Residual Stress and Buckling Patterns of Free-standing Yttria-stabilized-zirconia MembranesFabricatedbyPulsedLaser Deposition

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1 DOI: /fuce Residual Stress and Buckling Patterns of Free-standing Yttria-stabilized-zirconia MembranesFabricatedbyPulsedLaser Deposition A. Evans 1 *, M. Prestat 1,R.Tölke 1,M.V.F.Schlupp 1,L.J.Gauckler 1,Y.Safa 2, T. Hocker 2,J.Courbat 3,D.Briand 3,N.F.deRooij 3, D. Courty 4 1 ETH Zurich, Nonmetallic Inorganic Materials, Wolfgang-Pauli-Strasse 10, CH-8093 Zurich, Switzerland 2 ZHAW Winterthur, Institute of Computational Physics, Wildbachstrasse 21, CH-8400 Winterthur, Switzerland 3 École Polytechnique Fédérale de Lausanne (EPFL), Institute of Microengineering, Rue Jaquet-Droz 1, CH-2002 Neuchâtel, Switzerland 4 ETH Zurich, Laboratory for Nanometallurgy, Wolfgang-Pauli-Strasse 10, CH-8093 Zurich, Switzerland Received February 13, 2012; accepted May 07, 2012 Abstract The residual stress and buckling patterns of free-standing 8 mol.% yttria-stabilized-zirconia (8YSZ) membranes prepared by pulsed laser deposition and microfabrication techniques on silicon substrates are investigated by wafer curvature, light microscopy, white light interferometry, and nanoindentation. The 300 nm thin 8YSZ membranes (390 lm 390 lm) deposited at 25 C are almost flat after free-etching, whereas deposition at 700 C yields strongly buckled membranes with a compressive stress of 1,100 ± 150 MPa and an out-of-plane-displacement of 6.5 lm. These latter membranes are mechanically stable during thermal cycling up to 500 C. Numerical simulations of the buckling shape using the Rayleigh Ritz-method and a Young s modulus of 200 GPa are in good agreement with the experimental data. The simulated buckling patterns are used to extract the local stress distribution within the freestanding membrane which consists of tensile and compressive stress regions that are below the failure stresses. This is important regarding the application in, e.g., microsolid oxide fuel cell membranes which must be thermomechanically stable during microfabrication and device operation. Keywords: Buckling, Free-standing Membrane, Micro-solid Oxide Fuel Cell, Pulsed Laser Deposition, Stress, Thin Film, Yttria-stabilized-zirconia 1 Introduction Miniaturized devices such as gas sensors [1] and microsolid oxide fuel cells (micro-sofcs) [2 6] consist of microfabricated free-standing membranes which have the advantages of low thermal inertia, shorter mass transport lengths resulting in smaller ohmic resistances, and also larger active areas due to the nanostructure at the thin-film surface. The asdeposited thin films can have intrinsic stresses originating from the growth mechanism and extrinsic stresses arising from thermal expansion mismatches, which can be tensile or compressive depending on the deposition method and the substrate [7, 8]. These stresses are partially released during free-etching of the membrane and during thermal treatment of the free-standing thin films [9]. It is thus essential to find suitable deposition parameters and thereby tailor the amount of stresses within the free-standing membrane to ensure structural integrity and device reliability, and also to prevent delamination, fracturing, or cracking of the membrane. More than 10 years ago, Ziebart et al. [10] investigated experimentally and analyzed theoretically the buckling behavior of free-standing ~1 lm thick Si 3 N 4 membranes fabricated by plasma-enhanced chemical vapor deposition (PECVD) with lateral dimensions between 600 and 1,980 lm. The Si 3 N 4 membranes have an average pre-strain of e 0 = and are strongly buckled. It was found that, [ * ] Corresponding author, anna.evans@mat.ethz.ch FUEL CELLS 00, 0000, No. 0, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1

2 with an increasing side length, the membranes undergo symmetry-breaking buckling transitions. More recently, Yamamoto et al. [11] performed detailed structural and thermomechanical analyses on sputtered freestanding yttria-stabilized-zirconia (YSZ) electrolyte membranes. It was found that the YSZ buckling pattern changes its symmetry as a function of the membrane side length and that, for sputtered Pt-YSZ (150 nm) YSZ (150 nm) Pt-YSZ (150 nm) membranes annealed up to 625 C, a lower stress was observed for the larger membranes. The authors set up a failure-resistant temperature stress design space in the postbuckling regime for membranes with different lateral sizes and thicknesses [11]. In contrast to the conventional SOFC technology which consists of lm thick ceramic layers on microporous supports that are operated at temperatures of 600 1,000 C [12], the micro-sofcs have an operating temperature of below 550 C. The cathode electrolyte anode (CEA) thin-film membrane