- Email: [email protected]
Mastering the biaxial stress state in nanometric thin films on flexible substrates
Applied Surface Science 306 (2014) 70–74
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Mastering the biaxial stress state in nanometric thin films on flexible substrates D. Faurie a,∗ , P.-O. Renault b , E. Le Bourhis b , G. Geandier c , P. Goudeau b , D. Thiaudière d a
LSPM-CNRS, UPR3407, Université Paris 13, Villetaneuse, France Institut Pprime UPR3346, CNRS – Université de Poitiers, Futuroscope, France Institut Jean Lamour, CNRS UMR7198, Université de Lorraine, Nancy Cedex, France d SOLEIL Synchrotron, Saint-Aubin, Gif-Sur-Yvette, France b c
a r t i c l e
i n f o
Article history: Received 28 October 2013 Received in revised form 7 February 2014 Accepted 7 February 2014 Available online 18 February 2014 Keywords: Mechanical behavior of thin films Synchrotron radiation X-ray diffraction Biaxial deformation
a b s t r a c t Biaxial stress state of thin films deposited on flexible substrate can be mastered thanks to a new biaxial device. This tensile machine allows applying in-plane loads Fx and Fy in the two principal directions x and y of a cruciform-shaped polymer substrate. The transmission of the deformation at film/substrate interface allows controlling the stress and strain field in the thin films. We show in this paper a few illustrations dealing with strain measurements in polycrystalline thin films deposited on flexible substrate. The potentialities of the biaxial device located at Soleil synchrotron are also discussed. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Nanometric thin films are generally submitted to complex stress conditions when they are used in manufacturing applications [1]. In order to better understand the mechanical behavior of thin films, it is of utmost importance to assess the material mechanical behavior under complex combined multiaxial stress conditions. A few experiments have been developed to investigate the mechanical behavior of thin films under biaxial conditions such as Bulge test [2–5] and the ring-on-ring test [6]; however, these mechanical tests are limited to equi-biaxial loading. On the other hand, equi-biaxial stress states can also be applied to the film by annealing the thin film/substrate samples at elevated temperatures [7–9] profiting from the thermal expansion mismatch between film and substrate. Up to now, mechanical test of thin films supported by flexible substrates have only been carried out for single strain path (uniaxial tensile or compressive tests on the film-substrate composite [10–16]). Recently, we have developed a tensile testing device that allows mastering biaxial loading on thin films deposited onto cruciform compliant substrates. The biaxial device is available at DiffAbs beamline of the French synchrotron radiation
∗ Corresponding author. Tel.: +33 149403484. E-mail address: [email protected] (D. Faurie). http://dx.doi.org/10.1016/j.apsusc.2014.02.032 0169-4332/© 2014 Elsevier B.V. All rights reserved.
facility (SOLEIL, Saint-Aubin) [17,18]. A cruciform specimen is used for applying a longitudinal and a transverse loading simultaneously. By varying the ratio of these loadings, we are able to vary the biaxial stress state in the thin film in a controlled manner. In the present paper, we make a short overview of the experimental approach based on the synchrotron biaxial tensile device for studying the mechanical behavior of films under various loadings. The studied systems are W/Cu nanocomposite thin films and ultra-thin Au films deposited on polyimide cruciform substrate. Synchrotron X-ray diffraction (XRD) is used to measure strains in the film and digital image correlation (DIC) is used to determine strains in the substrate. This method provides important information regarding thin film behavior, the stress and strain field occurring in the film and in the compliant substrate. Especially, the initiation of plasticity and/or damaging in thin films can be scrutinized, thanks to combined measurements of very small strains in both film and substrate with high accuracy [19].
2. Experimental methodology We have employed the DIFFABS-SOLEIL biaxial tensile device working in the synchrotron environment for in situ diffraction characterization of thin polycrystalline films mechanical response [17]. The setup is shown in Fig. 1 in the DiffAbs experimental station at Soleil (Saint-Aubin, France). The biaxial tester is shown
D. Faurie et al. / Applied Surface Science 306 (2014) 70–74
71
Fig. 2. Graph showing the potentialities of the biaxial tensile device in term of loading paths.
Fig. 1. (a) Biaxial tensile device mounted on the goniometer of DiffAbs beamline (SOLEIL Synchrotron). A 2D detector allows capturing the Debye–Scherrer diffraction rings. (b) Photography of a cruciform-shaped sample (the metallic thin film is deposited at the center of the polyimide substrate) set on the device.
