Disentangling Epitaxial Growth Mechanisms of Solution Derived Functional Oxide Thin Films

This study investigates the mechanisms of epitaxial development and functional properties of oxide thin films (Ce0.9Zr0.1O2−y, LaNiO3, and Ba0.8Sr0.2TiO3) grown on single crystal substrates (Y2O3:ZrO2, LaAlO3, and SrTiO3) by the chemical solution deposition approach. Rapid thermal annealing furnaces are very powerful tools in this study providing valuable information of the early stages of nucleation, the kinetics of epitaxial film growth, and the coarsening of nanocrystalline phases. Advanced transmission electron microscopies, X‐ray diffraction, and atomic force microscopy are employed to investigate the film microstructure and morphology, microstrain relaxation, and epitaxial crystallization. This study demonstrates that the isothermal evolution toward epitaxial film growth follows a self‐limited process driven by atomic diffusion, and surface and interface energy minimization. All investigated oxides experience a transformation from the polycrystalline to the epitaxial phase. This study unequivocally evidences that the film thickness highly influences the epitaxial crystallization rate due to the competition between heterogeneous and homogeneous nucleation barriers and the fast coarsening of polycrystalline grains as compared to epitaxial growth. The investigated films possess good functional properties, and this study successfully confirms an improvement at long annealing times that can be correlated with grain boundary healing processes. Thick epitaxial films can be crystallized by growing sequential individual epitaxial layers.


DOI: 10.1002/admi.201600392
devices in multiple applications due to the broad variety of chemical and physical properties exhibited such as ferromagnetism, ferroelectricity, colossal magnetoresistance, multiferroicity, superconductivity, buffer layers in heterostructures or coated conductors, ionic conductivity, resistive random access memories (RRAM) memories, and catalysis. [ 1 ] Physical techniques like sputtering or pulsed laser deposition are often used to grow epitaxial oxide materials and heterostructures, but they require expensive vacuum systems. Chemical solution deposition (CSD) is an appealing methodology for the fabrication of oxide devices that provides signifi cant advantages being a versatile and low-cost alternative that allows deposition over large areas and provides good stoichiometric control. [ 2 ] For instance, inkjet printing is an innovative approach combining the advantages of solutions based methods with the fast, industrial-oriented production of electronic and functional oxide devices on organic and inorganic fl exible substrates (e.g., plastic, metals, paper, or textile). [ 3 ] The scientifi c and industrial relevance of CSD for functional oxide growth has driven researchers to study the fundamental thermodynamic and kinetic aspects associated to it. Particularly, there have been notable contributions to study the mechanisms leading to the self-assembling of epitaxial oxide nanoislands, [ 2c,d,4 ] establishing a solid background for more complex fi lm growth. Some works have studied the crystallization kinetics of polycrystalline oxide fi lms such as lead zirconium titanate (PZT) and cerium oxide. [ 5 ] Also, even if an enormous effort has been dedicated to understand the epitaxial growth of high-temperature superconducting yttrium barium copper oxide (YBCO) fi lms, [ 2e,6 ] there still exists few knowledge on the epitaxial development of solution derived functional oxides. Conventional sample processing in CSD is based on electrical resistance furnaces, also known as conventional thermal annealing or CTA. These furnaces have a large thermal inertia which leads to long temperature stabilization times and slow heating/ cooling ramps around 0.05-0.5 °C s −1 (3-30 °C min −1 ). Thus, a strong microstructural evolution cannot be avoided during heating cycles. Instead, rapid thermal annealing (RTA) furnaces, where sample heating is done through infrared lamp furnaces, develop heating/cooling ramps orders of magnitude faster (1−250 °C s −1 ), therefore, offering many advantages to

Introduction
Epitaxial complex functional oxides (e.g., La 1− x Sr x MnO 3 , Ba 1− x Sr x TiO 3 , PbZr x Ti 1− x O 3 , BiFeO 3 , YBa 2 Cu 3 O 7− x , CeO 2 , LaNiO 3 , etc.) are valuable candidates for the fabrication of novel investigate the mechanisms of epitaxial fi lm crystallization and to achieve unique processing paths. For instance, RTA has proven useful to lower the crystallization temperature and time of PZT fi lms by preventing the formation of an intermediate phase slowing down the perovskite phase formation or in the fabrication of thick oxide fi lms for electronic devices. [ 5a,7 ] Although RTA seems ideal for the study of epitaxial oxide crystallization, most of the reported works have been related up to now to oxide polycrystalline fi lm growth, for instance ZrO 2 , PbZr x Ti 1− x O 3 or SrBi 2 Ta 2 O 9 . [ 8 ] Heteroepitaxial growth involves single crystal substrates and high temperature thermal treatments and it is desired over polycrystalline growth in many fi lm functionalities where physical properties are highly infl uenced by structural and chemical disorder associated to grain boundaries. [ 9 ] A precise control of the crystalline quality, induced strain and fi lm microstructure which are highly dependent on the processing conditions is also needed in order to fabricate functional devices with excellent performances. This work reports on a new insight on the thermodynamic and kinetic mechanisms