assembly is typically thinner than 1 lm and is deposited onto a smooth surface of a micromachinable substrate. The gas access to the bottom electrode is achieved by etching the substrate and thereby creating a free-standing micro-sofc membrane (Figure 1) [2 6]. The thermomechanical stability of the free-standing membrane which separates the oxidant and the fuel is therefore crucial for the functioning of the fuel cell and constitutes the main substance of this work. The different materials used in the various CEA layers have different coefficients of thermal expansion, different elastic moduli and also different microstructures: whereas a Fig. 1 (a) Schematic cross-section of a free-standing micro-sofc membrane on a Si substrate. (b) Focussed ion beam cross-sectional image of a free-standing yttria-stabilized-zirconia (YSZ) electrolyte membrane with sputtered Pt thin-film electrodes. dense thin electrolyte is needed to ensure a gas-tight layer with a small ohmic resistance, electrodes with nanoporous structures are favored in order to obtain large surface exchange areas. Recent reports show the buckling patterns of free-standing CEA micro-sofc membranes with an YSZ electrolyte fabricated by sputtering [5, 13 19] or pulsed laser deposition (PLD) [9, 20, 21]. In these studies, the change of the membrane buckling pattern as a function of the fabrication steps [14, 17], the deposition parameters such as the temperature [20, 21], pressure [19], or membrane thickness [13], the annealing temperature [5, 16, 17, 21], and the influence of the gas flow [5] is described. However, in most studies only photographs of the buckled membranes are shown without any detailed explanation for the shape of the buckling pattern. In the first part of this study, the thermomechanical characteristics of free-standing 8 mol.% YSZ membranes with different thicknesses deposited by PLD at temperatures between room temperature (RT) and 700 C are described. In a second part, the buckling patterns of the free-standing membranes are simulated using the experimental data as input parameters. In the final part, the local distribution of stress within the membrane is extracted from the simulation data. 2 Experimental 2.1 Fabrication of Free-standing Yttria-stabilized-zirconia Membranes The fabrication of the free-standing YSZ membranes is depicted in Figure 2. Silicon wafers (4-in. diameter, 380 lm thick, [100]-oriented single crystals) were double-side coated with a 200 nm-thick low-stress silicon nitride layer by low-pressure chemical vapor deposition (LPCVD). A photolithographic step using a ma-n 1410 photoresist was carried out on the backside of the Si wafer to define the opening windows on the Si 3 N 4 (Figure 2b). The reactive ion etching to remove the backside silicon nitride layer was performed in CHF 3 (50 sccm) and O 2 (5 sccm) at 100 W during 220 s (RIE80, Oxford Instruments, UK). Backside anisotropic etching of the Si wafer was done in a 20% aqueous KOH solution at 90 C with a reflux condenser to obtain 2.5 cm 2.5 cm Si chips with 30 free-standing 390 lm 390 lm Si 3 N 4 membranes (Figure 2c). The 8YSZ thin films were prepared by PLD (Surface PLD workstation, Hückelhoven, Germany) from a sintered (Y 2 O 3 ) 0.08 (ZrO 2 ) 0.92 target with an 248 nm excimer laser (fluence: 2.9 J cm 2, pulse repetition rate: 10 Hz) through a molybdenum-free stainless steel mask at a substrate-target distance of 8.5 cm. The substrate temperature was varied between RT and 700 C (heating and cooling rate of 5 C min 1 ), and the oxygen chamber pressure was 2.66 Pa (Figure 2d). The 8YSZ layers exhibit thicknesses WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim FUEL CELLS 00, 0000, No. 0, 1 10

3 Fig. 2 Microfabrication process flow of the free-standing yttria-stabilized-zirconia membranes. between 30 and 300 nm. After 8YSZ deposition, the remaining Si 3 N 4 layer was removed again by reactive ion etching to yield Si chips with 30 free-standing 390 lm 390 lm 8YSZ membranes (Figure 2e). The 3 mol.% YSZ thin film membranes used for comparison were prepared in an identical way from a sintered (Y 2 O 3 ) 0.03 (ZrO 2 ) 0.97 PLD target. 