises to about 79 K, and at
higher temperatures the discontinuity disappears completely.
The same trends were observed in our experimental range of
magnetic fields up to 5 T and temperatures down to 65 K. In
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©1998 The American Physical Society
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FIG. 1. Current-voltage characteristics of a YBa2Cu3O72d microbridge in a magnetic field of 0.5 T and at different temperatures
as assigned to each curve. The vertical solid lines indicate the voltage jumps. The critical current I * and the critical voltage V * ,
shown as an example for the isotherm at 65 K, are the current and
voltage values of the last point before the voltage jump to higher
than 2 V occurs. I m is the current at which a discontinuity appears
before the main voltage jump at I * .
experiments, no thermal hysteresis of the I-V characteristics
below I * was observed. In a low-T c superconductor,1,11
however, a current history effect was observed at I m . The
reason is possibly that the voltage difference induced by the
temperature change due to the heating effect below and
above I m is out of our experimental resolution. Further investigation is needed here, especially for the possible hysteresis at the main jump I * .
Figures 2~a! and 2~b! present the temperature dependence
of the critical current I * and the critical voltage V * related to
the main voltage jumps as defined in Fig. 1. Although the
critical current I * decreases with increasing magnetic field
and temperature, its temperature and magnetic-field dependence at low and high temperatures is quite different. For
example, when the magnetic field increases from 0 to 5 T, I *
decreases only about 8% at 65 K compared to 45% at 78 K;
meanwhile at low temperatures the critical voltage V * decreases slightly with increasing temperature, whereas at high
temperatures it increases strongly with temperature. Furthermore, the critical voltage V * falls on a common curve below
a characteristic value T 1 depending on the magnetic field.
These results clearly indicate that the causes for the voltage
jumps at low and high temperatures should be different. In
order to show the different ranges more clearly, we replotted
as an example the temperature dependence of I * and V * at
0.5 T in Fig. 3~a!. Below the characteristic temperature denoted by T 1 , the V * coincide on a common curve. The temperature T 2 , where a curvature change of V * (T) and I * (T)
appears, was also introduced to classify the temperature
ranges. Both T 1 and T 2 shift to lower temperatures with
increasing magnetic fields.
The current-voltage characteristics in low temperatures in
Fig. 1 present the typical behavior caused by the hot-spot
effect.1,11 Based on the hot-spot model the I m and I * , shown
in Fig. 1 for the current-voltage characteristic at 65 K, are the
minimal and maximal current for the existence of a resistive
FIG. 2. Temperature dependence of the critical current I * ~a!
and the critical voltage V * ~b!. Symbols in ~a! and ~b! are identical.
Temperatures T 1 and T 2 are introduced as an example for the data
in a magnetic field of 0.5 T to classify the temperature ranges;
below T 1 the V * falls on a common curve, whereas at T 2 a curvature change of V * (T) and I * (T) appears.
domain, respectively. When the current I is lower than I m ,
the film is in the superconducting state. If the current I is
greater than I m , a resistive domain arises in the sample. Between I m and I * the domain remains localized. In this current range the voltage increases with increasing current and
depends approximately linearly on the current near I m . At
I * , the propagation of the resistive phase occurs and leads to
a voltage jump. The temperature dependence of the critical
current I * caused by the hot-spot effect was given as1,10
I * 5 @ 2hdw 2 T c / r N # 1/2~ 12T/T c ! 1/2,
~1!
where h is the heat-transfer coefficient, w and d are the width
and the thickness of the microbridge, respectively, r N is the
resistivity in the normal state.
The temperature dependence of the critical current I * in
the low-temperature range (T,T 2 ) can be fitted with Eq. ~1!
