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Thickness dependence of microcrack formation in YBa2Cu3O6 + x thin films on NdGaO3 (001) substrates
Thin Solid Films 519 (2011) 8058–8062
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Thin Solid Films j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t s f
Thickness dependence of microcrack formation in YBa2Cu3O6 + x thin films on NdGaO3 (001) substrates H. Palonen a, b,⁎, H. Huhtinen a, P. Paturi a a b
Wihuri Physical Laboratory, Department of Physics and Astronomy, FI-20014, University of Turku, Finland Graduate School of Materials Research, Turku, Finland
a r t i c l e
i n f o
Article history: Received 27 January 2011 Received in revised form 21 June 2011 Accepted 29 June 2011 Available online 8 July 2011 Keywords: YBaCuO Thin films Microcracks
a b s t r a c t Thickness dependence of parallel microcrack formation in YBa2Cu3O6 + x thin films prepared by pulsed laser deposition from nano- (n) and microcrystalline (μ) targets on NdGaO3 (001) is systematically investigated. Atomic force microscope and x-ray diffraction measurements show parallel microcracks normal to uniaxial twin boundaries. The amount of microcracks increases with film thickness. Superconducting properties of the films decrease very strongly with film thickness as a result of microcrack formation. The n-films have more rigid lattice and thus show more extensive cracking than μ-films. It is found that the μ-films have a thickness threshold (∼ 70 nm) where the first signs of cracking appear. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The current carrying capacity i.e. the critical current density, jc, of a superconductor in high magnetic field is determined by its flux pinning properties. Furthermore, the flux pinning is determined by the structural defects present in the crystal lattice. Most of the visions of future superconductor applications involve YBa2Cu3O6 + x (YBCO) as the material used. A quite compact review on the current state of YBCO thin film development and its challenges was written by Foltyn et al. [1]. One of the challenges in flux pinning research is to be able to separate the contributions of different flux pinning sources. This is difficult because many different crystal defects are present in thin films simultaneously. YBCO grown on NdGaO3 (NGO) cut in (001) plane forms uniaxial twins because of a directional preference that arises from the pseudo-orthorhombic growth of YBCO [2]. While flux pinning in dislocations is rather well understood many questions still remain about the role of twin boundaries as pinning sites [1,3] and about their role in the Hall-resistance of YBCO [4–7]. A uniaxially twinned film would enable us to study separately vortex pinning along and normal to twin boundaries. However, films grown on NGO (001) tend to have microcracks which prevent any resistance measurements [8]. The aim of this work is to demonstrate the importance of film thickness in preparing uncracked films on NGO
⁎ Corresponding author at: Wihuri Physical Laboratory, Department of Physics and Astronomy, FI-20014, University of Turku, Finland. E-mail address: heikki.palonen@utu.fi (H. Palonen). 0040-6090/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2011.06.106
(001) by presenting a systematic study of the properties of YBCO thin films of different thicknesses. The problem of cracks is removed if the substrate is cut in (110) direction but so is the uniaxiality of twins too which is undesired because the goal is to deduce the role of twins in Hall-resistance and flux pinning [9]. When grown on NGO (001) YBCO aligns its cell diagonal in the abplane with NGO's b-axis. This orientation gives a lattice mismatch of 0.8–0.9% [10] which is smaller than the mismatch of 1.4% [11] with SrTiO3. A high lattice mismatch can lead to a critical thickness above which microcracking occurs in a thin film [11]. This can be explained by the competing energy terms where homogeneous strain is proportional to the sample volume while many defect-related terms are proportional to the area of the film-substrate interface and crack formation energy is related to crack surface area and surface energy. If defects cannot relieve completely the strain induced by lattice mismatch eventually crack formation will be energetically more favorable than homogeneous strain. Since with NGO lattice mismatch is small, it cannot be used to explain the appearance of microcracks. Instead, NGO has highly anisotropic thermal expansion coefficients which give rise to a large thermoelastic stress component in the NGO b-axis direction [10]. This combined with the inability to relieve stress via twinning in b-direction explains the NGO a-axis oriented cracks appearing in YBCO thin films on NGO. Important in fabricating different pinning structures is the choice of target materials for the pulsed laser deposition (PLD) process. Targets with grainsize in nanometer scale (n-films) and in micrometer scale (μ-films) were used in this work. Comparing to μ-films, n-films are known to have better critical currents as a result of a higher pinning site density which is caused by smaller growth islands and more rigid elasticity of the lattice [12–14]. Other benefits of
H. Palonen et al. / Thin Solid Films 519 (2011) 8058–8062
n-films include smaller surface roughness and easier relaxation of the twin system with film thickness [15,16]. In this report we will discuss the role of film thickness in the properties of YBCO grown on NGO (001) substrates, compare n- and μ-films and discuss the possibilities of making intact and uncracked samples. The results have been divided into structural and magnetic properties.
2. Experimental details Pulsed laser deposition (PLD) was used to make superconducting thin film samples for this work. The PLD setup is similar to the one described in [15] but the resistive heater has been updated to IR-laser heater. The growth parameters used in ablation were the same as optimized for SrTiO3 (STO) substrates: the energy used in XeCl excimer UV-laser (λ = 308 nm) pulses was 80 mJ (1.7 J/cm 2) at 5 Hz deposition rate, a nominal substrate temperature of 750 °C was used during deposition at 40 Pa pressure of pure oxygen and an oxygenation step of 10 min was made after deposition at 700 °C in 1 atm of pure O2. The cooling rates were 10 °C/min before oxygenation step and 25 °C/min after it. Two sets of YBCO thin films of varying thicknesses were grown on NGO (001) substrates by PLD. The number of pulses used in ablation was 600–3000 in each set and to compare n- and μ-films a different target was used between the sets (see Table 1). Also a reference sample was grown on STO (100) at the same conditions with 2000 pulses. The targets used were both undoped YBCO but different in grainsize: a solid state reaction μ-target with grainsize of a few micrometers and a nanocrystalline target made by the citrate-gel method described in [17] with grainsize of about 50 nm. For structural analysis of YBCO thin films x-ray diffraction (XRD) measurements with a Philips X'pert MPD were carried out using a Schultz texture goniometer and CuKα x-ray tube. The measurement setup also includes a Ni-filter, a thin film collimator with 0.18° slit, 0.04 rad sollers and 1 × 4 mm cups. The samples were characterized with a general 2θ-screening, a rocking curve of YBCO (005) and 2θ − φ scans of the (122), (212) and (102)-peaks. The surface structure of the thin films was characterized with the atomic force microscope (AFM) Autoprobe CP which was used to measure the surface roughnesses (RMS) of the samples with image sizes of 20 × 20 μm 2, 10 × 10 μm 2 and 5 × 5 μm 2. After all other measurements the thin films were etched by photolithography to be able to measure the thickness of the films with AFM. A Quantum Design Physical Properties Measurement System magnetometer was used for measuring the superconducting properties of the samples. Temperature dependence of ac-magnetization was measured between 100 K and 10 K at 0.1 mT ac-field. Hysteresis loops were measured between −8 T and 8 T for dc-magnetization between 10 K and 80 K at 10 K intervals.
