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Physica C 405 (2004) 96–102

Microstructure and temperature dependence of microwavepenetration depth of Ag doped Y1Ba2Cu3O7�x thin films

Davinder Kaur a,*, S.P. Pai b, J. Jesudasan b, R. Pinto b

a Department of Physics, Indian Institute of Technology, Roorkee 247667, Indiab Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India

Received 16 December 2003; received in revised form 22 December 2003; accepted 27 January 2004

Available online 5 March 2004

Abstract

We report the measurements of magnetic penetration depth kðT Þ of Ag-doped YBa2Cu3O7�d (YBCO) thin films in

the thickness range 1500–4000 A and temperature range 18–88 K. The films are in situ grown by laser ablation onh100iLaAlO3 substrates. The penetration depth measurements are performed by microstrip resonator technique. A corre-

lation of kðT Þ with the film microstructure observed with atomic force microscopy has shown that kðT Þ depends

critically on the film microstructure. Temperature dependence of magnetic penetration depth has also been studied for

best quality films. The experimental results are discussed in terms of BCS theory (s-wave pairing) and d-wave Pairing

with and without unitary scattering. The results are found to be best fitted to the d-wave model with unitary scattering

limit. Near Tc, we have also compare the (3D) XY critical regime and the Ginzburg–Landau (GL) behaviour.

� 2004 Elsevier B.V. All rights reserved.

1. Introduction

The characteristic depth to which supercurrents

flows inside a superconductor is known as pene-tration depth k. This penetration depth is tem-

perature dependent and is also sensitive to the

properties of the superconductor near its surface.

The measurement of the temperature dependence

of kðT Þ in high-Tc superconductors is of great

interest as the penetration depth is directly related

to the density of superconducting carriers, and

gives an important information regarding thenature of pairing mechanism (whether s-wave or d-

* Corresponding author. Tel.: +911-332285407.

E-mail address: dkaurfph@iitr.ernet.in (D. Kaur).

0921-4534/$ - see front matter � 2004 Elsevier B.V. All rights reserv

doi:10.1016/j.physc.2004.01.029

wave in clean and unitary scattering limit). In

conventional superconductors order parameter Wis isotropic (s-wave symmetry). Evidence is now

growing that the order parameter in hole dopedhigh-Tc superconductors is anisotropic with direc-

tional dependence in the real space of the x� yplane coinciding with the Cu–O planes which

varies as x2 � y2 (d-wave symmetry) [1,2]. Such

evidence comes from various types of measure-

ment [3–6] including microwave measurements of

the low-temperature variation of k which show a

linear or quadratic temperature dependence ratherthan exponential dependence expected for s-wave.

Unlike s-wave superconductors, d-wave materials

do not exhibit a finite gap structure with essentially

zero states with in an energy gap when averaged

over all directions. The gap function, averaged

ed.

D. Kaur et al. / Physica C 405 (2004) 96–102 97

over all spatial directions, always has available

states with in it, even at T ¼ 0. As a result the

density of quasiparticles will depend much more

slowly on temperature than for s-wave material

and the temperature dependence of the penetra-

tion depth shows a power law at low temperature,where exponent is an integer number related to the

fermiology of the superconductor.

Various methods have been used for the mea-

surement of kðT Þ of high-Tc superconductors bothin single crystals [7,8] and thin films [9–11]. In the

present study, we report the microstructure and

temperature dependence of penetration depth of

Ag-doped YBCO thin films in the temperaturerange 18–88 K using highly sensitive microstrip

resonator technique.

Fig. 1. Schematic diagram of YBCO thin film microstrip res-

onator.

Fig. 2. Schematic diagram of microwave measurement setup.

2. Experimental

Ag-doped YBCO films were in situ grown at 750

�C by pulsed laser deposition (PLD) using 15 mmdiameter 5 wt% Ag-doped targets. The targets were

prepared using standard solid state reaction

method. The films were grown on 10 · 10 mm2, 0.5

mm thick double side polished h100i LaAlO3

substrates. An excimer laser (KrF, 248 nm) was

used for in situ growth of the films. The film growth

rate was nearly 150 �A /min. at the beginning of

growth. The film of various thickness in the rangeof 1500–4000 �A were prepared. Structural charac-

terization of films was carried out using XRD and

atomic force microscopy (AFM). Critical temper-

ature, TcðR ¼ 0Þ of the films was 90 K with DTaround 0.5 K. Critical current density (Jc) of thefilms was >106 A cm�2 at 77 K. The best quality

films measured were c-axis oriented and show

superior structural properties, with a high degree ofepitaxy and low value of Rs at 77 K and 10 GHz.

