Second Harmonic Generation Studies of Interfacial Strain Engineering in BaZr0.2Ti0.8O3

Film ferroelectrics demonstrate large breakdown strength, high energy density, and many unique phenomena not found in bulk materials. In this investigation, a rhombohedral BaZr0.2Ti0.8O3 (BZT) solid solution and various film‐substrate misfit strains are utilized to optimize the energy storage performance of ferroelectric thick films. Optical second harmonic generation is applied in both reflection and transmission geometries to reveal the renovation of entangled rhombohedral and tetragonal phases in the BZT films under compressive misfit strains. It is shown that the interfacial strain between the BZT film and substrate introduces the tetragonal domains. The competition between the tetragonal and rhombohedral phases creates the self‐assembled, anisotropically strained morphotropic structures to effectively accommodate the elastic and electrical stress fields through inside the thick BZT film. The BZT films demonstrate exceptional energy storage performance because of the adaptable nano‐domain structure within the bulk of the BZT films and may be engineered to optimize the superior performance of BZT films in energy storage.


Introduction
Ferroelectric film capacitors, due to their high breakdown strength, energy density, and fast discharge speeds, offers potential solutions for next-generation energy storage devices. [1]However, to further improve the energy performance of a ferroelectric DOI: 10.1002/aelm.202300497film, a slim P-E hysteresis loop with a decreasing remnant polarization and a delaying polarization saturation must be obtained to achieve a higher energy density and better energy conversion efficiency.The ferroelectric films withstand higher electric fields and store more electrostatic energy with lower energy loss during charge-discharge cycles.0] The polydomains have been primarily observed in BiFeO 3 [11][12][13][14] and Pb(Zr,Ti)O 3 (PZT) ferroelectric films. [15]Under an imposed electric field, the heterophase polydomains in the films continuously adapt in response to the competing elastic and electrical stresses.This competition delays saturation of the films' polarization since the elastic (barrier) and electrostatic (driving force) energy contributions cannot easily overcome one another.This delay allows the films to store higher energy densities compared to bulk materials or single-phase films.Moreover, the heterophase polydomain structures decrease the remnant polarization, leading to a further increase in the energy storage efficiencies.
In this work, we engineered the heterophase polydomain nanostructures for optimizing the energy storage performances in BaZr 0.2 Ti 0.8 O 3 (BZT) ferroelectric films by the compressive film-substrate misfit strain.The superior energy storage densities (up to 166 J cm −3 ) and recycling efficiencies (up to 96%) have been demonstrated in the BZT films of 350 nm, 900 nm, and 1800 nm thickness epitaxially grown on LaAlO 3 (LAO), (La,Sr)(Al,Ta)O 3 (LSAT), and SrTiO 3 (STO) substrates.We utilized optical second harmonic generation (SHG) to probe coexisting tetragonal and rhombohedral domains in both reflection and transmission geometries.We reveal that the interfacial misfit strain between the BZT film and substrate introduces the tetragonal domains, and the rhombohedral phase grows with increasing film thickness as the strain relaxes away from the film-substrate interface.The performance of energy storage in these films can be optimized by engineering the ultra-adaptive nanodomain structures to effectively accommodate the competing elastic and electrical stress fields during charge-discharge cycles.

Sample Preparation
Ferroelectric BZT films with a thickness from 350 to 1800 nm and a SrRuO 3 (SRO) bottom electrode of ≈100 nm thick were epitaxially grown on the (100)-oriented LAO, LSAT, and STO substrates.The substrates and SRO sputtering targets were prepared by the Anhui Institute of Optics and Fine Mechanics (Chinese Academy of Sciences, Hefei, China).The BZT ceramic target was prepared in-house with the same shape and size as the SRO target via a solid-state reaction method.RF-magnetron sputtering, at a deposition pressure of 1.2 Pa and a substrate temperature of 650 °C, was applied for the deposition of ≈100 nm SRO electrode layers and the ferroelectric BZT thick films.We noted that the polydomain structures in the BZT films are strongly dependent on the film preparation parameters.The phase structures and crystallographic orientations of the BZT films were analyzed by X-ray diffraction (XRD, Rigaku D/max-RC, Tokyo, Japan) for 2 scans.Transmission Electron Microscopy (TEM, JEOL, JEM-2010, Tokyo, Japan) was used to investigate the nanoscale polymorphic phase structures.Ferroelectric polarization-applied field (P-E) hysteresis loops were measured using an RT-Precision LC ferroelectric testing system (Radiant Technology, NM, USA).The details are discussed. [8,16]