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3. Results and discussion 3.1. Structure of the films The YBCO n-films show extensive cracking with increasing thickness as can be seen from AFM images in Fig. 1 which have parallel stripe-like shapes on the surfaces of the films. These shapes look like ridges at first but reveal cracks after removing part of the surface with phosphoric acid (Fig. 1f). The images in Fig. 1 are from nfilms while images of the μ-films showed similar features only with the thicker films and not so clearly even with them. The cracks are at almost regular intervals of 2 μm–5 μm normal to the twin boundaries which is consistent with earlier reports of cracking [8,2]. Cracks, if any, are no longer visible in the thinnest film with AFM. The length of the visible cracks varied from about 50 μm to almost 1 mm increasing with film thickness while the average distance between cracks is unchanged. Surface roughnesses of the thin films in Table 1 were determined from AFM images as an average of results from different image sizes. Surface roughnesses of the n-films are significantly lower compared to μ-films which has also been observed in [15]. The lower RMS roughness is related to the difference in growth mechanisms in the deposition between n-films and μ-films: it has been shown that particles deposited from n-target have smaller height and diameter than particles deposited from μ-target [13]. Film thickness seems not
a
b
5 μm
5 μm
c
d
5 μm
5 μm
e
f
5 μm
5 μm
Table 1 The YBCO thin films ablated with n- and μ-targets on NGO (001), their surface roughnesses with standard deviations (σ) and Tc (onset). Pulses
Thickness (nm)
Roughness (nm) n-films
σ
μ-films
σ
n-films
μ-films
600 800 1000 1500 3000 2000a
70 100 130 180 330 190
9 6 – 3.3 3.8 6.6
3 2 – 0.2 0.9 0.9
11 17 19 22 16 –
5 3 3 7 5 –
89 90 – 89 91 92
87 88 87 89 90 –
a
Tc (K)
This is the reference film grown on STO with n-target.
Fig. 1. AFM images of n-films showing parallel shapes that contain a crack inside. The film thicknesses are (a) 70 nm, (b) 100 nm, (c) 130 nm, (d) 180 nm, (e) 330 nm and f is the same sample as in e but the surface has been partially etched with phosphoric acid. The linear z-scale from black to white is 50 nm in a, b, and f and 20 nm in c, d, and e.
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to have any clear impact on the surface roughnesses of the samples in the thickness range used here. At higher (over 300 nm) thicknesses the RMS roughness should increase because of the developing island growth mode [18]. The XRD data on 2θ − φ scans of the (102)-peak showed clear epitaxial growth with the percentage of a-oriented (c-axis in plane) grains less than 1% for all the samples except the thickest of μ-films for which a-orientation was of the order of several percent. The exact proportion is difficult to determine because there is an overlapping tail of a substrate peak. The height of the YBCO unit cell was calculated from the relative positions of the (005) and (007) peaks giving 11.69 Å–11.72 Å for all the films which is larger than 11.68 Å [19,20] measured for a single crystal but agrees well with the multitude of values measured for thin films: 11.68 Å–11.70 Å [21] on NGO, 11.69 Å [22] on MgO with BaZrO3 buffer layer and 11.63 Å [23] on STO. The c-lattice parameter in YBCO thin films depends not only on the oxygen content but also on the growth conditions and the lattice mismatch [24]. Thus the oxygen content of thin films cannot simply be derived from the c-values and a more detailed look into XRD data is necessary. J. Ye and K. Nakamura [24] have shown that the intensity ratios of YBCO I(005)/I(004) and I(005)/I(007) peaks correlate with the oxygen content of the thin films offering an alternative method. The oxygen content of YBCO was estimated to be better than 6.8 in all the films where the estimation is based on the intensity ratios. Neither the height of the unit cell nor the oxygen content showed any dependence on the film thickness in either series. The twinning of the films was determined from 2θ − φ scans of the (122)/(212)-peaks. Fig. 2a shows the measured 2θ − φ scan of the reference film grown on STO which has a typical four-peak system of a biaxially twinned thin film [16]. The uniaxial twinning is seen in 2θ − φ scan as only two diffraction peaks in Fig. 2b instead of the four peaks. All n- and μ-films grown on NGO showed similar uniaxial twinning. The orthorhombicity of the YBCO-films, defined as = 2(b − a)/(a + b), was calculated by fitting Gaussian surfaces on the (122)/(212) peaks and extracting accurate peak positions. The calculated values of from the fit were all between 1.4% and 1.7%. The values are normal for YBCO thin films but no thickness dependence was found in either film series which is different from what has been reported for STO substrates where fully relaxed twins are formed already at about 150 nm thickness [16]. A constant orthorhombicity means that the a/bratio does not relax to its bulk value of 98.2% ( ≈ 1.8 %) [25] with NGO substrates like it does with STO. The difference in film relaxation between the substrates is to be expected because the relaxation happens through forming twins and uniaxial twinning leaves less freedom to relax the lattice than biaxial. The Gaussian fits to (122)/(212) peaks were also used to extract the full width at half maximum (FWHM) values in both φ- and 2θdirections. While no relaxation was observed in the orthorhombicity,
some rotational relaxation of YBCO can be seen in the decrease of φFWHM of (122) and (212) peaks with increasing film thickness which is shown in Fig. 3. While φ-FWHM shows a clear decrease no similar dependence was found in 2θ-FWHM which indicates that the relaxation in the films has to do with the angles of the pseudo-orthorhombic cell rather than its lattice parameters. The main difference in the φ-FWHM between n- and μ-films is with the thinnest films where μ-film has onethird higher value and is thus under more stress. Comparing φ-FWHMs and rocking curve FWHMs (Fig. 3), there is a one-third jump in the values between the first and the second thinnest μ-film in both cases. This could indicate a critical threshold of thickness where most of the cracking occurs. The FWHM values of nfilms have more variation and show no indication of a similar critical threshold. A detailed rocking curve of the (005)-reflection was measured in two different sample orientations: the incident beam parallel and normal to the ridge-like shapes seen in Fig. 1. The FWHM of the rocking curves measured incident beam normal to the shapes show a clear increase with film thickness (Fig. 3: inset) while no such peak broadening was observed in the parallel case. This broadening is related to the parallel structures seen in AFM images (Fig. 1) and is a measure of deformation of the film around the cracks. The deformation is also seen as additional shoulders at about ±0.5° in rocking curves measured incident beam normal to the cracks (Fig. 4). The thinnest films show no shoulders at all while the thickest films have clear additional shapes. These shoulders are more distinct in μfilms while n-films have smoother and broader rocking curves. While a smoothly broadening rocking curve means a continuous variation of the YBCO unit cell direction these shoulders could be due to a discontinuous variation. The shoulders could be a result of a sum of three peaks which would mean that the unit cell is distributed in three discrete directions around the cracks. The measured FWHM values of (005) rocking curves are between 0.20° and 0.35° which agrees well with earlier reports of 0.25° [26] and 0.28°–0.43° [27].
