Thickness and roughness dependence of magnetic flux penetration and critical current densities in YBa2Cu3O7−δ thin films

PHYSICA® ELSEVIER

Physica C 266 (1996) 235-252

Thickness and roughness dependence of magnetic flux penetration and critical current densities in YBa2Cu307_ 8 thin films Ch. Jooss a, A. Forkl a, R. W a r t h m a n n a, H.-U. Habermeier h, B. Leibold h H. Kronmiiller * .a ,p

a Max-Planck-lnstitutffir Metallforschung, Heisenbergstr. 1, D-70569 Stuttgart, Germany b Max-Planck-lnstitutff~r Festk6rperforschung, Heisenbergstr. 1, D-70569 Stuttgart, Germany

Received 8 March 1996; revised manuscript received 10 May 1996

Abstract

As a result of the island growth mode all epitactic YBa2Cu307_ ~ thin films show surface roughness. To investigate a possible surface pinning mechanism, combined magneto-optical and atomic force microscopy studies were carried out. Measurement of the spatial distribution of magnetic flux density on the surface of thin YBa2Cu30 7_ n films by means of the magneto-optical Faraday effect (MOFE) under application of external magnetic fields allows an accurate determination of critical current densities Jc. In order to have a quantitative comparison between the Bean model for thin films and experiment, a new nonlinear calibration technique for the flux densities was developed. For determining the thickness and roughness dependence of jc, samples with YBaCuO-strips of different thickness and roughness were patterned from one film. With the roughness determined experimentally by afm measurements, a satisfactory agreement between the measured and calculated thickness dependence of j~ is achieved. Surface pinning is found to cause between 10%-30% of the critical current densities of epitactic YBa2Cu30 7_ 8 thin films. Additionally microscopic deviations of the flux profiles from the Bean model are detected. Evidence for matching effects of the vortex line distribution with the density of surface pins is given.

1. Introduction Strong vortex line pinning in YBa2Cu3OT_ 8 (YBaCuO) is typically observed in thin epitaxial films. Their critical current densities Jc are about three orders of magnitude larger than for the monocrytalline material and reach some 10 ]l A / m 2 in high quality films at He-temperature. To analyze the origin of flux pinning the influence of many

* Corresponding author. Fax +49 711 689 1010.

types of structural defects as point defects like oxygen vacancies [1-3], grain boundaries [4,5], precipitates [6], intrinsic pinning [7], growth steps on film surfaces [8], dislocation chains in growth terraces [9] and others has been studied. Presently the most important pinning mechanisms and related structural defects are unknown. In this paper experimental results concerning the thickness and roughness dependence of Jc of thin YBaCuO-films are presented. As a result of the island growth mode, all epitactic YBaCuO thin films show surface roughness with a thickness variation of A d > 10 nm [10-12]. Com-

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Ch. Jooss et a l . / Physica C 266 (1996) 235-252

putational simulation of type-II superconductivity in thin films with thickness variation [13] shows that the vortices are attracted to thin regions. If the anisotropy ratio F = Ac/Aab is not too large (YBaCuO: F ~ 5), surface pinning takes places also in a layered superconductor. In this case a correlation length of the approximate two-dimensional pancake vortices along the c-axis of the order of the film thickness is preserved, since films with thickness of more than 50 nm are considered. This follows from linear elasticity theory of the vortex lattice in high-Tc superconductors [14,15]. The line tension P, which is related to the tilt-wavelength Az dependent tilt modulus c44(Az) is a measure, whether local vortex tilt is favoured or not. In YBaCuO the ratio between line tension and line energy per unit length is small ( P / g L < 1) only for short wavelength tilt Az < 50 am. However a systematic study of the influence of surface pinning on the high critical current densities at YBaCuO thin films is still lacking. Therefore the aim of this paper was to investigate a possible contribution of surface pinning of the vortex lines to the high it-values. Because of the sensitive dependence of the material morphology and the defect structure on the fabrication parameters [16], the separation of volume and surface pinning is quite difficult. To analyze these problems a special sample geometry was produced, where superconducting strips with different thickness and roughness were prepared from one YBaCuO film. For such samples, we may expect that they do not differ in their volume defect structure and differences in j~ are caused only by surface pinning.

