Geometric defects induced by strain relaxation in thin film oxide superlattices

Realizing engineered composite functional materials that are stable in extreme environments such as high temperature or oxidizing conditions is a key challenge for many applications. Engineered nanocomposite structures, such as nanoparticle matrices, vertically aligned nanocomposites, and superlattice heterostructures have many unique and exotic properties.¹ These include multiferroic properties,^2,3 negative capacitance,⁴ and directional emission,^5,6 as well as many other emerging functional properties.^7–11 For example, spectral control over thermal emission at high temperatures can unlock high operating efficiencies in thermophotovoltaic systems.¹² Such thermo-optic properties may require multilayer heterostructures or superlattices,^13,14 especially those that are crystalline, as they can exhibit novel transport and optical properties in the out-of-plane direction. The production of highly crystalline, photonic superlattices that are stable at high temperature, however, requires lattice and thermal expansion matching, refractive index mismatching, and immiscibility between the constituent materials. This greatly limits the number of available configurations.¹⁵ In particular, for high temperature applications, heterostructures of materials have significant issues with grain growth, thermal stresses, delamination, oxidation, and intermixing.^16,17

Here, we consider thin film superlattices of Ba(Zr_0.5Hf_0.5)O₃/MgO deposited on MgO (001) substrates heated to 700 °C. In our prior work, we developed a high throughput screening method for superlattice oxide pairs based on parameters obtained from materials project such as lattice matching, differing crystal structures, and thermal expansion.¹⁸ This was done to minimize differential thermal strain and to reduce the likelihood for intermixing of the two materials. In that work, it was found that Ba(Zr_0.5Hf_0.5)O₃/MgO superlattices were stable up to 1100 °C in dry air, to our knowledge, the highest temperature currently achieved, and demonstrated tunable spectral selectivity. However, achieving stability and enhanced performance above 1100 °C was challenged by the emergence of a secondary ZrO₂ type phase.

In this work, we report on geometric defects that emerge from overgrowths due to a strain relaxation mechanism¹⁹ in Ba(Zr_0.5Hf_0.5)O₃/MgO superlattice deposited by pulsed laser deposition. Once nucleated, the defect grows in volume through the surface of the crystal. It retains the superlattice structure but is spatially out-of-phase with the bulk matrix. The three-dimensional structure of these defects is shown to be an inverted pyramid. With in situ high temperature transmission electron microscopy, it is observed that these defects serve as the nucleation point for decomposition of the perovskite Ba(Zr_0.5Hf_0.5)O₃ into a (Zr_0.5Hf_0.5)O₂ phase and destruction of the superlattice structure at high temperature.

Alternating thin films of ∼4 nm BaZr_0.5Hf_0.5O₃ (BZHO) and ∼4 nm MgO were deposited by pulsed laser deposition onto a 5 × 5 mm² (001)-oriented MgO substrate (see Sec. IV for more details) from 8 up to 18 bilayers. Single layer BZHO films of ∼200 nm thickness were deposited similarly. Scanning electron microscopy (SEM) was used to determine the surface morphology and growth mode of the superlattice. <100>-orientated quadrate islands, averaging ∼100 nm in length and at a density of ∼70 per μm², are observed on the surface of the thick BZHO single layer film [Fig. 1(a)].

Moving to superlattice samples, a systematic change in the surface defect morphology, density, and size occurs with an increase in the number of bilayers. In the 8 N (eight bilayers) sample [Fig. 1(b)], multiple types of surface defects are observed. In a top-down view of the sample, these defects appear as quadrates, equilateral triangles, and isosceles triangles, orientated almost entirely along <100> and <110> directions for the quadrates and isosceles triangles, respectively. The size and density of triangular-plane surface defects is observed to generally increase as the number of bilayers increases in the samples shown in Figs. 1(b)–1(d). Only triangular-plane defects are observed on the surface of the 12 N [Fig. 1(c)] and 16 N [Fig. 1(d)] samples. We hypothesize that this is because the quadrate surface defects evolve during growth into these more complex defects as more layers are added. As well as being seen in top-down SEM, some of these surface defects have been observed in cross section using transmission electron microscopy (TEM) and are shown in the supplementary material (Figs. S1a and S1b). These defects are 10–50 nm in height depending on defect morphology type and appear to retain the superlattice structure.