governing the epitaxial crystallization of functional oxides derived from chemical solutions by using RTA to precisely control their microstructural evolution from the amorphous/nanocrystalline phases obtained after the decomposition of the solution precursors. In order to provide a general perspective of the phenomena involved, we investigate multiple epitaxial oxide systems displaying different functionalities and nucleation modes. Zirconium-doped ceria (Ce 0.9 Zr 0.1 O 2− y or CZO) grown on yttria-stabilized zirconia (Y 2 O 3 :ZrO 2 or YSZ), lanthanum nickelate (LaNiO 3 or LNO) on strontium titanate (SrTiO 3 or STO), and barium strontium titanate (Ba 0.8 Sr 0.2 TiO 3 or BST) on lanthanum aluminate (LaAlO 3 or LAO). These systems are chosen because of their chemical and structural compatibility, due to the relatively small lattice mismatches favorable for epitaxial growth, i.e., −4.5% for CZO/YSZ, 1.4% for LNO/STO and −5.1% for BST/LAO, and their remarkable functional properties. Ceria-based oxide fi lms are often used in electronic devices or in high temperature superconducting coated conductors due to their high dielectric constant, mechanical and chemical stability. [ 6b,c,10 ] The application of CZO in oxygen sensors, solidoxide fuel cells, solar thermochemical hydrogen generation, oxygen buffer, and active support for noble metals in catalysis is also under investigation. [ 1e,11 ] Lanthanum nickelate (LaNiO 3 or LNO) is used for the integration of oxide materials with silicon and as electrode in electronic devices due to its low electrical resistivity at room temperature. [ 12 ] Barium strontium titanate (Ba 0.8 Sr 0.2 TiO 3 or BST) possesses highly remarkable optical and dielectric properties and it is being used in non-linear optics, infrared detectors, thermal imaging, microwave dielectrics, or capacitors. [ 13 ] BST also shows ferroelectric response at room temperature for Ba/Sr ratios above 0.7/0.3. [ 13a,14 ] We have conducted systematic investigations to evaluate the fi lm morphology and microstructural relaxation at different experimental conditions, i.e., annealing times and fi lm thickness. 2D X-ray diffraction (2D-XRD) measurements are performed to evaluated and quantify the transformation to the epitaxial structure and correlate it with the microstructure. The results are supported by appropriate thermodynamic and kinetic theoretical descriptions. Finally, we have measured the functional properties of the fi lms and correlated the results with those from the fi lm microstructure and epitaxial growth.

Grain Growth and Microstructural Relaxation
Thermal treatments by conventional or rapid thermal annealing have heat radiation as the source for fi lm growth. We performed, fi rst of all, crystallization experiments with both types of furnaces using the same heating rates. We verifi ed that, indeed, no signifi cant differences exist for fi lms processed at the same conditions. This is demonstrated in Figure S1 in the Supporting Information which shows equivalent fi lm morphologies, root mean square (RMS) roughness and XRD peak intensities for BST fi lms grown on LAO substrates. CTA and RTA furnace treatments are done at 900 °C, 0.5 °C s −1 for 30 min in oxygen ambience. Equivalent experiments for CZO and LNO fi lms have reported similar results. [ 15 ] Thus, tubular furnaces will be employed only where long annealing times are required.
In order to investigate epitaxial fi lm development, we have performed isothermal annealing experiments with different durations, after annealing at very fast heating ramps with RTA (20 °C s −1 ). This heating ramp has been used recently to analyze separately nucleation and coarsening phenomena of oxide nanostructures, [ 2c,15 ] and it was found that RTA is fast enough to avoid any signifi cant coarsening during the heating ramp (≈35-45 s in the present case). Therefore, it is very likely that a similar phenomenology holds for fi lms.
The atomic force microscopy (AFM) characterization of BST fi lms grown on LAO substrates by RTA (900 °C, 20 °C s −1 in O 2 for 1, 5, and 30 min) shows the morphological evolution of fi lms with time and fi lm thickness ( Figure 1 a). We observe a transformation with time from rounded grains to fl at terraces and a denser structure refl ecting an improved coalescence of the 3D nucleated grains after epitaxial growth. [ 1c , 2a ] AFM images of CZO and LNO fi lms grown on YSZ and STO substrates at 900 and 700 °C, respectively, show an equivalent morphological transformation of the fi lm surface ( Figure S2, Supporting Information). CZO fi lm growth is also 3D, while we will see later that 2D nucleation may occur in LNO fi lms. Data analysis reveals that the grain dimensions (Figure 1 b) increase approximately from 13 to 60 nm (CZO), 16 to 50 nm (LNO), and 24 to 90 nm (BST). On the other hand, Figure 1 c shows a decrease of fi lms RMS roughness with the annealing time from around 1.4 to 0.7 nm (CZO), 1.5 to 0.7 nm (LNO), and 6.5 to 3.0 nm (BST). Generally, grain coarsening is associated with an increase of the RMS roughness due to the presence of spherical grains and a progressively larger peak-to-valley difference. [ 16 ] However, kinetic mechanisms present during grain growth such as atomic mobility and grain boundary (GB) zipping processes help lowering the RMS roughness in epitaxial growth. [ 17 ] In this case, surface energy minimization is the driving force leading to the formation of fl at terraces, thus, infl uencing roughness reduction. [ 2c , 5c , 6b,18 ] The presence of some large grains is likely causing the unusually high fi lm roughness for the BST case.
