Growth and properties of laser-ablated Bi2Sr2CaCu2O8+δ thin films

Physica C 199 ( 1992 ) 112-120 North-Holland

Growth and properties of laser-ablated Bi2Sr2CaCu208 +6 thin films R. Seemann, F. H~inisch, A. Sewing and R.L. Johnson II. Institut J~r Experimentalphysik, UniversittitHamburg, Luruper Chaussee 149, W-2000Hamburg 50, Germany

R. de Reus ~ and M. Nielsen Department of Solid State Physics, Rise National Laboratory, DK-4000 Roskilde, Denmark

Received 11 June 1992

Thin films of Bi2Sr2CaCu2Os+~have been fabricated by laser ablation on single crystal MsO (001 ), LaA103 (001) and NdGaO3 (001) substrates. The superconducting transition temperature Tco is above 80 K with critical current densities of 4× 105 A/cm 2 at 55 K. The structure and morphology of the films were investigated using scanning electron microscopy, scanning tunnel microscopy and X-ray diffraction. All films show c-axis orientation with a texture of less than 0.2 ° . Films deposited on MgO (001) are mostly randomly oriented in the a, b-plane although preferential orientations with rotational angles of 11.5° and 45 ° were observed close to the substrate/film interface. On LaA103 (001) and NdGaO3 (001) substrates the a, b-plane orientation is improved and about half of the film is epitaxiallyoriented.

1 Introduction High-quality superconducting thin films are required for a wide range o f technological applications in such diverse fields as m i c r o w a v e resonators, infrared r a d i a t i o n detectors a n d superconducting q u a n t u m interference devices ( S Q U I D s ) . Thus, it is o f p a r a m o u n t importance to optimize the growth and properties o f superconducting thin films. Since the a n n o u n c e m e n t o f high t e m p e r a t u r e superconductivity in the B i - S r - C a - C u - O system by M a e d a et al. [ 1 ] a lot o f research has been p e r f o r m e d on these materials. The family o f B i - S r - C a - C u - O superconductors can be classified according to the n u m b e r o f CuO2 layers in the unit cell a n d described by the form u l a Bi2Sr2Can_lCunO4+2n. The most c o m m o n c o m p o s i t i o n s are BiESrECuO6 +~ with one CuO2 layer ( n = l or 2201 p h a s e ) , BiESr2CaCu2Os+a with two CuO2 layers (n=2 or 2212 phase) and Bi2SrECa2Cu3Olo+~ with three CuO2 layers ( n = 3 or 2223 p h a s e ) . The c-axis lattice constants o f these c o m p o u n d s are 2.46, 3.06 a n d 3.71 n m a n d the corl Present address: Mikroelektronik Centret, DTH bdg 345 - O DK-2800 Lyngby, Denmark.

responding critical t e m p e r a t u r e s where the resistivity vanishes (Too) are 10 K, 85 K and 1 10 K; compounds with four and five CuO2 layers have also been reported [2,3 ], but to date single phase samples could not be synthesized. N u m e r o u s techniques can be used to prepare superconducting thin films; magnetron sputtering [4,5 ], coevaporation [6,7 ], ion-beam sputtering [8 ], electron-beam evaporation [ 5 ] and laser ablation [ 9 ] are all used routinely. We e m p l o y pulsed laser deposition because it is known that this technique can p r o v i d e stoichiometric transfer o f material from the target to the substrate. The m e t h o d is c o m p a r a t i v e l y recent - it was first used for deposition o f high-To superconductors by D i j k k a m p et al. in 1987 [ 10]. In the past most efforts have concentrated on preparing thin films o f the 1-2-3 c o m p o u n d s , such as YBa2Cu307 -x, a n d great progress has been achieved. In particular high quality thin films with excellent electrical properties can be p r e p a r e d routinely using " i n situ" deposition techniques in which the material is deposited at a m o d e r a t e substrate t e m p e r a t u r e 5 0 0 ° C - 7 0 0 ° C and superconducting films are obtained without subsequent high t e m p e r a t u r e annealing. The chemical stability a n d layered structure

0921-4534/92/$05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.

