Depolarization field tuning of nanoscale ferroelectric domains in (001)PbZr_0.4Ti_0.6O₃/SrTiO₃/PbZr_0.4Ti_0.6O₃ epitaxial heterostructures

The last decade has seen a tremendous surge in the interest in understanding non-trivial topologies in nanoscale ferroelectrics.^1–3 These include vortices,^4,5 antivortices,⁶ bubble domains,¹ and flux-closure domains.³ The presence of such topological defects is attributed to the interplay between various competing factors, e.g., the mechanical and electrical boundary conditions,^1,2,7,8 composition inhomogeneity,^2,5,8 and flexoelectric effects.^3,9 A common feature of such complex ferroelectric topologies is that the ultimate polarization configuration adopted by the ferroelectric system is driven by the magnitude and direction of the residual depolarization field.^10–15 Specifically, in ultrathin heterostructures, the depolarization field is known to strongly influence polarization stability and hence engender emergent domain structures¹⁵ and the corresponding ferroelectric characteristics, such as electromechanical response,¹⁶ imprint,^17–19 and coercive voltages.^19–21 

The remarkable progress made in the fabrication of high quality heterostructures and superlattices with atomically sharp interfaces²² has allowed in-depth investigation on the effects of depolarization field.¹⁶ While it is conventionally tailored by changing the ferroelectric layer thickness,^23–26 a recently adopted approach is by depositing a dielectric spacer within the ferroelectric film.^15,19,27 For example, the introduction of an SrTiO₃ layer modifies the screening at the interfaces and hence influences the depolarization field.¹⁵ The latter, in turn, affects parameters such as the coercive voltage, imprint, and the domain nucleation time.¹⁹ 

In this report, we exploit the spacer approach and vary the thickness of each ferroelectric layer to tune the depolarization field in (001) ultrathin PbZr_0.4Ti_0.6O₃/SrTiO₃/PbZr_0.4Ti_0.6O₃ (PZT/STO/PZT) sandwich heterostructures and investigate how their domain configuration, polarization stability, and switching behavior are affected. Here, the thickness of the STO spacer is maintained at 2 unit cells (u.c.) for all samples, while the thickness of each PZT layer is systematically decreased from 15 nm (PZT-15), to 13 nm (PZT-13), 9 nm (PZT-9), and 8 nm (PZT-8) by tuning the number of laser pulses in the pulsed laser deposition (PLD) process. High-resolution x-ray diffraction (XRD) demonstrates that this decrease in the PZT layer thickness drives a moderate change in the mechanical boundary conditions, going from a fully relaxed state (PZT-15) to partially in-plane compressive strained states (PZT-13, PZT-9, and PZT-8). This decrease in the PZT layer thickness results in an increase in the depolarization field, which manifests itself as changes to the domain morphology, viz., a decrease in domain wall length and domain size. Piezoresponse force microscopy (PFM) investigations demonstrate a domain transition from continuous labyrinthine²⁸ domains for samples with thicker PZT layers (15 nm and 13 nm) to disjointed and individual nanoscale domains for samples with thinner PZT layers (9 nm and 8 nm). A fractal dimensionality has been observed for the domains, at all thicknesses. The local coercive voltage measured by switching spectroscopy piezoresponse force microscopy (SSPFM) is found to be linked with the depolarization field-induced changes to domain wall features (i.e., length and roughness). Hence, there is a complex interplay between various ferroelectric factors such as depolarization field, coercivity, domain wall roughness, and tetragonality. A thorough understanding of the combined effect of these features will aid the design of ultrathin ferroelectric films with emergent topological properties.

Epitaxial PbZr_0.4Ti_0.6O₃/SrTiO₃/PbZr_0.4Ti_0.6O₃ (PZT/STO/PZT) heterostructures were grown on a 35 nm thick La_0.67Sr_0.33MnO₃ (LSMO) bottom electrode buffered (001) STO substrates (Shinkosha, Japan) by PLD (Neocera, USA). The deposition temperature for the LSMO, PZT, and STO layers was 800 °C, 700 °C, and 700 °C, respectively. During ablation, the oxygen pressure was kept at 100 mTorr for LSMO, 50 mTorr for PZT, and reduced to 20 mTorr for STO. After deposition, the films were cooled to room temperature at a rate of 20 °C/min in an oxygen atmosphere of 450 Torr. Care was taken to maintain the effective laser energy (at the target location) constant for each layer [i.e., 77 mJ (LSMO), 87 mJ (PZT), and 70 mJ (STO)] for all the depositions.