The growth rate of grains slightly decreases over time anticipating that a maximum grain size should be achieved. Since grain growth is a kinetic process associated to the movement of GBs, [ 19 ] crystalline defects and the dependence of atomic diffusion with grain size are frequently factors that limit GB migration, especially in the nanometer range. Previous works have referred to this behavior as self-limited growth which is described by a phenomenological law of the kinetic evolution of grain sizes [ 5c,e,f,20 ] where S 0 and S max are respectively the initial and fi nal grain diameter, t is the instantaneous time, and τ S is the character- The calculated diffusion coeffi cients for CZO, LNO, and BST are respectively (3.3 ± 0.6) × 10 −19 , (1.6 ± 0.9) × 10 −19 and (9.4 ± 0.7) × 10 −19 m 2 s −1 at their annealing temperatures (900 °C for CZO and BST, and 700 °C for LNO). These numbers reveal that atoms diffuse signifi cantly faster in BST fi lms than in CZO fi lms. It is also important to highlight that diffusion in LNO fi lms is high; despite they are produced at temperatures 200 °C lower than CZO and BST. Overall, these diffusion coeffi cients are approximately one order of magnitude larger than those reported for polycrystalline CeO 2 and Ce 1− x Gd x O 2 (CGO) fi lms grown by CTA (900 °C, 3 °C min −1 ). [ 5c ] Some works have proposed that the heating ramp highly infl uences nucleation and crystallization rates leading to different kinetic evolutions in fi lms processed by RTA. [ 5a,21 ] We will show later that epitaxial growth could also be related with the origin of the fast kinetics.
Film thickness has also a great infl uence over the microstructural evolution, and thus, the surface morphology. It has been reported previously in polycrystalline fi lms that grains enlarge with fi lm thickness and, consequently, surfaces become rougher. [ 5f,22 ] Thicker fi lms are prepared using the procedure described in the Experimental section. After three depositions, thicknesses are expected to be 60 nm (CZO), 70 nm (LNO), and 100 nm (BST), i.e., thrice the thickness of single coatings ( Figure S3, Supporting Information). Figure 1 a and Figure S2 in the Supporting Information illustrate the surface morphology of thicker CZO, LNO, and BST three-layer fi lms grown by RTA for 30 min. The fl at terraces observed in single-layer coatings disappear and fi lm surfaces present more rounded grains. Unexpectedly, grain dimensions also become smaller than in single-layer fi lms, from 60 to 25 nm (CZO), 50 to 20 nm (LNO), and 90 to 75 nm (BST). We will see later that these quasi-spherical grains very likely correspond to polycrystalline phases which are usually smaller than epitaxially terraced grains. As a result, the RMS roughness (Figure 1 c) rises signifi cantly compared to equivalent single-layer coatings from 0.7 to 2.1 nm (CZO), 0.7 to 3.0 nm (LNO), and 3.0 to 4.9 nm (BST). This is caused by the larger peak-to-valley difference as mentioned before. Another parameter which is signifi cantly correlated to the microstructural evolution of epitaxial fi lms is the RMS microstrain, i.e., the standard deviation of atomic positions from the mean value. [ 23 ] The microstrain µ , i.e., strain associated to the local distortions of the lattice, is particularly infl uenced by grain coarsening and GB zipping processes. [ 23 ] The determination of RMS µ values is done for single-layer epitaxial fi lms by evaluating the peak broadening of (00l) refl ections in θ -2 θ scans with the Williamson-Hall method ( Figure S4, Supporting Information). [ 23 ] Figure 2 a shows that µ depends on the particular oxide and also that it decreases with the annealing time. The evolution can be described with an exponential decay function [ 5c ] t exp , r 0 where µ r and µ 0 are the residual and initial microstrain, and τ µ is the relaxation time. CZO has a larger µ 0 than LNO and BST, while µ r values are almost identical (≈0.2%-0.3%). This means that CZO fi lms have an increased number of disordered GBs, as compared to LNO and BST fi lms. τ µ values for CZO, LNO, and BST fi lms are approximately 400, 370, and 60 s, respectively; much shorter than the relaxation times for grain coarsening. This suggests that grain coarsening continues after the residual microstrain has been stabilized. Essentially, microstrain evolution refl ects healing of defects at GBs while grain coarsening involves GB displacement. The faster microstrain relaxation of BST, as compared to CZO and LNO, can be related to a larger atomic diffusion during the GB zipping process. Equivalent values of µ have been reported by Rupp et al. for CGO fi lms grown by CTA (900 °C, 3 °C min −1 ). [ 5c ] However, the relaxation is signifi cantly faster in our fi lms grown by RTA. As we mentioned before, this could be related to the fast RTA heating ramps and the modifi cation of nucleation and crystallization rates, as reported elsewhere. [ 5a,21 ]

Transformation to Epitaxial Oxide Films
Crystal growth in CSD fi lms is thermodynamically driven by a decrease in the Gibbs free energy from the initial amorphous/ nanocrystalline phase to the fi nal crystalline fi lm. [ 2b-d ] The energy provided through thermal annealing allows overcoming the heterogeneous nucleation barrier responsible of the epitaxy development throughout the fi lm thickness. [ 2b ] In our case, the temperatures selected ensure that fi lms achieve a complete epitaxial growth. The parameters involved in this crystallization process are atomic diffusion, interfacial, surface and elastic energies minimization and GB recrystallization. [ 24 ] Figure 2 b, Figures S5a,c in the Supporting Information show the XRD diffraction patterns for single layers of CZO on (001) YSZ, LNO on (001) STO, and BST on (001) LAO heterostructures at different annealing times. We observe the (002) refl ection of YSZ, STO, and LAO substrates at 35.0°, 46.5°, and 48.0°, and the weak signal associated to the K β refl ection at 31.4°, 41.8°, and 43.1°. The (002) refl ections of CZO (33.4°), LNO (47.3°), and BST (45.9°) are also present. The (002) fi lm peak intensities grow with the annealing time; a phenomenon more pronounced at short annealing times, also revealing very high crystallization speeds. In addition, we can identify a very weak (111) CZO orientation at 28.8° for annealing times below 10 min which disappears for longer treatments. No other orientations are observed for LNO and BST besides (002) peaks. Three-layer fi lms present comparable (002) intensities as illustrated in Figure 2 c, Figure S5b,d in the Supporting Information, whereas the intensity of (111) CZO refl ection is stronger. We also detect other peaks associated to (011) LNO, (011), and (111) BST orientations. The shift observed in the (002) LNO refl ection ( Figure S5c,d, Supporting Information) is caused by fi lm relaxation mechanisms discussed elsewhere. [ 15,25 ] These results would suggest that fi lms have grown epitaxially, as we will see later by TEM and 2D-XRD.