Microstrip pattern was delineated in the YBCO

films using UV lithography and chemical etching.

The microstrip width was 175 lm and length, 9

mm. Au ground plane was used for Rs measure-

ments. For the measurement of kðT Þ a 25 lm thick

Teflon (Dupont) sheet was sandwiched between

the YBCO thin film strip and the YBCO groundplane film in a �flip-chip� configuration as shown in

Fig. 1. The Teflon dielectric sheet was metallized at

the lower surface with Ag/Au film (except in region

which forms the microstrip line) to enable contact

between the ground plane YBCO film and the

Au-plated microwave measurement jig. All mea-

surements were carried out in a closed cycle He

cryocooler.

Fig. 2 shows the block diagram of microwavemeasurement set up. Microwave measurement

were carried out over a swept frequency range of

1–12 GHz using HP8757C scalar network analyzer

and Hp83620 A synthesized sweeper. The micro-

wave power used was in the range �20 to 13 dBm.

The temperature was varied in the range 15–88 K

using a Si diode sensor and a temperature

98 D. Kaur et al. / Physica C 405 (2004) 96–102

controller. The Q-factor of resonators were mea-

sured from scalar network analyzer at various

resonant frequencies and temperature by calcu-

lating the ratio f =Df , where f is the center fre-

quency and Df is the 3 dB bandwidth of resonator

curves. Since the device was loosely coupled with18–20 dB insertion loss the measured Q-factor is

nearly equal to Q0, the unloaded Q-factor. The Q-factor due to conductor loss Qc, is given by

1

Qc

¼ 1

Q0

� 1

Qd

� 1

Qr

where Qd and Qr are Q-factors due to dielectric and

radiation losses respectively. Here Qd ¼ 1= tan d �104 for LaAlO3. The losses due to radiation have

been minimized by providing effective shielding at

k=2 spacing around the device, hence can be ne-

glected as compared to Qd. The values of Rs cor-responding to values of Qc were than calculated

using the expressions given by Pucel et al. [19].

Details of YBCO film growth by PLD and

microwave penetration depth measurements are

reported elsewhere [12,13].

Fig. 3. Variation of Reff (77 K) and kð0Þ with film thickness.

3. Theory

The microstrip resonator technique used for the

measurement of Rs and k of superconducting films

is based on a finite length of superconducting mi-

crostrip transmission line separated by capacitive

gaps at the input/output ports. The series induc-

tance of this transmission line, which is determined

by kðT Þ affects the propagation velocity of micro-wave signals. The phase velocity of an ideal loss-

less superconducting microstrip transmission line

is given by an expression [21]

vp ¼c=

ffiffiffiffiffiffieeff

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ ð2k=dÞ cot h t

k

� �þ gccsch t

k

� �q ð1Þ

where c is the velocity of light in vacuum, w is the

width of stripline, d and t are the dielectric and film

thickness, respectively. eeff is the effective dielectricconstant of the mixed dialectic system. Use of thin

dielectric in the range 10–50 lm thickness increases

the sensitivity of k measurement. The factor gctakes into account the contributions from fringing

field. The term gccschð tkÞ can be neglected from Eq.

(1) for aspect ratio w=d � 1. Both vp and eeff canbe determined experimentally from the resonant

frequency of the microstrip resonator. The phase

velocity is related to the resonance frequency fnthrough the relation

vp ¼ 2Lfn=n ð2Þwhere fn is the nth resonant frequency, n is the

mode number and L is the geometric length of the

microstrip. The fundamental resonant frequency fis given by an expression

f ¼ c2L

ffiffiffiffiffiffieeff

p ð3Þ

4. Results and discussion

The correlation between kðT Þ and film micro-

structure has been studied by varying the thickness

of Ag-YBCO films in the range 1500–4000 �A. Fig.

3 shows the variation of microwave surface resis-

tance with thickness of Ag-YBCO thin films along

with penetration depth data measured at 77 K.

The surface resistance decreases with increasing

thickness to an optimum thickness 3000 �A deter-mined by growth conditions. However the mea-

sured penetration depth keff does not change with

thickness and is constant to 3000 �A; both Rs and

keff increase as the thickness is further increased.