The crystallographic structure and strain conditions of the PZT/STO/PZT sandwich heterostructures were investigated by analyzing θ–2θ x-ray diffraction patterns (SmartLab, Rigaku, Japan) and reciprocal space mapping (PHILIPS X’Pert PRO Materials Research Diffraction system, Malvern Panalytical, Netherlands). The thickness of each individual layer was estimated by fitting the θ–2θ patterns in a custom-made MATLAB fitting program.²⁹ The number of laser pulses for LSMO and STO layers was kept constant at a value of 20 000 and 390, respectively. This results in fixed thicknesses for LSMO (35 nm) and STO layers [2 unit cells (u.c.)] in all samples, whereas the thickness of each individual PZT layer is reduced from 15 nm to 8 nm. Table I lists the detailed configuration of all samples.

Surface topography and ferroelectric domains were investigated by atomic force microscopy (AFM) and dual AC resonance tracking (DART) piezoresponse force microscopy (PFM), respectively, on a commercial scanning probe microscope (Cypher S, Asylum Research, USA). During scanning, an AC bias of 0.3 V at ∼350 kHz was applied to the Pt/Cr coated conductive probes (ElectriMulti 75G, BudgetSensors, Bulgaria), which have an average radius of <25 nm. Switching Spectroscopy Piezoresponse Force Microscopy (SSPFM) was performed to acquire piezoresponse-voltage hysteresis loops using a 0.2 Hz, 4 V peak–peak triangle pulse bias function.

Figure 1(a) shows the schematic of the PZT sandwich heterostructures and the variation across the sample series—only the PZT layer thickness changes between 8 nm and 15 nm, while thicknesses of the LSMO layer and the STO spacer stay constant. Figure 1(b) plots the XRD θ–2θ patterns of these samples around the (002) reflection. The presence of only (0 0 2) peaks (corresponding to the PZT, STO substrate, and LSMO from left to right) in the 2θ range of 40°–50° shows no evidence of PZT in other orientations, nor secondary phases.

These θ–2θ scans were fitted using a custom-made MATLAB programme²⁹ to estimate the thickness of each individual layer (Table I) and confirm their corresponding out-of-plane lattice parameter. The details of the fitted graphs are given in the supplementary material (S1–S3). The out-of-plane lattice parameter of the LSMO layer is constant at 3.85 Å for all samples. This is below its bulk value (c lattice parameter of bulk LSMO is 3.89 Å), consistent with the LSMO layer being under in-plane tensile strain, as expected. On the other hand, the out-of-plane lattice parameter for the PZT layer varies among the samples, as evidenced by its (002) peaks which shift toward a lower 2θ value with decreasing PZT thickness. In PZT-15, the out-of-plane lattice parameter is equal to the bulk lattice parameter at a value of 4.12 Å.³⁰ In other samples, this parameter is increased to 4.13 Å, suggesting that the PZT layer changes from a state of full relaxation (PZT-15) to partial in-plane compressive strain (PZT-8, PZT-9, and PZT-13). Note that the out-of-plane lattice parameter of STO is found to be 4.00 Å for thicker samples (PZT-15 and PZT-13) and 4.02 Å for thinner samples (PZT-9 and PZT-8). These values are much larger than that of bulk STO (i.e., 3.905 Å). This has been previously attributed to an induced polarization in the STO layer.^1,19

Figures 1(c)–1(f) are the asymmetric (103) reciprocal space maps (RSMs) of the sample set. They show the crystal truncation rods (CTRs) for the LSMO layer and the STO substrate align perfectly with each other along the Q_x (horizontally) direction for all films. This proves a pseudomorphic growth of the LSMO layer on the STO substrate. In contrast, the CTRs for the PZT layers take Q_x values lower than those of LSMO and STO. This is a result of the strain relaxation between the PZT and LSMO layers ascribed to a higher theoretical misfit between PZT and STO, i.e., 1.92% (using bulk lattice parameter, a, of PZT to be 3.98 Å).³⁰ The Q_x value increases (and Q_y value decreases) with decreasing PZT thickness, and this corresponds to an increase in the tetragonality of PZT. This confirms the change from fully relaxed to partially in-plane compressive strained condition with decreasing PZT thickness, as depicted already by the normally coupled θ–2θ scans [Fig. 1(b)]. The lattice parameters of PZT and LSMO layers for each film obtained from the above XRD and RSM analysis are summarized in Table II.

Next, the ferroelectric domain patterns of each film are studied using a high-resolution PFM technique to map the effect of the change in electrical boundary conditions. Figures 2(a)–2(h) show the amplitude and phase images, where the dark purple and yellow contrasts in the phase images indicate upward and downward domains, respectively.