2.2 Characterization of the Free-standing Yttria-stabilizedzirconia Membranes The buckling of the free-standing 8YSZ membranes was characterized by light microscopy (Polyvar MET, Reichert- Jung, Depew NY, USA). For the observation of the buckling patterns as a function of temperature, the Si wafers were cut down into 0.5 cm 0.5 cm pieces (with ~4 free-standing membranes) in order to fit into the LINKAM heating stage which was placed under the light microscope. The temperature, heating and cooling rates, as well as the cooling water flow were controlled by the LINKAM TMS 92 and PS 1500 units. All samples were heated and cooled at 10 C min 1 in ambient air. Optical analysis of the buckling amplitude was performed by optical profilometry (Wyko NT1100 white light interferometer, Veeco, Plainview, NY, USA), whereby the precision of the interferometer is in the sub-nanometer range. The buckling amplitude measurements as a function of temperature were performed in a custom-made heating system consisting of alumina with a screen-printed platinum resistor as a heater. The thicknesses of the free-standing 8YSZ membranes were determined from scanning electron microscopy (SEM, Leo 1530, Carl Zeiss SMT, Germany) cross-sectional images taken with an in-lens detector at an acceleration voltage of 3 kv or from focused ion beam (NVISION 40, Zeiss, Germany) cross-sectional images. 2.3 Wafer Curvature Measurements of Supported Yttriastabilized-zirconia Thin Films Yttria-stabilized-zirconia thin films (200 nm) were prepared by PLD using a custom-made sample holder onto 300 lm thick 1-in. Si wafers coated with 200 nm Si 3 N 4 (LPCVD) on both sides. The stress in the YSZ thin films was determined by wafer curvature (Tencor FLX- 2320A measurement system, Milpitas, CA, USA) with a scan length of 20 mm and a maximum of 50 measured points. First, the radius of curvature of the blank substrate was measured and then the substrate with the deposited 8YSZ thin film. This allowed the stress of the 8YSZ thin film to be obtained by subtraction of the substrate data and using Stoney s equation [22]. 2.4 Nanoindentation of Supported Yttria-stabilizedzirconia Thin Films Yttria-stabilized-zirconia thin films (300 nm) were deposited onto 380 lm thick Si wafer pieces (1 cm 1 cm) coated with 200 nm Si 3 N 4 (LPCVD). Nanoindentation was performed using a TriboIndenter (Hysitron Inc., USA) with a Berkovich diamond tip. Load partially unload indentation tests were performed with a maximum load of 4,000 ln. The small indentation depths had to be discarded due to the surface roughness, and thus only the measurements with penetration depths between 35 and 60 nm were taken into account for further evaluation. The Young s modulus was calculated from the reduced modulus E r using 1/E r = (1 m i 2 )/E i + (1 m s 2 )/E s. E i (1,141 GPa) and m i (0.07) are the Young s modulus and Poisson s ratio of the diamond indenter tip, respectively; and m s is the Poisson s ratio of YSZ which is between 0.3 and 0.32 [23]. 2.5 Input Parameters for the Simulation The simulation of the buckling pattern is based on the Rayleigh Ritz-method [24] for minimization of the total energy and is implemented as an in-house Mathematica code. The details of the modeling are given elsewhere [25]. As input parameters, we used the free-standing membrane dimensions and thickness, the residual stress from wafer curvature measurements, the Young s modulus obtained from nanoindentation, and the buckling amplitude from investigations by white light interferometry. These input values are implemented as (dimensionless) reduced values [10]. The coordinates x and y are thus given as a fraction of the side length a, i.e., x/a and y/a. The buckling amplitude w is evaluated with respect to the film thickness h, i.e., w/h. The input strain values e are given as fraction value or as multiple values of the critical buckling strain e critical = 4.365/(1 + m) r 2 = , where m is the Poisson s ratio and r = h/a is the aspect ratio of the film thickness h to the side length a. 3 Results and discussion 3.1 Thermomechanical Properties of Free-standing 8YSZ Thinfilm Membranes The free-standing 390 lm 390 lm 200 nm-thick Si 3 N 4 membrane (Figure 2c) has no visible buckling under the light FUEL CELLS 00, 0000, No. 0, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 3

4 Fig. 3 Influence of the deposition temperature on the residual stress in 8YSZ thin films. Light microscopy images taken at RT of the buckling patterns of 390 lm 390 lm free-standing 300 nm-thick 8YSZ membranes prepared by PLD at different deposition temperatures. The percentage indicates the membrane survival rate (i.e., number of surviving membranes) after deposition and free-etching. The stress was obtained by wafer curvature; for each deposition temperature, the average and standard deviation were derived from three samples. microscope between RT and 500 C [26]. This is expected for a low-stress low-pressure chemical vapor deposited Si 3 N 4 as the thermal expansion coefficients of the silicon support (a Si = C 1 at RT and C 1 at 826 C) [27, 28] and Si 3 N 4 (a Si3N4 = C 1 at RT) [29] do not differ much. The stress within the Si 3 N 4 layer was measured at RT by wafer curvature to be slightly tensile with 125 ± 8 MPa, which is typical for precursor-based methods such as CVD [30]. After 8YSZ deposition at 400 or 700 C onto a free-etched flat Si 3 N 4 membrane (Figure 2d), the sample is cooled down to RT