mounted on the goniometer (Fig. 1a) and allows X-ray diffraction in reflection mode at glancing angles (no shadowing edges). Two couples of motors and force sensors are fixed to the device frame. The four motors can be actuated separately in order to keep the studied area at a fixed position in the goniometer. The cruciform compliant substrates are coated by a thin film in their central area of 20 mm in diameter only and gripped by a cam rotating in a cylindrical fixation (Fig. 1b). As shown in Fig. 2, this tensile device allows applying simple or complex loadings in a controlled manner. Strain measurements can be performed for different loading paths using both X-ray diffraction and DIC techniques: (i) Synchrotron XRD is used to measure lattice strains within the thin film over coherent diffraction domains. Classically, changes in interplanar spacing dhkl can be used with Bragg’s law = 2dh k l sin h k l to determine the elastic strain εϕ through the knowledge of the incident wavelength and the change in the Bragg scattering angle. Employing an X-ray area detector, grain selective strain measurements can be monitored for several directions of the diffraction vector k = kd − ki during straining. This vector gives the direction of the strain measurement and
can be differently oriented during a same experiment either by placing a 2D X-ray detector close to the sample in order to acquire an important part of Debye–Scherrer rings (Fig. 3), or by rotating the sample and the detector (0D or 2D) using the 7-Circle goniometer of the DiffAbs beamline. (ii) DIC is used to assess the strain in the polyimide cruciform substrate. An image of the bottom of the substrate (the uncoated side) is captured with a CCD camera. Image correlation is used to determine displacement and strain fields on the surface of an object by capturing images of the surface at different states [20]. One state is recorded before loading, i.e. the reference image, and the other states are subsequent images of the deformed object. DIC uses random patterns of gray levels of the sample surface to measure the displacement via the correlation of a pair of digital images. Knowing the macroscopic strains εxx and εyy in the substrate, and assuming a complete strain transfer at the film/substrate interface, the in-plane stresses xx and yy can be deduced using Hooke’s law. One interesting way is to compare the measured strain and stress field in both film and substrate in order to study the strain transmission during elastic deformation [18] and to find signature of plastic deformation and/or damaging when it occurs (separation of the two curves) [21].
Fig. 3. Sketch of the experimental set-up developed at DiffAbs beamline. The thin film elastic strains are measured by X-ray diffraction while the substrate macroscopic strains are measured by digital image correlation.
72
D. Faurie et al. / Applied Surface Science 306 (2014) 70–74
Fig. 4. In-plane strains as a function of applied loads in the case of nearly biaxial loading of {W/Cu nanocomposite thin/Kapton® substrate} system, in the elastic domain. Full symbols show strains in the W phase of the film estimated by XRD while open symbols show substrate strains measured by DIC.
3. Illustrative results 3.1. Equi-biaxial loading of thin films in the elastic domain The first illustration presents a study of strain field in a nanocomposite W/Cu thin film (150 nm) deposited at room temperature by sputtering alternatively W and Cu onto Kapton® substrate (127.5 m) [18]. Sputtering deposition was achieved with an argon ion-gun sputtering beam at 1.2 keV where the base pressure in the chamber was 7 × 10−5 Pa and the working pressure during film growth was 10−2 Pa. The deposition rate was about 0.05 nm/s and 0.07 nm/s for W and Cu components, respectively. The high intensity of the synchrotron radiation and the use of a hybrid pixel detector (XPAD3.1) allowed measuring the lattice strain in short counting times with good accuracy [22]. Fig. 4 shows the results of the in-plane strains εxx and εyy , estimated by XRD (in the W phase of the films) and DIC (at the surface of the substrate) as a function of applied load being nearly equi-biaxial. The strain evolutions are linear, as expected for loadings within the elastic domain. This figure shows that the two strain components are slightly different, and that this difference increases with the applied force. Moreover, the DIC and XRD strains are superimposed, within experimental uncertainty, for each component. It is clear that the difference between εxx and εyy is significant, and equivalent for both techniques. This difference is attributed to the in-plane elastic anisotropy of Kapton® . A comparison of the two approaches for measuring in situ plane strains shows that the strain measurements are of good accuracy and adaptability for various stress conditions. The strains obtained by the DIC and XRD techniques are equal to within 10−4 . From the results of these tests, we can be confident that combined synchrotron XRD and DIC analyses could be used with efficiency and reliability in biaxial tensile tests of thin films deposited on polymer substrates. The main consequence of the accuracy of the two strain measurement techniques is that the applied strain is shown to be transmitted unchanged in the elastic domain through the metallic film–polymeric substrate interface, although no adhesion layer was used, even with such a high elastic mechanical contrast (two orders of magnitude between Young’s moduli of W and Kapton). Similar result is reported for gold films by Geandier et al. [23]. 3.2. Strain pole figure measurements during complex loading of thin films As a second illustration, we show X-ray diffraction strains measured along many orientations of the diffraction vector k. By using
Fig. 5. {2 0 0} Strain Pole Figures measured in a 40 nm thick Au film deposited on Kapton® substrate for (a) an equibiaxial loading (Fx = 150 N and Fy = 150 N) and (b) a non-equibiaxial loading Fx = 50 N and Fy = 125 N.