For the films with thicker PZT layers (i.e., PZT-15 and PZT-13), labyrinthine structures of upward polarization are observed [Figs. 2(a), 2(b), 2(e), and 2(f)]. As the thickness of the PZT layer is decreased, there is a moderate change in the epitaxial strain conditions. However, the PZT layer is subject to a significantly increased depolarization field. Now, we have two competing effects: (i) the in-plane mechanical (or epitaxial) compressive strain (which stabilizes the out-of-plane polarization component and, in turn, favors a longer c axis) and (ii) the depolarization field, which acts to suppress the out-of-plane polarization (and hence shorten the c axis) to minimize the electrostatic energy costs.^24,31,32 As a result, the depolarization field for such thinner PZT films (i.e., PZT-9) drives the breakdown of labyrinthine domains into uniformly distributed disjointed nanodomains¹⁵ [Figs. 2(c) and 2(g)]. When the PZT thickness is reduced to 8 nm, ultrafine nanoscale domains are observed [Figs. 2(d) and 2(h)]. Note these nanoscale domains can only be distinguished from their darker amplitude contrast as their phase contrast becomes blurry. Our reports have shown this to be a signature of bubble domains with Néel and Bloch type domain walls;¹ thus, we ascribe these features to be bubble domains.

With respect to the domain polarization, Fig. 2(i) statistically summarizes the ratio of upward/downward domains among all samples. The colors in the bar chart correspond to the contrast of PFM phase images. In PZT-15 and PZT-13, the upward polarized labyrinthine domains cover 36 ± 5% and 38 ± 8%, respectively, with a dominant downward polarized matrix. This preferential downward polarization occurs due to a mismatch in the valence band at the bottom ferroelectric/electrode interface.³³ With the change in nanoscale disjointed domain patterns, the upward domain portion reduces dramatically to 8 ± 2% for PZT-9 and 5 ± 2% for PZT-8. This shift in favored polarization distribution is often linked with a variation in the defect accumulation at the top and bottom interfaces, which is manifested as a change in the magnitude of the built-in field.^18,34

Next, SSPFM hysteresis loops of different samples are acquired to understand how the switching behavior changes with the PZT layer thickness and domain patterns (Fig. 3). Note that the large error bars occur as the coercive voltage value varies at different areas of the film due to the highly localized nature of SSPFM as a measurement technique. Statistical measurements have been carried out to obtain reliable coercive voltage values. The coercive voltage, V_c (2V_c = |V⁺| + |V⁻|) peaks for PZT-13 at 2V_c = 3.8 ± 0.3 V. When the PZT layer thickness is less than 13 nm, the 2V_c value decreases to 3.5 ± 0.6 V for PZT-9 and 2.5 ± 0.6 V for PZT-8. This decrease in the coercive voltage is attributed to the decrease in volume to be switched and an additional contribution by the depolarization field as a result of polarization instability.³⁵ 

On the other hand, the PZT-15 film shows, anomalously, the lowest coercive voltage at 2V_c= 2.6 ± 0.1 V, despite being the thickest of the sample series. Although Fig. 3 plots voltages, the combined effect of the lowest coercive voltage and the highest thickness implies that the PZT-15 has the lowest coercive field. At this thickness, the depolarization field becomes less significant and other contributions become prominent. According to Merz's law,³⁶ domains nucleate at a rate exponential to the activation field. This activation field that depends on the domain wall energies also increases with tetragonality.³⁷ Despite having similar domain patterns, PZT-15 has a smaller tetragonality as compared to PZT-13, which contributes to the low coercive voltage in PZT-15. In addition to the film thickness, tetragonality, and depolarization field, the coercive voltage can also be strongly affected by the characteristics of domain walls.^38,39 Therefore, we next investigate how the domain features (domain size, domain wall length, and domain wall roughness) vary with the change in the ferroelectric layer thickness.

The domain configurations and the corresponding switching behaviors in ferroelectric thin films and nanostructures, which are often determined by the domain (volume) and domain wall (surface)⁴⁰ energy parameters, hinge on the mechanical and electrical boundary conditions. To better explain the above observations, the relationships between domain size/domain wall length and PZT thickness/boundary conditions are carefully investigated using WSxM software.⁴¹ 

The domain fraction (upward domains) and the domain wall length of the PZT/STO/PZT films (in a 1 × 1 μm² area) vs thickness of the PZT layer are compared in Fig. 4(a). The inset shows the correlation between domain fraction and domain wall length for each sample. Here, the domain fraction is obtained by calculating the statistical average of the ratio of area with upward polarization to total area (i.e., 1 × 1 μm²), and domain wall length is the total wall length separating upward and downward phase.