and the free-standing 8YSZ Si 3 N 4 membrane is buckled [26], thereby evidencing the release of compressive stress. During cooling to RT (in the PLD chamber), these compressive stresses are reduced slightly due to the extrinsic tensile stress contribution resulting from the different coefficients of thermal expansion of 8YSZ (a YSZ = C 1 at RT) [28] and the underlying Si 3 N 4. Upon free-etching, the supporting Si 3 N 4 layer is removed and the 8YSZ membrane is released (Figure 2e). This free-standing 8YSZ membrane is still buckled (Figure 3c) and the compressive stress within the thin film is attributed to atomic peening during growth of the pulsed-laser deposited 8YSZ film [9, 19, 21, 31]. Figure 3 shows the light microscopy images taken at RT of free-standing 300 nm 8YSZ membranes deposited at RT, 400 and 700 C along with the percentage of surviving membranes from several Si chips consisting of 30 membranes. The 8YSZ membranes deposited at RT had a slight compressive stress of 270 ± 80 MPa, looked flat under the light microscope and were obtained with a high survival rate (Figure 3a). These RT-deposited PLD membranes, however, do not survive thermal treatment, as can be seen in the optical micrographs taken at different temperatures for a membrane placed on a heating stage (Figure 4a). There are several possible reasons for this: firstly, the 8YSZ (PLD) films deposited at a low temperature tend to be rich in defects and disorder. Upon annealing, these defects heal out and the ions pack closer. The crystallization leads to a free volume shrinkage of around 3 5% (similar to the solidification shrinkage observed for glasses [32]) which would correspond to a linear shrinkage of 1 2%. Only 10% of this shrinkage would be sufficient strain to exceed the yield strength of the thin-film membrane. Secondly, the 8YSZ thin films deposited by PLD tend to be slightly oxygen deficient [33, 34], resulting in a sub-stoichiometric oxide with excessive oxygen vacancies and some zirconium ions in the three-valent state. The subsequent re-oxidation of the 8YSZ during annealing in air leads to reincorporation of oxygen into the lattice and to chemical strain [35]. The re-oxidation of the 8YSZ films might influence their stress state by two concurrent processes. The re-oxidation fills up the excess oxygen vacancies which would expand the zirconia lattice resulting in a compression of the YSZ films. At the same time, the radii of some zirconium ions change from r Zr3+ =0.78Åtor Zr4+ =0.72Å[36] resulting in an overall lattice contraction and thereby exerting a tensile stress on the YSZ film. It should be noted that the membranes always cracked within the free-standing area and that no delamination of the thin film from the substrate was observed at the edge of the membrane. The 8YSZ membranes deposited at 400 C were all cracked (Figure 3b), whereas those deposited at 700 C exhibit a buckling pattern characteristic for compressive stress and were obtained with a survival rate of >99% (Figure 3c). The wafer curvature measurements of as-deposited Si Si 3 N 4 -substratesupported 8YSZ films showed that the 8YSZ films deposited at 400 C had a compressive stress of 2,900 ± 340 MPa (Figure 3b), whereas the 8YSZ films deposited at 700 C had a lower compressive stress of 1,100 ± 150 MPa (Figure 3c). Fig. 4 Light microscopy images taken as a function of temperature of a 390 lm 390 lm free-standing 300 nm-thick 8 mol.% yttria-stabilized-zirconia membrane deposited by pulsed laser deposition (a) at RT and (b) at 700 C. The membrane was placed onto a heating stage and heated at a rate of 10 C min 1 in air WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim FUEL CELLS 00, 0000, No. 0, 1 10

5 Garbayo et al. [9] found similar results by micro-x-ray diffraction (micro-xrd) for both as-deposited and annealed free-standing 8YSZ PLD membranes (820 lm 820 lm). The authors reported stress values of 4.5 and 2.2 GPa for 120 nm thin 8YSZ membranes deposited at 400 and 700 C, respectively. After annealing at 600 C, the amount of compressive stress was reduced to 1.9 and 1.7 GPa, respectively [21]. The survival rate of the 8YSZ PLD membranes deposited at 400 C decreased from >99% down to 70% after annealing at 600 C, whereas all the membranes deposited at 700 C survived the thermal treatment [9]. One possible reason for the small amount of surviving 8YSZ membranes deposited at 400 C in our study is an excessively high compressive stress leading to a buckled membrane with locally too high tensile stress (see section 3.3). The reported decrease in compressive stress upon annealing at 600 C for the 8YSZ membranes deposited by PLD at 400 C [9] can be attributed to further crystallization during thermal treatment at temperatures above the deposition temperature which results in