PHYSICAL REVIEW B 66, 184518 ~2002!

Effect of strain on the structure and critical temperature in superconductingNd-doped YBa2Cu3O7Àd

M. Salluzzo,1 C. Aruta,2 G. Ausanio,1 A. D’Agostino,3 and U. Scotti di Uccio1,4

1INFM-COHERENTIA and Dipartimento di Scienze Fisiche, Universita` di Napoli ‘‘Federico II’’ Piazzale Tecchio 80,I-80125 Napoli, Italy

2INFM-COHERENTIA, Universita’ di Roma ‘‘Tor Vergata,’’ Dipartimento di Ingegneria, Meccanica,Via del Politecnico 1, 00133 Roma, Italy

3PROMETE S.r.l.–INFM Spin off Company, via Buongiovanni 49, 80046 San Giorgio a Cremano (NA), Italy4Universitadi Cassino, Cassino, Italy

~Received 31 May 2002; published 27 November 2002!

A detailed study of the correlation between the superconducting critical temperature and the strain inas-grown, high-quality,c-axis epitaxial, Nd-doped YBa2Cu3O72d ~YBCO! films is reported. Samples withthicknesses ranging from 8 to 250 unit cells have been deposited by high-pressure oxygen sputtering onLaAlO3 ~100! single-crystal substrates. Thea, b, andc axis of the films have been accurately determined byx-ray diffraction from the measurements of the~005! and the~038!-~308! reflections. Below a certain thickness,a crossover from orthorhombic to tetragonal structure is observed, together with a decrease of the criticaltemperature. These results cannot be explained by the elastic deformation of the film, but point to inelasticstrain induced by the large mismatch with the substrate related to an oxygen reorganization in the Cu~1!-Oplane.

DOI: 10.1103/PhysRevB.66.184518 PACS number~s!: 74.76.Bz, 74.62.2c, 74.62.Dh

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I. INTRODUCTION

The recent, extensive research activity demonstratesthe full control of structural and superconducting propertis crucial for applications of Y1Ba2Cu3O72d ~YBCO! thinfilms to superconducting devices. A key issue is the relatbetween stress and superconducting critical tempera(Tc). Experimentally, the effect of compressive or tensstress is achieved resorting to deposition on substratespresent suitable mismatch with the film. The strain depeon film thickness, so that very thin films are required. Hoever, the results are controversial. While YBCO single crtals subject to suitable uniaxial pressure slightly increasecritical temperature,1 Tc is always depressed in strained thfilms.2 This behavior is not related to general propertieshigh-Tc superconductors. For instance, theTc ofLa1.9Sr0.1Cu2O6 can be doubled by growing sufficiently thifilms subject to in-plane compressive stress.3 It is not clearwhat mechanism is responsible for the behavior of YBCfilms, and if any structural change is correlated toTc in thiscase. The interpretation of the results is complicated byleast three effects:~a! superconductingc-axis films of YBCOhave a rectangular in-plane lattice (a50.3820 nm,b50.3886 nm), while most substrates have a square in-plattice; ~b! the dependence of theTc on uniaxial pressurealonga andb axis is opposite;~c! Cu~1!-O chain ordering isvery sensitive to any kind of structural changes~like compo-sitional changes, cationic disorder or simply strain-inducstructure modifications!.

Both structure and microstructure investigations, togetwith transport measurements, are required in order tosome insight on the thickness dependence ofTc . In spite ofa quite large number of studies, the structure of very tYBCO samples is not completely understood. Indeed, a c

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plete structural refinement of very thin YBCO films is vedifficult. An accurate refinement has been reportedY1Ba2Cu3O72d /Pr1Ba2Cu3O72d multilayers deposited onSrTiO3 substrates, characterized by a fixed Pr1Ba2Cu3O72d

~PBCO! thickness layer and variable YBCO thickness dowto 1 unit cell.4 Since the diffraction from symmetrical peakcontains meaningful features associated with the multilamodulation, the coordinates of the YBCO and PBCO catioalong thec axis can be accurately determined. The authfound that the YBCO layers are characterized by ac-axiscontraction when reducing the thickness from 12 to 1 ucell, due to the simultaneous contraction of the Cu~2!-Cu~2!,Cu~2!-Cu~1!, and Ba-Cu~1! distances. As only symmetricaq22q measurements are considered, the structure alonga and b axes is not resolved. This information is insterelevant, because it is related to the actual mechanismin-plane strain. Dislocations and antiphase boundariesformed in the first layers of YBCO film,5,6 so even 2–3 unitcell films must contain such defects that modify the strfield and the film structure. Similar conclusions have bereached by some of us for the case of varioR11xBa22xCu3Oy (R denotes rare earth or Y! films resortingto accurate transmission electron microscopy~TEM!, ultra-high vacuum–scanning tunneling microscopy~UHV-STM!and x-ray diffraction measurements.7