B Z

/

~~W ....................... X Fig. 1. Sketch of geometry of the YBaCuO strips and choice of the coordinates.

thickness d and width W >> d in the x-direction according to Fig. 1. Because of the geometry the current density reduces to j = Jx ex and the force densities are given by fp = - f t = J × B = jx( Bzey - Byez) = jxBzey.

(1)

2. Theory

The z-component of the force density causes a curvature of the vortex line and is compensated by the elastic forces of the vortex line lattice. In the conventional Bean model [18], which assumes a B-independent critical current density j~(r)=Jc = const., the demagnetizing effects, that become important in flat superconductors are disregarded. Hence, the critical current density is given from Amp~re's law by jc = OBJOy. In the thin film case, j~ is determined by the gradient of the in-plane component OBy/OZ [19], which however cannot be measured by using the MOFE. Hence, the critical current density cannot be determined by measuring the By-gradient, but can be calculated solving Biot-Savart's law for a thin strip, extending infinitely in the x-direction,

2.1. Bean-model for thin strips

Bz( y, Z)= ~P J-w/2J-d/2

The critical state in type-II superconductors is given by the balance between the macroscopic pinning force density fp and the driving force density ft on the vortex distribution. For very small Hot ~ 0, which is fulfilled in YBaCuO thin films, the driving force is identical with the Lorentz force [17] of the flowing critical current density Jc on the vortex lines. We consider an infinitely extended thin strip of

Jx( Y', Z')( y - Y') X (y_y,)2+(z_z,) 2 dr' dz',

fw/2 f /2

(2) B y ( y , z ) = - ix----~°f w / 2 f a / 2 2 p , _ w/2" - d/2 L ( Y', Z')( Z-- Z') × (y_y,)2+(Z_Z,)

2 dy' dz',

Ch. Jooss et al./ PhysicaC 266 (1996)235-252 and comparing the calculated and measured Bz(y)profiles. Brandt et al. [20] found an analytic solution for the current distribution,

2jcn. arctan

Jx(Y)

=

( y ( ( W /,2 ) 2 - Q. '2 ), 1/2 "~ / 2 ( Q--'--7_- ,2 ~,/---" T

0.16Bz

0.12-

[T]

0.08-

oo4,

0 0.04

By

l Yl < Q ,

i ,oo ,.T

0.02

JcY/I Y[, a
IT] (3)

in the thin strip structured SC's and analytic solutions of (2) for the corresponding fields Bz(y) and By(y) at the surface z = d/2. As in the conventional Bean model for extended type-II superconductors, a constant critical current density j¢ is flowing along the strip edges in areas, where the magnetic flux has penetrated. In the Bean model for thin films (d << W) an additional sheet current I j l < j c according Eq. (3) flows in the flux free area. The relation between the penetration depth P of the magnetic flux measured from the strip edge and the external field B a is

P=(W/2)[1-cosh-I(

237

Ban" )1

(4)

0 -0.02

-0.0~ 3 Jx 21011

~ j

I

I ,oo m,

10

A/m 2 - 1 -

/ ~

~-2~ ,,,

-2" --3'

W-20O,w~ J¢'2'5"1011A/m2

-1'oo

6

16o

2( o

Y [um] Numerical calculation of the B: and By profiles for a height of 350 nm over the film surface. The film thickness is 250 nm and a Jc of 2.5X l0 II A/m E was used. Fig. 2.

~ tXoJcd ] ] ' which allows an accurate determination of Jc. Forkl et al. [21] give an analytic solution for Biot-Savarts' law from developing Jx(Y) into a Taylor series, which allows us to calculate the field distribution B( y, z) of the current distribution (3) in the whole space around and inside the superconducting strip. The two-dimensional integrals with integrand (3) can easily be integrated numerically. The results for B, and By and the current density (5) are shown in Fig. 1 for a strip with W = 2 0 0 txm, d = 250 nm and Jc = 2.5 X 10 l~ A / m 2. In Fig. 2 the fields and the sheet current j , d are shown for different film thicknesses between 100 nm and 700 nm, all with the same penetration depth Q = w / 2 - P = 50 /a,m.