Figure 1(e) shows a representative 2θ − ω x-ray diffraction (XRD) pattern of the as-synthesized superlattices around the MgO 002 peak. Provided the layers in the superlattice are thin and smooth enough, the interfaces act like additional scattering centers, resulting in satellite peaks around an average 2θ − ω XRD diffraction peak for the constituent materials.²⁰ The XRD pattern shows clear satellite peaks out to second order indicating well defined superlattice structure. Secondary or polycrystalline peaks are not present in the full range x-ray diffraction pattern and indicate that misoriented surface defects represent a small volume fraction of the sample. Further, Fig. 1(f) shows a reciprocal space map for a 14 bilayer superlattice sample also about the MgO 202 peak. Again, there is no indication of defect regions, and the Q_x value of the film 202 peak suggests that the film is partially relaxed from the substrate.

TEM was used to investigate the origin and evolution of the defects in the bulk of the superlattice structure. Figure 2(a) shows a large-scale view of a 10 N superlattice while Fig. 2(b) shows a more detailed view of a defective region. Clear structural defects are observed that start in the bulk, grow in size along a facet toward the film surface, and result in the surface defects observed in Figs. 1(b)–1(d). Defect-free interfaces are observed until the third BZHO layer of the superlattice, ∼16 nm or 40 monolayers of BZHO and MgO. In the third BZHO layer, nucleation of defects is observed. Using a simplistic model, the equation for critical thickness is given below:²¹ 

where a_s is the substrate lattice parameter and a_f is the film lattice parameter. Using a_BZHO ≈ 4.18 Ź⁸ and a_MgO ≈ 4.21 Å, the critical thickness is estimated as 30 nm for a BZHO film on MgO. Considering that this simplistic model is typically an overestimate, this agrees reasonably with what is observed in TEM for BZHO/MgO bilayers and suggests that these defects occur beyond the critical thickness, possibly as a result of misfit dislocations.

In the thick (∼200 nm) BZHO films, these overgrowths are clear on the surface as quadrate protrusions. However, in the superlattice structure, soon after the first islands form, the growth is terminated and an MgO layer is grown over it. We hypothesize that this leads to the overall defect structure in a way akin to layering a fabric over an uneven surface; with the bump increasing in size with each layer of fabric that is added. From Fig. 2(b), it is clear that there is an initial overgrowth in the third BZHO layer of the superlattice, as indicated by Z contrast, and is consistent with the islands observed in the thick BZHO film in Fig. 1(a). This eventually progresses into an inverse-pyramidal structure, which can be observed both in cross section [Fig. 2(b)] and on the surface of these superlattice samples [Figs. 1(b)–1(d)]. This progresses symmetrically at 30° from the growth direction (60° total angle). However, no difference in nanobeam electron diffraction is observed in these regions. In these regions, the superlattice appears to be offset by half a period but preserved, explaining why there is no clear evidence of these defects in diffraction.

Figure 2(c) shows the Mg, Ba, Zr, and Hf concentrations as measured by TEM EDS for the region in Fig. 2(b). Figures 2(d) and 2(e) compare a composition linescan through a regular, defect-free superlattice region and through a geometric defect, respectively, along the growth direction. The defect begins with an ∼8 × 3 nm overgrowth of BZHO from the third superlattice layer. This is seen as a bump in the Ba, Zr, and Hf concentrations and a commensurate dip in Mg concentration, seen in the EDS analysis in Fig. 2(e). A sine curve is overlaid with the net intensity of the elements along with the HAADF, to help show the disorder that is present due to the overgrowth, compared to Fig. 2(d) which passes through a defect-free region. Although the layers are shifted, these defects do not form due to composition inhomogeneities.

By comparing TEM cross sections along the <100> and <110> directions, which reveal a different faceting angle (Fig. 2 in the supplementary material), these 3D geometric defects appear pyramidal in nature. This is supported by atom probe topography (APT) measurements shown in Figs. 3(a) and 3(b). There is a clear triangular outline to the overall defect in two arbitrary views at 90°. Additionally, Fig. 3(a) shows a clear rectangular protrusion in the fourth BZHO layer from the substrate, which corroborates our findings from TEM [Fig. 2(b)]. This follows logically from the hypothesis that the quadrate protrusions act as the origin of these geometric defects. This also shows a bump in the third BZHO layer initiating the growth of the geometric defect, confirming what was observed in the TEM HAADF images. This then leads to an antiphase region, where the superlattice is shifted up approximately half a layer compared to a normal region. Figures 3(a) and 3(b) also appear to show regions of high Mg concentration in the BZHO layers around the edge of the defect structure. We believe that these regions may be able to act as diffusion channels, hence the high Mg concentration. There are already reports of extended defects such as misfit dislocations acting as easy diffusion paths in superlattice materials due to lower barriers to diffusion.²² 