In YBCO films, strong changes in the superconductiproperties, in particularTc , occurs at very low thicknessnamely less than 10 unit cells.2,3 Unfortunately, conventionax-ray setup sensitivity is too weak to measure the in-planaandb parameters in this thickness range. For this reasonfocused our attention on Nd-doped YBCO~YNdBCO! films.YNdBCO structural and superconducting properties are vsimilar to YBCO, but this compound exhibits a stronger rduction of the critical temperature with thickness. Thus

©2002 The American Physical Society18-1

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SALLUZZO, ARUTA, AUSANIO, D’AGOSTINO, AND DI UCCIO PHYSICAL REVIEW B66, 184518 ~2002!

conventional x-ray diffractometer can be employed to fudetermine the structure of films with sensitive reductionTc .

In this report we present data on the correlation betwthe critical temperatures and the structure of high quac-axis Nd-doped films~YNdBCO! with thickness rangingbetween 9 to 250 unit cells deposited on 10310 mm2

LaAlO3 ~LAO!. The choice of LAO substrates is relatedthe fact that its matching with YNdBCO is worse than fSrTiO3. Consequently the effect of the strain in thin filmsexpected to be more important. Moreover, LAO inducecompressive strain on the film. A compressive strainYBCO single crystals can enhanceTc ; but as reported inRef. 2, theTc of YBCO films deposited on LaAlO3 decreaseswith thickness. We considered this discrepancy worthyspecific investigation. On the other hand, LaAlO3 substratespresent twinning domains due to the transition to the rhobohedral form. The possible effect of twinning on film proerties will be discussed in the following.

The LAO substrates have been prepared by followinvariant of the Kawasaki8 technique, which has been usedKoster et al. for the preparation of clean TiO2-terminatedSrTiO3 substrates.9 The as-received substrates were ultsonically soaked in demineralized water maintained100 °C for 10 min. Finally the substrate was etched usinBHF solution (pH55.5) and annealed at 950 °C in 103 Pa ofpure oxygen before the deposition, in order to clean areconstruct the terrace structure. Friction and topogrameasurements performed in contact mode using a NANSCOPE III ~Digital Instruments! atomic force microscope~AFM! show a well-ordered, mainly single terminated aslightly vicinal, surface with a terrace width of 80 nm@Fig.1~a!#. No attempt was made to identify the terminating layof treated substrates.

The samples have been grown by on-axis diode sputtein high oxygen pressure, as reported in Ref. 10 using a tawith a stoichiometry Y1Nd0.1Ba1.9Cu3O72d . The film-targetdistance is 15 mm, the deposition temperature is 850 °C,the oxygen pressure is 200 Pa. Two different oxidation pcesses have been adopted. The first procedure consistannealing in oxygen at 2.53103 Pa and 700 °C for 20 minthe second consisted in a longer annealing~1 h! in 2.53104 Pa oxygen at 500 °C. In both cases, thick films shTc>86 K, DTc.0.8 K, Jc(77 K)>23106 A/cm2 andJc(4.2 K) of 3.53107 A/cm2, as measured by an inductivtechnique.11

The surface morphology of the films has been invegated by AFM in contact mode. As shown in Figs. 1~b!–1~d!,the surface of YNdBCO is composed of islands. The islathickness is equal to one unit cell~u.c.! or multiples. Boththe mean terrace width and the meanRq

2 roughness increasin thicker films. Compared to YBCO sputtered films, fewgrowth spirals are present. The islands show a squared shwith sharp edges parallel to the substrate principal axSmall precipitates, probably Nd2O3 or Y2O3 grains, are ran-domly dispersed on the surface. In contrast, large precipitare absent.

The film thicknesst has been determined accuratelyfitting Pendello¨sung fringes that can be clearly distinguish

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around symmetric~001! reflections for the thinnest sample~up to 36 unit cells films!, as shown in Fig. 2. For thickesamples, the determination is instead based on the sputtetime. Films with different thickness~250, 125, 62, 32, 16, 10and 8 u.c.! have been analyzed to measure thea-, b- and

FIG. 1. AFM topography obtained in contact mode of~a! anetched and thermal treated LaAlO3 substrate and~b! a 10 u.c.,~c! a32 u.c., and~d! a 125 u.c. YNdBCO film. The horizontal scale5003500 nm2 for each image while the height scales~black towhite! are~a! 0–3 nm,~b! 0–6 nm,~c! 0–12 nm, and~d! 0–16 nm.