a 2D detector combined with a rotation of the sample around its normal, it is possible to measure at least one Strain Pole Figure for each applied biaxial loading in a reasonable time (a few minutes). This method has been applied to a gold ultra-thin film (40 nm) submitted to different loadings. The Au thin film was deposited by ion-beam sputtering on Kapton® substrate. The base pressure in the growth chamber was 7 × 10−5 Pa, while the working pressure during film growth was approximately 10−2 Pa. Gold deposition was carried out at room temperature with an Ar+-ion-gun sputtering beam at 1.2 keV. The {1 1 1} fiber-texture that generally occurs for gold films has been found to be weak, mainly because of the small thickness. Diffraction experiments have been carried out on DiffAbs beamline, X-ray diffracted signal being recorded by a MAR SX-165 CCD detector placed just behind the sample (at 160 mm from it), in order to get a big part of the Debye–Scherrer diffraction rings. This method is obviously applicable if the crystallographic texture is weak that is generally the case for ultra-thin films deposited on polymer substrates. In order to measure a complete SPF, an azimuthal rotation (angle ) is needed. Thus, a 2D diffractogram was recorded every each two-degree step. In the absence of shear strains, the symmetry makes sufficient a range of 180◦ to describe the whole strain fields. Fig. 5 shows the {2 0 0} Strain Pole Figure for two different applied loads. Fig. 5a corresponds to Fx = 150 N and Fy = 150 N (equibiaxial loading), while Fig. 5b corresponds to a non-equibiaxial loading state of Fx = 50 N and Fy = 125 N. The complex loading path induced a significant shape change of the Strain
D. Faurie et al. / Applied Surface Science 306 (2014) 70–74
Fig. 6. Loading path of similar {W/Cu nanocomposite thin/Kapton® substrate} systems for different loading ratios (R = 0.2, R = 0.33, R = 0.5, R = 0.9).
Pole Figure. The equibiaxial stress applied to the thin films, corresponding to Fig. 5a, is evidenced by a rotational symmetry of the strain field around the normal to the surface, with negative strains in the region close to the center of the Strain Pole Figure and positive strains in the region close to the extremity. In contrast, this rotational symmetry is obviously lost in the case of a non-equibiaxial stress state (Fig. 5b) as encountered for uniaxial tensile tests. These measurements can be simultaneously made for a few {h k l} plane families, depending on the number of accessible Bragg angles on the 2D X-ray detector. This kind of measurements are rare, especially in the thin film community, and allow scrutinizing load transfer from one grain family to another during plastic deformation. The experimental data is of great interest and is to be compared to elastoplastic models suitable for thin films. 3.3. Effect of load ratio on the thin films mechanical behavior The present illustration encompasses experimental results for 4 cruciform specimens coated by W/Cu nanocomposites thin films (similar to those presented in Section 3.1) having similar as-deposited configuration (residual stresses, grain size and crystallographic texture). These 4 specimens were subjected to biaxial stress tension with variable loading paths. All in situ tensile tests were conducted at a strain rate of ε˙ = 8 × 10−6 s−1 along the two main tensile axes. As shown in Fig. 1 and inset of Fig. 4, the loading axes (Fx and Fy ) are taken parallel to the arms of the specimen. The loadings were controlled in order to maintain the tensile loads Fx and Fy in a fixed proportion and Fy axis was taken as the direction of the higher applied tension. The applied load ratios were of R = Fx /Fy = 0.9, 0.5, 0.33 and 0.2. Fig. 6 shows the evolution of Fy as function of Fx for each loading ratio. In all cases, a pre-load is applied to the sample (Fx = Fy = 15 N) in order to avoid significant height changes of the sample during mechanical loading. The evolution of the curves is almost linear, slight drifts being attributed to the anisotropic visco-elastic behavior of the Kapton® substrate. Fig. 7 shows the evolution of εyy as function of εxx , measured both by XRD (in the W phase of the film, full symbols) and DIC (on the substrate, open symbols), for each loading ratio. For each technique, the pre-loading state (Fx = Fy = 15 N) is considered as the reference state to determine the applied strains. For each loading ratio, the macroscopic strains of the substrate measured by DIC increased almost linearly, as for applied loads. It should be noted
73
Fig. 7. In plane strains of {W/Cu nanocomposite thin/Kapton® substrate} systems for each loading ratio (R = 0.2, R = 0.33, R = 0.5, R = 0.9). Full symbols show strains in the W phase of the film estimated by XRD while open symbols show substrate strains measured by DIC. The saturation of X-ray strains along y direction (εyy ) is the signature of the brittle behavior of thin film (cracks).