film shrinkage [31]. This is, however, not desirable when the thin film is used as an electrolyte layer in a micro-sofc membrane, where it should not undergo phase transformation during fuel cell operation. On the other hand, the 8YSZ films deposited at 700 C are already in a fully crystallized state (as evidenced by the selected area electron diffraction patterns; not shown here) and are stable during micro-sofc operation at C. In addition, they are under compressive stress due to the atomic peening, and this compressive stress state remains frozen in the thin film even when it is heated up to 700 C again. This is in good agreement with the in situ observations of the buckling pattern under the optical microscope as a function of temperature (Figure 4b) which show that the membrane buckling shape did not undergo visible changes during heating (and the subsequent cooling). However, the buckling amplitude measured by white light interferometry of the 8YSZ membranes changes with temperature. The buckling profiles of the 8YSZ and 3YSZ membranes obtained by optical profilometry between RT and 600 C are shown in Figure 5a and b, with the 3YSZ membranes only given for purposes of comparison, since the change in the buckling shape is more obvious and evidences the importance of extrinsic stresses. Figure 5c depicts the out-of-plane displacements and buckling shapes as a function of the temperature of 8YSZ and 3YSZ membranes during the first heating after deposition at 700 C. The 8YSZ membranes are already buckled at RT with a maximum out-of-plane displacement of 6.5 lm. This buckling amplitude increases almost linearly with an increasing temperature and reaches 14.1 lm at 600 C, whereby the shape of the buckling pattern remains the same (Figure 5c). Height / μm Height / μm Distance / μm Distance / μm Deformation amplitude / µm Temperature / C Fig. 5 Profiles of the (a) 8YSZ and (b) 3YSZ free-standing membranes obtained from line scans by optical profilometry between RT and 600 C of the membranes depicted in (c). The dashed lines have been inserted to guide the eye as some data points are missing in the steep walls of the buckling pattern due to the high surface angle which exceeds the critical angle for collecting the reflected beam. (c) Maximum out-of-plane-displacements obtained by white light interferometry versus temperature and optical micrographs of the corresponding buckling patterns of 390 lm 390 lm free-standing 300 nm thin 8YSZ and 3YSZ for membranes (during the first heating after deposition at 700 C). FUEL CELLS 00, 0000, No. 0, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 5

6 This shows that the post-buckling shape is stable and does not change much due to small perturbations, e.g., those caused by a change in temperature. Furthermore, this evidences that the square 8YSZ membrane is already in an advanced stage of buckling at RT due to the intrinsic stresses originating from atomic peening during PLD growth, and that the buckling amplitude increases due to the extrinsic compressive stresses originating from the mismatch of thermal expansion coefficients between the Si Si 3 N 4 substrate and the YSZ thin film. In contrast, the free-standing 3YSZ square membranes are flat at RT, and a buckling amplitude of 1.2 lm is detectable only at 200 C. This is attributed to the smaller grains and to a higher stiffness of the 3YSZ which lead to a higher critical buckling mode compared to 8YSZ (i.e., the mode where tensile stresses occur that cause a spontaneous crack growth or rupture of the film). At 600 C, the 3YSZ membranes have a maximum out-of-plane displacement of 12.0 lm and a similar buckling pattern compared to the 8YSZ. It can be summarized that the effect of the different coefficients of thermal expansion of the 8YSZ membrane and the Si-based substrate lead to an increase of the buckling amplitude with an increasing temperature, but the shape of the buckling pattern does not change much. These observations are slightly different compared to the membrane buckling patterns of RT-sputtered YSZ thin films that changed their shape with increasing temperature reported by Lai et al. [16] presumably due to crystallization of their films which leads to a higher density, and thus to lateral shrinkage of the thin films. For the above-mentioned reasons, we will focus only on 8YSZ PLD membranes deposited at 700 C in the following sections. The shape of the buckling patterns not only depends on the size of the free-standing area [11] and on the deposition temperature, but also on the thickness of the membrane. Figure 6 shows the optical micrographs taken at RT of 8YSZ membranes deposited by PLD at 700 C with thicknesses between 30 and 300 nm, and the corresponding membrane survival rates after fabrication. Besides a high survival