Optical Second Harmonic Generation Polarimetry
Two detection geometries were utilized in our optical SHG measurements, as shown in Figure 1.In the reflection geometry, a mode-locked Ti:Sapphire pulse laser (80 MHz, 10 nJ per pulse, 100 fs) was used as the fundamental light source (810 nm, ≈1 mJ cm −2 ) and the BZT films were aligned with surface normal axes at  = 45 o .Both p-polarized and s-polarized SHG intensities were measured as a function of the incident light polarization angle, , and used to assess the effective symmetry of the films.In the transmission geometry, laser pulses from a regenerative amplifier (Coherent RegA9000, 250 kHz, 5 μJ per pulse, 200 fs) were used as the fundamental light source (810 nm, ≈100 mJ cm −2 ).The BZT films were aligned with surface normal axes at  = 0 o with respect to the incident light.In both geometries, a fundamental light wave of frequency  first passes through a Glan Polarizer to ensure linear polarization before passing through a half-wave plate.The half-wave plate, which was controlled by an electronic motion controller (Universal Motion Controller / Driver ESP300, Newport) through LabVIEW, was used to rotate the polarization angle, , of the incident light on the sample.In all the experiments, p-polarized optical fields were considered as traveling parallel to the optics table while s-polarized optics fields travel perpendicular to the optics table.After the half-wave plate, the fundamental light wave was then passed through a long-pass filter (LPF) which blocks optical wavelengths below 780 nm.This is to make sure that no SHG signals from the pulse lasers or optical components will enter the PMT.A converging lens (L1), with a focal length of 35 mm, was then used to focus the fundamental light onto the sample in order to achieve a high enough energy density for eliciting a measurable nonlinear response.After the signal is generated from the sample's non-centrosymmetric surface, interface, or bulk, it was passed through a second Glan Po- larizer used to analyze either p-polarized or s-polarized SHG intensities as functions of the incident polarization angle, , which are measured by the PMT.More details are described. [17]Whether or not to detect SHG in the reflection or transmission geometry depends on whether one is probing a surface, interface, or bulk region.In general, the reflection geometry was used for probing surface and interface structure, while the transmission geometry was used to probe bulk regions.