that εxx for R = 0.2 and R = 0.33 is negative because of Poisson’s ratio effect; in these two cases the applied load along the x direction is not high enough to compensate this effect. Obviously, the in-plane strain ratio is therefore strongly different from the load ratio. In contrast to substrate macroscopic strains, the film elastic strains εxx and εyy saturate before attaining 1%. It has been already suggested by Djaziri et al. [21] that three deformation domains occur in such brittle nanocomposite films: I purely elastic, II micro-plasticity and/or cracks initiation, III fracture of the films. Domain I corresponds to the good match between film and substrate strains. Domain II can be detected when XRD strains depart from DIC strains by more than 0.2% (clearly seen in the case R = 0.5). Domain III has a clear signature corresponding to the saturation or slight decrease of the XRD strain along the highest load direction (εyy in our cases). As cracks develop perpendicularly to the y direction, the strain relaxation is not observed in the x direction, so that εxx still decreases in domain III for R = 0.2 and R = 0.33 while it increases for R = 0.5 and R = 0.9. This representation, which is not usual in the thin films community, allows showing the anisotropic behavior of the mechanical properties of thin films. Noteworthy three deformation domains have also been evidence in Ni nanocrystalline bulk materials [24,25]: I elastic, II microplastic, and III macroplastic. Bulk and film nanocrystalline materials should obviously exhibit similar mechanical behavior. But the third domain is obviously completely different in the present case of thin film. It is only possible in thin film because even after crack or microcrack initiation some parts of the film are still attached to the substrate and can sustain more deformation [26]. 4. Concluding remarks We have shown in this paper how the DiffAbs biaxial tensile device allows mastering the stress and strain fields in thin films deposited on flexible substrates. The combination of synchrotron X-ray diffraction and digital image correlation allows measuring simultaneously the strains in the thin film and in the substrate. It appears to be pertinent to study the mechanical behavior of the whole film/substrate system and to discretize the different deformation modes of the thin film. This method can be applied to any
74
D. Faurie et al. / Applied Surface Science 306 (2014) 70–74
crystalline film deposited on any compliant substrate and shall be of great interest for studying the mechanical behavior of materials used in stretchable electronics [27]. References [1] S. Massl, J. Keckes, R. Pippan, Acta Materialia 55 (2007) 4835–4844. [2] J.J. Vlassak, W.D. Nix, Journal of Materials Research 7 (1992) 3242–3249. [3] P.A. Gruber, J. Böhm, F. Onuseit, A. Wanner, R. Spolenak, E. Arzt, Acta Materialia 56 (2008) 2318–2335. [4] A.F. Jankowski, T. Tsakalakos, Thin Solid Films 290 (1996) 243–247. [5] M.P. Orthner, L.W. Rieth, F. Solzbacher, Review of Scientific Instruments 81 (2010) 055111. [6] S. Eve, N. Hubert, O. Kraft, A. Last, D. Rabus, M. Schlagenhof, Review of Scientific Instruments 77 (2006) 103902. [7] G. Cornella, S.H. Lee, W.D. Nix, J.C. Bravman, Applied Physics Letters 71 (1997) 2949. [8] S.P. Baker, A. Kretschmann, E. Arzt, Acta Materialia 49 (2001) 2145–2160. [9] J. Keckes, Journal of Applied Crystallography 38 (2005) 311–318. [10] S.P. Lacour, D. Chan, S. Wagner, T. Li, Z. Suo, Applied Physics Letters 88 (2006) 204103. [11] P.A. Gruber, C. Solenthaler, E. Arzt, R. Spolenak, Acta Materialia 56 (2008) 1876–1889. [12] D. Faurie, P. Djemia, E. Le Bourhis, P.O. Renault, Y. Roussigné, S.M. Chérif, R. Brenner, O. Castelnau, G. Patriarche, Ph. Goudeau, Acta Materialia 58 (2010) 4998–5008. [13] D.Y.W. Yu, F. Spaepen, Journal of Applied Physics 95 (2004) 2991.
[14] J. Andersons, Y. Leterrier, Thin Solid Films 471 (2005) 209–217. [15] S. Cai, D. Breid, A. Crosby, Z. Suo, J. Hutchinson, Journal of the Mechanics and Physics of Solids 59 (2011) 1094–1114. [16] M. Hommel, O. Kraft, E. Arzt, Journal of Materials Research 14 (1999) 2373–2376. [17] G. Geandier, D. Thiaudière, R.N. Randriamazaoro, R. Chiron, S. Djaziri, B. Lamongie, Y. Diot, E. Le Bourhis, P.O. Renault, P. Goudeau, A. Bouaffad, O. Castelnau, D. Faurie, F. Hild, Review of Scientific Instruments 81 (2010) 103903. [18] S. Djaziri, P.O. Renault, F. Hild, E. Le Bourhis, Ph. Goudeau, D. Thiaudière, D. Faurie, Journal of Applied Crystallography 44 (2011) 1071–1079. [19] S. Djaziri, D. Faurie, P.O. Renault, E. Le Bourhis, Ph. Goudeau, D. Thiaudière, G. Geandier, Acta Materialia 13 (2013) 5067–5077. [20] G. Besnard, F. Hild, S. Roux, Experimental Mechanics 46 (2006) 789–803. [21] S. Djaziri, D. Faurie, E. Le Bourhis, Ph. Goudeau, P.O. Renault, C. Mocuta, D. Thiaudière, F. Hild, Thin Solid Films 530 (2013) 30–34. [22] C. Le Bourlot, P. Landois, S. Djaziri, P.O. Renault, E. Le Bourhis, P. Goudeau, M. Pinault, M. Mayne-L’Hermite, B. Bacroix, D. Faurie, O. Castelnau, P. Launois, S. Rouzière, Journal of Applied Crystallography 45 (2012) 38–47. [23] G. Geandier, P.O. Renault, E. Le Bourhis, Ph. Goudeau, D. Faurie, C. Le Bourlot, Ph. Djemia, O. Castelnau, S.M. Chérif, Applied Physics Letters 96 (2010) 041905. [24] H. Van Swygenhoven, S. Van Petegem, Materials Characterization 78 (2013) 47–59. [25] S. Van Petegem, L. Li, P.M. Anderson, H. Van Swygenhoven, Thin Solid Films 530 (2013) 20–24. [26] A.L. Volynskii, D.A. Panchuk, S.L. Bazhenov, M.Y. Yablokov, A.B. Gilman, A.V. Bolshakova, L.M. Yarysheva, N.F. Bakeev, Thin Solid Films 536 (2013) 179–186. [27] D.S. Gray, J. Tien, C.S. Chen, Advanced Materials 16 (2004) 393–397.