rate, it is desirable to have a gas-tight 8YSZ layer that is as thin as possible in order to minimize the ohmic resistance. The 8YSZ thin film deposition at 700 C yielded buckled membranes with survival rates above 95% for the thicknesses between 50 and 300 nm (Figure 6). It was possible to deposit membranes even thinner than 30 nm, but only a small number survived the free-etching step (Figure 2e). Fig. 6 Influence of the membrane thickness on the survival rate after deposition and free-etching. Light microscopy images taken at RT of the buckling patterns of free-standing 8YSZ membranes deposited at 700 C with different thicknesses. The buckling patterns of the 30 and 50 nm thin 8YSZ membranes (390 lm 390 lm) have an axial and fourfold rotational symmetry. This has also been observed for 60 nm 8YSZ PLD membranes deposited at 200 C with dimensions of 620 lm 620 lm [9] and for r.f. sputtered LSCF (65 80 nm) YSZ(60 nm) 250 lm 250 lm multilayer membranes [16]. In the slightly thicker 75 nm YSZ PLD membranes, only the rotational symmetry remains. Such a buckling pattern has been observed by other researchers: for 120 nm 8YSZ thin films made by PLD at 400 C with dimensions of 620 lm 620 lm [21], RT-sputtered 100 nm thin YSZ [37], sputtered 590 nm YSZ thin films (282 lm 282 lm) [11], and r.f. sputtered Pt (80 nm, RT) 8YSZ(100 nm, 550 C) Pt(80 nm, RT) and LSCF(65 nm, 500 C) YSZ(60 nm, 500 C) LSCF(65 nm, 500 C) 160 lm 160 lm micro-sofc membranes [17, 18]. The 150 and 300 nm thick 8YSZ PLD membranes again show both axial and fourfold rotational symmetries, which were also found for sputtered Pt- YSZ(150 nm) YSZ(150 nm) Pt-YSZ(150 nm) 80 lm 80 lm membranes after thermal cycling [11]. It can be summarized that different buckling pattern shapes can be obtained by PLD and sputtering for 8YSZ membranes on Si substrates, and that the out-of-plane deformation depends on the membrane side length, thickness, deposition temperature, stiffness of the materials, and also occurs in multilayer membranes. The Young s modulus of a 300 nm thick 8YSZ thin film deposited by PLD at 700 C onto a Si Si 3 N 4 substrate was determined from nanoindentation measurements to be 205 ± 20 GPa, which is slightly lower than for bulk YSZ [38]. It should be noted that only the penetration depths between 35 and 60 nm were taken into account in the calculation in order to avoid any influence from the surface roughness and from the underlying substrate. 3.2 Numerical Simulation of the Buckling Patterns of Freestanding 8YSZ Membranes The simulation of the buckling pattern was performed using the Rayleigh Ritz method for minimization of the total energy [24]. For the numerical simulation, the following input parameters were used: membrane side length a = 390 lm and thickness h = 300 nm, and a Young s modulus of 200 GPa. The reduced strain was varied in order to observe the changes in buckling patterns. Figure 7 shows the simulation results of the buckling patterns for different input values for the strain (and corresponding stress values). In order to show the buckling shape in a pre-buckling stage, in the first and advanced stages of the primary buckling, as well as in an advanced stage of the secondary buckling, we have selected some examples where the input strain values e are given as fraction value or as multiple values of the critical buckling strain e critical = An initial strain of e = 0.9 e critical leads to a WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim FUEL CELLS 00, 0000, No. 0, 1 10

7 Fig. 7 Influence of the reduced stain input value on the simulated out-of-plane displacements and buckling patterns with the input parameters: side length 390 lm, thickness 300 nm, Young s modulus 200 GPa, and different strain values (a d). Experimental data determined from ( * ) wafer curvature measurements and ( ** ) white light interferometry of a free-standing 300 nm thick 8YSZ membrane. (e) Light microscope image taken at RT. reduced out-of-plane displacement of 10 2, which corresponds to an almost flat membrane in the pre-buckling stage (Figure 7a). By increasing the reduced strain value to e =2 e critical, the reduced out-of-plane-displacement is increased to 1.29 and the membrane is slightly bent, as an amount of energy is released (with respect to the pre-buckling path) by a mirror and C 4z -rotational symmetric deformation of the membrane due to the early stage of the primary buckling mode (Figure 7b). For a strain of e = 20 e critical, the reduced buckling amplitude increases to 5.49 in an advanced stage after the onset of the primary buckling mode (Figure 7c). By further increasing the strain to e = 571 e critical, i.e., corresponding to a residual stress value of 307 MPa, the outof-plane displacement increases to 8.08 lm. Folds start to appear within the membrane