The growth mode of a fi lm on top of a substrate can be predicted from a thermodynamic point of view by evaluating the wetting condition of a fi lm on a substrate. The wetting condition is derived from Young's equation and it is defi ned as the change in surface energy Δ γ = γ f + γ i − γ s , where γ f , γ i , and γ s are respectively the surface energies of the fi lm, the fi lmsubstrate interface, and the substrate. [ 26 ] If we reach a full wetting condition ( γ f + γ i < γ s ), the growth mode will be 2D or layer-by-layer, whereas if γ f + γ i > γ s the system will grow following a 3D or Volmer-Weber growth mode. We can consider that γ f and γ s correspond the energy of the (001) surface since it is the orientation of the single crystals employed, but also the epitaxial orientation of fi lms. The interface energies for the heterostructures evaluated is considered close to 0 J m −2 since fi lms are grown on substrates with the same crystallographic structure (fl uorite/fl uorite and perovskite/perovskite). CZO should present a 3D growth since γ CZO = 3.25 J m −2 and γ YSZ = 1.75 J m −2 , [ 27 ] while the growth mode of LNO and BST fi lms should be layer-by-layer Figure 3 illustrates the high resolution transmission electron microscopy (HRTEM) analysis of the single-layer oxide fi lms investigated. CZO fi lms annealed at 900 °C, 20 °C s −1 for 10 min in O 2 have areas where the fi lm is completely epitaxial (Figure 3 a). Figure 3 b shows another region presenting truncated CZO pyramids, common of 3D Volmer-Weber epitaxial growth, [ 2c ] together with particles of around 5-10 nm further up from the substrate. The power spectrum in Figure 3 c confi rms the random orientation of the particles, as well as the epitaxial orientation of nanopyramids. These pyramids are fully relaxed on top of the YSZ substrate with a lattice parameter a CZO,exp = a CZO,bulk = 5.385 Å ( a YSZ,bulk = 5.143 Å). Similar studies have been conducted on LNO fi lms grown at 700 °C, 20 °C s −1 for 10 min in O 2 . Figure 3 d-f show that most of the fi lm is epitaxial with some polycrystalline regions of around 10 nm close to the surface. In addition, it seems that LNO grows following a 2D layer-by-layer growth mode, confi rming the results obtained from the wetting condition. The layer-by-layer growth is better observed from the fl at surfaces in Figures 4 a,b which show the AFM image and corresponding line scan of a LNO fi lm obtained from a diluted precursor solution with a concentration of 0.04 M and annealed at 700 °C, 10 °C min −1 for 1 h in O 2 . The epitaxial region of the LNO fi lm is strained to match the STO substrate with a lattice parameter a LNO,exp = a STO,bulk = 3.903 Å ( a LNO,bulk = 3.850 Å), as calculated from the power spectrum in Figure 3 e. The HRTEM characterization of a single-layer BST fi lm, annealed at 900 °C, 20 °C s −1 for 5 min in O 2 , reveals a completely epitaxial fi lm (Figure 3 g,h). The power spectrum in Figure 3 h reveals a fully relaxed BST fi lm ( a BST,exp = a BST,bulk = 3.993 Å) on top of the LAO substrate ( a LAO,bulk = 3.790 Å). Interestingly, Figure 4 c-e shows that BST fi lms follow a 3D Volmer-Weber growth instead of the 2D layerby-layer growth calculated from the wetting condition. It has been reported before that strain can have a relevant infl uence in nucleation barriers, fi lm morphology and epitaxial growth. [ 2a,c,29 ] The surface and interface energies considered before are usually for unstrained nuclei. It has been suggested that an additional energy term in γ f should be included to account for the contribution of strain [ 30 ] S ij ij i j ij ijkl ijkl kl where σ ij is the surface stress tensor, ε ij the lattice mismatch and S ijkl is the second order stress tensor. But also, the infl uence of strain in γ i must be considered [ 29b ] Adv. Mater. Interfaces 2016, 3, 1600392 www.advmatinterfaces.de www.MaterialsViews.com Figure 3. HRTEM characterization of single-layer CZO grown on YSZ at 900 °C, 20 °C s −1 for 10 min in O 2 : a) completely epitaxial zone, b) partially polycrystalline area, and c) power spectrum of the orange frame in (b). Investigation of single-layer LNO grown on STO at 700 °C, 20 °C s −1 for 10 min in O 2 : d) HRTEM image of the system, and e) and f) power spectra of epitaxial and polycrystalline regions. Analysis of single-layer BST grown on LAO at 900 °C, 20 °C s −1 for 5 min in O 2 : g) HRTEM image, and h) power spectrum calculated at the colored frame in (g).