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Mastering the biaxial stress state in nanometric thin films on flexible substrates D. Faurie a,∗ , P.-O. Renault b , E. Le Bourhis b , G. Geandier c , P. Goudeau b , D. Thiaudière d a
LSPM-CNRS, UPR3407, Université Paris 13, Villetaneuse, France Institut Pprime UPR3346, CNRS – Université de Poitiers, Futuroscope, France Institut Jean Lamour, CNRS UMR7198, Université de Lorraine, Nancy Cedex, France d SOLEIL Synchrotron, Saint-Aubin, Gif-Sur-Yvette, France b c
a r t i c l e
i n f o
Article history: Received 28 October 2013 Received in revised form 7 February 2014 Accepted 7 February 2014 Available online 18 February 2014 Keywords: Mechanical behavior of thin films Synchrotron radiation X-ray diffraction Biaxial deformation
a b s t r a c t Biaxial stress state of thin films deposited on flexible substrate can be mastered thanks to a new biaxial device. This tensile machine allows applying in-plane loads Fx and Fy in the two principal directions x and y of a cruciform-shaped polymer substrate. The transmission of the deformation at film/substrate interface allows controlling the stress and strain field in the thin films. We show in this paper a few illustrations dealing with strain measurements in polycrystalline thin films deposited on flexible substrate. The potentialities of the biaxial device located at Soleil synchrotron are also discussed. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Nanometric thin films are generally submitted to complex stress conditions when they are used in manufacturing applications [1]. In order to better understand the mechanical behavior of thin films, it is of utmost importance to assess the material mechanical behavior under complex combined multiaxial stress conditions. A few experiments have been developed to investigate the mechanical behavior of thin films under biaxial conditions such as Bulge test [2–5] and the ring-on-ring test [6]; however, these mechanical tests are limited to equi-biaxial loading. On the other hand, equi-biaxial stress states can also be applied to the film by annealing the thin film/substrate samples at elevated temperatures [7–9] profiting from the thermal expansion mismatch between film and substrate. Up to now, mechanical test of thin films supported by flexible substrates have only been carried out for single strain path (uniaxial tensile or compressive tests on the film-substrate composite [10–16]). Recently, we have developed a tensile testing device that allows mastering biaxial loading on thin films deposited onto cruciform compliant substrates. The biaxial device is available at DiffAbs beamline of the French synchrotron radiation
∗ Corresponding author. Tel.: +33 149403484. E-mail address: [email protected] (D. Faurie). http://dx.doi.org/10.1016/j.apsusc.2014.02.032 0169-4332/© 2014 Elsevier B.V. All rights reserved.
facility (SOLEIL, Saint-Aubin) [17,18]. A cruciform specimen is used for applying a longitudinal and a transverse loading simultaneously. By varying the ratio of these loadings, we are able to vary the biaxial stress state in the thin film in a controlled manner. In the present paper, we make a short overview of the experimental approach based on the synchrotron biaxial tensile device for studying the mechanical behavior of films under various loadings. The studied systems are W/Cu nanocomposite thin films and ultra-thin Au films deposited on polyimide cruciform substrate. Synchrotron X-ray diffraction (XRD) is used to measure strains in the film and digital image correlation (DIC) is used to determine strains in the substrate. This method provides important information regarding thin film behavior, the stress and strain field occurring in the film and in the compliant substrate. Especially, the initiation of plasticity and/or damaging in thin films can be scrutinized, thanks to combined measurements of very small strains in both film and substrate with high accuracy [19].
2. Experimental methodology We have employed the DIFFABS-SOLEIL biaxial tensile device working in the synchrotron environment for in situ diffraction characterization of thin polycrystalline films mechanical response [17]. The setup is shown in Fig. 1 in the DiffAbs experimental station at Soleil (Saint-Aubin, France). The biaxial tester is shown
D. Faurie et al. / Applied Surface Science 306 (2014) 70–74
71
Fig. 2. Graph showing the potentialities of the biaxial tensile device in term of loading paths.
Fig. 1. (a) Biaxial tensile device mounted on the goniometer of DiffAbs beamline (SOLEIL Synchrotron). A 2D detector allows capturing the Debye–Scherrer diffraction rings. (b) Photography of a cruciform-shaped sample (the metallic thin film is deposited at the center of the polyimide substrate) set on the device.