FIG. 2. Low-angleq –2q x-ray diffraction spectra for a~a! 8u.c.,~b! 12 u.c., and~c! 32 u.c. YNdBCO film deposited on LaAlO3substrates. Each spectrum is shifted for clarity. Note the Pend¨-sung fringes around the~001! reflection from which an accurateestimation of film thickness is obtained.

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EFFECT OF STRAIN ON THE STRUCTURE AND . . . PHYSICAL REVIEW B66, 184518 ~2002!

FIG. 3. v –2q maps aroundthe ~038!-~308! reflections ofYNdBCO characterized by differ-ent thickness:~a! 10 u.c., ~b! 16u.c., ~c! 32 u.c., ~d! 63 u.c., ~e!125 u.c., and~f! 250 u.c. The datahave been fitted using a standa2D Lorentian profile~not shown!.

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c-axis lengths. X-ray diffraction of the~005! peak allowedc-axis length determination. The full width at half maximuof the rocking curve around the~005! reflection is less than0.12° for all the samples considered in this work.a and bevaluation is instead achieved resorting tov –2q mapsaround the~038!-~308! reflections~Fig. 3!. In order to im-prove the statistics, long acquisition times~up to 3 days!were employed in the case of very thin films. The~005! peakhas been detected before and after long data acquisitioorder to exclude possible oxygen loss during the measments. No sensitive variation of thec-axis length has beendetected, even in the case of very thin samples. The valua, b, andc have been obtained by a fitting procedure, invoing a one-dimensional Lorentian profile for~005! peaks, anda two-dimensional~2D! Lorentian for the~038!/~308! maps.In Figs. 4 and 5 the results are resumed. The YNdBCOa-andb-axis lengths approach each other with decreasingthickness, but remain far from the substrate lattice spac(as50.379 nm). At the same time, thec axis remains ap-proximately constant down to a 32 unit cell sample, andslightly increases in the 10 unit cell film. Finally thec axisincreases substantially in the 8 u.c. thin film, for which wwere not able to determine the in plane structure.

The critical temperature of samples with different thic

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ness has been determined either inductively or resistiv~using a zero-resistivity criterion!, obtaining consistent results~Fig. 6!. The YNdBCO films haveTc lower than YBCOfilms prepared in the same deposition setup~which is 91 K!.Moreover, the slope of theTc vs t plot is steeper than for

FIG. 4. Measureda (m) and b (d) lattice parameters of theYNdBCO films deposited on LaAlO3 substrates plotted againssample thickness. The solid line is a theoretical estimation folloing Eq. ~2! ~see text!.

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SALLUZZO, ARUTA, AUSANIO, D’AGOSTINO, AND DI UCCIO PHYSICAL REVIEW B66, 184518 ~2002!

YBCO deposited on the same substrates.2 Both effects areprobably related to a reduction of the carrier densityn, asseen by Hall-effect measurements on thick films (n.231021 cm23), due to the Nd31 doping.

II. DISCUSSION

Our data allow us to discuss two distinct features of tYNdBCO films, namely the structural effects of the strainduced by the substrate and the depression of the critemperature with decreasing film thickness. A first result tdeserves some attention is the fact that the YNdBCOa andbaxes come closer and closer to each other, but their vdoes not seem to approach the lattice spacing of thestrate, nor does in-plane area of the film cell approachsubstrate cell area. This result is quite surprising at first,it can be understood in terms of a standard model of stdue to interface effects. To this aim, we note that the eqlibrium length of the lattice parameters is given by the mimization of the Gibbs energy~per unit area! of the film. Therelevant terms are the elastic energy, which is proportionathe film thickness, and the interface energy:

FIG. 5. Measuredc axis (L) of YNdBCO films plotted againstfilm thickness and calculatedc axis (d) determined using Eq.~3!.In the inset the measured cell volume vs sample thickness isshown.

FIG. 6. The measured critical temperature of the YNdBCO filvs sample thickness (d) and the theoretical critical temperatuaccording to an elastic stress model@Eq. ~4!, L symbol#.