3.2. Superconducting properties of the films Critical temperatures of the samples were determined from acmagnetization measurements as the onset temperature of the transition to superconducting state. The Tc values in Table 1 show a slight increase from 87 K to 91 K from thinner to thicker films which is consistent with the XRD results where the FWHM values indicate more stressed state of the films. The lattice mismatch between the film and the substrate induces misfit dislocations as a stress relieving process near the film-substrate interface [1,28]. In thinner films the stressed volume near the substrate interface constitutes a larger volume fraction and thus thinner films are under more stress than thicker ones.
60 30
60
(a)
(b) 50
50 72
28
30
(122) (212)
20
40
ϕ (°)
ϕ (°)
40
30 20
70
10 26 54
56
2θ(°)
58
0
10 54
56
58
0
2θ(°)
Fig. 2. (a) The four-peak system of (122)/(212) peak measured from a 190 nm thick n-film on STO showing biaxial twinning and (b) the same peak system measured from a 180 nm thick n-film on NGO showing uniaxial twinning.
H. Palonen et al. / Thin Solid Films 519 (2011) 8058–8062
0.9
0.6
0.30 0.25 0.20 100 200 300 Thickness (nm)
150
200
250
300
350
30
10
1
20
0.4 100
0 50
400
100
150
Fig. 3. The FWHM in φ-direction of (122)/(212) peaks (see Fig. 2) measured from nfilms (filled circles ) and μ-films (filled squares ■) on NGO plotted against film thickness. The inset shows FWHM of (005) rocking curves in 2θ against film thickness.
•
n 70 nm n 180 nm n 330 nm
300
350
Counts (a.u.)
where jc is the critical current density, Δm = m−(B) − m+(B) is the opening of the hysteresis loop and a, b are the dimensions of a rectangular sample (a ≤ b), was used. The Bean formula is not really valid for our cracked samples so we can only make an estimate of the local jc with it. For a square sample of thickness t, Eq. (1) gives
0.4
0.6
b3 t
:
ð2Þ
Now assume that the sample is split into n slabs so that a = b/n. If the pieces do not interact, the magnetic moment of one slab is Δm′/n. Now Eq. (1) gives the local critical current for one slab as
0.8
Relative ω (°) Fig. 4. Normalized rocking curves of the YBCO (005)-reflection measured with the incident beam normal to the ridge-like shapes seen in Fig. 1. The curves with different thicknesses have been shifted upwards with their baselines for clarity. Solid lines are μfilms and dashed lines are n-films.
The magnetic moments (actually half of the opening of the hysteresis loops) of the samples in zero field and at 40 K in Fig. 5 show a drastic decrease of more than two orders of magnitude with film thickness. Similar trends in zero-field values of moments were seen also at all other temperatures. If the samples were crack-free magnetic moments would increase with thickness since all the samples have otherwise the same dimensions except film thickness. Only low field moments are discussed here because the paramagnetic substrate NGO has a very strong moment at lower temperatures which makes accurate magnetic measurements of YBCO thin films difficult in high fields. The reduction of magnetic moment with film thickness seen in Fig. 5 is due to the cracking of the film which cuts the currents circulating the whole film. Also the increase in the length of the cracks further hinders the currents inside the film. The cracks get longer in thicker films which has also been confirmed with transmission electron microscope images [8]. The fact that the cracks get gradually shorter could possibly be used to confirm whether a film really is crack-free or not. The smallest cracks form weak links in the films which could be seen with a careful ac-magnetization measurement as power dissipation. In this work only the thinnest μ-film seems crackfree judging by the lack of imaginary part of ac-magnetization. To calculate the critical current density of our samples the Bean formula [29] 2Δm ; aV ½1−a = ð3bÞ
250
•
jc =
jc;H∥c =
200
Fig. 5. Magnetic moments of n-films (filled circles, ) and μ-films (filled squares, ■) both on NGO plotted against film thickness measured in zero field and at 40 K. The inset shows the same plot but with lin–log axes. For comparison the value measured for n-film on STO was 402 μAm2. Magnetic moments of the samples were extracted as half of the opening of the hysteresis loop.
h i 3Δm Am2
0.2
300
Thickness (nm)
Thickness (nm)
0
200
Thickness (nm)
10
0.5
100
B < 1 mT T = 40 K
40 m (μAm2)
ϕ−FWHM (°)
0.7
60
0.35
m (μAm2)
RC−FWHM ( )
50
0.8
0.4 50
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ð1Þ
jc;local ≈
2Δm′ = n 2Δm′ =n 3 ; 2 a bt b t
ð3Þ
where it has been approximated that 1 − a/(3b) ≈ 1 since a ≪ b in a slab. Setting the two critical currents equal gives Δm′ = 3Δm/(2n). Thus cutting the sample into n pieces reduces the magnetic moment roughly by n when n ≫ 1. Using 5 μm as the average crack distance gives respectively local critical current of 10 and 11 MA/cm 2 for the 180 and 330 nm thick nfilms. For μ-films the estimation of local critical current gives too high (N30 MA/cm 2) values. This is expected because the average crack distance used in estimation was measured from n-films while in μfilms the crack distance is too long to be easily measured by AFM. None of the films grown on NGO reach the value of the reference film on STO for which a critical current density of 5.4 MA/cm 2 at 70 K was obtained. The best jc calculated from Eq. (1) assuming crack-free film was the thinnest μ-film for which 0.93 MA/cm 2 at 70 K was measured which is slightly below the values reported in the literature for YBCO thin films on NGO (001) at 77 K: about 1 MA/cm 2 [30,31] (DC sputtering films), 4–5 MA/cm 2 [27] (metal-organic chemical vapor deposition) and 2–4 MA/cm 2 [32,33] (PLD). The higher values in literature is partly explained by the fact that our jc is extracted from magnetic measurements and compared to values from resistance measurements which give 2–3 times higher jc [34]. The rest of the difference between our result and literature values can be attributed to the film thickness. It has been reported that jc decreases rapidly for films thinner than ∼ 100 nm [35,36]. The magnetic moment of μ-films has a clear jump between 70 nm and 100 nm thick films, which is consistent with similar jump in the XRD data and could indicate a cracking threshold and thus a crack-free film. However, the 70 nm thick μ-film still has four times smaller jc than the reference film on STO.
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A clear distinction between n- and μ-films in terms of magnetic moment can be seen in Fig. 5. The μ-films have larger moments than n-films throughout all thicknesses which contradicts the usual results of n-films being better because of their higher defect density [15,37]. In this work the better values of μ-films can be attributed to the smaller amount of cracking. This is consistent with the AFM images that showed cracking related structures in n-films while in μ-films the cracks were hardly visible. The reason for n-films to develop more cracks than μ-films is the less elastic lattice which is due to a smaller growth island size and a larger amount of lattice defects, especially dislocations [13,14]. The lesser elasticity of n-films can be deduced from the variation of φ-FWHM of XRD peaks with film thickness [14].