Results and Discussions
Figure 2a shows the charged areal energy densities (W area ) and energy storage efficiencies ( = ) for the ferroelectric BZT films of 350 nm, 900 nm, 1400 nm, and 1800 nm thickness grown on LAO, LSAT, and STO substrates.If W C is used to denote the charged/stored energy density, and W re is the discharged/released energy density, i.e., the recyclable energy density, and W loss is the energy density loss during the discharging process.While the storage efficiencies of BZT/LSAT and BZT/STO clearly increase (from 68% to 88% in BZT/LSAT and from 77% to 96% in BZT/STO) with growing thickness of the BZT layers, the  in BZT/LAO shows a fluctuation between 73% and 84% and with an average ≈80%.A similar trend is revealed in the areal energy densities: W area of BZT/LAO, BZT/LSAT, and BZT/STO films increase from 4 × 10 −5 J cm −2 , 5 × 10 −5 J cm −2 and 6 × 10 −5 J cm −2 to 10 × 10 −5 J cm −2 , 10.1 × 10 −5 J cm −2 and 10.3 × 10 −5 J cm −2 , as the BZT layer thickness increases from 350 to 1400 nm. Figure 2b shows the representative ultra-slim P-E hysteresis loops and energy storage characteristics of the 350-nm, 700-nm, 1400-nm, and 1800-nm-thick BZT/STO films.Similar trends in P-E loops are also observed for the BZT film grown on LSAT and LAO substrates. [9]It is important to note that both the remnant polarization P r and the maximum polarization P m decrease with the growing BZT layer thickness.The interfacial strain between the BZT layer and the STO substrate is crucial for optimizing the energy storage performances in the BZT films.Strains were imparted into the BZT films through differences in lattice parameters and thermal expansion behavior between the film and the underlying substrate. [18]The bulk rhombohe-dral structure was confirmed in the BZT polycrystalline ceramic with a lattice parameter ≈4.060 Å via XRD analysis. [10]e verified that the LAO, LSAT, and STO substrates have lattice parameters of ≈3.790 Å, ≈3.870 Å, and ≈3.905 Å, respectively. [19]The interfacial lattice misfits of the BZT films grown on the STO, LSAT, and LAO substrates are therefore estimated to be −3.8%,−4.7%, and −6.65%, respectively.In the meantime, all the BZT films are buffered by the 100-nm SRO electrode layer (≈ −2% misfit with BZT), which leads to a smaller misfit strain than the initial estimated ones: The lattice parameter of SRO is ≈4.0 Å in the 1800-nm BZT/LAO film, indicating that it is in a strained state (vs bulk SRO lattice parameter of ≈3.93 Å).The out-of-plane lattice parameters of the mixed R/T phases are calculated to be ≈4.200Å for the BZT film grown on the LAO substrate (the out-of-plane lattice parameters of the rhombohedral and tetragonal phases (c-axis) near the interface are calculated to be 4.210 Å and 4.190 Å, respectively), by using our previous published selected area electron diffraction (SAED) data. [9][22] This yields an effective substrate lattice parameter at the interface of ≈3.840 Å, which is a bit larger than that of the bulk LAO (3.790 Å).The in-plane strain for the tetragonal phase at the interface was computed to be ≈−3.7% by the same method using an estimated bulk tetragonal c-lattice parameter of ≈4.090 Å (computed from the XRD pattern of the thickest film grown on STO, i.e., 1.8 μm BZT on the substrate with the smallest misfit strain). [9]Based on the same effective substrate lattice parameter, the a-axis lattice parameter of the tetragonal phase was estimated: 3.840/(1-0.037)≈3.990 Å.The self-strain between a rhombohedral phase and a tetragonal phase is about (3.990-4.060)/4.060≈−1.7% in the BZT/STO films.The internal stress field is essential to create anisotropically-strained morphotropic nanodomains throughout the whole BZT bulk film.Similarly, the in-plane strains in the BZT films grown on the STO substrate decrease slightly from −3.8% to ≈−2.37% according to the (002) peak positions from the XRD −2 scan data. [10]The substrate and the film materials are both of the perovskite structure (ABO 3 ) and they have similar thermal expansion coefficients.We therefore neglected the thermal expansion mismatch. [22,23]o understand the phase segregated tetragonal and rhombohedral structures, we first measured SHG intensities in the reflection geometry.In our analysis, we assume that: (a) ferroelectric domains are much smaller (10-100 nm) than the wavelength of the second harmonic light (≈400 nm), and the incident probe size, such that one is truly averaging over many domains; (b) to calculate the total SHG intensity, the individual nonlinear polarization contributions are not correlated (no interference from multiple domains).Tetragonally strained domains with orientations along the film thickness are the dominant component of the reflected SHG.Rhombohedral polydomains predominate in the transmitted SHG signals.The SHG signal is free of artifacts arising from leakage current and electrostatic interference.Additionally, because the BZT films lack inversion symmetry and the SHG signals produced by the bulk are much larger than those produced by surface or interface nonlinear polarizations, the SHG responses at interface layers are ignored in our analysis to simplify the approximate model; (c) the SHG intensities generated by domain wall are mostly negligible due to its much smaller relative area fraction compared with domains.
Figure 3 shows the p-polarized ( = 0 • ) and s-polarized ( = 90 • ) SHG intensities as functions of the incident polarization angle for ferroelectric BZT thick films grown on various substrates.The reflected SHG signals (at a tilt angle of  = 45°) are clearly dominated by tetragonally strained domains oriented along the thickness of the film, i.e., z-axis.To assess rhombohedral signatures, we analyze the SHG intensities by the second-order susceptibility components,  zxx ,  xxz ,  zzz ,  xxy ,  yxx , and  yyy .The SHG intensity can be expressed as, where  (2)   eff is the effective nonlinear second-order susceptibility, F T and F R are the volume fraction of the tetragonal and rhombohedral domains, respectively.For the 3m symmetry, the SHG intensities, I 2 p−out (), I 2 s−out () can be expressed as functions of the polarization angle  of the incident pump pulses for an effective surface region [24] : where where L  and L 2 are the diagonal elements of the Fresnel transformation tensors regarding the fundamental and SHG light at frequencies  and 2, respectively.And  = 0°and  = 90°are for the p-polarized and s-polarized input laser light, respectively.For P-polarized SHG output: Rhombohedral phase: pp = 0 ( 8 ) The total p-polarized SHG output intensity is: With a p-polarized input laser light ( = 0°), we have: For S-polarized SHG output: 14) Rhombohedral phase: 16) The total S-polarized SHG output intensity is: With a p-polarized input laser light ( = 90°), we have: A straightforward method to measure the increase in rhombohedral characteristics within BZT films is by establishing the ratio between the second-order nonlinear susceptibility-induced SHG responses of rhombohedral and tetragonal phases: Figure 4 shows the ratio, R/T as a function of film thickness for the BZT films grown on the LAO, LSAT, and STO substrates.In all three BZT films, the rhombohedral susceptibility components ( xxy ,  yxx , and  yyy ) exhibit a positive correlation with the film thickness, and their contributions become more pronounced as the thickness increases.This demonstrates a lowering of structural symmetry as strain relaxations occur away from the film-substrate interface, introducing more elastic rhombohedral phases.The increase slopes of R/T ratios in Figure 4 reflect the distribution of interfacial strain field in the BZT films.The BZT/LAO system exhibits the lowest slope, indicating the slowest relaxation of strain within the BZT film layer.We observe the best energy conversion efficiency, ƞ in the 350-nm BZT/LAO film.The slow relaxation of interfacial misfit strain (≈−5.5%)explains well the fluctuations