R. Seemann et al. /Properties of Bi:,SreCaCu2Os+6thinfilms

of the B i - S r - C a - C u - O system (BSCCO) make it particularly suitable for technological applications and attempts have been made to develop "in situ" processes for BSCCO [ l l - 1 6 ] . One problem with "in situ" methods for BSCCO is the loss of Bi due to its high vapour pressure during high temperature processing; however, this can be compensated by using targets with an excess of Bi. Nevertheless, the electrical properties of such films are generally not as good as the electrical properties of films prepared with post-annealing [ 17 ]. In this paper we discuss the preparation of post-annealed thin Bi2SrECaCu208+6 films with optimized electrical properties. The analysis of the X-ray diffraction results provides some insight into the growth mechanisms of the films on different substrates.

2. Preparation of

Bi2Sr2CaCu2Os+athin

films

113

To achieve high-quality superconducting thin films it is essential to have stoichiometric transfer of the material from the target to the substrate [ 19 ]. The substrate temperature has to be high enough to form the correct bonding configurations in the material deposited [ 20 ] yet below the temperature at which the material reevaporates. As a first step in optimizing the deposition parameters the electrical resistivity and the stoichiometry of the films were studied as a function of the energy density of the laser beam. The deposition temperature was held constant at 450°C and the furnace temperature was fixed at 830°C for the post-annealing. Some of the electrical properties used to characterize the quality of the films are shown in fig. l; namely the onset of the superconducting transition To on, the transition temperature Too, the transition width 6(85%-15%) and the ratio of the film resistances at 300 K and 150 K (R3oo/R15o). A good single-phase film should have a high Too, small 6, Tcon should be close to T~o, and

The Bi2SrECaCu208+ 6 films were prepared by pulsed laser ablation using a XeC1 excimer laser operating at 308 nm with a repetition rate of 5 Hz and a pulse length of l0 ns. The total energy of the beam was around 90 mJ per pulse, but in order to obtain a well-defined focus at the target an aperture was used to mask offthe edges of the beam which reduced the energy to 50 mJ per pulse. The beam was rastered and focused onto the target at an angle of incidence of 25 ° and the distance from the target to the substrate was 28 mm. The target was a sintered cylinder of 20 m m diameter with the nominal composition Bi2SrECaCu208 + a [ 18 ]. Polished MgO single-crystal substrates were used for the optimization of the growth parameters. The substrates were mounted on a 15 m m diameter, 2 m m thick stainless steel disc with stainless steel clamps and the temperature was monitored with an encapsulated N i - C r N i thermocouple inserted in the sample holder. The substrate was heated using IR-radiation coupled to the sample holder via a quartz light-pipe from a 2 kW quartzhalogen lamp outside the vacuum chamber. The apparatus was evacuated with a turbomolecular pump to a pressure of 2 × 10- 7 mbar but during the ablation process the chamber was filled with oxygen to 0.2 mbar. After deposition air was let into the system and the annealing was performed at atmospheric

Fig. I. Electrical properties of Bi2Sr2CaCu2Os+6 thin films on M g O (001 ) for differentenergy densitiesof the laserbeam at the target.The following symbols are uscd: (~) is Tc o~,the onset of the superconducting transition, ( [] ) R3oo/R~5o, the ratio of the resistancesat 300 K and 150 K, ((3) T~o, the superconducting transitiontcmpcraturc, and ( A ) J, the transition width using the

pressure.

85°/o-150/ocriterion.

Tc [Z] [] : Rs0o/R15o

loo

1.6 1.4

80 1.2

60

A : d(K)

40

10

•

9 8 7 0

I

0

0.75

I

I

I

1.5

2.25

3

Y

Z/A (J/cm')

114

R. Seemann et al. /Properties of Bi2SreCaCu2Oe+a thin films

(R3oo/Rlso) should be 2. From fig. 1 it can be seen that Too and R3oo/Rlso have maxima and J has a

minimum for an energy density of 0.75 J / c m 2. The stoichiometry of the films was determined by X-ray photoelectron spectroscopy (XPS), total-reflection fluorescence analysis (TRFA) and Rutherford backscattering spectroscopy (RBS). The nominal composition of our films was Bi: 1.7, Sr: 2, Cu: 2, Ca: 1.1; i.e. the Bi content was always lower than that of the target. It can be concluded that even at a deposition temperature of 450°C some Bi is lost during the ablation process. Figure 2 shows the effect of varying the deposition temperature on the electrical properties of the films. The annealing temperature of the furnace was fixed at 830°C and the energy density was kept constant at 0.75 J/cm 2. Although T~on increases linearly with deposition temperature from room temperature to 800°C, the resistance ratio (R3oo/R15o) and T¢o show broad maxima at around 320°C and distinct maxima between 450 and 520°C. The minimum value of J occurs at about 500°C, so this deposition temperature should yield the best superconducting films.

