Misfit Dislocation Guided Topographic and Conduction Patterning in Complex Oxide Epitaxial Thin Films

Interfacial dissimilarity has emerged in recent years as the cornerstone of emergent interfacial phenomena, while enabling the control of electrical transport and magnetic behavior of complex oxide epitaxial films. As a step further toward the lateral miniaturization of functional nanostructures, this work uncovers the role of misfit dislocations in creating periodic surface strain patterns that can be efficiently used to control the spatial modulation of mass transport phenomena and bandwidth‐dependent properties on a ≈20 nm length scale. The spontaneous formation of surface strain‐relief patterns in La0.7Sr0.3MnO3/LaAlO3 films results in lateral periodic modulations of the surface chemical potential and tetragonal distortion, controlling the spatial distribution of preferential nucleation sites and the bandwidth of the epilayer, respectively. These results provide insights into the spontaneous formation of strain‐driven ordered surface patterns, topographic and functional, during the growth of complex oxide heterostructures on lengths scales far below the limits achievable through top‐down approaches.


DOI: 10.1002/admi.201600106
of materials properties by altering the subtle energy landscape of competing interactions through epitaxial strain and dissimilarity. [ 1,2 ] Notably, this strategy has led to the discovery of exotic interfacial phenomena, [ 3,4 ] while opening the possibility to tune the bulk transport, magnetic, ferroelectric, and multiferroic properties of thin fi lms. [5][6][7][8][9] However, next generation nanodevices demand a further step toward miniaturization, facing challenging strategies to controllably manipulate the lateral modulation of atomic length scales. In semiconductor epitaxy, this goal can be achieved through the Stranski-Krastanov growth mode, leading to the formation of self-assembled quantum dots on a wetting layer [ 10 ] driven by lateral gradients in the surface chemical potential. [ 11 ] This strategy, however, typically leads to nanostructures exhibiting broad size distributions and poor positional order. Strained fi lms, on the other hand, usually relax by misfi t dislocations (MDs) above a critical thickness at which their elastic energy exceeds the energy of the interfacial dislocation network. [ 12 ] The overlapping of strain fi elds emanating from individual dislocations causes lateral modulations of lattice distortions which may extent up to the free surface. Therefore, highly organized MD networks buried at the substrate-fi lm interface not only modulate the physical properties of thin fi lms, but in addition can promote the growth of ordered nanostructures on their surfaces. In this sense, MDs have been used to produce strain guided patterned surfaces in semiconductor [ 13,14 ] and metal [ 15,16 ] systems, and more recently to tune Dirac surface sates in topological insulators. [ 17 ] However, to date, the extension of this concept to oxide epitaxy remains elusive.
A unique property of dislocations, that make them highly appealing for creating new functional nanostructures, is their multiscale character. While being essentially linear defects, they store their elastic energy at comparatively large distances (several nanometers) from their sub-nanometer core. As a consequence, they can modify the properties of the host material in two different length scales. On the one hand, dislocation lines can be considered as a separate phase exhibiting its own physical behavior. [ 18 ] A clear manifestation of their singularity, for instance, comes from the observation that oxygen defi cient dislocations in SrTiO 3 [19][20][21][22] exhibit bistable resistive switching, [ 23 ]

Introduction
Thin fi lm heteroepitaxy of complex oxides has evolved in recent years to a fascinating platform for the manipulation Adv. Mater. Interfaces 2016, 3,1600106 www.advmatinterfaces.de www. MaterialsViews.com or that their nonsuperconducting cores induce pinning of the magnetic fl ux lines in type-II superconductors. [ 24,25 ] On the other hand, owing to the strong sensitivity of the electronic structure to strain, MD long range strain fi elds are key for the realization of periodic functional (magnetic, electronic or catalytic) [ 26 ] bulk and surface patterns. Particularly, in manganite thin fi lms, theoretical studies show that the sign of the misfi t strain profoundly alters their magnetotransport response. [ 6 ] A compressive/tensile biaxial strain promotes a stronger/weaker Mn 3 d -O 2 p orbital overlapping leading to a broader/narrower bandwidth, allowing a local control on the electrical conduction by imposing spatial strain modulations. As MDs typically form square networks, they provide positional order along two mutually perpendicular directions for the creation of self-organized surface templates, [13][14][15][16][17] in contrast with substrate steps which only induce unidirectional ordering. [ 27 ] Notably, dislocation spacings within the 10-20 nm range are commonly obtained, which is far below the miniaturization limits achievable in oxides by top-down approaches, [ 28 ] and can be manipulated through an appropriate choice of the substrate and the thickness of the fi lm.