of ƞs for the BZT films, as the thickness of BZT layer is between 700-nm and 1800-nm, as shown in Figure 2a.In contrast, the magnitude of the slope for the R/T ratio is significantly higher in both the BZT/LSAT and BZT/STO films.However, both ƞ and W area are improved with a thicker BZT layer due  intensities as functions of the incident polarization angle were fitted according to the following equation [25][26][27] : 2,j sin 2 2,j sin 2 3,j sin 2 (2) For Equation 29, the subscript j denotes x = ⟨ 110⟩ or y = 〈110〉 to designate an analyzer output polarization angle of either  = − 45 o or + 45 o , respectively.The total dpolarized SHG intensity is expressed as an incoherent sum of polarization-resolved SHG intensities from rhombohedral domains throughout the bulk and rhombohedral domains near the surface in Equation 23a.Otherwise, some SHG intensity polar plots cannot be fitted without violating the important reciprocity condition, 2,y = 1. [28,29]In Equation 23b,c, The SHG detection geometry and film orientation are important factors for probing domain structures.The complex domain components and their distributions can be determined by an azimuth-polarization-dependent and tilting second harmonic generation measurements as previously discussed by Trassin et al., and Kumar et al. [30,31] The incident optical fields are orthogonal to the tetragonal polarizations ([ 100] and [100]) when the film is probed at normal incidence.The d-polarized SHG signals are therefore dominated by rhombohedral domains within a coherence length from the surface of the film and the d-polarized SHG intensities can be used as a tool for the growth of rhombohedral domains with increasing film thickness in BZT films. [32]igure 5 shows the sum of both d-polarized SHG maxima from rhombohedral domains.To demonstrate the relative changes in SHG values, a second Y-axis is incorporated to feature a distinct scale for BZT/STO.We show that the d-polarized SHG signal sum increases with increasing thickness of the BZT films in all BZT/LAO, BZT/LSAT, and BZT/STO films.The results agree well with the data shown in Figure 4.More elastic rhombohedral phases are introduced into the BZT film, while the interfacial strain relaxation occurs away from the film-substrate interface.We reveal that the d-polarized SHG intensity is the greatest in BZT/ STO, but the lowest in BZT/LAO.The highest and lowest degrees of bulk rhombohedral symmetry are consistent with the lowest and highest epitaxial misfit strains in the BZT/STO and BZT/LAO films, respectively.It is important to note that the increase of the d-polarized SHG signal lasts even in the 1800nm BZT films.This indicates that the strain field distributes along the microscale instead of the nanoscale due to the interfacial lattice mismatch.More importantly, the self-assembled, anisotropically-strained morphotropic nanodomains are generated by the difference of internal lattice misfit strains between the rhombohedral and tetragonal phases inside the BZT film.The internal strains are initiated by the interfacial lattice misfits between the BZT film and the substrate as we discussed above.The internal elastic strain between the two-phase phase boundaries prevents a fast relaxation of the film-substrate misfit, significantly delaying the saturation of the electric polarization.
The SHG results are further supported by XRD and transmission electron microscopy (TEM) data.The XRD patterns for the 1800-nm BZT films grown on LAO, LSAT, and STO substrates are shown in Figure 6.We observe the (100) diffraction peaks for both the bottom SRO electrode layer and the BZT film.The presence of mixed rhombohedral and tetragonal phases is clearly revealed in the broadening diffraction peaks near 44 o .The diffraction data from XRD patterns of the remaining films are summarized in Table 1 below.The BZT films have shown an epitaxial quality and the phases are mixed (labeled as "R") in all films except the 1.8 mm film on STO, which shows split diffraction peaks for the T and R phases.The residual strains are well correlated with the substrate ("initial strain") and film thickness (relaxed with an increasing thickness).The mixed rhombohedral/tetragonal phase structure in the BZT films is consistent with the reciprocal space mapping (RSM) as we previously discussed. [10]The RSM analysis of the 1250 nm thick BZT/STO film distinctly revealed the observable split peaks originating from the (103) plane due to the rhombohedral and tetragonal phases, respectively (figure S3 in Ref. [10]).The phase entangled tetragonal and rhombohedral domains are also demonstrated in the TEM images for the same 900-nm BZT/STO film as shown in Figure 7.The internal elastic strain induced columnar microdomains (fish bone structures) are clearly observable along the thickness direction of the BZT film.The embedded tetragonal domains within the rhombohedral polytwins are consistent with previous reported TEM diffraction results in the 900nm BZT film. [9,10]We further take the low mag.TEM image from the "fish bone" regions as shown in Figure 7b.Analysis of the domain structure in the figure reveals the {101} type of domain boundary in the "fish bone" structure, which indicates a rhombohedral symmetry and a second-order domain structure as discussed. [9]For the regions corresponding to these "fish bone" like R-domains, we performed higher resolution TEM analyses.The result is shown in Figure 7c.We confirmed that these regions are of both tetragonal and rhombohedral symmetries from the FFT-SAED analyses.This is consistent with our previous HAADF-STEM (atomically resolved) analyses of the BZT films.As indicated in Figure 2b of Ref. [10], the T-like and R-like polar structures as well as their phase boundaries were determined according to the projected displacements of the B-site cations relative to the centers of the perovskite unit cells on the {100} plane.The R-phase is a single-variant rhombohedral domain with a {111} polar vector while the T phase shows (001) ("Ta") and (100) ("Tc") polar vectors.
In the absence of an interfacial misfit strain, BZT exhibits rhombohedral (3m) symmetry.The compressive misfit strain from the substrate squeezes the in-plane lattice, inducing the formation of columnar, tetragonal domain structures with polar axes parallel to the [100] direction.These strain-induced tetragonal domains relax with increasing film thickness and columns of rhombohedral polytwins form along the thickness direction.Both microscale and nanoscale rhombohedral domains are identified from TEM imaging, and they are mixed in with tetragonal nanodomains away from the substrate.In addition to the interfacial strain between the substrate and BZT film, the elastic internal strains arising from the displacement of the nanoscale morphotropic-like phase boundary are essential to maintain the strain field through the microscale BZT films.During application of an electrical field, these mixed polydomain nanostructures progress from their remnant, neutral state to a poled, charged state.Polarization saturation is delayed while the electrical field is unable to overcome the elastic energy barriers between elastic rhombohedral domains.Since breakdown typically occurs after saturation of the dielectric polarization, higher breakdown electrical fields are achieved, and thus higher electrical energy densities can be stored in the films.In addition to delaying polarization saturation in these films, lower remnant polarizations are also achieved due to the low self-strain of elastic rhombohedral polytwin domains. [9,10]Having a low self-strain allows these domains to self-assemble in a "head-to-tail" polar ordering which promotes electroneutrality within the film, thus lowering the remnant polarization without an external field as the schematic shown. [9]The self-strained polar ordering induces the low remnant polarizations, which ultimately increases the energy storage efficiency of the BZT films.