very well. The resulting curve with a fitting parameter
@ 2hdw 2 T c / r N # 1/2576.76 mA for data in a magnetic field of
0.5 T is indicated by the solid line in Fig. 3~a!. From this fit
we can determine the heat-transfer coefficient h. Using r N
597 m V cm ~the measured resistivity at 100 K! and the experimentally obtained data for w ~59 mm!, d ~5200 nm!,
and T c ~587.6 K!, the calculated heat-transfer coefficient h
is 208 W/cm2 K. This value of the heat-transfer coefficient is
lower than the reported one (103 W/cm2 K) for the boundary
between YBCO film and SrTiO3 substrate.12 As shown in
Ref. 13, the temperature rise in the film can also be caused
from the heat flow in the substrate and it is given as DT s
5 b Pt 0 / $ 2l(Dt 0 ) 1/2@ 4(Dt 0 ) 1/21w # c p % , where b 54/p 1/2, P
is the dissipated power in the film, t 0 is the duration of the
current pulse, D is the heat diffusion constant of the sub-
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FIG. 3. ~a! Temperature dependence of the critical current I *
and the critical voltage V * in a magnetic field of 0.5 T. The solid
line indicates the fit with Eq. ~1!, Temperatures T 1 and T 2 are the
same as those defined in Fig. 2. ~b! Temperature dependence of the
critical current I * near T c . The solid lines are fits to a power-law
form I * 5I * (H)(12T/T c0 ) 3/2. The symbols are the same as shown
in Fig. 2~a!. The extracted values of I * (H) are given in inset and
the solid line presents a fit of I * (H)5C/(11H/H 0 ) a with C
5926.3 mA, m 0 H 0 51.326 T, and a 50.67.
strate, l is the length of the microbridge. Using c p
51 J/cm3 K, D50.18 cm2/s ~Ref. 13!, and the values of w
~59 mm!, l ~5500 mm!, and t 0 ~51.5 s! we derived a heattransfer coefficient h s @ 5 P/(lwDT s ) # of the SrTiO3 substrate of 708 W/cm2 K. Thus the effective heat-transfer coefficient considering both the heat resistance at the filmsubstrate boundary and in the substrate is 414 W/cm2 K,
which is more reasonably consistent with our experimental
value. The disparity may be caused by the heat resistance at
the boundary between the SrTiO3 substrate and the copper
sample holder.
Equation ~1! is predicted for a long microbridge with the
length l@ h , where h 5(Kd/h) 1/2 is a characteristic thermal
length ~thermal healing length! with K being the thermal
conductivity of the superconducting film. To check selfconsistency of the hot-spot model we use the experimentally
derived heat-transfer coefficient h5208 W/cm2 K to calculate the thermal healing length h. For this 200-nm-thick
YBCO microbridge we obtained the value of h of 0.7 mm
using the value of thermal conductivity K50.05 W/cm K for
YBCO.14 Clearly, the thermal healing length is very short
when compared to the length of the microbridge.
The voltage jump at I m corresponds to the resistance
change in the microbridge due to the appearance of the hot
spot. The resistance of the hot spot can be estimated using
the form of R H 5DV/I m and it decreases with increasing
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temperature ~1.73 V at 65 K and 1.07 V at 71 K!. Furthermore, we can derive the length of the hot spot l H
(5lR H /R N ) using the obtained resistance of the hot spot and
the resistivity in normal state, where R N (5 r N l/wd) is the
resistance of the microbridge in the normal state. Corresponding to the hot-spot resistance at 65 and 71 K we obtained the related length of the hot spot of 3.14 and of 1.95
mm, respectively. These values demonstrate that the hot spot
is localized in a small area of the microbridge.
The above results indicate that the voltage jumps at low
temperatures (T,T 2 ) are caused by the hot-spot effect. At
high temperatures (T.T 2 ), however, Fig. 3~a! shows a deviation between the experimental data and the theoretical
curve of the hot-spot model. Therefore, the voltage instability can be caused by another mechanism. In analysis of the
data we found that the temperature dependence of the critical
current I * is the same as that reported in Ref. 7, i.e., it can be
well fitted with a power-law form I * 5I * (H)(1
2T/T co ) 3/2. The related results are shown in Fig. 3~b!,
where T co 589.4 K was used. The fitting parameter I * (H),
which presents the magnetic-field dependence of the I * extrapolated to zero temperature, has the form 1/(11H/H 0 ) a
with a 50.67. These results suggest that the origin of the
voltage jumps in the high-temperature range (T.T 2 ) is the
same as reported in Ref. 7. Although such temperature and
magnetic-field dependence could be induced by other
mechanisms,15 the recent experiments on voltage instability
in Bi2Sr2CaCu2O81d superconducting films8 show clear evidence for the mechanism of flux-flow instability in combination with consideration on the influence of self-heating.16
There the temperature dependence of the critical current is
related to the temperature-dependent inelastic scattering time
of quasiparticles; meanwhile, its magnetic-field dependence
is caused by the different temperature change in the films
induced by the dissipated power in magnetic fields.