Despite the strong potential of MDs in oxide heterostructures to create ordered functional patterns, their associated long range strains remain poorly understood. In particular, previous studies have been mainly focused on ferroelectric fi lms, where MD strains have been shown to induce piezoelectric couplings at different length scales, [ 29 ] alter the chemical composition around dislocation cores, [ 30 ] and cause a local decrease of the spontaneous polarization, [ 31 ] leading to the formation of interfacial dead layers, [ 32,33 ] or to the suppression of ferroelectricity in lattice-mismatched nanoislands. [ 34 ] On the other hand, theoretical analysis shows that threading segments of the MDs induce a smearing of the ferroelectric phase transformation over a range of temperatures. [ 35 ] Exploiting the profound impact of these defects on the material's properties in a deterministic way, however, is challenged by the diffi culty to predict the misfi t relaxation behavior of the framework structure building these materials, as well as to the requirement of correlating local surface properties with localized buried strain sources.
In this work we address these issues using thin fi lms of the highly spin-polarized room temperature ( T C ≈ 370 K) half-metal ferromagnet, La 0.7 Sr 0.3 MnO 3 (LSMO), [ 36 ] as a model system. The interest on strategies to functionalize their surfaces stems from its strong potential in technological applications such as tunneling junctions and spin fi lters, [ 37 ] high-density data storage media, [ 38 ] nanosensors or catalysts. [ 39 ] It is shown that strain modulated thin fi lms constitute an ideal scenario to investigate the complex interplay between strain and functionality at a local level, while providing a clue for the realization of spontaneous functional nanostructures in the ≈20 nm range. close to that derived for tensile strained LSMO/STO fi lms in their elastic regime, ν = 0.33. [ 7 ] As shown in Figure 1 b, the 3.5 nm thick fi lm, on the other hand, exhibits an undulated surface and a dislocated interface (see the encircled MD).

Dislocation Structure and Strain Evolution
Careful inspection of this image shows that the surface undulations are due to both, a downward bending of the horizontal atomic rows above the dislocation core (see also Figure 1 c), and outgrowths, as indicated by arrowheads, that as a general trend form on the surface at each side of the projected line of the buried MDs, ≈4 nm away from them (see Figure 1 b). In thicker fi lms, the outgrowths are no longer present, while the bending of atomic planes prevails independently of fi lm thickness, Figure S1 (Supporting Information). An enlarged view of the core structure of the encircled MD is presented in Figure 1 c. The Burgers circuit yields a Burgers vector b x = [100], parallel to the interface, as indicated in the fi gure. The two arrowed vertical atomic rows terminating at the slip plane bare witness of a split core: . It is worthy to mention that similarly dissociated cores have been theoretically predicted for oxygen defi cient b x = [100] edge dislocations in SrTiO 3 , [ 22 ] and also identifi ed as a polymorphic form of b x = [100] dislocations in MgO. [ 40 ] In fact, analysis of several MD cores indicated that this core splitting is a general trend among the observed MDs. The two adjacent b 1 and b 2 partial dislocations build a rather compact core structure. The displacement fi eld above the core is clearly manifested as a downward bending of the atomic rows, with a maximum amplitude of ≈1.25 Å at the horizontal locus of the buried dislocation. Figure 1 d shows maps of the in-plane, ε xx ( x,z ), and out-of-plane, ε zz ( x,z ), strain components around the MD, computed from the experimental image shown in panel (c) using Geometrical Phase Analysis. [ 41 ] The positions of the two partials in the composite core are clearly discerned, along with the compressive (red, yellow) and tensile regions (magenta, blue) extending into the substrate and the fi lm, respectively. It can be observed that the misfi t relieving tensile strains, ε xx , draw two arms propagating up to the fi lm surface, whilst normal strains, ε zz , rapidly vanish as a result of the boundary condition of a free (001) surface, σ zz = σ zx = σ yx = 0 ( σ ii are components of the stress tensor).