Fig. 4. Rs vs. T plots for Ag-YBCO films of various thickness at

10 GHz.

D. Kaur et al. / Physica C 405 (2004) 96–102 99

Fig. 4 shows the temperature variation of surfaceresistance for Ag-doped YBCO thin films of vari-

ous thicknesses. We found a minimum value of Reff

of 215 lX at 77 K and 10 GHz for a film thickness

of about 3000 �A and kð0Þ of 1400 �A.

Finite films thickness effects [20] can give

thickness (t) dependence of Reff and keff which are

actual experimentally measured values of surface

resistance and penetration depth respectively, asfollows:

Reff ¼ Rs cothðt=kÞ"

þ ðt=kÞsinh2 ðt=kÞ

#þ Rtrans ð4Þ

where Rtrans is due to power transmission into the

substrate and

Xeff ¼ Xs cothðt=kÞ ð5ÞWhere DkeffðT Þ ¼ DXeffðT Þ=xl0. Thus if finite

thickness effects are playing a role, both Reff andkeff should vary with thickness of the film. The fact

that our measured penetration depth (keff ) does

not change with thickness rules out any finite

thickness effects. However beyond 3000 �A film

thickness, both Reff and keff increases. This may be

due to degradation in the microstructure of the

films of thickness greater than optimum thickness

as seen in the AFM images. Fig. 6(a) and (b)shows the AFM images of films with thickness

3000 and 4000 �A respectively. Highly aligned grain

structure with large grains has been observed for

films of thickness 3000 �A. However, 4000 �A thick

Ag-YBCO film shows more surface roughness

with less aligned grain structure.

We explore two other important possibilities forthe decrease of Rs with increase in thickness of the

film, namely: (i) percolation effects and (ii) for-

mation of defects during film growth. However,

the films from a continuous highly oriented

microstructure beyond 500 �A; and hence the per-

colation effects do not exist in the thickness range

of 900–3000 �A studied here. Therefore, we ex-

plored the possibility of defects influencing thethickness dependence of Reff .

It is well known that highly oriented YBCO

thin films support very high critical current den-

sities of the order of 106 �Acm�2 (at 77 K) due to

presence of a high density of flux pinning centers.

These pinning centers are basically nanodefects

such as strain, oxygen vacancies, lattice defects etc.

generated during the growth of the thin films.Therefore in highly oriented YBCO thin films Jcvalues increase with increasing density of flux

pinning centers. We have observed a high Jc valueof 3 · 106 A cm�2 (77 K) for YBCO film of 900 �Athickness; and the value increases with increas-

ing thickness reaching 5.8 · 106 A cm�2 (77 K) for

thickness of 2500 �A as shown in Fig. 5. This in-

crease in the value of Jc with thickness can be ex-plained due to the increase in the number of

defects which act as flux pinning centers. This

Implies that as the film thickness increases, the

number of defects also increases.

In the following, we explore the role of these

defects formed during growth of the film in

microwave surface resistance using the physical

picture describe by Hardy et al., [7] and Zhanget al., [6]. In this description, the surface resistance

Rs can be written as

Rsðx; T Þ ¼8p2

c4x2k3ðT Þr1ðx; T Þ ð6Þ

where kðT Þ is the penetration defect and r1 is the

real part of the conductivity associated with the

normal fluid response. r1 is given as

r1ðx; T Þ ¼1

l0k2ð0Þ

XnðT ÞsðT Þ

1þ x2s2ðT Þ ð7Þ

Fig. 6. (a) AFM image of 3000 �A thick Ag-YBCO film. (b)

AFM image of 4000 �A thick Ag-YBCO film.

Fig. 5. Variation of Jc with thickness for Ag-YBCO films.

Fig. 7. Variation of normalized phase velocity vp=c vs. nor-

malized temperature T=Tc.

100 D. Kaur et al. / Physica C 405 (2004) 96–102

where Xn ¼ 1� Xs ¼ 1� ðkð0Þ � kðT ÞÞ2 is the

normal fluid fraction, Xs is the superfluid fractionand s is scattering time. The addition of defects

can put a limit on the increases in sðT Þ and thus

cause an overall decrease in loss. In the present

study an increase in thickness of the film implies an

increase in growth time which in turn increases the

number of defects and decreases the scattering

time, and thereby r1. thus an increase in thickness

of the film leads to decrease in r1 and thenaccording to equation (6), cause a decrease in

surface resistance Rs.

Fig. 7 shows the plot of normalized phase

velocity vp=c vs. normalized temperature, T=Tc for3000 �A thick Ag-YBCO film. From these phase

velocity data kðT Þ values were calculated at vari-

ous temperatures.