Despite the fact that the voltage jump at T.T 2 can originate from the flux-flow instability, the self-heating is unavoidable there and it could induce a hot spot. In order to
rule out the possible existence of the hot spot at T.T 2 we
check the Stekly parameter s5 r N j 2c d/ @ h(T c 2T) # , which is
the ratio of the characteristic heat generation r N j 2c in the
normal state to the heat transfer (T c 2T)h/d, where j c is the
depinning critical current density and the parameters r N , d,
h are the same as defined above. If s,1 the hot spot cannot
appear in the sample. As shown in Ref. 7, the voltage jumps
near T c can be caused by the flux-flow instability occurring
close to the depinning. Then the depinning critical current I c
could be approximately I * . Therefore we use I * 5I * (H)(1
2T/T c ) 3/2 instead of I c to estimate the Stekly parameter for
this film. Fitting the data for 0.5 T we found I * (H)
5743.3 mA. Using h5208 W/cm2 K and the values of r N ,
d, T c for this film, we obtained s52.3731022 (T c 2T) 2 .
Thus the Stekly parameter will be smaller than 1 when the
temperature is higher than 81.1 K, which corresponds approximately to the experimentally observed T 2 as shown in
Fig. 3~a!. Figures 2~a! and 2~b! indicate that the temperature
T 2 depends on the magnetic field. This is due to the
magnetic-field dependence of the critical current density j c .
The calculated temperatures above which the hot-spot effect
cannot appear are 82.4, 81.1, 80, 77.9, 76.2, 74.5, and 72.7 K
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for the magnetic fields of 0, 0.5, 1, 2, 3, 4, and 5 T, respectively, using the I * (H) obtained by fitting I * (T) in corresponding magnetic fields near T c . All of those values are
consistent with the experimentally determined temperatures
T 2 . Thus the hot spot should not appear in the microbridge if
T.T 2 , whereas it is a reasonable origin for the voltage
jumps at temperatures lower than T 2 .
Although the temperature dependence of the critical current I * can be explained with the hot-spot model up to T 2 ,
the critical voltage V * has different temperature dependence
in the temperature range of T,T 1 and T 1 ,T,T 2 . This is
possibly due to the temperature dependence of the dissipation induced by the thermally activated flux motion in the
superconductive part of the microbridge because the measured voltage across the microbridge is the sum of the dissipation both in the hot spot and in the superconductive part.
The dissipation in the latter one can cause the strong increase
of the critical voltage V * with increasing temperature in T 1
,T,T 2 . Consequently, we can classify temperatures into
three ranges of T.T 2 , T 2 .T.T 1 , and T,T 1 . In the range
of T.T 2 and T,T 1 the critical current I * and the critical
voltage V * present the characteristics of the flux-flow instability ~under the influence of self-heating! and a pure hotspot, respectively; meanwhile in range of T 2 .T.T 1 the
critical voltage V * includes the dissipation in the superconductive part of the microbridge, despite the fact that the voltage jump is caused by the hot-spot effect. The temperature
range T.T 2 , where the flux-flow instability is responsible
for the voltage jumps, is small for this film compared to that
in the previous report. The characteristic shape of the I-V
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curves I * (T,H) and V * (T,H) of the hot-spot effect reported
here were not observed in other films. The appearance of a
hot spot in this film could be caused by the existence of weak
spots of the microbridge due to inhomogeneities in heat
transfer or the superconducting medium, despite the fact that
it was not detected by the x-ray analysis and the temperature
dependence of the resistance (R2T) measurement. Therefore the voltage instability is tightly related to the quality of
the sample. It is possible to observe different kinds of voltage instability by controlling the quality of the microbridge.
In other words, the investigation of the voltage instability in
the current-voltage characteristics at high current densities
can reveal information about the quality of the microbridge.
In conclusion, we observed two kinds of high currentinduced voltage instability in the same YBa2Cu3O72d superconducting film. The voltage jumps in I-V characteristics
close to T c and at low temperatures were, respectively, interpreted as due to a flux-flow instability and a hot-spot effect
that manifest themselves as distinctive shapes of I-V characteristics, different temperature and magnetic-field dependence of the critical current and the critical voltage associated to the voltage jumps. The observation of the different
kinds of high current-driven voltage instability may depend
on temperature, magnetic field, and the quality of the
samples.
The experiment was carried out in Universität Konstanz,
Germany. We thank J. Haering for preparing the films, P.
Voss-de Haan, and R. Newsome for the critical reading of
the manuscript.
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