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wheret1 andt2 are two length scales that depend onCi j andgi j . The continuous line plots superimposed on the expmental data in Fig. 4 are obtained from Eq.~2!, with t151u.c. andt2510 u.c. Notice that this is not the result offitting procedure; the choice of these values is based ontuitive considerations. In particular, the choice oft1 impliesthat a perfect match with the substrate is only possiblefilm thickness of the order of 1 u.c., while the value oft2 hasbeen chosen supposing that in our case at 10 u.c. therecrossover from a tetragonal to an orthorhombic unit cUnfortunately, no experimental data have been collectedthe 1–10 u.c. range due to sensitivity limitations of the x-rsetup. Such experimental results can be obtained by usynchrotron radiation.13 Note that whent1.t2 another ex-pression is obtained for thea andb parameter versus the filmthickness. In particular, in that case no pseudomorpgrowth is expected even at 1 unit cell, and the film becomorthorhombic upon cooling at room temperature just afone unit cell is deposited.

In spite of the qualitative agreement, we believe thatwhole experiment cannot be interpreted in the frameworkan elastic theory for small lattice deformations alone. Oproblem with Eq.~2! is the choice of a meaningful paramett1, which is assumed to be 1 u.c. in the case of our samand in Fig. 3. This choice is quite arbitrary and not realistThe second and probably more important reason for wh

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EFFECT OF STRAIN ON THE STRUCTURE AND . . . PHYSICAL REVIEW B66, 184518 ~2002!

we think that elastic strains alone cannot explain the pnomena comes from the application of the model tostructural changes along thec axis. In the case of an elastideformation due to in-plane stress, that is when the stcomponentscc is zero, the equilibriumc-axis strain«c isrelated to thea- andb-axis strains («a and«b, respectively!through the equation

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We can evaluate«c from Eq. ~3!, given the experimentavalues of«a ,«b , and taking the elastic moduliCi j of YBCOsingle crystals from the literature.12 Note that this last assumption is justified by the fact that our samples are vsimilar to YBCO films since the amount of Nd-Ba substittion is very small~about 5%!. The results are reported in Fig6. The disagreement between calculated and experimec-axis values is striking, since Eq.~3! foresees a decreasethe c-axis length with decreasing film thickness, that isbehavior opposite from the experimental evidence. Moover, based on our measurements, the cell volume is founchange with the thickness, which is again in contrast wpure elastic deformation.

This result differs from that of Varelaet al.4 The authorscalculated thec axis of YBCO layers in their YBCO/PBCOmultilayers, resorting to Eq.~3!. Assuming that a 1 u.c. thickYBCO film would perfectly match a PBCO lattice inYBCO/PBCO multilayer, they found good agreement wexperimentalc-axis length values. There are several diffeences, however, between YBCO/PBCO multilayers andYNdBCO films on LAO substrates. First of all, the sandwistructure of a multilayer implies that YBCO is subject to twinterface stresses, instead of one. Moreover, the latticematch of YBCO with respect to PBCO is smaller than tmismatch between relaxed YNdBCO films and LAO. Itreasonable that an elastic strain takes place in very thin fiin the case of moderate mismatch.

In order to see if elastic strain can explain theTc depen-dence on the film thickness in a simple way, we have triedcompare the measured values with data calculated byequation

DTc~«a ,«b ,«c!5]Tc

]«aD«a1

]Tc

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]Tc

]«cD«c . ~4!

Here we assumed that the change ofTc with uniaxial defor-mation is determined by the uniaxial]Tc/]« i pressure coef-ficients of YBCO.14,15 The results are shown in Fig. 6; thmodel gives a slight increase ofTc with decreasing filmthickness, in striking contrast to experiment. It shouldmentioned that, concerning the electronic properties,samples are slightly different from YBCO films and in paticular are characterized by a lower concentration of mobholes per CuO2 plane. However, it is well known that undedoped~oxygen deficient or cation substituted! YBCO crys-tals are characterized by a more pronounced, positive, dedence ofTc on the pressure.16 The more pronounced effect iunderdoped YBCO samples has been attributed in Ref. 1

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a change of the mobile holes with pressure. Thereforeincrease ofTc is expected to be even larger in our sampthan the values predicted by Eq.~3! using the coefficientsassigned to an optimally doped YBCO crystal. This is, in oopinion, a direct proof that the mechanism of supercondtivity depression in thin YBCO films cannot be relatedelastic strain. Other authors reached similar conclusionsthe case of YBCO thin films deposited onto SrTiO3 andLaAlO3 substrates.2 In Ref. 2 the slower reduction of thecritical temperature of YBCO deposited on LaAlO3 sub-strates compared to SrTiO3 is claimed to be opposite to thexpectation. However, as we have shown here, it is not psible to suppose thata andb axes of YBCO films are equal tothe substrate axis for any thickness. Therefore our resdemonstrate, in our opinion with a more solid experimenbasis, that uniaxial pressure effects cannot explain the crittemperature change in YNdBCO and YBCO samples.