2.2. Approximate calculation of jsc due to surface pinning Due to the reduction of their line energy, vortex lines prefer positions of small thickness in the film.

At a position r in the x-y-plane with film thickness to the c-axis is given by

d(r) the total energy of a vortex parallel E(r)

= eLd(r ) -- 4n./x0A2ao [In(K) + 0 . 5 ] d ( r ) ,

(5)

where e L denotes the line energy per unit length and r = ( x 2 + 22) 1/2 the position of the vortex line. This is a result of Ginzburg-Landau theory, where the layered structure of a high-Tc superconductor is taken into account with anisotropic superconducting parameters Ac, Aab, ~c and ~:~b" Since the magnetic penetration length A~b is of the same magnitude as the wavelength of thickness modulation lr, it is not possible to consider a vortex line as a point particle in a potential of the thickness variation as in Eq. (5). The densities of the kinetic energy of the superconducting currents around the vortex and the field energy are delocalized over the length-scale of sur-

Ch. Jooss et al.// Physica C 266 (1996) 235-252

238

face roughness and therefore must be integrated over the surface-geometry.

Bz

0.20.15-

2.3. Approximations

[T]

An exact calculation of the line energy of a vortex line in a thickness modulated thin film within the framework of Ginzburg-Landau theory is a very complicated problem. The structure of the vortex including order parameter, magnetic field and current distribution is strongly influenced by the thickness modulation. Additionally the curvature of the vortex lines due to demagnetizing effects must be considered. For a first approximate calculation, presented in a forthcoming paper [22], the following approximations are assumed: We consider only vortex lines parallel to the c-axis (cll z). The roughness is approximated by a periodic thickness variation of amplitude A d and w a v e l e n g t h I r. The influence of the thickness modulation on the field and current distribution and the order parameter of a vortex is neglected. Therefore the Ginzburg-Landau bulk energy density of a vortex line is integrated over the surface geometry. The film thickness is influencing the vortex by vortex line widening, where the magnetic penetration depth A~b is replaced by an effective penetration depth Aeel= 2A2ab/d. For calculating the pinning force on a single vortex line, the energy difference A E of the vortex sitting in a maximum or minimum of the thickness modulation is divided through the distance l J 2 between both positions. The macroscopic volume density of the pinning force is calculated from the single vortex pinning force by direct summation. Finally Jc is described with a thickness and roughness independent iv, due to volume pinning and jS(d, Ad, lr) resulting from surface pinning due to film roughness by j¢ = j v +j~,

(6)

Ar

0.05

o=5o.,,,~_______.j~/~/ee~~

0 By

O. 1

I ~

I

I

I

(7)

A E is the energy difference of a vortex line between positions of maximal and minimal thickness of the thickness modulated film being determined in a forthcoming paper [22].

B0=97.0mT 69.3mT 55,5 mT 41,6 m7 27,7 13.8raT mT

0.05 IT]

0 - -0.05 -0.1 2.8

jx,d

2.1 1.4

10 5

0.7O-

A/m

I

-0.7-

-1.4.-2.1 -2.8

W=200~u'n

j¢-2,5"10~ A/m:

oo

-1'oo

6 16o Y [.ml

21

Fig. 3. Calculated fields and sheet currents for different film thickness d = 100, 200, 300, 400, 500 and 700 nm. For all films a penetration depth of P = W / 2 - Q = 50 p,m was used.

As described in detail in Ref. [22], the critical current density jc~ due to surface pinning is determined by three parameters: averaged thickness, thickness variation and leading wavelength of thickness variation, characterizing the microscopic geometry variations of the films. With increasing thickness variation Ad, j~ is enlarged. A maximum of j~ is expected for film thickness d = 2Aab. Vortex line widening reduces j~ for film thickness d < 2A,b, while for d > 2 A a b J cs follows a law, giving for the total critical current density

Jc =jv + c(lr)(Ad)/d,

1 a e ( d , ad, jc~ = - dqO0

o.1

(8)

where c ( l r) has been determined in Ref. [22]. If the wavelength dependence of j~ is considered, a maximum of j~ occurs for roughness wavelength of the magnetic spacing of the vortex line at l r -~ 2Aab. For higher roughness wavelength the energy gradient of the vortex line is reduced, while for l r < 2A~b the

Ch. Jooss et al./ Physica C 266 (1996) 235-252

magnetic and current energy of the vortex line is averaged over the geometry variation and therefore the pinning force and j~ is reduced. In section 4 the experimentally determined critical current densities for various YBaCuO films with different roughness parameters are compared with the calculated Jc, where the only free parameter is the constant j v in Eq. (6).