A projection of the MD network on the interface plane obtained by orientation contrast scanning electron microscopy (SEM) is shown Figure 2 a. The MD network is formed by irregularly spaced short (≈100 nm) dislocation segments along the [100] and [010] directions, with average spacing < S > = 25 ± 10 nm (see Figure S1, Supporting Information). These lines correspond to the projection of half-loops onto the interfacial plane, where they leave a MD segment which increases in length as the threading segments move apart. With increasing fi lm thickness to 6 nm, < S > reduces to 19 ± 6 nm, while most of dislocations run across the limits of the imaged 1000 nm × 1000 nm areas (see Figure S1, Supporting Information). The theoretical dislocation spacing for full relaxation, b x /ε = 16.5 nm, is achieved for the 14 nm thick fi lm, with < S > = 16 ± 3 nm. According to equilibrium theory, the energy barrier needed for a half-loop of critical radius to survive increases with decreasing misfi t strain. [ 42 ] Therefore, as the misfi t is relieved by expansion of existing half-loops, the nucleation of new ones becomes kinetically suppressed. As a consequence, the average dislocation length increases whilst their lateral spacing narrows as the fi lms thicken, in excellent agreement with experimental observations (see Figure S1, Supporting Information). Since the glide plane coincides with the interface plane, the MDs can easily rearrange their positions on that plane to minimize their elastic interactions, resulting in increasingly ordered patterns. According to this evolution, the density of threading arms of MDs rapidly decreases as the fi lms thicken, while the strain state of the fi lms becomes determined by the increasingly ordered interfacial MD network.
In order to analyze the morphological transition occurring between 2 and 3.5 nm, Figure 2 compares the MD network shown in panel (a) with a topographic atomic force microscopy (AFM) image of the same fi lm panel (b). In agreement with the cross-section HRTEM image shown in Figure 1 b, it is clearly seen that the surface topography consists of a network of ridges and terraces mimicking the underlying dislocation network. Hence, the outgrowths shown in Figure  images from the 6 nm thick fi lm (see Figure 3 a,b) and compared them with the spatial distribution of the residual in-plane strain ε xx ( x,y ) + ε 0 , ( ε 0 = −2.3% is the background misfi t strain), arising from a square network of b x = [100] and b y = [010] dislocations, using continuum isotropic elasticity (see Figure 3 c). We employed the isotropic-average shear modulus of LSMO derived from the Voigt-Reuss-Hill averaging, [ 43 ] using the cubic elastic stiffness coeffi cients reported by Darling et al. [ 44 ] G = 50.98 GPa. Note that the LSMO is softer than the LAO substrate ( G = 133.10 GPa). [ 45 ] In this situation, the core of the dislocation is predicted to lie in the fi lm very close to the interface, [ 46 ] in agreement with the present observations. The calculated strain map shows good match with the LAADF experimental image, in which darker areas correspond to a lower degree of misfi t relaxation between dislocations. Minimum relaxation levels are also attained along the locus of dislocation lines and, to a lower extent, at the crossing points, as also resolved in the experimental image (see Figure 3 b). This suggests that the observed topography results from preferential growth at surface sites with a minimum level of residual strain.
Since here we are interested on the effect of strains on surface phenomena, to confi rm this hypothesis, here we estimate the strain state of the free fi lm surface using displacement fi elds derived from the image dislocation approach. [ 43 ] The vertical and horizontal atomic displacements, u z and u x , at the free surface of a fi lm with thickness d , induced by an interfacial dislocation with Burgers vector b x , are given by [ 47 ] From Equation ( 1) , the amplitude of the downward atomic displacement at the dislocation coordinate x = 0 is b x /π ≈ 1.20 Å Adv. Mater. Interfaces 2016, 3, 1600106 www.advmatinterfaces.de www.MaterialsViews.com The tensile strain given by Equation ( 2) is superimposed over the background compressive misfi t strain due to the substrate, ε 0 , yielding a residual surface strain, ε xx ( x ) + ε 0 , as plotted in Figure 4 a for the 3.5 and 6 nm thick fi lms, respectively. The fi gure includes three dislocations, the central one at x = 0. For the 3.5 nm thick fi lm, assuming a dislocation spacing of 25 nm, almost total relaxation ( ε xx ( x ) + ε 0 ) ≈ 0 occurs at each side of the dislocation line at a distance of about 4 nm. For the 6 nm thick one, assuming a dislocation spacing of 19 nm, the overlapping of strain fi elds erases the fl uctuation between adjacent MDs. In this case complete relaxation is achieved within a region of size similar to the thickness of the fi lm located between adjacent dislocations. However, for those two thicknesses, specially for the thinner fi lm, the dispersion of S values is still high enough to expect the coexistence of both types of modulation in the same sample.