mounted on the goniometer (Fig. 1a) and allows X-ray diffraction in reflection mode at glancing angles (no shadowing edges). Two couples of motors and force sensors are fixed to the device frame. The four motors can be actuated separately in order to keep the studied area at a fixed position in the goniometer. The cruciform compliant substrates are coated by a thin film in their central area of 20 mm in diameter only and gripped by a cam rotating in a cylindrical fixation (Fig. 1b). As shown in Fig. 2, this tensile device allows applying simple or complex loadings in a controlled manner. Strain measurements can be performed for different loading paths using both X-ray diffraction and DIC techniques: (i) Synchrotron XRD is used to measure lattice strains within the thin film over coherent diffraction domains. Classically, changes in interplanar spacing dhkl can be used with Bragg’s law = 2dh k l sin h k l to determine the elastic strain εϕ through the knowledge of the incident wavelength and the change in the Bragg scattering angle. Employing an X-ray area detector, grain selective strain measurements can be monitored for several directions of the diffraction vector k = kd − ki during straining. This vector gives the direction of the strain measurement and
can be differently oriented during a same experiment either by placing a 2D X-ray detector close to the sample in order to acquire an important part of Debye–Scherrer rings (Fig. 3), or by rotating the sample and the detector (0D or 2D) using the 7-Circle goniometer of the DiffAbs beamline. (ii) DIC is used to assess the strain in the polyimide cruciform substrate. An image of the bottom of the substrate (the uncoated side) is captured with a CCD camera. Image correlation is used to determine displacement and strain fields on the surface of an object by capturing images of the surface at different states [20]. One state is recorded before loading, i.e. the reference image, and the other states are subsequent images of the deformed object. DIC uses random patterns of gray levels of the sample surface to measure the displacement via the correlation of a pair of digital images. Knowing the macroscopic strains εxx and εyy in the substrate, and assuming a complete strain transfer at the film/substrate interface, the in-plane stresses xx and yy can be deduced using Hooke’s law. One interesting way is to compare the measured strain and stress field in both film and substrate in order to study the strain transmission during elastic deformation [18] and to find signature of plastic deformation and/or damaging when it occurs (separation of the two curves) [21].
Fig. 3. Sketch of the experimental set-up developed at DiffAbs beamline. The thin film elastic strains are measured by X-ray diffraction while the substrate macroscopic strains are measured by digital image correlation.
72
D. Faurie et al. / Applied Surface Science 306 (2014) 70–74
Fig. 4. In-plane strains as a function of applied loads in the case of nearly biaxial loading of {W/Cu nanocomposite thin/Kapton® substrate} system, in the elastic domain. Full symbols show strains in the W phase of the film estimated by XRD while open symbols show substrate strains measured by DIC.
3. Illustrative results 3.1. Equi-biaxial loading of thin films in the elastic domain The first illustration presents a study of strain field in a nanocomposite W/Cu thin film (150 nm) deposited at room temperature by sputtering alternatively W and Cu onto Kapton® substrate (127.5 m) [18]. Sputtering deposition was achieved with an argon ion-gun sputtering beam at 1.2 keV where the base pressure in the chamber was 7 × 10−5 Pa and the working pressure during film growth was 10−2 Pa. The deposition rate was about 0.05 nm/s and 0.07 nm/s for W and Cu components, respectively. The high intensity of the synchrotron radiation and the use of a hybrid pixel detector (XPAD3.1) allowed measuring the lattice strain in short counting times with good accuracy [22]. Fig. 4 shows the results of the in-plane strains εxx and εyy , estimated by XRD (in the W phase of the films) and DIC (at the surface of the substrate) as a function of applied load being nearly equi-biaxial. The strain evolutions are linear, as expected for loadings within the elastic domain. This figure shows that the two strain components are slightly different, and that this difference increases with the applied force. Moreover, the DIC and XRD strains are superimposed, within experimental uncertainty, for each component. It is clear that the difference between εxx and εyy is significant, and equivalent for both techniques. This difference is attributed to the in-plane elastic anisotropy of Kapton® . A comparison of the two approaches for measuring in situ plane strains shows that the strain measurements are of good accuracy and adaptability for various stress conditions. The strains obtained by the DIC and XRD techniques are equal to within 10−4 . From the results of these tests, we can be confident that combined synchrotron XRD and DIC analyses could be used with efficiency and reliability in biaxial tensile tests of thin films deposited on polymer substrates. The main consequence of the accuracy of the two strain measurement techniques is that the applied strain is shown to be transmitted unchanged in the elastic domain through the metallic film–polymeric substrate interface, although no adhesion layer was used, even with such a high elastic mechanical contrast (two orders of magnitude between Young’s moduli of W and Kapton). Similar result is reported for gold films by Geandier et al. [23]. 3.2. Strain pole figure measurements during complex loading of thin films As a second illustration, we show X-ray diffraction strains measured along many orientations of the diffraction vector k. By using
Fig. 5. {2 0 0} Strain Pole Figures measured in a 40 nm thick Au film deposited on Kapton® substrate for (a) an equibiaxial loading (Fx = 150 N and Fy = 150 N) and (b) a non-equibiaxial loading Fx = 50 N and Fy = 125 N.