(6 of 12)
where E str is the interface strain energy per unit area and E dis is the misfi t dislocation energy per unit area. If we consider the lattice mismatch between fi lm and substrate ( ε ≈ a substrate − a fi lm /a fi lm ; a fi lm , and a substrate are the lattice parameters of fi lm and substrate, respectively), we can see that LNO fi lms on STO have a relatively low mismatch ( ε LNO−STO ≈ 1.4%) which may lead to a small strain energy enough to prevent a 3D growth. On the other hand, the strain energies of CZO on YSZ and BST on LAO should be signifi cantly large given that the lattice mismatch are ε CZO−YSZ ≈ −4.5% and ε BST−LAO ≈ −5.1%. Thus, it would be feasible that the nucleation of BST fi lms on LAO transitions from a 2D to a 3D growth mode. The results shown until now clearly demonstrate that RTA is an adequate tool to fabricate and study epitaxial crystallization which occurs at very short annealing times. Despite that, an accurate evaluation of the epitaxial growth requires the use of more general tools not limited to out-of-plane information or local regions of fi lms such as 1D-XRD and HRTEM. The degree of epitaxy can be precisely calculated with a methodology that uses a 2D-XRD detector. [ 31 ] 2 θχ scans are conducted at fi xed ϕ angles to simultaneously collect multiple fi lm crystalline orientations. The amount of (001)   and polycrystalline material are displayed as a central "spot" and a ring, respectively. Equivalent studies for CZO and LNO fi lms can be found in the Supporting Information ( Figure S6, Supporting Information). We observe that the epitaxial fraction in one-layer fi lms grows rapidly at expenses of the polycrystalline material. Full epitaxy is reached after 15-30 min of annealing by RTA for CZO and LNO fi lms, whereas epitaxial growth is completed after ≈5-10 min for BST fi lms. Instead, fi lms with three layers show a slower evolution toward full epitaxy ( Figure 5 a and Figure S6 in the Supporting Information). Interestingly, the amount of time required to achieve complete epitaxial growth for single-layers is shorter than the time needed to reach full microstrain relaxation which is approximately around 1-2 h for CZO and LNO, and 30 min for BST (Figure 2 a). Equivalent results have also been reported for YBCO fi lms grown by conventional thermal annealing of chemical solutions. [ 6a ] Therefore, these results indicate that healing of GB defects is still in progress after fi lms are completely epitaxial. Figure S7 in the Supporting Information shows 2D-XRD (022)-centered pole fi gure measurements for CZO, LNO, and BST fi lms respectively grown on YSZ, STO, and LAO substrates at 20 °C s −1 , and temperatures of 900 °C (CZO and BST) and 700 °C (LNO). The annealing times are 30 min for CZO and LNO, and 45 min for BST fi lms. These results indicate that CZO, LNO, and BST fi lms have four poles at χ = 45° corresponding to the (002) orientation characteristic of epitaxial growth. No other signal has been detected, thus, confi rming the achievement of full epitaxy in our fi lms. After a good optimization process, the fi nal epitaxial fi lms are very compact and have very low residual porosity as demonstrated previously. [ 2c , 5d,32 ] Homogeneous and heterogeneous nucleation events (polycrystalline and epitaxial crystallization) may have similar probabilities since processing temperatures are far from the oxide melting point ( T mp,CZO ≈ 2400 °C, T mp,LNO ≈ 1680 °C, T mp,BST ≈ 1625 °C [ 33 ] ). [ 2b,d ] However, the results indicate that there is a strong driving force to transform highly energetic polycrystalline material into an ordered epitaxial fi lm with reduced surface and interface energies. Up to our knowledge, this is the fi rst time that epitaxial growth is suggested to derive from polycrystalline material of the very same oxide phase in the case of binary oxides. For at least some ternary oxides such as YBCO, [ 2e,34 ] this process clearly involves several intermediate phases.
The self-limited growth model described previously [Equations ( 1) and ( 2) ] is also used to describe the crystallization kinetics from data in Figure 5 a and Figure S6 in the Supporting Information. Comparison of the epitaxial diffusion coefficients ( D epi ) of one-and three-layer CZO, LNO, and BST fi lms ( Figure 6 a) show a faster crystallization kinetics of one-layer BST fi lms compared to LNO and CZO, as it could be envisaged from HRTEM results in Figure 3 . This trend is also maintained for three-layer fi lms which show a reduction in D epi of about one order of magnitude. We have also extracted the transformation rates by converting the epitaxial fraction percentage to epitaxial fi lm thickness, i.e., multiplying by the fi lm thickness reported before. Figure 6 b illustrates an equivalent behavior to that described for the epitaxial diffusion coeffi cients. The initial values of the epitaxial growth rates for one-layer fi lms range from 0.04 nm s −1 (CZO) to 0.2 nm s −1 (BST), while threelayer fi lms have epitaxial growth rates more than one order of Adv. Mater. Interfaces 2016, 3, 1600392 www.advmatinterfaces.de www.MaterialsViews.com Figure 6. a) Epitaxial diffusion coeffi cients ( D epi ), and b) dependence of the epitaxial growth rates with the annealing time ( t annealing ) of one-and threelayered CZO, LNO, and BST fi lms. A scale √2 has been used in the Y -axis of (b) for better visualization. c) Evolution of polycrystalline particle size of three-layered CZO, LNO, and BST fi lms during isothermal annealing extracted from (111) CZO, (011) LNO, and (011) BST refl ections. d) Polycrystalline diffusion coeffi cients ( D poly ) obtained from data in (c). magnitude smaller [ from 0.001 nm s −1 (CZO) to 0.01 nm s −1 (BST)]. Interestingly, there is a decrease of the epitaxial growth rates with the annealing time. This could be understood as a reduction in the driving force toward epitaxy as the transformation proceeds due to microstructural evolution of the remaining polycrystalline material being available for recrystallization.