In contrast, when the mismatch becomes larger, inelastrain is more plausible. Such inelastic effects may be dua reordering of the oxygen sublattice in the Cu~1!-O planes,whena andb parameters become comparable. This mecnism may also be responsible of the abrupt crossover totetragonal structure, that is in fact not correctly describedthe elastic model of Eq.~2! for physically meaningful valuesof the scale lengtht1 as discussed above. In contrast, intrducing inelastic effect accompanied by oxygen sublatticeorganization, it is possible to explain the observed changthe c axis and the observed increase of the cell volumWhile we think that very thin films contain the same oxygconcentration as thicker films~also confirmed by the fact thatwo different annealing procedures in the thinnest filmsnot change the structure!, an expandedc axis and cell vol-ume in the thinnest films can be produced by inelasstrains.

At present, we are not able to determine directly the rson forTc suppression. However, our data suggest that soplausible mechanisms can be ruled out:~a! The Tc depres-sion takes place at relatively high film thickness, so that ato 2D transition in the electronic properties of the materiaexcluded.~b! The effect can hardly be related to oxygedeficiency in thinner films. Nd-doped YBCO presents an ecess oxygen concentration in the Cu~1!-O planes. In fact, foreach Nd31 that substitutes a Ba21 ion, 1

2 O22 is allowed inthe structure to preserve the charge neutrality.17 Since thefilms have roughly 5% of Nd31 at Ba sites, we expec'2% –3% oxygen excess. Moreover, the films are eaoxygenated during the cooling, quite independently ofemployed procedure, and are very stable as demonstratex-ray measurements. Surface oxygen depletion cannoruled out; however, this effect, if present, is generally blieved to affect only the topmost layers, whileTc depressionis sensitive for 50 u.c. thick films. Finally, oxygen depletioshould determine a much larger increase of thec-axis length,with respect to observed values.~c! An increased cationicdisorder in thinnest films~that is, exchanges between Nd anBa! may affect the superconducting properties. Howeva reduction of thec-axis length is expected, contrary to eperimental evidence.~d! Also the twinning of the LAO sub-strate may have a minor role on the superconductivity

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SALLUZZO, ARUTA, AUSANIO, D’AGOSTINO, AND DI UCCIO PHYSICAL REVIEW B66, 184518 ~2002!

ultrathin films. AFM shows that twin domains are certainlarger than 535 mm2 in our substrates. Then, hundreds2D YNdBCO islands will be formed during deposition insingle LAO domain. Therefore, the density of defects tcan be related to substrate twinning should be much lothan the density of twin boundaries of the YNdBCO filitself and of its columnar defects formed during the depotion process.

On the other hand, structural data support the idea ofelastic strain in thin YNdBCO films. Our results are a clthat inelastic structural changes related to oxygen reordeplay an important role. For this reason we believe that inot unconceivable that, due to the strain field, stable ortrhombic domains in thinner films, which are characterizedlower bulk condensation energy and higher surface eneare less stable than tetragonal ones and that therefore oxis not able to form ordered chains. Indeed the reducedference betweena- and b-axis lengths suggests that somreordering of the oxygen ions within the Cu~1!-O plane maytake place, leading in the end to the suppression of‘‘chain’’ structure. This in turn affects the electronic prope

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ties of samples, for example, by decreasing the hole dopand consequently the superconducting transition tempture.

In conclusion, we have performed accurate measuremof the a-, b-, andc-axis lengths of YNdBaCuO films deposited on LaAlO3 substrates. We investigated the correlatibetween the stress due to the substrate and the obsestrain, as a function of film thickness. Finally, we related tsuperconducting critical temperature of thin films to tstrain. A clear picture of the structure deformation duemismatch with the LaAlO3 substrate emerges from our datWe discussed the experimental results in terms of an inelastrain of the films, due to oxygen reordering in the Cu~1!-Oplanes under stress, also arguing that this is the mecharesponsible forTc depression.

ACKNOWLEDGMENTS

The present work has been partially supported byCIPE A3, 5% CNR Projects. The authors are grateful toZegenhagen, L. Lanotte, and F. Miletto Granozio for the uful discussions and suggestions on data interpretation.

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