Conclusion
The heterophase polydomain nanostructures in BZT films are optimized by the film-substrate interfacial misfit strains for superior energy storage performance.High energy storage densities (up to 166 J cm −3 ) and recycling efficiencies (up to 96%) have been demonstrated in the BZT films with a thickness from 350 to 1800 nm grown on LAO, LSAT, and STO substrates.We utilized the polarization resolved SHG to probe the revolution of tetragonal and rhombohedral domains in both reflection and transmission geometries.We reveal that the distribution of interfacial strain field relaxes rapidly in BZT/LAO due to a large lattice misfit, and the best performance in ƞ and W area is achieved in the 350-nm BZT/LAO film.In contrast, both ƞ and W area are improved with a thicker BZT layer (up to 1800-nm) in BZT/LSAT and BZT/STO with a moderate interfacial misfit strain.We show that the strains can be imparted into the BZT films through differences in lattice parameters and control the internal phase boundaries between different domains.The interfacial strains accommodate the competing elastic and electrical stress fields to intro-duce the self-assembled, anisotropically-strained morphotropic nanodomains, which maintain the strain field distribution in the microscale.The phase entangled nanodomains can be used as a tool to effectively engineer the polydomain structures for optimizing the performance in energy storage of BZT films.

Figure 1 .
Figure 1.Schematics for the polarization-resolved SHG detection in the a) reflection and b) transmission geometry.Focusing lenses are marked as L1, L2, and L3.A band-pass filter (BPF) is used to block fundamental light from entering the photomultiplier tube (PMT).A long-pass filter (LPF) is placed before the sample to filter out any SHG light arising from the laser system and prior optical components.An initial polarizer (POL) is used to ensure that the fundamental light is linearly polarized before being rotated by a half-wave plate (/2).The second polarizer (POL) acts as the analyzer for selecting specific SHG polarization orientations.