[4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
4. Conclusions In this work the structural and superconducting properties of YBCO thin films grown on NGO (001) were investigated. Two series of films with varying thicknesses were laser ablated with μ- and ntargets. The superconducting properties of the films decrease very strongly with film thickness as a result of extensive cracking. The main difference found between the two series was that the n-films crack more quickly with film thickness. This is attributed to the more rigid lattice of n-films as compared to μ-films [14]. Furthermore, some indications of a critical cracking threshold around 70 nm was found in μ-films meaning that less than 70 nm thick μ-films could be completely crack-free. In contrast, all of the n-films (70–330 nm thick) showed at least some microcracks. In conclusion, thin μ-films are plausible candidates for further measurements that utilize the uniaxial twin boundaries. Resistivity and Hall-conductance measurements will be made in the future to clarify the pinning mechanisms parallel and normal to twin boundaries.
[16] [17] [18] [19]
[20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31]
Acknowledgment The Wihuri Foundation is acknowledged for financial support. References [1] S.R. Foltyn, L. Civale, J.L. Macmanus-Driscoll, Q.X. Jia, B. Maiorov, H. Wang, M. Maley, Nat. Mater. 6 (2007) 631. [2] J. Nam, R.A. Hughes, J.P. Castellan, B.D. Gaulin, J.F. Britten, J.S. Preston, J. Appl. Phys. 97 (2005) 123906. [3] B. Dam, J.M. Huijbregtse, F.C. Klaassen, R.C.F. van der Geest, G. Doornbos, J.H. Rector, A.M. Testa, S. Freisem, J.C. Martinez, B. Stauble-Pumpin, R. Griessen, Nature 399 (1999) 439.
[32] [33] [34]
[35] [36] [37]
Z.D. Wang, J. Dong, C.S. Ting, Phys. Rev. Lett. 72 (1994) 3875. N.B. Kopnin, V.M. Vinokur, Phys. Rev. Lett. 83 (1999) 4864. R. Ikeda, Phys. C 316 (1999) 189. M. Safonchik, K. Traito, S. Tuominen, P. Paturi, H. Huhtinen, R. Laiho, Phys. C 469 (2009) 1983. G. Koren, E. Polturak, N. Levy, G. Deutscher, N.D. Zakharov, Appl. Phys. Lett. 73 (1998) 3763. I.K. Bdikin, P.B. Mozhaev, G.A. Ovsyannikov, P.V. Komissinski, I.M. Kotelyanskii, Phys. C 377 (2002) 26. O. Chaix-Pluchery, B. Chenevier, J.J. Robles, Appl. Phys. Lett. 86 (2005) 251911. R. Wördenweber, Supercond. Sci. Technol. 12 (1999) R86. P. Paturi, H. Huhtinen, K. Laajalehto, R. Laiho, Supercond. Sci. Technol. 13 (2000) 622. H. Huhtinen, J. Järvinen, R. Laiho, P. Paturi, J. Raittila, J. Appl. Phys. 90 (2001) 1521. M. Peurla, H. Huhtinen, Y.Y. Tse, J. Raittila, P. Paturi, IEEE Trans. Appl. Supercond. 17 (2007) 3608. H. Huhtinen, P. Paturi, E. Lähderanta, R. Laiho, Supercond. Sci. Technol. 12 (1999) 81. P. Paturi, M. Peurla, K. Nilsson, J. Raittila, Supercond. Sci. Technol. 17 (2004) 564. J. Raittila, H. Huhtinen, P. Paturi, Y.P. Stepanov, Phys. C 371 (2002) 90. C. Jooss, A. Forkl, R. Warthmann, H.U. Habermeier, B. Leibold, H. Kronmuller, Physica C 266 (1996) 235. J.D. Jorgensen, M.A. Beno, D.G. Hinks, L. Soderholm, K.J. Volin, R.L. Hitterman, J.D. Grace, I.K. Schuller, C.U. Serge, K. Zhang, M.S. Kleefisch, Phys. Rev. B 36 (1987) 3608. H. Casalta, P. Schleger, P. Harris, B. Lebech, N.H. Andersen, R. Liang, P. Dosanjh, W.N. Hardy, Phys. C 258 (1996) 321. M. Mukaida, S. Miyazawa, M. Sasaura, H. Yonezawa, J. Appl. Phys. 69 (1991) 3399. M. Mukaida, Y. Yamazaki, Y. Shingai, S. Makino, M. Kusunoki, A. Saito, S. Ohshima, Supercond. Sci. Technol. 17 (2004) 337. H. Huhtinen, K. Schlesier, P. Paturi, Supercond. Sci. Technol. 22 (2009) 075019. J. Ye, K. Nakamura, Phys. Rev. B 48 (1993) 7554. A. Rosová, C. Boulesteix, I. Vávra, Phys. C 214 (1993) 247. H. Yamada, H. Yamasaki, K. Develos-Bagarinao, Y. Nakagawa, Y. Mawatari, H. Obara, Phys. C 392 (2003) 1068. A. Abrutis, J.P. Sénateur, F. Weiss, V. Kubilius, V. Bigelytė, Z. Šaltytė, B. Vengalis, A. Jukna, Supercond. Sci. Technol. 10 (1997) 959. H. Wang, S.R. Foltyn, P.N. Arendt, Q.X. Jia, X. Zhang, Phys. C 444 (2006) 1. H.P. Wiesinger, F.M. Sauerzopf, H.W. Weber, Phys. C 203 (1992) 121. C. Villard, G. Koren, D. Cohen, E. Polturak, B. Thrane, D. Chateignier, Phys. Rev. Lett. 77 (1996) 3913. M.L. Lucia, J. Santamaria, F. Sánchez-Quesada, W. Lopera, M.E. Gómez, P. Prieto, Phys. C 260 (1996) 149. H.Y. To, G.J. Valco, K.B. Bhasin, Supercond. Sci. Technol. 5 (1992) 421. H. Yamasaki, Y. Nakagawa, A. Sawa, H. Obara, K. Develos, Phys. C 372 (2002) 1885. J. Hudner, O. Thomas, F. Weiss, D. Boursier, E. Mossang, J.P. Senateur, J.C. Villegier, H. Moriceau, M. Schwerdtfeger, A. Jäger, H. Ohlsén, Supercond. Sci. Technol. 7 (1994) 195. H. Huhtinen, J. Raittila, P. Paturi, V.-P. Huhtala, S. Mattila, J. Salminen, IEEE Trans. Appl. Supercond. 13 (2003) 2777. T. Venkatesan, X.D. Wu, B. Dutta, A. Inam, M.S. Hedge, D.M. Hwang, C.C. Chang, L. Nazar, B. Wilkens, Appl. Phys. Lett. 54 (1989) 581. M. Peurla, H. Huhtinen, P. Paturi, Supercond. Sci. Technol. 18 (2005) 628.