3. Experiment and sample characterization

3.1. Sample preparation All films were deposited by pulsed laser ablation on SrTiO 3 (100) substrates [16]. The energy density at the YBaCuO target was 2 J / c m 2, the oxygen pressure 100 Pa and the substrate temperature was hold at 1050 K during deposition. Afterwards they were cooled in oxygen atmosphere to room temperature. X-ray diffraction [12] and Raman studies show that the films are highly epitactic and c-axis oriented up to film thickness of 500 nm. An exception is the 700 nm thick film NLY 437 of S1, which has possibly a small fraction of a-axis oriented grains. This could also be concluded from the presence of rod-like features in Fig. 5d. The transition temperature of all films was between 88.5 K and 91.8 K. After film fabrication two different kinds of sample series S1 with $2, and $3, were patterned by means of standard photoresist lithography and chemical 1 mm

YBaCuO

220

]'l~

480 nm

V "-' ~._.]sample 1

seriesS2 2 3

i<

330

- - ~ 4

etching. In S1 from each of the six different YBaCuO-films with thickness from 140 nm to 700 nm one strip with rectangular cross-section was pattemed. Each strip has a width of W = 200 I~m and length of more then 2 mm. In series $2, and $3, five strips with a length of 3 mm were patterned from one film. In a first step 5 strips with equal thickness were etched from the film. Then each strip was etched by ion milling and so reduced in its thickness. A cross-section of $2 after etching is sketched in Fig. 4. The ion milling was performed with 500 V Ar ions with an ion current density of 0.2 m A / c m 2. The ions were discharged before they hit the YBaCuO film to avoid charging. The penetration depth of the 500 V Ar particles perpendicular to the film surface is limited to 1-2 monolayers. Therefore the actual surface layer of the YBaCuO film is taken off by the transfer of the Ar momentum to the surface atoms. The momentum transfer is increased in the surface holes because of multiple scattering of the particles. Hence, the roughness of the films enlarges with decreasing thickness due to ion milling. After ion milling the two series $2 and $3 were annealed in pure oxygen at T = 775 K to reduce the volume damage and guarantee equal oxygen content in all strips. Finally the five films of series $2 and $3 are distinct merely with respect to their surface roughness and thickness, since a homogenous distribution of the defects, resulting from epitaxial film growth within the film thickness, is assumed (see the discussion in section 4).

3.2. Surface characterization

210_pm 430 nm

239

170

1.7 5 1_.~ )l

7,1 m m Fig. 4. Cross-section of series $2 after successive reduction in film thickness. Note that the scale is stretched in the z-direction. The thickness of the unetched film was d = 480 nm, which correspondents to the thickness of sample 2.

For determining the surface structure of all strips, atomic force microscopy (arm) measurements were performed. In Fig. 5 afm images of four films of S1 with different thickness are shown. The transversal size of the growth islands increases from 200-300 nm at the thinnest film NLY 438 of S1 (d = 140 nm) to 520-580 nm at NLY 437 with d = 700 nm. This is a result of the island mediated growth mode, where different growth islands coalesce with increasing film thickness [11]. Whether the coalescence of the growth islands is related with a thickness dependence of the volume defect structure will be discussed in section 4 including the critical current

240

Ch. Jooss et a l . / Physica C 266 (1996) 235-252

100 n m

i

SO n m

0 nm

NI ;5

~!ili 2 pm

Fig. 51. Afm images from the surfaces of four films of series S1. (a) NLY 438 with d = 140 nm; (b) NLY 440 with d = 250 nm; (c) NLY 434 with d = 290 nm; (d) NLY 437 with d = 700 nm. The roughness enhancement with increasing film thickness can be seen clearly. densities. Additionally the height of the islands and the depth of the adjacent holes or trenches increases. Hence, the roughness is correlated to the film thickness, which is shown in Fig. 6, where the standard deviation