a 2D detector combined with a rotation of the sample around its normal, it is possible to measure at least one Strain Pole Figure for each applied biaxial loading in a reasonable time (a few minutes). This method has been applied to a gold ultra-thin film (40 nm) submitted to different loadings. The Au thin film was deposited by ion-beam sputtering on Kapton® substrate. The base pressure in the growth chamber was 7 × 10−5 Pa, while the working pressure during film growth was approximately 10−2 Pa. Gold deposition was carried out at room temperature with an Ar+-ion-gun sputtering beam at 1.2 keV. The {1 1 1} fiber-texture that generally occurs for gold films has been found to be weak, mainly because of the small thickness. Diffraction experiments have been carried out on DiffAbs beamline, X-ray diffracted signal being recorded by a MAR SX-165 CCD detector placed just behind the sample (at 160 mm from it), in order to get a big part of the Debye–Scherrer diffraction rings. This method is obviously applicable if the crystallographic texture is weak that is generally the case for ultra-thin films deposited on polymer substrates. In order to measure a complete SPF, an azimuthal rotation (angle ) is needed. Thus, a 2D diffractogram was recorded every each two-degree step. In the absence of shear strains, the symmetry makes sufficient a range of 180◦ to describe the whole strain fields. Fig. 5 shows the {2 0 0} Strain Pole Figure for two different applied loads. Fig. 5a corresponds to Fx = 150 N and Fy = 150 N (equibiaxial loading), while Fig. 5b corresponds to a non-equibiaxial loading state of Fx = 50 N and Fy = 125 N. The complex loading path induced a significant shape change of the Strain
D. Faurie et al. / Applied Surface Science 306 (2014) 70–74
Fig. 6. Loading path of similar {W/Cu nanocomposite thin/Kapton® substrate} systems for different loading ratios (R = 0.2, R = 0.33, R = 0.5, R = 0.9).
Pole Figure. The equibiaxial stress applied to the thin films, corresponding to Fig. 5a, is evidenced by a rotational symmetry of the strain field around the normal to the surface, with negative strains in the region close to the center of the Strain Pole Figure and positive strains in the region close to the extremity. In contrast, this rotational symmetry is obviously lost in the case of a non-equibiaxial stress state (Fig. 5b) as encountered for uniaxial tensile tests. These measurements can be simultaneously made for a few {h k l} plane families, depending on the number of accessible Bragg angles on the 2D X-ray detector. This kind of measurements are rare, especially in the thin film community, and allow scrutinizing load transfer from one grain family to another during plastic deformation. The experimental data is of great interest and is to be compared to elastoplastic models suitable for thin films. 3.3. Effect of load ratio on the thin films mechanical behavior The present illustration encompasses experimental results for 4 cruciform specimens coated by W/Cu nanocomposites thin films (similar to those presented in Section 3.1) having similar as-deposited configuration (residual stresses, grain size and crystallographic texture). These 4 specimens were subjected to biaxial stress tension with variable loading paths. All in situ tensile tests were conducted at a strain rate of ε˙ = 8 × 10−6 s−1 along the two main tensile axes. As shown in Fig. 1 and inset of Fig. 4, the loading axes (Fx and Fy ) are taken parallel to the arms of the specimen. The loadings were controlled in order to maintain the tensile loads Fx and Fy in a fixed proportion and Fy axis was taken as the direction of the higher applied tension. The applied load ratios were of R = Fx /Fy = 0.9, 0.5, 0.33 and 0.2. Fig. 6 shows the evolution of Fy as function of Fx for each loading ratio. In all cases, a pre-load is applied to the sample (Fx = Fy = 15 N) in order to avoid significant height changes of the sample during mechanical loading. The evolution of the curves is almost linear, slight drifts being attributed to the anisotropic visco-elastic behavior of the Kapton® substrate. Fig. 7 shows the evolution of εyy as function of εxx , measured both by XRD (in the W phase of the film, full symbols) and DIC (on the substrate, open symbols), for each loading ratio. For each technique, the pre-loading state (Fx = Fy = 15 N) is considered as the reference state to determine the applied strains. For each loading ratio, the macroscopic strains of the substrate measured by DIC increased almost linearly, as for applied loads. It should be noted
73
Fig. 7. In plane strains of {W/Cu nanocomposite thin/Kapton® substrate} systems for each loading ratio (R = 0.2, R = 0.33, R = 0.5, R = 0.9). Full symbols show strains in the W phase of the film estimated by XRD while open symbols show substrate strains measured by DIC. The saturation of X-ray strains along y direction (εyy ) is the signature of the brittle behavior of thin film (cracks).