Evolution of Film Topography
The link between the morphological evolution of a free surface and its strain state is given by the surface chemical potential µ ( x ) = µ 0 + γΩκ ( x ) + Ω w ( x ), [ 11 ] where µ 0 is the chemical potential of the unstressed fl at surface, γ is the surface free energy per unit area, Ω is the volume of a growth unit, κ ( x ) is the surface curvature, and w ( x ) is the local surface strain energy density. [ 48 ] Assuming a fl at surface, κ ≈ 0, the modulation of the driving force for strain induced surface mass transport due to an underlying pure edge MD located at can be expressed as where M = 2 G (1 + ν )/(1 − ν ). According to Equation ( 3) , growth units will migrate from highly strained regions to fi nd stable positions at locations exhibiting minimum Δ µ 0 ( x ) values at each side of the dislocation. To illustrate this, Figure 4 b depicts the chemical potential reduction relative to the position of the MD, as a function of distance, the surface chemical potential at the position of the MD) for the 3.5 and 6 nm thick fi lms, with < S > = 25 and 19 nm, respectively. For the 3.5 nm thick fi lm, the fl uctuation draws two minima at each side, ≈4 nm away from the MDs, where the chemical potential is reduced by 17 meV. This abrupt gradient in Δ µ d ( x ) should induce the preferential nucleation of LSMO at each side of the MDs, leading to the formation of the observed topographic pattern. It should be noted, however, that since in this case the glide plane is parallel to the interface plane, MDs can easily move to rearrange their positions and, therefore, those surface features do not necessarily appear associated with them. It is to be noted that there exists a kinetic limitation for the vertical growth of the ridges: Once a ridge is formed, the rapid increase in surface curvature at that point causes the competition between the surface energy, γκ ( x ), and strain energy, w ( x ), terms of the chemical potential, eventually hindering its vertical growth. This scenario drastically changes as the fi lm surface moves further apart from the dislocation strain sources (and those ones get closer), as exemplifi ed by the 6 nm thick fi lm (see Figure 4 b). The plot clearly shows that a thickness increase of 2.5 nm results in nearly a 50% decrease in the amplitude of the fl uctuation in Δ µ d ( x ). This effect contributes to homogenize the chemical potential throughout the surface, resulting in fl atter fi lms, in agreement with experimental observations (see Figure S1, Supporting Information). Therefore, the formation of terraces in the 3.5 nm thick fi lm, exhibiting a wider dispersion in S values, can be attributed to the overlapping of the strain fi eld in regions with locally enhanced MD densities.

Strain Effects on Surface Currents
Before considering the local effect of buried MDs on surface currents, we will take into consideration the bulk transport Adv. Mater. Interfaces 2016, 3, 1600106 www.advmatinterfaces.de www.MaterialsViews.com  behavior of the fi lms. Figure 5 a depicts standard four-point electrical resistivity measurements as a function of the thickness of the fi lms. As seen in the fi gure, room temperature resistivity values decrease as the fi lm thickness, thereof the relaxation level as manifested by the variation in the c/a lattice parameter ratio, increases. The temperature dependence of the resistivity of the different fi lms, on the other hand, indicates bulk-like insulating behavior for the 2 nm and 3.5 nm thick fi lms, and metallic behavior for larger thicknesses (6 and 14 nm), see Figure S2 (Supporting Information). As far as the surface electrical properties of the fi lms are concerned, however, current maps indicate local resistivity fl uctuations that appear associated with the formation of MDs. Starting with the 3.5 nm thick fi lm, Figure 5 b shows an AFM image corresponding to the I(x,z) current map shown in Figure 5 c. Despite its bulk insulating behavior, this fi lm exhibits surface metallic behavior. Current enhancements are clearly seen as dark contrasts decorating surface steps, which are attributed to the extended tipsurface contact area along their ledges. Within the terraces, brighter lines of depressed current are also observed along the in-plane <100> directions. Both, topographic and conduction images are correlated with the underlying MD network. For the 6 nm thick fi lms, the topographic ridge/terrace pattern is no longer present ( Figure 5 d and Figure S1, Supporting Information) and exhibits unit cell height steps (Figure 5 f), the corresponding current map still exhibits current depressions along lines parallel to the in-plane <100> directions, as clearly seen in Figure 5 e. The infl uence of strain on the magnetotransport properties ABO 3 perovskite compounds is intimately correlated to tilt and distortion processes of the MnO 6 octahedral framework. Strain affects magnetotransport properties by acting on different mechanisms at a microscopic level. First strain affects both <Mn O Mn> bond angle and the Mn O