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Thin Solid Films j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t s f
Thickness dependence of microcrack formation in YBa2Cu3O6 + x thin films on NdGaO3 (001) substrates H. Palonen a, b,⁎, H. Huhtinen a, P. Paturi a a b
Wihuri Physical Laboratory, Department of Physics and Astronomy, FI-20014, University of Turku, Finland Graduate School of Materials Research, Turku, Finland
a r t i c l e
i n f o
Article history: Received 27 January 2011 Received in revised form 21 June 2011 Accepted 29 June 2011 Available online 8 July 2011 Keywords: YBaCuO Thin films Microcracks
a b s t r a c t Thickness dependence of parallel microcrack formation in YBa2Cu3O6 + x thin films prepared by pulsed laser deposition from nano- (n) and microcrystalline (μ) targets on NdGaO3 (001) is systematically investigated. Atomic force microscope and x-ray diffraction measurements show parallel microcracks normal to uniaxial twin boundaries. The amount of microcracks increases with film thickness. Superconducting properties of the films decrease very strongly with film thickness as a result of microcrack formation. The n-films have more rigid lattice and thus show more extensive cracking than μ-films. It is found that the μ-films have a thickness threshold (∼ 70 nm) where the first signs of cracking appear. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The current carrying capacity i.e. the critical current density, jc, of a superconductor in high magnetic field is determined by its flux pinning properties. Furthermore, the flux pinning is determined by the structural defects present in the crystal lattice. Most of the visions of future superconductor applications involve YBa2Cu3O6 + x (YBCO) as the material used. A quite compact review on the current state of YBCO thin film development and its challenges was written by Foltyn et al. [1]. One of the challenges in flux pinning research is to be able to separate the contributions of different flux pinning sources. This is difficult because many different crystal defects are present in thin films simultaneously. YBCO grown on NdGaO3 (NGO) cut in (001) plane forms uniaxial twins because of a directional preference that arises from the pseudo-orthorhombic growth of YBCO [2]. While flux pinning in dislocations is rather well understood many questions still remain about the role of twin boundaries as pinning sites [1,3] and about their role in the Hall-resistance of YBCO [4–7]. A uniaxially twinned film would enable us to study separately vortex pinning along and normal to twin boundaries. However, films grown on NGO (001) tend to have microcracks which prevent any resistance measurements [8]. The aim of this work is to demonstrate the importance of film thickness in preparing uncracked films on NGO
⁎ Corresponding author at: Wihuri Physical Laboratory, Department of Physics and Astronomy, FI-20014, University of Turku, Finland. E-mail address: heikki.palonen@utu.fi (H. Palonen). 0040-6090/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2011.06.106
(001) by presenting a systematic study of the properties of YBCO thin films of different thicknesses. The problem of cracks is removed if the substrate is cut in (110) direction but so is the uniaxiality of twins too which is undesired because the goal is to deduce the role of twins in Hall-resistance and flux pinning [9]. When grown on NGO (001) YBCO aligns its cell diagonal in the abplane with NGO's b-axis. This orientation gives a lattice mismatch of 0.8–0.9% [10] which is smaller than the mismatch of 1.4% [11] with SrTiO3. A high lattice mismatch can lead to a critical thickness above which microcracking occurs in a thin film [11]. This can be explained by the competing energy terms where homogeneous strain is proportional to the sample volume while many defect-related terms are proportional to the area of the film-substrate interface and crack formation energy is related to crack surface area and surface energy. If defects cannot relieve completely the strain induced by lattice mismatch eventually crack formation will be energetically more favorable than homogeneous strain. Since with NGO lattice mismatch is small, it cannot be used to explain the appearance of microcracks. Instead, NGO has highly anisotropic thermal expansion coefficients which give rise to a large thermoelastic stress component in the NGO b-axis direction [10]. This combined with the inability to relieve stress via twinning in b-direction explains the NGO a-axis oriented cracks appearing in YBCO thin films on NGO. Important in fabricating different pinning structures is the choice of target materials for the pulsed laser deposition (PLD) process. Targets with grainsize in nanometer scale (n-films) and in micrometer scale (μ-films) were used in this work. Comparing to μ-films, n-films are known to have better critical currents as a result of a higher pinning site density which is caused by smaller growth islands and more rigid elasticity of the lattice [12–14]. Other benefits of
H. Palonen et al. / Thin Solid Films 519 (2011) 8058–8062
n-films include smaller surface roughness and easier relaxation of the twin system with film thickness [15,16]. In this report we will discuss the role of film thickness in the properties of YBCO grown on NGO (001) substrates, compare n- and μ-films and discuss the possibilities of making intact and uncracked samples. The results have been divided into structural and magnetic properties.
2. Experimental details Pulsed laser deposition (PLD) was used to make superconducting thin film samples for this work. The PLD setup is similar to the one described in [15] but the resistive heater has been updated to IR-laser heater. The growth parameters used in ablation were the same as optimized for SrTiO3 (STO) substrates: the energy used in XeCl excimer UV-laser (λ = 308 nm) pulses was 80 mJ (1.7 J/cm 2) at 5 Hz deposition rate, a nominal substrate temperature of 750 °C was used during deposition at 40 Pa pressure of pure oxygen and an oxygenation step of 10 min was made after deposition at 700 °C in 1 atm of pure O2. The cooling rates were 10 °C/min before oxygenation step and 25 °C/min after it. Two sets of YBCO thin films of varying thicknesses were grown on NGO (001) substrates by PLD. The number of pulses used in ablation was 600–3000 in each set and to compare n- and μ-films a different target was used between the sets (see Table 1). Also a reference sample was grown on STO (100) at the same conditions with 2000 pulses. The targets used were both undoped YBCO but different in grainsize: a solid state reaction μ-target with grainsize of a few micrometers and a nanocrystalline target made by the citrate-gel method described in [17] with grainsize of about 50 nm. For structural analysis of YBCO thin films x-ray diffraction (XRD) measurements with a Philips X'pert MPD were carried out using a Schultz texture goniometer and CuKα x-ray tube. The measurement setup also includes a Ni-filter, a thin film collimator with 0.18° slit, 0.04 rad sollers and 1 × 4 mm cups. The samples were characterized with a general 2θ-screening, a rocking curve of YBCO (005) and 2θ − φ scans of the (122), (212) and (102)-peaks. The surface structure of the thin films was characterized with the atomic force microscope (AFM) Autoprobe CP which was used to measure the surface roughnesses (RMS) of the samples with image sizes of 20 × 20 μm 2, 10 × 10 μm 2 and 5 × 5 μm 2. After all other measurements the thin films were etched by photolithography to be able to measure the thickness of the films with AFM. A Quantum Design Physical Properties Measurement System magnetometer was used for measuring the superconducting properties of the samples. Temperature dependence of ac-magnetization was measured between 100 K and 10 K at 0.1 mT ac-field. Hysteresis loops were measured between −8 T and 8 T for dc-magnetization between 10 K and 80 K at 10 K intervals.