At higher temperatures a significant loss of Bi was observed. The results of the optimization of the post-annealing temperature are summarized in fig. 3. In this case the energy density was fixed at 0.75 J/cm 2 and the deposition temperature at 450°C. The results shown here were obtained by annealing the samples in air in a separate tubular furnace. By annealing the samples in the deposition chamber back-filled with air without cooling to room temperature between deposition and annealing smoother films were produced (see fig. 4) hut the electrical properties hardly changed. The best films were achieved by annealing at 852°C which is only about 7°C lower than the temperature at which the film starts to reevaporate from the MgO (001) substrate. With these optimised deposition parameters for our laser deposition process we are able to fabricate routinely thin films of BiESr2CaCu2Os+~ with Too> 80 K. The deposition rate with our experimental setup is 0.2 nm/s and the films used in this study were typically 150 nm thick.

1 I0

100 I

~-0"

80 ~---Tc0

~,

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60

~

_

.

.

.

1.7

50

1.6 1.5 1.4

4O ~ ! e (K) 20

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0

0

200

400

600

800

Td.p¢C) Fig. 2. Electrical properties of Bi2Sr2CaCu2Os+6thin films for differentdepositiontemperatures.

L

i

J

I

825 835 845 855 865 875

Tpo.t (~C) Fig. 3. Variation of the electricalpropertiesof Bi2Sr2CaCu20.+ thin films as a functionof the annealingtemperature.

R. Seemann et al. /Properties of Bi2Sr2CaCu208+~ thin films

Fig. 4. (a) SEM image of a Bi2Sr2CaCu2Os+6thin films on MgO(001 ) post-annealed in a furnacewith intermediate cooling to roomtemperature between deposition and annealing; (b) SEM image of a film annealed in the deposition chamber. Note the remarkable difference in surface roughness.

3. Properties of the films The surface morphology of the thin films was investigated with scanning electron microscopy (SEM) and scanning tunneling microscopy (STM). Figure 4(a) shows an SEM image of a furnace-annealed sample and fig. 4 (b) an image of a sample annealed in the growth chamber. It can be seen that the film annealed inside the apparatus is smoother and the domains are larger than for the sample annealed in the furnace. Using optical microscopy we found that holes in the films are correlated with defects on the substrate which induce local desorption of the film. Energy dispersive X-ray analysis shows that regions

115

near holes (e.g. as indicated by the arrow in fig. 4) have a stoichiometry of Bi2Sr2CuO6+a (the n = 1 phase). On the surface of furnace-annealed samples defects in the form of needles of length I - 4 lam and width ~0.5 ~tm were found with composition (Sr, Ca) CuOx. it is likely that the bismuth deficiency of the films together with defects in the substrate promote the local growth of Bi2Sr2CuO6+~ and (Sr, Ca)CuOx-phases. Our STM measurements show that Bi2Sr2CaCu2Os+a grows in a completely different manner to YBa2fu307_x thin films. Platelets are formed with horizontal dimensions of several ~tm on each side with step heights of around 3 nm, which corresponds to the c-axis length of Bi2Sr2CaCu2Os+~. Step heights of one half, three-halves and twice the c-axis are also found. Films with some of the above mentioned defects also have 2.5 nm steps which correspond to Bi2Sr2CuO6+a, the n = 1 phase, and steps which can be assigned to the n = 3 phase are sometimes observed. Figure 5 shows a grey scale STM image recorded over an area 200 × 200 nm 2 of a film annealed in the deposition chamber. The STM measurement was performed in constant current mode with a tunnel current of 50 pA and a tunnel voltage 0.5 V. The dynamic range of the grey scale is 10 nm. Two typical growth columns with a c-axis of 3.06 nm can be seen along with a number of characteristic growth defects.

O tt~

O O v-4

O tt~

O

Ohm

50nm

lOOnm

150nm

Fig. 5. STM image of the surface of a Bi2Sr2CaCu2Os+afilm on MgO(001 ). The dynamic range of the grey scale is 10 nm and the tunnel parameters were Vt...~l=0.5 V, I~...~j=50 pA.