bond length, thus modifying the strength of the double exchange ferromagnetic (DEF) interactions. For the same reasons strain also affects antiferromagnetic (AF) superexchange interactions. In addition, strain may introduce an orbital bias since in-plane compressive or tensile strains may promote selective d 3 z 2r 2 or d x 2y 2 orbital occupancy, respectively. Therefore, as a fi rst approximation, an elongation of the Mn O distances or a decrease of the <Mn O Mn> bond angle would promote a reduction of the strength of DEF interactions and therefore, a reduction of the ferromagnetic Curie temperature, T C , and an increase of electrical resistivity. On the contrary, the reduction of Mn O distances or the straightening of the <Mn O Mn> bond angle promotes the strengthening of DEF interactions and a reduction of resistivity. The observation of enhanced conductivity at (100)-type twin walls in LSMO/STO thin fi lms, which are submitted to a severe compressive strain, indeed Adv. Mater. Interfaces 2016, 3, 1600106 www.advmatinterfaces.de www.MaterialsViews.com supports these arguments. [ 49 ] Nevertheless, this scenario may be strongly affected by selective orbital occupancy and AF superexchange interactions. The balance between these competing effects is controlled by the ratio between perpendicular and in-plane lattice parameters c/a , refl ecting the degree of tetragonal distortion of the structure. [ 50 ] In such scenario, increasing c/a >1.0 works against the metallic ferromagnetic behavior and would promote an increment of the resistivity. Since according to our analysis above, the behavior of the present fi lms is well described by the continuum isotropic elasticity theory, the infl uence of rigid octahedral tilting mechanisms can be safely neglected, which otherwise would manifest as noticeable anomalies in the behavior of lattice parameters. [ 7 ] Accordingly, the image contrast in the AFM current maps may be analyzed in terms of local c/a values, directly governed by the residual misfi t strain, ( ε xx +ε 0 )( x ) shown in Figure 4 a. The lateral modulation of the c/a ratio at the fi lm surface is given by where ε xx is given by Equation ( 2) , and ε zz is solely determined by the outward relaxation determined by the Poisson's effect, ε zz = 2 νε xx /( ν −1). In the case of the 6 nm thick fi lm, using the Poisson's ratio derived for the 2 nm thick fi lm, ν = 0.35 (see above), a c/a ratio of ≈1.03 can be estimated at the locus of the dislocation ( ε xx ≈ −0.013) while c/a ≈ 1.0 in a large area between dislocations ( ε xx ≈ 0). As a result, the metallic character is expected to be depressed at the dislocations that would exhibit a higher resistivity. Thus, the pattern observed in current maps is a close mimic of the dislocations pattern. The very same reasoning may be applied to explain the low conducting paths observed on the surface of the 3.5 nm thick fi lm. In this case we fi nd c/a = 1.05 ( ε xx ≈ −0.020) above the dislocation lines. Experimental determinations of the c/a ratio from the GPA derived strain maps indeed support the above behavior. Figure 6 a shows the c/a ( x ) dependence at two different levels above the dislocation analyzed in Figure 1 c,d, corresponding to the 3.5 nm thick fi lm. The blue and red curves are taken close to the fi lm surface and at half way from the buried dislocation core, as indicated in Figure 6 b. It can be clearly observed that the c/a ratio locally increases above the dislocation, reaching values closely similar to those derived from linear elasticity. It can be also observed that the average c/a level increases toward the fi lm surface, which can be attributed to an elastic relaxation perpendicular to the fi lm surface. Identifying the strained regions as less conducting is also in agreement with the insulating behavior observed in the 2 nm thick fi lm, prior to the appearance of dislocations. In those fi lms, c/a ≈ 1.06 ( ε xx ≈ −0.023), i.e., they are expected to lie well within an antiferromagnetic insulating phase. [ 6 ] Above the onset of plastic relaxation, this analysis yields a view of partly relaxed LSMO/LAO thin fi lms as a conducting compressed matrix, decorated with nanometric paths of higher resistance material aligned with the in-plane <100> directions coinciding with the positions of the buried MDs, in agreement with experimental I ( x,y ) maps. As shown above, the topological distribution of strained, high-resistivity regions, throughout the volume of the fi lms varies with the fi lm thickness. Just after the onset of plastic relaxation, the MD density is low, but their associated strains occupy a signifi cant fraction of the fi lm volume owing to its reduced thickness. Thus, in the 3.5 nm thick fi lm, the average bulk insulating behavior can be understood by considering that the connectivity between metallic regions is below the percolating threshold. At larger thicknesses, the increased dislocation density promotes a higher average level of relaxation consistent with the metallic behavior observed in the 6 nm thick fi lm.