due to an amount of energy that is released by elongation and due to an additional amount of membrane energy that is transferred to a stored bending energy by a local increase of the thin film curvature (Figure 7d). Furthermore, the elastic shear energy causes the folds to rotate slightly. This is attributed to the (mirror) symmetrybreaking secondary buckling mode. This simulated buckling pattern looks similar to the light microscopy image shown in Figure 7e for a 300 nm 8YSZ membrane deposited at 700 C which also includes the negative buckling areas at the edge of the membrane. In addition, the resulting out-ofplane displacement is in good agreement with the experimental findings from optical profilometry investigations and with literature data where a maximum central deflection of 9 lm was obtained for a 120 nm thin YSZ membrane deposited by PLD at 700 C [21] and 6 lm for a sputtered LSCF(15 nm) YSZ(75 nm) Pt(100 nm) membrane [15] of similar size. The input residual stress value of 307 MPa deviates from the calculated value of 1,100 MPa which was obtained from the wafer curvature using the Stoney s equation. This is attributed to the fact that the substrate-supported 8YSZ thin films used for the wafer curvature measurements may not have exactly the same residual stress as the free-standing membranes where the stress may have changed during the free-etching step. The etching of an underlying silicon substrate leads to more compliance in the structure and allows the 8YSZ membrane to undergo a larger bending deformation, and thereby reduce an amount of its compressive stress. Further refinement of the simulation (e.g., by using a high-order degree of the Rayleigh Ritz expansion) may also lead to a more realistic representation of the secondary branching on the edges. This branching enables the buckled film to absorb more energy without increasing its buckling amplitude, and would subsequently lead to a smaller deviation of the residual stress values. The buckling pattern with a C 4z -rotational and mirror symmetries (Figure 3c) was also simulated (not shown here) and indicated that less membrane energy is stored as shearing energy since there is no loss of the mirror symmetry. FUEL CELLS 00, 0000, No. 0, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 7

8 In summary, the experimental buckling patterns imaged at RT and the simulated shapes form a consistent picture. It is found that different amounts of stored energy (of the membrane and the bending), as well as their significance depend on the membrane dimension, thickness, residual stress, and temperature. The thickness of the membrane is not only a geometrical parameter, since it was observed that the deformation amplitude of thin membranes is smaller than that of thicker membranes with a higher packing factor (not shown here). The temperature also plays two roles: on the one hand, the deposition temperature has an impact on the intrinsic stress coming from the kinetic energy of the particles during PLD growth (atomic peening) and the resulting microstructure (more defects and less dense for low deposition temperatures). On the other hand, the temperature influences the extrinsic stress from the mismatch of the coefficients of thermal expansion between the YSZ thin film and the Si Si 3 N 4 substrate. In the next section, the simulated buckling patterns are used to extract the local stress distribution in the free-standing membrane. 3.3 Simulated Local Stress Distribution in Buckled Membranes In brittle materials such as ceramics, failure is primarily dominated by flaws. In the case of our microfabricated membranes, flaws can arise, e.g., from dirt on the substrate or ejection debris particles from the PLD target during thin film deposition [39], leading to a local stress concentration. When none of such primary failure sources are present, secondary effects such as tensile and compressive stresses can determine the thermomechanical stability of a free-standing membrane. For this reason, the buckling pattern simulated in Figure 7d was used to extract the local stress distribution within the free-standing membrane. Figure 8 shows the stress distribution seen from the top (Figure 8 a and b) and bottom (Figure 8 c and d) side of the buckled membrane. The principal stresses are often used as failure criteria for brittle materials such as ceramics. The left images (Figure 8 a and c) depict the principal stresses r I, whereas the right images (Figure 8 b and d) show the principal stresses r II. The principal stresses are obtained by choosing a basis in which the shear stress components of the stress tensor become 0. It should be noted that these stress calculations are based on a purely elastic theory. Therefore this model does not include the self-adaptation phenomena which