The interpretation of these results involves several factors. The simple evaluation of the ratio between growth temperature and melting point ( T / T mp ) for each oxide confi rms that the atomic mobility of BST ( T / T mp,BST ≈ 0.55) must be larger than that of LNO ( T / T mp,LNO ≈ 0.42) and CZO ( T / T mp,CZO ≈ 0.38). The measurement of the polycrystalline particle size for three-layer fi lms could help explain the reduction with time of the epitaxial growth rates. It is worth mentioning that the transformation of a polycrystalline phase to epitaxial material involves a reorientation or recrystallization of grains. These processes are more diffi cult for large grains and, therefore, epitaxial growth should be slowed down.  (011) BST refl ections. We observe coarsening of the polycrystalline grains with the annealing time. Specifi cally, CZO fi lms show a much larger growth, from 15 nm after 30 min of annealing to 32 nm after 240 min, while the polycrystalline grain dimensions of LNO and BST evolve with a much contained growth; from 12 and 16 nm after 30 min of annealing, and 16 and 22 nm after 240 min. Figure 6 d shows the polycrystalline diffusion coeffi cients ( D poly ) calculated from data fi tting of Figure 6 c with the self-limited growth model described previously. These are effective values of atomic diffusion since many parameters have an infl uence over it (grain boundaries, porosity, etc). D poly,CZO is almost two times larger than D poly,LNO and D poly,BST as expected from the grain sizes in Figure 6 c. These results confi rm our suspicions; epitaxial crystallization of CZO is slower compared to LNO and BST due to a faster polycrystalline grain coarsening. Full epitaxial growth should be possible in three-layer fi lms since D epi are more than one order of magnitude larger than D poly . Our data predicts that the epitaxial growth of CZO, LNO, and BST fi lms should be completed after long annealing times in the range of 80, 16, and 10 h, respectively. Figure 7 illustrates the process toward epitaxial growth. Essentially, epitaxy proceeds as long as polycrystalline grains are small. Otherwise, it is slowed down and longer annealing times will be required to achieve complete epitaxial fi lms. Nucleation barriers are also a factor to consider in epitaxial crystallization. The calculation of heterogeneous and homogeneous nucleation barriers requires exact values of thermodynamic data for each oxide that are unavailable. Nevertheless, the heterogeneous epitaxial nucleation barrier is usually smaller than the homogeneous one and, thus, epitaxial growth should always be promoted at the right conditions. [ 2d , 29a ] The physical properties of the fi lms investigated are likely infl uenced by their degree of epitaxy and the local microstructure. Figure S8a in the Supporting Information shows the measurement of electrical resistivity for LNO fi lms annealed at 700 °C by RTA (20 °C s −1 for 15 min) and CTA (0.5 °C s −1 for 1 h). The metallic response of LNO fi lms is remarkably good with values comparable to those reported in the literature. [ 35 ] The higher electrical resistivity values observed for the sample annealed by RTA is caused by the large amount of microstructural defects accumulated at low angle GB as compared to fi lms grown by CTA, i.e., grain coalescence after 2D grain nucleation has not been fully completed and, hence, some intergranular pores remain. [ 6a ] The longer dwell times used in CTA allow for additional healing of GB defects ( Figures S9a,b, Supporting Information), and thus, lower resistivity values. [ 36 ] We conducted piezoresponse force microscopy (PFM) measurements for BST fi lms grown at 900 °C by RTA (20 °C s −1 for 45 min) and CTA (0.5 °C s −1 for 4 h). Figure S8b presents the dependence of the effective piezoelectric constant d 33 as a function of the electric fi eld which have been extracted from amplitude and phase loops reported in the Supporting Information ( Figure S10, Supporting Information). The inset shows the results of writing experiments obtained by polarizing inverse ferroelectric domains at ±7 V. The loops have good saturation shapes with coercive fi elds of 6.2-7.5 × 10 7 V m −1 . The values of the piezoelectric constant for an AC voltage of 2.5 V and a resonance frequency of 130 kHz are approximately 8.5 (900 °C, 20 °C s −1 , 45 min) and 27 pm V −1 (900 °C, 0.5 °C s −1 , 4 h). These values are lower than the d 33 constant for bulk BaTiO 3 ( d 33 BTO,bulk ≈ 0 pm V −1 ), [ 37 ] equivalent to those reported for highly (001)-oriented BaTiO 3 layers produced by conventional thermal CSD on (001)LNO/Pt/TiO 2 /SiO 2 /Si substrates, [ 38 ] and Adv. Mater. Interfaces 2016, 3, 1600392 www.advmatinterfaces.de www.MaterialsViews.com Figure 7. Schematic representation of the competition between epitaxial and polycrystalline growth in the case of Volmer-Weber heteroepitaxial nucleation mode. A similar behavior should be expected for fi lms with a 2D layer-by-layer nucleation.