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3. Results and discussion 3.1. Structure of the films The YBCO n-films show extensive cracking with increasing thickness as can be seen from AFM images in Fig. 1 which have parallel stripe-like shapes on the surfaces of the films. These shapes look like ridges at first but reveal cracks after removing part of the surface with phosphoric acid (Fig. 1f). The images in Fig. 1 are from nfilms while images of the μ-films showed similar features only with the thicker films and not so clearly even with them. The cracks are at almost regular intervals of 2 μm–5 μm normal to the twin boundaries which is consistent with earlier reports of cracking [8,2]. Cracks, if any, are no longer visible in the thinnest film with AFM. The length of the visible cracks varied from about 50 μm to almost 1 mm increasing with film thickness while the average distance between cracks is unchanged. Surface roughnesses of the thin films in Table 1 were determined from AFM images as an average of results from different image sizes. Surface roughnesses of the n-films are significantly lower compared to μ-films which has also been observed in [15]. The lower RMS roughness is related to the difference in growth mechanisms in the deposition between n-films and μ-films: it has been shown that particles deposited from n-target have smaller height and diameter than particles deposited from μ-target [13]. Film thickness seems not
a
b
5 μm
5 μm
c
d
5 μm
5 μm
e
f
5 μm
5 μm
Table 1 The YBCO thin films ablated with n- and μ-targets on NGO (001), their surface roughnesses with standard deviations (σ) and Tc (onset). Pulses
Thickness (nm)
Roughness (nm) n-films
σ
μ-films
σ
n-films
μ-films
600 800 1000 1500 3000 2000a
70 100 130 180 330 190
9 6 – 3.3 3.8 6.6
3 2 – 0.2 0.9 0.9
11 17 19 22 16 –
5 3 3 7 5 –
89 90 – 89 91 92
87 88 87 89 90 –
a
Tc (K)
This is the reference film grown on STO with n-target.
Fig. 1. AFM images of n-films showing parallel shapes that contain a crack inside. The film thicknesses are (a) 70 nm, (b) 100 nm, (c) 130 nm, (d) 180 nm, (e) 330 nm and f is the same sample as in e but the surface has been partially etched with phosphoric acid. The linear z-scale from black to white is 50 nm in a, b, and f and 20 nm in c, d, and e.
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to have any clear impact on the surface roughnesses of the samples in the thickness range used here. At higher (over 300 nm) thicknesses the RMS roughness should increase because of the developing island growth mode [18]. The XRD data on 2θ − φ scans of the (102)-peak showed clear epitaxial growth with the percentage of a-oriented (c-axis in plane) grains less than 1% for all the samples except the thickest of μ-films for which a-orientation was of the order of several percent. The exact proportion is difficult to determine because there is an overlapping tail of a substrate peak. The height of the YBCO unit cell was calculated from the relative positions of the (005) and (007) peaks giving 11.69 Å–11.72 Å for all the films which is larger than 11.68 Å [19,20] measured for a single crystal but agrees well with the multitude of values measured for thin films: 11.68 Å–11.70 Å [21] on NGO, 11.69 Å [22] on MgO with BaZrO3 buffer layer and 11.63 Å [23] on STO. The c-lattice parameter in YBCO thin films depends not only on the oxygen content but also on the growth conditions and the lattice mismatch [24]. Thus the oxygen content of thin films cannot simply be derived from the c-values and a more detailed look into XRD data is necessary. J. Ye and K. Nakamura [24] have shown that the intensity ratios of YBCO I(005)/I(004) and I(005)/I(007) peaks correlate with the oxygen content of the thin films offering an alternative method. The oxygen content of YBCO was estimated to be better than 6.8 in all the films where the estimation is based on the intensity ratios. Neither the height of the unit cell nor the oxygen content showed any dependence on the film thickness in either series. The twinning of the films was determined from 2θ − φ scans of the (122)/(212)-peaks. Fig. 2a shows the measured 2θ − φ scan of the reference film grown on STO which has a typical four-peak system of a biaxially twinned thin film [16]. The uniaxial twinning is seen in 2θ − φ scan as only two diffraction peaks in Fig. 2b instead of the four peaks. All n- and μ-films grown on NGO showed similar uniaxial twinning. The orthorhombicity of the YBCO-films, defined as = 2(b − a)/(a + b), was calculated by fitting Gaussian surfaces on the (122)/(212) peaks and extracting accurate peak positions. The calculated values of from the fit were all between 1.4% and 1.7%. The values are normal for YBCO thin films but no thickness dependence was found in either film series which is different from what has been reported for STO substrates where fully relaxed twins are formed already at about 150 nm thickness [16]. A constant orthorhombicity means that the a/bratio does not relax to its bulk value of 98.2% ( ≈ 1.8 %) [25] with NGO substrates like it does with STO. The difference in film relaxation between the substrates is to be expected because the relaxation happens through forming twins and uniaxial twinning leaves less freedom to relax the lattice than biaxial. The Gaussian fits to (122)/(212) peaks were also used to extract the full width at half maximum (FWHM) values in both φ- and 2θdirections. While no relaxation was observed in the orthorhombicity,
some rotational relaxation of YBCO can be seen in the decrease of φFWHM of (122) and (212) peaks with increasing film thickness which is shown in Fig. 3. While φ-FWHM shows a clear decrease no similar dependence was found in 2θ-FWHM which indicates that the relaxation in the films has to do with the angles of the pseudo-orthorhombic cell rather than its lattice parameters. The main difference in the φ-FWHM between n- and μ-films is with the thinnest films where μ-film has onethird higher value and is thus under more stress. Comparing φ-FWHMs and rocking curve FWHMs (Fig. 3), there is a one-third jump in the values between the first and the second thinnest μ-film in both cases. This could indicate a critical threshold of thickness where most of the cracking occurs. The FWHM values of nfilms have more variation and show no indication of a similar critical threshold. A detailed rocking curve of the (005)-reflection was measured in two different sample orientations: the incident beam parallel and normal to the ridge-like shapes seen in Fig. 1. The FWHM of the rocking curves measured incident beam normal to the shapes show a clear increase with film thickness (Fig. 3: inset) while no such peak broadening was observed in the parallel case. This broadening is related to the parallel structures seen in AFM images (Fig. 1) and is a measure of deformation of the film around the cracks. The deformation is also seen as additional shoulders at about ±0.5° in rocking curves measured incident beam normal to the cracks (Fig. 4). The thinnest films show no shoulders at all while the thickest films have clear additional shapes. These shoulders are more distinct in μfilms while n-films have smoother and broader rocking curves. While a smoothly broadening rocking curve means a continuous variation of the YBCO unit cell direction these shoulders could be due to a discontinuous variation. The shoulders could be a result of a sum of three peaks which would mean that the unit cell is distributed in three discrete directions around the cracks. The measured FWHM values of (005) rocking curves are between 0.20° and 0.35° which agrees well with earlier reports of 0.25° [26] and 0.28°–0.43° [27].