The consequences of these defects on the stability of the superlattice were investigated using in-situ high temperature TEM. A 14 N bilayer sample was rapidly heated in vacuo to 1000 °C. Figures 4(a)–4(f) show the progression of degradation at the thinnest end of the cross section over ∼2 min. From this, degradation progressed from the thinnest region (at the right of the image), starting with the decomposition of BZHO into (Zr_0.5Hf_0.5)O₂, occurring at the third bilayer and beyond, consistent with the defects observed in Fig. 2. This decomposition causes the upper layers of the superlattice (around these defects) to degrade, while the lower layers are initially preserved. This is confirmed by elemental analysis on a region post-decomposition and cooling [shown in Figs. 4(g) and 4(h)], which shows an absence of Ba outside the superlattice regions. Decomposition seems to occur due to the loss of Ba and since the initial onset is at these defects, these observations support our hypothesis that the Mg-rich defect edges act as diffusion pathways. The survival of the remaining undamaged superlattice structure in Fig. 4(h) following heating at 1000 °C indicates that MgO and BZHO are highly immiscible, consistent with our prior findings.¹⁸ We hypothesize that this immiscibility contributes to the formation of the geometric defects. When layering each material, they are unable to mix to resolve the strain induced by the protrusion in the underlayer.

Using superlattices of BZHO/MgO, we show that under non-ideal conditions, small overgrowths that occur due to a strain relaxation mechanism can develop into complex inverse-pyramidal defects. These defects act as the limiting factor for thermal stability in vacuo, by being a nucleation center for decomposition of the superlattice. In addition, these superlattice defects express themselves on the surface as triangular based defects, resulting in an increased surface roughness. This work highlights the importance of optimum conditions for producing high-quality, geometric defect-free oxide thin film superlattices for optimal thermal stability and functional properties.

MgO and BaZr_0.5Hf_0.5O₃ (BZHO) targets were obtained from Kurt J. Lesker Co. Films were deposited on (001)-oriented MgO substrates by ablation from a 248 nm KrF laser fired at 6 Hz and 1.1 J cm⁻² for the BZHO target and 5 Hz, 1.8 J cm⁻² for the MgO target with a spot size of ∼0.05 and ∼0.11 cm², respectively. The substrates were baked at 950 °C in base vacuum for 20 min prior to being held at 700 °C in 100 mTorr of O₂ throughout the deposition. The substrate–target distance is 7 cm. Following the deposition, 2θ − ω x-ray diffraction scans were performed with a Rigaku Smartlab diffractometer, using a 1.54 Å Cu Kα source, a Ge 220 monochromator, and parallel beam geometry. For the reciprocal space maps, a Ge 220 analyzer was used on the detector side.

High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images and energy dispersive x-ray spectroscopy (EDS) data were collected using a Thermo Fisher Scientific Talos F200X G2 S/TEM operated at 200 kV and equipped with a Super-X EDS detector. High temperature TEM was performed using a Protochips Fusion Select holder with the sample deposited on a “Vacuum Only, Carbon Coated MEMS” chip, to a max temperature of 1000 °C at a rate of 100 °C/min; image series were recorded at 3 Hz for ∼60 min. Cross-sectional TEM samples were prepared by focused ion beam (FIB) lift-out on a Thermo Fisher Scientific Helios G4 DualBeam system equipped with a Xe-plasma ion source. Scanning electron microscopy (SEM) images were also obtained using a Thermo Fisher Scientific Helios 650 Nanolab operated at 2 kV. The APT volumes were prepared by a standard FIB lift-out also using the Thermo Fisher Scientific Helios 650 Nanolab. Analysis was done in a Cameca LEAP 5000 XR Atom Probe.

See the supplementary material for additional cross-sectional transmission electron microscope imaging of surface and bulk defects.

This work is supported by the Department of Defense, Defense Advanced Research Projects Agency under Grant No. HR00112190005. The views, opinions, and/or findings expressed are those of the authors and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government. The authors acknowledge the financial support of the University of Michigan College of Engineering and technical support from the Michigan Center for Materials Characterization.

The authors have no conflicts to disclose.

Matthew Webb: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Tao Ma: Formal analysis (supporting); Investigation (supporting); Visualization (supporting); Writing – review & editing (equal). Allen Hunter: Investigation (supporting); Software (supporting); Visualization (supporting); Writing – review & editing (supporting). Sean McSherry: Conceptualization (supporting); Methodology (supporting); Writing – review & editing (supporting). Jonathan Kaufman: Methodology (supporting); Writing – review & editing (supporting). Zihao Deng: Writing – review & editing (supporting). William Carter: Methodology (supporting); Project administration (supporting). Emmanouil Kioupakis: Funding acquisition (supporting); Writing – review & editing (supporting). Keivan Esfarjani: Funding acquisition (equal); Writing – review & editing (supporting). Andrej Lenert: Funding acquisition (equal); Project administration (equal); Writing – review & editing (supporting). John T. Heron: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.