116

R. Seemann et al. /Properties of Bi2Sr2CaCu2Os+~ thin films

X-ray diffraction measurements ( X R D ) were performed to investigate the orientation of the Bi2Sr2CaCu2Os+6 films relative to the single crystal substrates. The c-axis texture was determined with high angular resolution using a two-crystal-diffractometer [21 ]. Figure 6 shows a three-dimensional view of the (0 0 10) peak of a furnace-annealed BSCCO thin film. The intensity is displayed on a logarithmic scale. The position sensitive detector was fixed to detect all X-rays scattered between 25.3 ° and 32.3 ° in 20 while 0 was varied in steps Of 0.1 ° between 10.6 ° and 18.6 ° . Even though the film was furnace-annealed the texture of the c-axis is around 0.2 ° and films that were annealed in the growth chamber have an even smaller texture. The wide distribution of intensity around the Bragg reflection at 0 = 14.6 ° shows that there are misaligned regions. It should be noted that films deposited at 500°C and not annealed at higher temperatures are noncrystalline. It is known that the superconducting currents are strongly anisotropic and flow in the CuO2-planes so the orientation of the a, b-planes of individual domains should markedly influence the superconducting properties of thin films. Grain boundaries between misaligned and rotated domains limit the critical current density Jc [ 22 ]. The effect of sample microstructure on intergranular currents can be investigated with AC magnetic susceptibility measurements. The results from our samples show that the susceptibility as a function of the applied magnetic field varies about ten times more for furnace-annealed samples than for those annealed in the growth

chamber. The critical current densities obtained at 55 K with the Bean model [23] are l04 A / c m 2 for the furnace-annealed samples and 105 A / c m 2 for the growth-chamber annealed samples. Obviously the films annealed in the growth chamber have fewer weak links than the furnace-annealed films. The alignment of the a, b-plane of the epitaxially grown films was investigated using a four-circle Xray diffractometer with the geometry shown in fig. 7. In the Bragg-Brentano configuration ~0and Z are defined as the rotation angles of the crystal around the [001 ] and [010] axes of the film, respectively. Figure 8 shows a pole figure (Z-~o scan) of ( 115 ) Bragg peak of Bi2SrECaCu2Os+6 from a film 150 nm thick containing both epitaxial and randomly-oriented domains. The randomly-oriented regions produce the modulated ridge of intensity at Z~ 58 °. The peaks observed at ~0= 45 ° + n × 90 ° correspond to the wellaligned (115), (i15), ( 1 i 5 ) and (175) planes of the film. The two peaks at ~0=45 ° + 11.5 ° indicate the presence of domains which are rotated 11.5 ° in the a, b-plane. These peaks can be seen more clearly in fig. 8 (b), which shows the pole figure of the ( 115 ) peak of a film only 26 nm thick. The contribution from disordered regions is smaller than the peaks are narrower than for the thicker film. The first stage of thin film formation apparently takes place in an epitaxially rotated growth mode with ~0= 11.5 ° due to

co+O

u% c 0~ C 0% 0

0

,~,v

25,3

20

32,3

Fig. 6. High resolution X-ray diffraction measurement of the (0 0 10) peak of Bi2Sr2CaCu2Os+~.The FWHM in the 0 direction is 0.2 °.

Fig. 7. The geometryof the four-circlediffractometerused for the XRD measurements.

R. Seemann et al. /Properties of Bi2Sr2CaCu2Os+6 thin films

~

117

1(3~3

eo

o (a)

BSCCO(IO) M¢0(10) Fig. 9. Schematic to explain the epitaxially rotated peaks in fig. 8. The reciprocal lattice planes parallel to the surface (the basal plane) of both the B i2Sr2CaCu208 +a film and the MgO substrate are shown. Epitaxial rotations occur predominantly when the vector (j) is parallel to a high symmetry direction of either the film or the substrate. F o r j # [ 100 ] as shown the rotational angle (0 is given by sin (45 ° -q~) = sin ( 135 ° ) aMgo/aascco.