3.2. Superconducting properties of the films Critical temperatures of the samples were determined from acmagnetization measurements as the onset temperature of the transition to superconducting state. The Tc values in Table 1 show a slight increase from 87 K to 91 K from thinner to thicker films which is consistent with the XRD results where the FWHM values indicate more stressed state of the films. The lattice mismatch between the film and the substrate induces misfit dislocations as a stress relieving process near the film-substrate interface [1,28]. In thinner films the stressed volume near the substrate interface constitutes a larger volume fraction and thus thinner films are under more stress than thicker ones.
60 30
60
(a)
(b) 50
50 72
28
30
(122) (212)
20
40
ϕ (°)
ϕ (°)
40
30 20
70
10 26 54
56
2θ(°)
58
0
10 54
56
58
0
2θ(°)
Fig. 2. (a) The four-peak system of (122)/(212) peak measured from a 190 nm thick n-film on STO showing biaxial twinning and (b) the same peak system measured from a 180 nm thick n-film on NGO showing uniaxial twinning.
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0.9
0.6
0.30 0.25 0.20 100 200 300 Thickness (nm)
150
200
250
300
350
30
10
1
20
0.4 100
0 50
400
100
150
Fig. 3. The FWHM in φ-direction of (122)/(212) peaks (see Fig. 2) measured from nfilms (filled circles ) and μ-films (filled squares ■) on NGO plotted against film thickness. The inset shows FWHM of (005) rocking curves in 2θ against film thickness.
•
n 70 nm n 180 nm n 330 nm
300
350
Counts (a.u.)
where jc is the critical current density, Δm = m−(B) − m+(B) is the opening of the hysteresis loop and a, b are the dimensions of a rectangular sample (a ≤ b), was used. The Bean formula is not really valid for our cracked samples so we can only make an estimate of the local jc with it. For a square sample of thickness t, Eq. (1) gives
0.4
0.6
b3 t
:
ð2Þ
Now assume that the sample is split into n slabs so that a = b/n. If the pieces do not interact, the magnetic moment of one slab is Δm′/n. Now Eq. (1) gives the local critical current for one slab as
0.8
Relative ω (°) Fig. 4. Normalized rocking curves of the YBCO (005)-reflection measured with the incident beam normal to the ridge-like shapes seen in Fig. 1. The curves with different thicknesses have been shifted upwards with their baselines for clarity. Solid lines are μfilms and dashed lines are n-films.
The magnetic moments (actually half of the opening of the hysteresis loops) of the samples in zero field and at 40 K in Fig. 5 show a drastic decrease of more than two orders of magnitude with film thickness. Similar trends in zero-field values of moments were seen also at all other temperatures. If the samples were crack-free magnetic moments would increase with thickness since all the samples have otherwise the same dimensions except film thickness. Only low field moments are discussed here because the paramagnetic substrate NGO has a very strong moment at lower temperatures which makes accurate magnetic measurements of YBCO thin films difficult in high fields. The reduction of magnetic moment with film thickness seen in Fig. 5 is due to the cracking of the film which cuts the currents circulating the whole film. Also the increase in the length of the cracks further hinders the currents inside the film. The cracks get longer in thicker films which has also been confirmed with transmission electron microscope images [8]. The fact that the cracks get gradually shorter could possibly be used to confirm whether a film really is crack-free or not. The smallest cracks form weak links in the films which could be seen with a careful ac-magnetization measurement as power dissipation. In this work only the thinnest μ-film seems crackfree judging by the lack of imaginary part of ac-magnetization. To calculate the critical current density of our samples the Bean formula [29] 2Δm ; aV ½1−a = ð3bÞ
250
•
jc =
jc;H∥c =
200
Fig. 5. Magnetic moments of n-films (filled circles, ) and μ-films (filled squares, ■) both on NGO plotted against film thickness measured in zero field and at 40 K. The inset shows the same plot but with lin–log axes. For comparison the value measured for n-film on STO was 402 μAm2. Magnetic moments of the samples were extracted as half of the opening of the hysteresis loop.
h i 3Δm Am2
0.2
300
Thickness (nm)
Thickness (nm)
0
200
Thickness (nm)
10
0.5
100
B < 1 mT T = 40 K
40 m (μAm2)
ϕ−FWHM (°)
0.7
60
0.35
m (μAm2)
RC−FWHM ( )
50
0.8
0.4 50
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ð1Þ
jc;local ≈
2Δm′ = n 2Δm′ =n 3 ; 2 a bt b t
ð3Þ
where it has been approximated that 1 − a/(3b) ≈ 1 since a ≪ b in a slab. Setting the two critical currents equal gives Δm′ = 3Δm/(2n). Thus cutting the sample into n pieces reduces the magnetic moment roughly by n when n ≫ 1. Using 5 μm as the average crack distance gives respectively local critical current of 10 and 11 MA/cm 2 for the 180 and 330 nm thick nfilms. For μ-films the estimation of local critical current gives too high (N30 MA/cm 2) values. This is expected because the average crack distance used in estimation was measured from n-films while in μfilms the crack distance is too long to be easily measured by AFM. None of the films grown on NGO reach the value of the reference film on STO for which a critical current density of 5.4 MA/cm 2 at 70 K was obtained. The best jc calculated from Eq. (1) assuming crack-free film was the thinnest μ-film for which 0.93 MA/cm 2 at 70 K was measured which is slightly below the values reported in the literature for YBCO thin films on NGO (001) at 77 K: about 1 MA/cm 2 [30,31] (DC sputtering films), 4–5 MA/cm 2 [27] (metal-organic chemical vapor deposition) and 2–4 MA/cm 2 [32,33] (PLD). The higher values in literature is partly explained by the fact that our jc is extracted from magnetic measurements and compared to values from resistance measurements which give 2–3 times higher jc [34]. The rest of the difference between our result and literature values can be attributed to the film thickness. It has been reported that jc decreases rapidly for films thinner than ∼ 100 nm [35,36]. The magnetic moment of μ-films has a clear jump between 70 nm and 100 nm thick films, which is consistent with similar jump in the XRD data and could indicate a cracking threshold and thus a crack-free film. However, the 70 nm thick μ-film still has four times smaller jc than the reference film on STO.
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A clear distinction between n- and μ-films in terms of magnetic moment can be seen in Fig. 5. The μ-films have larger moments than n-films throughout all thicknesses which contradicts the usual results of n-films being better because of their higher defect density [15,37]. In this work the better values of μ-films can be attributed to the smaller amount of cracking. This is consistent with the AFM images that showed cracking related structures in n-films while in μ-films the cracks were hardly visible. The reason for n-films to develop more cracks than μ-films is the less elastic lattice which is due to a smaller growth island size and a larger amount of lattice defects, especially dislocations [13,14]. The lesser elasticity of n-films can be deduced from the variation of φ-FWHM of XRD peaks with film thickness [14].