Figure 2 .
Figure 2. a) Storable areal energy densities and charge-discharge efficiencies of the BZT films grown on LAO, LSAT, and STO substrates of 350-1800 nm thickness.The error for these measurements is no more than 3% of the shown values.b) P-E hysteresis loops for the BZT/SRO/STO films of thickness ranging from 350 to 1800 nm.

Figure 4 .Figure 5 .
Figure 4. Ratio between rhombohedral and tetragonal susceptibility components as a function of film thickness for BZT grown on LAO (3.790 Å), LSAT (3.870 Å), and STO (3.905 Å).SHG signals in the reflection geometry at  = 45 o are predominantly from tetragonal phases.Dashed lines show the increasing rhombohedral signature trend.

Figure 6 .
Figure 6.a) XRD −2 scan of the three thickest BZT films (1.8 mm) grown on LAO, LSAT, and STO substrates, b) representative Φ-scan pattern of the (001) oriented BZT film (using data from the 1800 BZT film grown on LAO).

Figure 7 .
Figure 7. a) A cross-sectional bright field TEM image of the 900 nm thick BZT/STO film, showing columnar rhombohedral microdomains along the thickness of the film; b) TEM image of the "fish bone" regions showing the local symmetry of the mixed phases c) Magnified TEM imaging of tetragonal (1) and rhombohedral (2) domain morphologies in the BZT/STO film.The FFT-SAED images distinctly unveil the presence of tetragonal and rhombohedral symmetries, respectively.

Table 1 .
Lattice parameters of the (001) BZT films grown on LAO, LSAT, and STO substrates.