¢

Q Fig. 8. X R D ;(-~ scans of the Bi2Sr2CaCu2Os+~ (115) reflection of films deposited on MgO. The thickness o f the films were (a) 150 nm, (b) 26 nm. The peak at ~ = 45 ° is the ( 115 ) Bragg peak of Bi2Sr2CaCu2Os+~.

the 10% mismatch in the corresponding crystallographic axes of BiESrECaCu2Os+8 and MgO (001). This rotational growth mode also has been observed recently by Hung et al. [24 ]. A simple explanation for this particular orientation of the film relative to the substrate may be found following the general method of ref. [25 ]. Consider the lattice planes parallel to the surface of both the film and the substrate (see fig. 9). We now rotate these relative to each other and look for particularly favourable orientations. The distortions produced by the mismatch of film and substrate are described by periodic functions with vectors joining the reciprocal lattice points in one lattice with points in the other. Favourable orientations are likely to be found where such vectors are parallel to a high symmetry direction in the substrate or in the film. The 11.5 ° rotational angle of the Bi2Sr2CaCu2Oa+a film found experimentally here constitutes an instructive example of this effect. A simple geometrical consideration shows that when the vector from the (110) reciprocal lattice point of MgO to (110) of

Bi2Sr2CaCu2Os+a is parallel to the [ 100] direction of Bi2Sr2CaCu2Os+a, the rotational angle is 11.5 °. Despite the fact that the lattice parameters of Bi2SrzCaCu2Os+a ( a = 0 . 5 4 0 nm, b=0.541 nm) and MgO (a=0.421 nm) have a mismatch of ~ 10% the resulting thin films have remarkably good electrical properties. By using different substrates which provide better lattice matching it should be possible to grow epitaxial films with even better electrical properties. To investigate this possibility we deposited Bi2SrzCaCu2Os+a on NdGaO3 (001) ( a = 0.384 nm, b=0.389 nm, c=0.385 nm; misfit ~ 1%) and LaA103 (001) (a=0.379 nm, misfit ~0.8%) single-crystal substrates with the same deposition parameters as for the MgO(001 ) substrates. Figure 10 shows pole figures of the (115) Bragg peak of a BizSr2CaCu2Os+a thin films grown on NdGaO3 (001 ). The ( 115 ) and ( i 15 ) Bragg peaks can be seen clearly at ~ o = - 4 5 ° and ~0=45 ° for X~ 57.5 ° in fig. 10 (a). However, a closer look at the data on an expanded scale (fig. 10 ( b ) ) reveals the presence of additional intensity at X~57.5 ° for arbitrary ~ which is due to the (115) reflections from domains randomly oriented in the a, b-plane. From the integrated intensities it can be estimated that approximately equal amounts of Bi2Sr2CaCu2Os +a are randomly a, b-plane oriented and truly epitaxial. Note that no preferred rotated orientations are ob-

118

R. Seemann et al. I Properties of Bi2SreCaCueOs+a thin films

~i %%%

(313

%° l

/1t

%0

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¢0%

%

<-9

-'~'~

< ~ " ~ ~

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Fig. 10. X R D measurements of a Bi2Sr2CaCu208+~ film on NdGaO3 (001); (a) shows a pole figure of the ( 115 ) reflection, The two sharp peaks at ( 0 = - 4 5 ° and + 4 5 ° indicate epitaxial growth. In (b) the intensity scale has been expanded to illustrate the presence of randomly in-plane oriented domains.

served in this case which reflects the closer lattice match between NdGaO3 and BiESr2CaCu2Os+6. Figure I 1 shows a pole figure of the ( 115 ) Bragg peak of a BiESr2CaCu208+~ thin film grown on LaAIO3 (001). The mosaic spread is 0.6 ° in ~p and 0.8 ° in X. Since the X-ray diffractometer has an angular resolution of 0.2 o in ~ and 0.8 ° in g the mosaic spread in Z is <0.8 ° . As in the case of Bi2Sr2CaCu2Os+~ on NdGaO3 substrates there are also randomly-oriented domains present in thin films grown on LaA103 and again about equal quantities of randomly in-plane oriented and fully epitaxial domains are present. It should be noted that the "background" due to randomly-oriented domains shows additional structures that can be seen better in fig. 12, which shows a (o scan at Z= 58.3 °. The additional peaks cannot be explained in terms of an orthorhombic splitting and they occur even though the lattice constant difference between LaAIO3 and

<-?