Conclusion
To conclude, the strain fi eld of MDs in a complex oxide heterostructure introduces a lateral modulation of the chemical potential and the bandwidth-dependent properties at the free surface of the fi lm. In particular, the present experiments shed light on the structural mechanisms underpinning the topographic and electrical conduction patterning of the surface of LSMO/LAO thin fi lms. It is shown that, even if perovskite thin fi lms may relax misfi t strains by combining octahedral distortions and octahedral tilting which may eventually elude the formation of Adv. Mater. Interfaces 2016, 3, 1600106 www.advmatinterfaces.de www.MaterialsViews.com MDs, the strain state of dislocated fi lms is well described by continuum elasticity. This allows straightforward modeling of the strain sate of the fi lms and their free surfaces, and the interpretation of their effect on local surface properties like the chemical potential and the bandwidth controlling the transport properties of these materials. These properties exhibit different dependencies on the amplitude of surface strain fl uctuations, which in turn depend on fi lm thickness and MD density. Chemical potential fl uctuations are rapidly smeared out, limiting the thickness range useful for topographic patterning. On the other hand, surface current patterning is shown to persist up to larger thicknesses. Interestingly, our analysis indicates that current depressions along the projection of dislocation lines on the fi lm surface are well described by the lateral modulation of the c/a axial ratio, controlling the balance between selective Mn d orbital occupation, in-plane Mn 3 d -O 2 p orbital overlapping, and AF interactions. [ 50 ] These results demonstrate the feasibility of using MDs in a controlled way to produce spontaneous, highly ordered, surface topographic and conduction patterns on a ≈20 nm length scale. Further optimization of each of the surface properties investigated in this work can be achieved through the magnitude of the misfi t strain and the strength of the Burgers vector of the MDs.

Experimental Section
Films : High-quality fi lms with (100) orientation and thicknesses of 2, 3.5, 6, and 14 nm were epitaxially grown under a biaxial compressive strain of ε 0 = −2.3% on LAO substrates by magnetron sputtering as reported elsewhere. [ 51 ] Electrical Resistivity : The in-plane electrical resistivity was measured using the standard four-point geometry with a constant applied current of 5 nA.
Conducting Atomic Force Microscopy : Local electrical conductivity maps were measured by conducting AFM under an N 2 environment, using commercial conductive CrPt-coated Si tips mounted on cantilevers with k = 40 Nm −1 (BudgetSensors). The lateral resolution of the technique is, in principle, limited by the tip radius of ≈10-20 nm. In the employed setup, the sample was grounded and the voltage was applied to the tip. An external I-V converter (Stanford Research Systems) was used to provide access to a wide range of compliance currents (1 pA to 1 mA).
High-Resolution X-Ray Diffraction : The lattice parameters of the fi lms were determined from HR-XRD using a four-angle goniometer and primary optics consisting of a parabolic mirror and a 4 x Ge(220) asymmetric monochromator (X'Pert Pro MRD-Panalytical). The in-plane lattice parameters were determined in the same equipment with a parabolic mirror in the incidence beam optics, fi xed grazing angle of 0.5° on the sample, and parallel plate collimator in the diffracted optics.
Transmission Electron Microscopy : Thin foil specimens were prepared by conventional cutting-gluing-grinding procedures, followed by Ar milling at a grazing incidence down to perforation. Cross-section atomic resolution images (HRTEM) were obtained at 200 kV using the fi eldemission gun FEI Tecnai F20 S/TEM and the Cs-corrected Tecnai F20 electron microscopes. The projected strain distribution on the plane of the fi lm was directly imaged by LAADF microscopy, [ 52 ] using a fi eld emission gun Tecnai F20 S/TEM electron microscope.
Orientation Contrast Scanning Electron Microscopy : Orientation contrast SEM images [ 53 ] were obtained in a QUANTA FEI 200 FEG-ESEM electron microscope in order to determine dislocation densities over large areas.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.