[4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
4. Conclusions In this work the structural and superconducting properties of YBCO thin films grown on NGO (001) were investigated. Two series of films with varying thicknesses were laser ablated with μ- and ntargets. The superconducting properties of the films decrease very strongly with film thickness as a result of extensive cracking. The main difference found between the two series was that the n-films crack more quickly with film thickness. This is attributed to the more rigid lattice of n-films as compared to μ-films [14]. Furthermore, some indications of a critical cracking threshold around 70 nm was found in μ-films meaning that less than 70 nm thick μ-films could be completely crack-free. In contrast, all of the n-films (70–330 nm thick) showed at least some microcracks. In conclusion, thin μ-films are plausible candidates for further measurements that utilize the uniaxial twin boundaries. Resistivity and Hall-conductance measurements will be made in the future to clarify the pinning mechanisms parallel and normal to twin boundaries.
[16] [17] [18] [19]
[20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31]
Acknowledgment The Wihuri Foundation is acknowledged for financial support. References [1] S.R. Foltyn, L. Civale, J.L. Macmanus-Driscoll, Q.X. Jia, B. Maiorov, H. Wang, M. Maley, Nat. Mater. 6 (2007) 631. [2] J. Nam, R.A. Hughes, J.P. Castellan, B.D. Gaulin, J.F. Britten, J.S. Preston, J. Appl. Phys. 97 (2005) 123906. [3] B. Dam, J.M. Huijbregtse, F.C. Klaassen, R.C.F. van der Geest, G. Doornbos, J.H. Rector, A.M. Testa, S. Freisem, J.C. Martinez, B. Stauble-Pumpin, R. Griessen, Nature 399 (1999) 439.
[32] [33] [34]
[35] [36] [37]
Z.D. Wang, J. Dong, C.S. Ting, Phys. Rev. Lett. 72 (1994) 3875. N.B. Kopnin, V.M. Vinokur, Phys. Rev. Lett. 83 (1999) 4864. R. Ikeda, Phys. C 316 (1999) 189. M. Safonchik, K. Traito, S. Tuominen, P. Paturi, H. Huhtinen, R. Laiho, Phys. C 469 (2009) 1983. G. Koren, E. Polturak, N. Levy, G. Deutscher, N.D. Zakharov, Appl. Phys. Lett. 73 (1998) 3763. I.K. Bdikin, P.B. Mozhaev, G.A. Ovsyannikov, P.V. Komissinski, I.M. Kotelyanskii, Phys. C 377 (2002) 26. O. Chaix-Pluchery, B. Chenevier, J.J. Robles, Appl. Phys. Lett. 86 (2005) 251911. R. Wördenweber, Supercond. Sci. Technol. 12 (1999) R86. P. Paturi, H. Huhtinen, K. Laajalehto, R. Laiho, Supercond. Sci. Technol. 13 (2000) 622. H. Huhtinen, J. Järvinen, R. Laiho, P. Paturi, J. Raittila, J. Appl. Phys. 90 (2001) 1521. M. Peurla, H. Huhtinen, Y.Y. Tse, J. Raittila, P. Paturi, IEEE Trans. Appl. Supercond. 17 (2007) 3608. H. Huhtinen, P. Paturi, E. Lähderanta, R. Laiho, Supercond. Sci. Technol. 12 (1999) 81. P. Paturi, M. Peurla, K. Nilsson, J. Raittila, Supercond. Sci. Technol. 17 (2004) 564. J. Raittila, H. Huhtinen, P. Paturi, Y.P. Stepanov, Phys. C 371 (2002) 90. C. Jooss, A. Forkl, R. Warthmann, H.U. Habermeier, B. Leibold, H. Kronmuller, Physica C 266 (1996) 235. J.D. Jorgensen, M.A. Beno, D.G. Hinks, L. Soderholm, K.J. Volin, R.L. Hitterman, J.D. Grace, I.K. Schuller, C.U. Serge, K. Zhang, M.S. Kleefisch, Phys. Rev. B 36 (1987) 3608. H. Casalta, P. Schleger, P. Harris, B. Lebech, N.H. Andersen, R. Liang, P. Dosanjh, W.N. Hardy, Phys. C 258 (1996) 321. M. Mukaida, S. Miyazawa, M. Sasaura, H. Yonezawa, J. Appl. Phys. 69 (1991) 3399. M. Mukaida, Y. Yamazaki, Y. Shingai, S. Makino, M. Kusunoki, A. Saito, S. Ohshima, Supercond. Sci. Technol. 17 (2004) 337. H. Huhtinen, K. Schlesier, P. Paturi, Supercond. Sci. Technol. 22 (2009) 075019. J. Ye, K. Nakamura, Phys. Rev. B 48 (1993) 7554. A. Rosová, C. Boulesteix, I. Vávra, Phys. C 214 (1993) 247. H. Yamada, H. Yamasaki, K. Develos-Bagarinao, Y. Nakagawa, Y. Mawatari, H. Obara, Phys. C 392 (2003) 1068. A. Abrutis, J.P. Sénateur, F. Weiss, V. Kubilius, V. Bigelytė, Z. Šaltytė, B. Vengalis, A. Jukna, Supercond. Sci. Technol. 10 (1997) 959. H. Wang, S.R. Foltyn, P.N. Arendt, Q.X. Jia, X. Zhang, Phys. C 444 (2006) 1. H.P. Wiesinger, F.M. Sauerzopf, H.W. Weber, Phys. C 203 (1992) 121. C. Villard, G. Koren, D. Cohen, E. Polturak, B. Thrane, D. Chateignier, Phys. Rev. Lett. 77 (1996) 3913. M.L. Lucia, J. Santamaria, F. Sánchez-Quesada, W. Lopera, M.E. Gómez, P. Prieto, Phys. C 260 (1996) 149. H.Y. To, G.J. Valco, K.B. Bhasin, Supercond. Sci. Technol. 5 (1992) 421. H. Yamasaki, Y. Nakagawa, A. Sawa, H. Obara, K. Develos, Phys. C 372 (2002) 1885. J. Hudner, O. Thomas, F. Weiss, D. Boursier, E. Mossang, J.P. Senateur, J.C. Villegier, H. Moriceau, M. Schwerdtfeger, A. Jäger, H. Ohlsén, Supercond. Sci. Technol. 7 (1994) 195. H. Huhtinen, J. Raittila, P. Paturi, V.-P. Huhtala, S. Mattila, J. Salminen, IEEE Trans. Appl. Supercond. 13 (2003) 2777. T. Venkatesan, X.D. Wu, B. Dutta, A. Inam, M.S. Hedge, D.M. Hwang, C.C. Chang, L. Nazar, B. Wilkens, Appl. Phys. Lett. 54 (1989) 581. M. Peurla, H. Huhtinen, P. Paturi, Supercond. Sci. Technol. 18 (2005) 628.