~ <~"='<_o Fig. 11. X R D measurements of a Bi2Sr2CaCu208+~ film on LaAIO3 (001 ); (a) shows a pole figure of the (115) reflection and (b) the intensity plotted on an expanded scale.

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Fig. 12.9scan at X=58.3 ° o f a Bi2Sr2CaCu2Os+6 film on LaA103 (001). The strong peaks at ~ = 0 °, 90 ° and 180 ° (intensity: 7>< 105 cts/50 s) indicate epitaxial growth. The smaller peaks are from domains rotated in the a, b-plane and the peaks at ~ = 4 5 ° and 135 ° are due to misoriented regions of the substrate.

R. Seemann et al. / Properties of Bi eSreCaCu 208+6 thin films

Bi2Sr2CaCu2Os+~ is smaller than for NdGaO3. It is possible that these extra peaks are i n d u c e d by the phase transition between the trigonal a n d cubic phases o f LaA103 at 435 °C. The electrical properties o f the films on LaAIO3 and NdGaO3 are quite similar to the Bi2Sr2CaCu208+~ thin films grown on M g O ( 0 0 1 ) , b u t higher critical current densities o f ~ 4 × 105 A / cm 2 were achieved. By using N d G a O 3 (001) substrates or substrates with suitable buffer layers o f L a A 1 0 3 / N d G a O 3 (001 ) a n d non-stoichiometric targets it should be possible to increase the d e p o s i t i o n t e m p e r a t u r e during the laser ablation process and thereby achieve better epitaxial growth.

4. Conclusions The parameters for the preparation of Bi2Sr2CaCu208 ÷~ thin films using laser ablation have been optimized. The best films were o b t a i n e d with a deposition t e m p e r a t u r e o f 500°C in an oxygen pressure o f 0.2 m b a r a n d subsequent annealing in air at a p p r o x i m a t e l y 852 °C for 5 min. X-ray diffraction studies on these films indicate a c-axis texture o f less than 0.2 °. The films d e p o s i t e d on MgO consists m a i n l y o f d o m a i n s in which the a, b-planes are rand o m l y rotated a r o u n d the c-axis. The films d e p o s i t e d on LaA103 (001) a n d N d G a O 3 (001) substrates consist o f b o t h epitaxial a n d r a n d o m l y a, b-plane oriented d o m a i n s in a p p r o x i m a t e l y equal amounts. On all substrates critical t e m p e r a t u r e Too o f above 80 K are achieved routinely. The critical current density is depressed due to intergranular weak links for films grown on MgO (001 ) substrates, however, films on LaAIO3 ( 0 0 1 ) a n d N d G a O 3 ( 0 0 1 ) substrates reach critical current densities o f 4 × 105 A / c m 2 at 55 K.

Acknowledgements We t h a n k J. Bock from H O E C H S T A G for providing Bi2Sr2CaCu2Os+~ targets. L. Briiggemann, R. Bloch a n d W. press helped with the X-ray diffraction m e a s u r e m e n t s at Kiel University. R. Behr ( U n i v e r sity H a m b u r g ) , P. Vase a n d T. Freltoft ( N K T Research Center, Brondby, D e n m a r k ) p e r f o r m e d magnetic susceptibility measurements. R. Gutschke and

119

R. Michaelis ( G K S S G e e s t h a c h t ) p r o v i d e d the TRFA-results a n d F. G o e r k e the scanning electron micrographs. The staff o f HASYLAB and in particular G.I. von A p p e n p r o v i d e d invaluable technical assistance. This work was s u p p o r t e d by the B M F T under project no. 05 490 CAB a n d the European Community Science Plan under contract ERBSCI*CT000352.

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R. Seemann et al. /Properties o f Bi2Sr2CaCu2Os+ ~ thin films

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[23] C.P. Bean, Phys. Rev. Lett. 8 (1962) 250; idem, Rev. Mod. Phys. 36 (1964) 31. [24] L.S. Hung, S.T. Lee, J.M. Mir, D.H. Shin, Jian Li, J. Silcox and J.W. Mayer, J. Appl. Phys. 71 ( 1992 ) 2356. [ 25 ] F. Grey and J. Bohr, in: Phase Transitions in Surface Films, vol. 267, NATO Advanced Study Institute, Series B: Physics, ed. H. Taub (Plenum, New York, 1991 ).