Suppression of mixed-phase areas in highly elongated BiFeO${}_3$ thin films on NdAlO${}_3$ substrates

Mixed-phase areas are produced in highly elongated BiFeO${}_3$ (BFO) thin films as a consequence of strain relaxation. A (001) neodymium aluminate (NdAlO${}_3$; NAO) substrate ($a\sim 3.747$ Å) prominently suppresses the strain relaxation effect and prevents the formation of mixed-phase regions. This creates a pathway to the thick, quasipure, highly elongated phases required for magnetoelectric applications. We characterize the crystal structure, the interface between film and substrate, the surface morphology, and the ferroelectric domain structure of BFO films on NAO substrates and compare them with those of films on typical lanthanum aluminate substrates. The underlying mechanisms are discussed based on the intriguing nature of phase competition in bismuth ferrite phases using first principles density functional calculations for the misfit strain-dependent total energy.

Figure 1

Thickness dependence of the $c$-axis lattice parameters of T-BFO. (a) X-ray θ-2θ scans of the BFO films grown on NAO and LAO substrates. (b) The $c$-axis lattice parameters of the T-BFO phases presented as a function of the BFO film thicknesses for the films grown on NAO and LAO substrates. The $c$-axis lattice parameters are calculated from the positions of the (001) diffraction peaks. The error bars are estimated from the full width at half maximum of each (001) peak.

Figure 2

Reciprocal space maps for the BFO film (56.2 nm in thickness) grown on NAO substrate. (a) HL scan around (002) reflections. (b) Twin structure of the NAO substrate displayed by HK scan at $L$ $=$ 2. (c) HL scan around (103) reflections. The RSMs are plotted on logarithmic scales.

Figure 3

Cross-sectional transmission electron microscopy at the interface between the pure T-BFO film and the NAO substrate. (a) HRTEM image. (b) SAED pattern. Yellow (red)-colored spots represent the diffraction peaks of the NAO substrate (T-BFO film).

Figure 4

Surface morphologies of the BFO films grown on LAO and NAO substrates. (a) Surface morphologies of BFO films grown on LAO substrates. As the film thickness increased, the mixed-phase areas indicated by dark contrast expanded. Each AFM image is supplemented by a histogram to show the height distribution. The thinnest film shows a pure T-BFO phase and a step terrace structure. The thicker films have mixed-phase areas and thus the histograms have double-peak shapes that are fitted to two Gaussian curves for quantitative analysis of the areal fraction. (b) Surface morphologies of BFO films grown on NAO substrates. None of the films with different thicknesses showed any mixed-phase areas, but rather exhibited smooth surfaces as a result of having only a quasipure T-BFO phase. Single-Gaussian fits are applied to all of the associated histograms because they have no shoulder peak. (c) A high-resolution AFM image over a 1 μm × 1 μm area for a representative BFO film (42 nm in thickness) on NAO. (d) Areal fraction of the mixed-phase regions for the film grown on LAO, calculated by fitting the two-Gaussian peaks. The error bars are estimated from the standard error of each fit parameter in the two-Gaussian function. The films analyzed by a single-Gaussian fit are assigned a zero value for the fraction and no error bars are shown. (e) The mixed-phase regions of the BFO/LAO fall in and the dips become deeper in proportion to the thickness of the BFO film. The scale bars represent 1 μm.

Figure 5

Film thickness dependence of the BFO films’ ferroelectric domain structures on the NAO substrates (left) and on the LAO substrates (right). For each sample, both ferroelectric domain structures along an out-of-plane direction and an in-plane direction were measured simultaneously using piezoresponse force microscopy (PFM) scanning in the ⟨100⟩ crystalline direction. Fine stripe domain structures along the ⟨110⟩ crystal axis occurred over the T-BFO regions, except for the mixed-phase areas. None of the samples show contrast in the out-of-plane PFM image. This represents the same polarization direction along the out-of-plane direction, which is typical due to a self-poling effect induced by different top-down interfaces. The scale bars indicate 1 μm. The Fourier transformed results of the in-plane PFM images are displayed nearby on logarithmic scales. The domain width can be estimated from the satellite peak position along the ⟨110⟩ direction. The size of the $k$ spaces is $\left(\frac{2\pi }{5\mu \mathrm{m}}\times 128\right)\times \left(\frac{2\pi }{5\mu \mathrm{m}}\times 128\right)$.

Figure 6

Double logarithmic plot of stripe domain width versus film thickness. From the Fourier transformed images of the in-plane PFM results, an average domain width (half period) perpendicular to the ⟨110⟩ direction was extracted as a function of film thickness. Because the typical domain width ($w$) grew with increasing film thickness ($t$), in accordance with $w\propto t^{\gamma }$, a least-squares linear fit was carried out in the log-log plot. The exponent ($\gamma$) was determined to be ∼1 for the NAO case.

Figure 7

Density functional calculation results for the phase competition between T-BFO and R-BFO. (a) Total energy per formula unit with respect to the ground state is presented as a function of the substrate lattice parameter. It is assumed that the films are fully strained to the substrates and that the in-plane lattice parameters of the strained films are the same as those of the substrates. The NAO substrate provides an in-plane lattice parameter of 3.747 Å on which the T-BFO is considerably more stable than R-BFO and coherent growth can be realistically achieved. (b) $c/a$ ratios plotted as a function of the substrate lattice parameter. For the R-BFO phase with an in-plane lattice parameter of less than 3.85 Å, the local minimum is barely stabilized due to the interference of the T-BFO phase. Given such highly compressive strains, the $c$-axis lattice parameter is fixed under the constraint of volume conservation while the atomic positions are relaxed.