330 nm) are shown. In series S2 an inverse correlation between the standard deviation and the film thickness in comparison to S 1 is obtained, as demon-

50

S=

. [d(ri) -d]2/(N

- 1)

(9)

I

I

40-

30is plotted over the thickness for all series. Other parameters for the characterization of the surface roughness are the thickness variation A d between deep holes and islands, which typically occur at Ir. The distance l~ is the leading wavelength in the Fourier transformation of the surface profile. These parameters are determined for each strip and summarized in Table 1. In Fig. 7 the afm-images of two strips of $2 with the unetched surfaces of $ 2 / 2 ( d = 480 nm) and the etched surface of $ 2 / 4 ( d =

I

[nm]

._.,....,----o

20I 0 -

o

/ e'~/

-Serie~l $3 o Serie~l S1 • Seriell $2

260

460 d

66o

a)o

[nm]

Fig. 6. Thicknessdependenceof the standarddeviation S of the film roughness.The differentthicknessdependenceof SI and $2 as a result of different fabrication methods can be seen.

Ch. Jooss et al. / Physica C 266 (1996) 235-252 strated in Fig. 6. An afm image of series $3 is shown in Fig. 8. The surfaces of all strips of series $3 are very similar. This also can be recognized from Fig. 6, where the standard deviation of $3 is almost a constant for all strips.

241

3.3. Magneto-optical Faraday effect Because YBaCuO is not showing a significant magneto-optical Faraday effect, a magneto-optical active layer is required in order to observe the

10000

~

5000

0

0

5000

10000

1707

6 2000 4600 6600 80oo Fig. 7. Afm images from the unetched original surface of $2 ($2/2) (top) with d = 480 nm and the etched surface $2/4 (bottom) with d = 330 nm.

242

Ch. Jooss et a l . / Physica C 266 (1996) 235-252

magnetic flux density [23,24]. In a MOL the polarization of a linearly polarized light beam is rotated by an angle or, which in EuSe is proportional to the component of the magnetic induction parallel to the beam direction. The strength of B parallel to the surface normal (Bz), can be seen in a polarization microscope as a variation of the intensity of the light beam reflected at the MOL/HTSC interface. As field detecting element two different MOLs were used: EuSe of thickness 250 nm [25,26], which was evaporated on the HTSC-film surface, allows a high spatial resolution of a few ixm. In Fig. 9 the magneto-optical detection of flux distribution by means of EuSe is demonstrated for the strip NLY 440 for different external fields B a. In order to improve the light reflection at the surface of the YBaCuO-films, a gold layer of 200 nm thickness is sputtered before evaporating the EuSe layer. Additionally a ferrimagnetic iron-garnet film [27] with in-plane anisotropy was used as MOL. The resulting magneto-optic images are presented in Fig. 10 for the strip $2/1. The iron-garnet has a larger

Table 1 Surface roughness characterization of all measured YBaCuO samples by means of analyzing afm images. The parameters /r, S and Ad are defined in the text. The thickness d is the averaged thickness of each strip measured by profilometer Series, strip

thickness d roughness S Ad [nm] 1, [nm] [nm] [nm]

S1/1 (NLY338) SI/2(NLY441) S1/3 (NLY440) S1/4(NLY434) S1/5 (NLY439) S1/6(NLY437) $2/5 $2/1 $2/4 $2/3 $2/2 $3/1 $3/4 $3/2 $3/5 $3/3

1404- 5 190-4- 5 2504- 10 290+ 10 520+ 10 7004- 10 1704- 5 2205: 5 3304- 10 4304- 10 4804- 10 1105: 5 1304- 5 1604- 5 165+ 5 2054- 5

6 10 14 14 25 27 40 40 40 30 20 14 20 14 15 16

10 50 60 50 70 80 110 120 120 100 70 35 80 45 50 45

OO"

4000

3000

~

.2000 o

,1000

non o

tooo

e6oo

3d~

4000

Fig. 8. Afro image of $ 3 / 2 surface d = 160 rim, which is typical for the other strips of this series.

200-300 380-440 380-440 500-550 470-530 520-580 750-800 750-800 750-800 600-830 730-800 540-560 590-610 510-530 590-610 300-400