that εxx for R = 0.2 and R = 0.33 is negative because of Poisson’s ratio effect; in these two cases the applied load along the x direction is not high enough to compensate this effect. Obviously, the in-plane strain ratio is therefore strongly different from the load ratio. In contrast to substrate macroscopic strains, the film elastic strains εxx and εyy saturate before attaining 1%. It has been already suggested by Djaziri et al. [21] that three deformation domains occur in such brittle nanocomposite films: I purely elastic, II micro-plasticity and/or cracks initiation, III fracture of the films. Domain I corresponds to the good match between film and substrate strains. Domain II can be detected when XRD strains depart from DIC strains by more than 0.2% (clearly seen in the case R = 0.5). Domain III has a clear signature corresponding to the saturation or slight decrease of the XRD strain along the highest load direction (εyy in our cases). As cracks develop perpendicularly to the y direction, the strain relaxation is not observed in the x direction, so that εxx still decreases in domain III for R = 0.2 and R = 0.33 while it increases for R = 0.5 and R = 0.9. This representation, which is not usual in the thin films community, allows showing the anisotropic behavior of the mechanical properties of thin films. Noteworthy three deformation domains have also been evidence in Ni nanocrystalline bulk materials [24,25]: I elastic, II microplastic, and III macroplastic. Bulk and film nanocrystalline materials should obviously exhibit similar mechanical behavior. But the third domain is obviously completely different in the present case of thin film. It is only possible in thin film because even after crack or microcrack initiation some parts of the film are still attached to the substrate and can sustain more deformation [26]. 4. Concluding remarks We have shown in this paper how the DiffAbs biaxial tensile device allows mastering the stress and strain fields in thin films deposited on flexible substrates. The combination of synchrotron X-ray diffraction and digital image correlation allows measuring simultaneously the strains in the thin film and in the substrate. It appears to be pertinent to study the mechanical behavior of the whole film/substrate system and to discretize the different deformation modes of the thin film. This method can be applied to any
74
D. Faurie et al. / Applied Surface Science 306 (2014) 70–74
crystalline film deposited on any compliant substrate and shall be of great interest for studying the mechanical behavior of materials used in stretchable electronics [27]. References [1] S. Massl, J. Keckes, R. Pippan, Acta Materialia 55 (2007) 4835–4844. [2] J.J. Vlassak, W.D. Nix, Journal of Materials Research 7 (1992) 3242–3249. [3] P.A. Gruber, J. Böhm, F. Onuseit, A. Wanner, R. Spolenak, E. Arzt, Acta Materialia 56 (2008) 2318–2335. [4] A.F. Jankowski, T. Tsakalakos, Thin Solid Films 290 (1996) 243–247. [5] M.P. Orthner, L.W. Rieth, F. Solzbacher, Review of Scientific Instruments 81 (2010) 055111. [6] S. Eve, N. Hubert, O. Kraft, A. Last, D. Rabus, M. Schlagenhof, Review of Scientific Instruments 77 (2006) 103902. [7] G. Cornella, S.H. Lee, W.D. Nix, J.C. Bravman, Applied Physics Letters 71 (1997) 2949. [8] S.P. Baker, A. Kretschmann, E. Arzt, Acta Materialia 49 (2001) 2145–2160. [9] J. Keckes, Journal of Applied Crystallography 38 (2005) 311–318. [10] S.P. Lacour, D. Chan, S. Wagner, T. Li, Z. Suo, Applied Physics Letters 88 (2006) 204103. [11] P.A. Gruber, C. Solenthaler, E. Arzt, R. Spolenak, Acta Materialia 56 (2008) 1876–1889. [12] D. Faurie, P. Djemia, E. Le Bourhis, P.O. Renault, Y. Roussigné, S.M. Chérif, R. Brenner, O. Castelnau, G. Patriarche, Ph. Goudeau, Acta Materialia 58 (2010) 4998–5008. [13] D.Y.W. Yu, F. Spaepen, Journal of Applied Physics 95 (2004) 2991.
[14] J. Andersons, Y. Leterrier, Thin Solid Films 471 (2005) 209–217. [15] S. Cai, D. Breid, A. Crosby, Z. Suo, J. Hutchinson, Journal of the Mechanics and Physics of Solids 59 (2011) 1094–1114. [16] M. Hommel, O. Kraft, E. Arzt, Journal of Materials Research 14 (1999) 2373–2376. [17] G. Geandier, D. Thiaudière, R.N. Randriamazaoro, R. Chiron, S. Djaziri, B. Lamongie, Y. Diot, E. Le Bourhis, P.O. Renault, P. Goudeau, A. Bouaffad, O. Castelnau, D. Faurie, F. Hild, Review of Scientific Instruments 81 (2010) 103903. [18] S. Djaziri, P.O. Renault, F. Hild, E. Le Bourhis, Ph. Goudeau, D. Thiaudière, D. Faurie, Journal of Applied Crystallography 44 (2011) 1071–1079. [19] S. Djaziri, D. Faurie, P.O. Renault, E. Le Bourhis, Ph. Goudeau, D. Thiaudière, G. Geandier, Acta Materialia 13 (2013) 5067–5077. [20] G. Besnard, F. Hild, S. Roux, Experimental Mechanics 46 (2006) 789–803. [21] S. Djaziri, D. Faurie, E. Le Bourhis, Ph. Goudeau, P.O. Renault, C. Mocuta, D. Thiaudière, F. Hild, Thin Solid Films 530 (2013) 30–34. [22] C. Le Bourlot, P. Landois, S. Djaziri, P.O. Renault, E. Le Bourhis, P. Goudeau, M. Pinault, M. Mayne-L’Hermite, B. Bacroix, D. Faurie, O. Castelnau, P. Launois, S. Rouzière, Journal of Applied Crystallography 45 (2012) 38–47. [23] G. Geandier, P.O. Renault, E. Le Bourhis, Ph. Goudeau, D. Faurie, C. Le Bourlot, Ph. Djemia, O. Castelnau, S.M. Chérif, Applied Physics Letters 96 (2010) 041905. [24] H. Van Swygenhoven, S. Van Petegem, Materials Characterization 78 (2013) 47–59. [25] S. Van Petegem, L. Li, P.M. Anderson, H. Van Swygenhoven, Thin Solid Films 530 (2013) 20–24. [26] A.L. Volynskii, D.A. Panchuk, S.L. Bazhenov, M.Y. Yablokov, A.B. Gilman, A.V. Bolshakova, L.M. Yarysheva, N.F. Bakeev, Thin Solid Films 536 (2013) 179–186. [27] D.S. Gray, J. Tien, C.S. Chen, Advanced Materials 16 (2004) 393–397.