(9 of 12) 1600392 wileyonlinelibrary.com larger than those reported for thicker epitaxial Ba 0.6 Sr 0.4 TiO 3 fi lms grown on LAO substrates. [ 39 ] It is known that the formation of piezoelectric domains is hindered at GBs which decrease the spontaneous polarization. [ 36 ] Films with small grains, i.e., those produced by RTA, have a large amount of GBs as compared to fi lms processed by CTA with longer annealing times (Figures S9c,d,Supporting Information) which explains the enhanced piezoelectric response of fi lms produced by CTA.

Route toward Thick Epitaxial Films
The long annealing times required to achieve full epitaxy in the investigated thick fi lms (≈60 nm) demand clearly to adopt a different strategy. When multideposition is performed with intermediate pyrolysis treatments, we have shown that the corresponding epitaxial growth rates decrease strongly when the total fi lm thickness increases because the driving force for epitaxial growth is reduced when the precursor nanoparticles coarsen (see Figure 6 b). Here, we propose a different strategy to avoid this limitation in achieving thick epitaxial fi lms. We have performed multideposition of individually grown epitaxial layers; thus, each precursor layer will grow on top of a similar one already epitaxial, i.e., after the second layer we induce an homoepitaxial growth. We have evaluated this case for BST fi lms in order to prevent the competition between polycrystalline and epitaxial material. Figure 8 shows a perfectly terraced surface of a BST bilayer grown on LAO at 900 °C, 0.5 °C s −1 for 4 h in O 2 . X-ray refl ectometry (XRR) measurements in Figure 8 b reveal that the fi lm thickness is twice the value of single-layer fi lms (≈72 nm). Figure 8 c,d illustrate that the bilayer is completely epitaxial without presence of polycrystalline phases. The surface pores observed arise from an incomplete coalescence of the Volmer -Weber nucleated grains. Figure S11 in the Supporting Information shows equivalent experiments for CZO fi lms grown on YSZ at 900 °C, 20 °C s −1 for 30 min in O 2 . Additional data can be found elsewhere. [ 15 ] Therefore, we have demonstrated that the competition between polycrystalline and epitaxial growth development which is mastered by the rather close homogeneous and heterogeneous nucleation barriers, by a reduction of the surface and interface energies due to GB healing, and by the atomic diffusion coeffi cients which are found to favor epitaxy. The evaluation of these parameters can be used to defi ne very effective strategies to grow thick epitaxial CSD-derived fi lms by multideposition of solutions separated by complete epitaxial fi lm development.

Conclusions
The analysis of the isothermal evolution of single-layer fi lms has allowed us to quantify the time dependence of the epitaxial growth rate, estimating the coarsening rates of epitaxial and polycrystalline grains, and the microstrain evolution. We have shown that three-layer fi lms display much reduced epitaxial grain growth rates, an issue which is correlated with an enhanced coarsening of the homogeneously nucleated grains. We have concluded that different processes control the kinetics of epitaxial grain growth, coarsening of polycrystalline grains and grain boundary defect healing. Epitaxial and polycrystalline grain coarsening are demonstrated to follow a thermally activated self-limited growth diffusion model with different diffusion coeffi cients, while grain boundary diffusion and zipping processes cause a faster exponential relaxation of the local fi lm lattice (microstrain), as compared to grain coarsening processes. The wetting condition used to evaluate the nucleation mode of the oxide fi lms confi rms the experimentally observed 3D Volmer-Weber nucleation for CZO fi lms on YSZ and 2D layer-by-layer nucleation for LNO fi lms on STO. However, 3D nucleation is experimentally detected for BST fi lms on LAO substrates which contradicts the 2D nucleation mode calculated from the wetting condition. The large contribution of strain which increases the surface energy of fi lms is the most probable cause for this change in nucleation modes.
The coexistence of polycrystalline and epitaxial material at early stages of growth reveals close values of homogeneous and heterogeneous nucleation barriers. Epitaxial crystallization is demonstrated to occur from polycrystalline material of the fi nal oxide phase and not from intermediate phases, and the driving force is the decrease of surface Adv. Mater. Interfaces 2016, 3, 1600392 www.advmatinterfaces.de www.MaterialsViews.com Figure 8. Growth of two independent and epitaxial BST layers on LAO: a) AFM characterization of the surface morphology, b) XRR measurements, c) 2D-XRD raw data, and d) line scan of (c) at χ = 0° and χ ≠ 0°.