would minimize the inter-grain stress; in addition, it does not account for chemical strain effects which would lead to a local volume change accompanied by local strain [40]. The residual stress of 307 MPa leads to a buckling pattern consisting of both tensile and compressive regions. Such stress distribution maps can help to predict failure of the free-standing thin films, and the stress values can be used to assess the reliability of the membrane. These stress distri- y / µm y / µm x / µm y / µm y / µm x / µm x / µm x / µm Fig. 8 Simulation of the local stress distribution within the buckling pattern of the free-standing membrane shown in Figure 7d. Surface stress distribution on the top side (a and b) and bottom side (c and d) of the buckled membrane, whereby the principal stress I is depicted in (a and c) and the principal stress II is shown in (b and d) WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim FUEL CELLS 00, 0000, No. 0, 1 10

9 bution maps can also be useful when evaluating whether certain deposition parameters are suitable for fabricating stable free-standing membranes or whether there are regions with (excessively) high tensile or compressive stresses which may cause the thin film to crack or to peel off from the substrate at the edge of the etched hole. In our case of free-standing 8YSZ thin film membranes deposited at 700 C, it can be summarized that all stresses are below these failure stresses. In the current stress engineering approach for the application of YSZ membranes in, e.g., micro-sofc membranes, a very high compressive stress is not desired, since this leads to cracked membranes (Figure 3b). YSZ membranes with tensile stresses or very low compressive stresses (Figure 3a) are not envisaged regarding the subsequent deposition of thin-film electrodes. Indeed, many high-performance SOFC electrode materials, such as LSCF [41], have a higher thermal expansion coefficient than the one of YSZ. Their deposition at a high temperature ( C, e.g., by PLD [41] or spray pyrolysis [42]) and the subsequent cooling to RT add a tensile component to the stress that has to be compensated in order to avoid rupture of the membrane under tension. Therefore, YSZ layers under moderate compressive stress are currently seen as the state-of-the-art electrolyte membranes for micro-sofc. 4 Conclusion The residual stress and buckling of free-standing 8YSZ membranes fabricated by PLD were investigated by light microscopy, wafer curvature, white light interferometry, as well as nanoindentation, and the buckling patterns were simulated. It was found that 8YSZ deposited by PLD at 25 C yielded flat membranes that cracked upon heating, whereas the 8YSZ membranes deposited at 700 C yielded buckled membranes which were stable during thermal cycling up to 600 C. The experimental buckling shapes and the simulated patterns form a consistent picture. The buckling pattern is a consequence of different amounts of energies that are stored in the form of membrane energy such as elongation and shearing and bending energy. The simulated buckling patterns were used to extract the local stress distribution within the free-standing YSZ membrane. These simulation results are important with regard to the application of free-standing membranes, e.g., in micro-sofcs which must be thermomechanically stable during microfabrication and device operation. Acknowledgements The authors thank Saša Karalić (ETH Zurich) for taking some of the light microscopy images. Dr. Christof Schneider (Paul-Scherrer-Institut, Villigen) is thanked for providing the heating stage. Prof. R. Spolenak (ETH Zurich) is thanked for stimulating discussions. Dr. Antonia Neels (CSEM, Neuchâtel) is thanked for detailed discussions on XRD and stresses in thin films. Dr. Ji-Won Son (Korea Institute of Science and Technology) is thanked for detailed discussions about residual stresses in thin films. Dr. Julia Martynczuk is thanked for her help during FIB image acquisition. The FIRST team (ETH Zurich) is acknowledged for providing the cleanroom facilities. Financial support from the Swiss National Science Foundation (SNF, Sinergia contract #CRSI ) and the Korean-Swiss Science and Technology Cooperation is gratefully acknowledged. References [1] M. Heule, L. J. Gauckler, Sens. Actuators B 2003, 93, 100. [2] A. Evans, A. Bieberle-Hütter, J. L. M. Rupp, L. J. Gauckler, J. Power Sources 2009, 194, 119. [3] H. Huang, M. Nakamura, P. C. Su, R. Fasching, Y. Saito, F. B. Prinz, J. Electrochem. Soc. 2007, 154, B20. [4] S. Rey-Mermet, Y. Yan, C. Sandu, G. Deng, P. Muralt, Thin Solid Films 2010, 518, [5] M. Tsuchiya, B.-K. Lai, S. Ramanathan, Nat. Nano 2011, 6, 282. [6] C.-W. Kwon, J.-W. Son, J.-H. Lee, H.-M. Kim, H.-W. Lee, K.-B. Kim, Adv. Funct. 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