For the sample case of s-wave pairing (BCS

theory) the best fit to the tabulated superfluid

fraction kðOÞkðT Þ

h i2data as shown by Muhlschlegel

et al. [14] is

kðOÞkðT Þ

� �2¼ ð1� tAÞB

with fit parameters A ¼ 2:9037 and B ¼ 1:2886,where, t ¼ T=Tc is the reduced temperature and

kð0Þ is the penetration depth at 0 K. According to

the best fit to the d-wave pairing model as pro-posed by Won and Maki [15] the values of fit

D. Kaur et al. / Physica C 405 (2004) 96–102 101

parameters are A ¼ 1:3056 and B ¼ 0:96595. Sim-

ilarly for dirty d-wave pairing model as proposed

by Sun and Maki [16], the values of fit parameter

comes out to be A ¼ 2:1721 and B ¼ 1:1368respectively.

We tried to fit our experimental data according

to these models for Ag-YBCO films. Fig. 8(a)

shows the plot of superfluid fraction kð0Þ2=kðT Þ2versus reduced temperature T=Tc. The lines in this

figure represent the various models proposed for

Fig. 8. (a) Variation of kð0Þ2=kðT Þ2 vs. reduced temperature

T=Tc. (b) Best fit of kð0Þ2=kðT Þ2 vs. reduced temperature T=Tc.

pairing mechanism. The best fit of our experi-

mental results as shown in Fig. 8(b) yields the fit

parameters A ¼ 1:81221 and B ¼ 1:05376 which

reflects that d-wave model with dirty limit de-

scribes the data best in these films. Reported re-

sults [7–11] for YBCO superconductor alsoindicate that the measured temperature depen-

dence of k does not show a self consistent fit to

BCS temperature dependence derived from a sin-

gle gap over the entire temperature range. For

YBCO thin films, quadratic temperature depen-

dence of kðT Þ in low temperature range has been

observed [9], which is indicative of d-wave super-

conductivity in dirty limit. It has been suggestedthat in the d-wave pairing state, strong potential

scattering by the defects present in thin films, can

easily push a superconductor into the gapless re-

gime where a quadratic rather than linear term

would be observed.

The physical properties of bulk, classic super-

conductors near the superconducting transition

temperature Tc can be well described by theGinzburg–Landau model. Estimates of the Ginz-

burg temperature TG, at which Ginzburg–Landau

theory is expected to break down, indicate that

critical behaviour in classic superconductors is

restricted to a temperature range that is extremely

close to Tc as a consequence of semimacroscopic

size of the coherence length. However soon it has

been realized that due to extremely short coher-ence lengths as well as elevated values of Tc of

high-Tc superconductors, the Ginzburg criterion

for the width of the critical region could lead to the

possibility of observing fluctuations and critical

scaling near the superconducting transition [17].

There are number of studies of thermodynamic

properties and transport properties which support

the view that there is indeed critical behaviour overa significant temperature interval with the critical

exponent being those of the three-dimensional

(3D) XY model.

Near Tc, we have also compare the three

dimensional (3D) XY critical regime and the

Ginzburg–Landau(GL) behaviour, using the

expression

kðT Þ ¼ k�ð1� T=TcÞ�n

where n ¼ 1=3 and 1/2 respectively.

Fig. 9. Log–log plot of kðT Þ vs. reduced temperature

t ¼ ð1� T=TcÞ.

102 D. Kaur et al. / Physica C 405 (2004) 96–102

Fig. 9 shows a log–log plot of kðT Þ vs. nor-malized temperature t ¼ ð1� T=TcÞ with in the

critical region. The best fit of the plot yields

k� ¼ 916 �A and n ¼ 0:39. The exponent is thus

found to be close to the (3D) XY critical regime

which is consistent with the other reports on

YBCO single crystal [18].

5. Conclusion

In conclusion, our experimental results show

that the penetration depth depends critically on

the microstructural quality of the films. Beyond

optimum thickness surface resistance as well as

penetration depth increases due to degradation of

microstructure of the films. Temperature depen-dence of penetration depth has been fitted to the

theoretical models (BCS theory and d-wave model

in clean and unitary scattering limit). The results

are found to be best fitted to the d-wave model

with unitary scattering limit. Near Tc, the tem-

perature dependence of the penetration depth has

been found to be consistent with the critical

behaviour of the three dimensional XY model.

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