Adv. Mater. Interfaces 2016, 3, 1600392 www.advmatinterfaces.de www.MaterialsViews.com and interfacial energies of the polycrystalline stage. The crystallization of individual layers is a route to adequately reach fast fully epitaxial thick fi lms by avoiding the excessive coarsening of polycrystalline grains which reduces the surface and interface energies. Rapid thermal annealing furnaces have proved to be ideal tools for the study of CSD-derived oxide fi lm grain coarsening and epitaxial crystallization, and to enhance growth rates. The fast heating ramps achieved compared with tubular furnaces have given access to very short annealing times, and allowed a precise study of nucleation modes and growth mechanisms of complex oxides. The thorough investigation of different CSD-derived oxide fi lms, as well as the theoretical modelling employed, has provided further insight on the mechanisms involved on CSD epitaxial growth of functional oxide fi lms, and has shown a path to develop larger epitaxial fi lm thickness at enhanced growth rates. We have also successfully correlated fi lm physical properties with GB healing mechanisms which indicates that longer annealing times contribute to the improvement of fi lm functionality. These methods and studies have been proved to be of general validity for complex oxides, and so they could be easily implemented on a wide range of epitaxial systems to evaluate their growth mechanisms, but also to optimize the industrial fabrication of functional devices for example by inkjet printing methods.

Experimental Section
CSD is the method used to grow the functional oxide fi lms. Solution synthesis of the oxides investigated has been described before. [ 31b,40 ] Briefl y, cerium (III) and zirconium (IV) acetylacetonate salts (Sigma-Aldrich) were added in propionic acid and stirred at 50 °C for 30 min to obtain 0.25 M Ce 0.9 Zr 0.1 O 2− y (CZO) precursor solutions. Secondly, lanthanum (III) nitrate and nickel (II) acetate precursor salts (Sigma-Aldrich) were diluted in 2-methoxyethanol and refl uxed at 125 °C for a few hours to prepare 0.2 M LaNiO 3 (LNO) solutions. Finally, barium (II) and strontium (II) acetate salts (Sigma-Aldrich) were mixed in propionic acid for 3 h with the addition of titanium (IV) isopropoxide to synthesize Ba 0.8 Sr 0.2 TiO 3 (BST) precursor solutions with a 0.3 M concentration. Solutions were then stabilized with acetylacetone. The CZO, LNO, and BST precursor solutions were respectively spun at 6000 rpm for 2 min onto thoroughly cleaned Y 2 O 3 :ZrO 2 (YSZ), LaAlO 3 (LAO), and SrTiO 3 (STO) single crystal substrates (Crystec Gmbh). The substrates had a (001) orientation and were 5 × 5 mm 2 in size. The fi lms with metalorganic precursors of CZO, LNO, and BST were respectively heated at 300 °C for 30 min, 350 °C for 30 min, and 450 °C for 10 min with a tubular furnace. That ensured a complete decomposition of the organic material with no detectable C residues, as determined by thermogravimetric analyses and Fourier transform infrared (FTIR) spectroscopy (see Figure S12 in the Supporting Information). [ 15,41 ] A detection limit for the FTIR instrument (Spectrum One, Perkin Elmer) of 0.8 wt% was estimated. Crystallization of the pyrolyzed amorphous/nanocrystalline fi lms, which had thicknesses of 25 nm for CZO and 40-45 nm for LNO and BST, [ 31b ] was done using an AS-Micro rapid thermal annealer (Annealsys) in static oxygen environment with heating ramps up to 20 °C s −1 . Temperatures of 900 °C for CZO and BST were selected as optimal processing conditions to study grain growth and epitaxial crystallization due to a large atomic mobility of the species at those temperatures. [ 6b,42 ] The annealing temperature for LNO was set to 700 °C due to a phase instability above ≈800 °C. [ 43 ] For purpose of comparison, CTA in tubular furnaces and an oxygen fl ow of 0.6 L min −1 was also performed to ascertain that gas exchange effects do not infl uence the microstructural evolution. Thicker fi lms (up to ≈100 nm) were prepared through two different multilayer processes that consisted of: ( 1) consecutive deposition and pyrolysis steps and a fi nal high temperature thermal treatment at the selected conditions of the whole architecture, and ( 2) sequential deposition, pyrolysis, and high temperature growth of each layer.
The surface morphology of fi lms was characterized by AFM using an Agilent 5100 system in the intermittent contact mode. MountainsMap 7.0 software (Digital Surf) was employed to examine the resulting topographic images. The structural characterization of fi lms was done through XRD. The crystallographic structure was determined from 1D θ -2 θ measurements using a Rigaku Rotafl ex RU-200BV diffractometer. This system was also used to measure the fi lm thickness by XRR at low diffraction angles. 2D-XRD analyses using a Bruker GADDS system allowed the quantitative evaluation of the epitaxial fraction. Additional information about the method used to calculate the epitaxial fraction can be found elsewhere. [ 1d,15 , 31a ] In addition, (022) pole fi gure measurements had been performed by integrating 360 2D XRD frames collected at steps of Δ ϕ = 1° for t = 20 s each frame. Microstrain was evaluated following the Williamson-Hall methodology described in the Supporting Information. [ 15,23 ] These crystallization studies were supported with additional HRTEM analyses. Cross-sectional specimens were prepared by mechanical polishing and ion milling and examined with FEI Tecnai F20 and JEOL J2010F microscopes operating at 200 kV with lateral resolutions of 0.14 nm. The physical properties of the fi lms were also characterized. The electrical resistivity of LNO fi lms was measured using a physical properties measurement system (PPMS) from Quantum Design Inc., setting the electrical contacts in a four-probe confi guration and following the van der Pauw method. [ 44 ] The piezoresponse of BST fi lms had been measured by PFM using an Agilent 5500LS system in contact mode and employing conductive diamond tips (AppNano).

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