With PZT layer thickness decrease from 15 nm to 8 nm, two main effects, namely, domain breakdown and domain shrinking, contribute to the domain transition. From PZT-15 to PZT-13, the upward domain fraction remains at a relatively constant value, while the domain length sum increases. This marks the initial breakdown of labyrinthine domains in PZT-15, where the decrease in individual domain size is negligible but the domain density increases [see the supplementary material (S5) for a schematic]. In thinner films (i.e., PZT-9 and PZT-8), where the depolarization field is stronger, PFM images suggest that the effect of domain shrinking becomes prominent with the nanoscale domain fraction of only 8% for PZT-9 and 5% for PZT-8. Table III describes the domain transitions as a function of PZT film thickness.

Further, statistical analysis of the individual domains [Fig. 4(b)] reveals that both domain size (area) and domain wall length of individual domains demonstrate a declining trend with decreasing PZT layer thickness. It is worth mentioning that the range of both individual domain area/domain wall length (as depicted by the error bars) reduces with decreasing PZT layer thickness [Fig. 4(b)]. For example, PZT-15 has larger error bars as compared to PZT-8 because it contains a wide spread of domains of varying sizes (sub-50 nm² to 0.6 μm²) and lengths (sub-20 nm to 5 μm). This observation shows that the domains tend to shrink toward a more homogenous configuration with an increase in depolarization field.

Next, the fractal dimensionality was calculated for all samples using the relationship between domain size and domain wall length, i.e., $P∝AH||2$⁠, where P is perimeter (individual domain wall length), A is individual domain area, and $H||$ is in-plane Hausdorff dimension of the domain walls.⁴² The $H||$ values are extracted from the slope of log(A)–log(P) plots for each sample [Fig. 4(c)], and the in-plane Hausdorff dimension values at different thicknesses are plotted in Fig. 4(d). When $H||=1$⁠, it signifies that the domains are completely smooth, else $1<H||<2$ indicates fractal dimensionality as well as a degree of domain wall roughness⁴² and this represents the spatial disorder.^43,44

Of the four systems’ studies, both the PZT-15 (with labyrinthine domains) and the PZT-9 (with disjointed domains) show relatively smaller $H||$ and thus smoother domain walls compared to PZT-13 (with labyrinth-disjointed transition domains) and PZT-8 (with the bubble domains). These domain wall features (i.e., length and roughness) can also explain the switching behavior discussed in Fig. 3. Previously, it was shown that 90° domain walls promote 180° domain switching by acting as preferred nucleation sites.^45,46 On the other hand, the defects, trapped at domain walls, can also result in random field disorder(so-called pinning potential), which can be manifested as an increase in domain roughness³⁸ and switching threshold. Recall that the coercive voltage of PZT-15 (2V_c = 2.70 V) is much lower than that of PZT-13 (2V_c = 3.84 V). Hence, the anomalously low coercive voltage of PZT-15 can now be fully explained; it is the combined effect of a low tetragonality, which reduces the switching barrier and smooth domain walls, that result in lower pinning sites.³⁹ In contrast, the higher domain wall roughness of PZT-13 possibly stems from the pinning sites. This could hinder local domain switching and thus explain its higher coercive voltage.

In summary, we report the ferroelectric domain evolution from labyrinthine to nanoscale disjointed domains in (001) ultrathin epitaxial PbZr_0.4Ti_0.6O₃ sandwich heterostructures, driven by the depolarization field. This is due to the combined effect of the presence of a dielectric spacer, i.e., 2 unit cells of STO, and thickness variation of the PZT layer from 15 nm to 8 nm. The coercive voltage is found to be dependent on both tetragonality and domain wall features (i.e., length and roughness). This study thus successfully links the interplay of ferroelectric film thickness, depolarization field, domain pattern, domain wall features, and switching behaviors in PZT/STO/PZT sandwiched structured films. These results should guide further experiments focused on manipulating topological transitions in ultrathin ferroelectric heterostructures.

See the supplementary material for the detailed structural data of the analyzed samples (XRD fittings along with the fitted lattice parameters and thicknesses, reciprocal space maps depicting a possible tilt) and a schematic depicting the domain transition.

The research was supported by DARPA under Grant No. HR0011727183-D18AP00010 (TEE Program), an Australian Research Council (ARC) Discovery Project, and partially supported by the Australian Research Council Centre of Excellence in Future Low-Energy Electronics Technologies (Project No. CE170100039) funded by the Australian Government. Q.Z. acknowledges the support of a Women in FLEET Fellowship.

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