Combined impact of strain and stoichiometry on the structural and ferroelectric properties of epitaxially grown $\mathrm{N}{\mathrm{a}}_{1+x}\mathrm{Nb}{\mathrm{O}}_{3+\delta }$ films on (110) $\mathrm{NdGa}{\mathrm{O}}_3$

We demonstrate that the strain of an epitaxially grown film, which is induced by the lattice mismatch between the crystalline substrate and film and relaxes with increasing film thickness, can be conserved beyond the critical thickness of plastic relaxation of the respective film/substrate heterostructure system by adding epitaxially embedded nanoprecipitates and/or nanopillars of a secondary phase. By doing so we modify the ferroelectric properties of the film in a very controlled way. For this purpose, strained $\mathrm{N}{\mathrm{a}}_{1+x}\mathrm{Nb}{\mathrm{O}}_{3+\delta }$ films are epitaxially grown on $\left(110\right)\mathrm{NdGa}{\mathrm{O}}_3$ and their structural and electronic properties are investigated. X-ray diffraction and transmission electron microscopy analysis indicate that in addition to the epitaxially grown majority phase $\mathrm{NaNb}{\mathrm{O}}_3$, a second phase $\mathrm{N}{\mathrm{a}}_y\mathrm{Nb}{\mathrm{O}}_{3+\delta }$ is present in the films and forms crystalline precipitates and vertically aligned pillars a few nanometers in diameter. For large enough concentrations, this secondary phase appears to be able to suppress the plastic relaxation of the $\mathrm{NaNb}{\mathrm{O}}_3$ matrix. In contrast to stoichiometric films and films with small Na excess, which demonstrate strain relaxation for film thickness exceeding a few nanometers and relaxor-type ferroelectric behavior, the $\mathrm{N}{\mathrm{a}}_{1+x}\mathrm{Nb}{\mathrm{O}}_{3+\delta }$ film with the largest off-stoichiometry (grown from a target with $x=17\%$) exhibits the “classic” ferroelectric behavior of unstrained $\mathrm{NaNb}{\mathrm{O}}_3$ with a hysteretic structural and ferroelectric transition. However, the temperature of this hysteretic transition is shifted from 616 K to 655 K for unstrained material to room temperature for the strained $\mathrm{N}{\mathrm{a}}_{1+x}\mathrm{Nb}{\mathrm{O}}_{3+\delta }$ film grown from the off-stoichiometric target.

Figure 1

Sketches of the different concepts of strain engineering of thin epitaxial films for the case of compressive in-plane strain: (a) due to the lattice mismatch between substrate and film, in-plane strain is introduced at the substrate-film interface and leads to an elastic deformation of the film's lattice, which relaxes (due to defects) with the increasing thickness of the film [19]; (b) similarly to (a), however, the elastic deformation is preserved by vertically aligned nanopillars of a secondary phase [20]; and (c) similarly to (a), however, the elastic deformation is preserved by nanoprecipitates of a secondary phase. The arrows indicate the amount of elastic deformation (strain) of the film, and the different colors characterize the different phases, i.e., primary phase (blue) and secondary phase (red).

Figure 2

(a) Powder XRD measurements of $\mathrm{N}{\mathrm{a}}_{1+x}\mathrm{Nb}{\mathrm{O}}_{3+\delta }$ targets prepared with Na excess compared to the stoichiometric $\mathrm{NaNb}{\mathrm{O}}_3$ ($x=0$) composition (see also Supplemental Material). For better visibility the signals are shifted by a factor of 10 for each successive composition; the compositions ($x$) are given in the figure. Reflection peaks indicated by “A” and “B” are attributed to the $\mathrm{NaNb}{\mathrm{O}}_3$ phase and the $\mathrm{N}{\mathrm{a}}_3\mathrm{Nb}{\mathrm{O}}_4$ secondary phase, respectively. (b) RSM in the vicinity of the ${\left(444\right)}_{\mathrm{o}}$ and ${\left(260\right)}_{\mathrm{o}}$ Bragg reflections of the $\mathrm{NdGa}{\mathrm{O}}_3$ substrate demonstrate the epitaxial growth of the $\mathrm{NaNb}{\mathrm{O}}_3$ phase for the $\mathrm{N}{\mathrm{a}}_{1.17}\mathrm{Nb}{\mathrm{O}}_{3+\delta }$ film on $\mathrm{NdGa}{\mathrm{O}}_3$, the white crosses marking the position of unstrained $\mathrm{NaNb}{\mathrm{O}}_3$.

Figure 3

(a) Magnified HRXRD scans of the reference sample grown from a stoichiometric $\mathrm{NaNb}{\mathrm{O}}_3$ target (lower curves) and a sample grown from a $\mathrm{N}{\mathrm{a}}_{1.17}\mathrm{Nb}{\mathrm{O}}_{3+\delta }$ target (upper curves; the intensity is shifted by a factor of 100) recorded at room temperature around the ${\left(220\right)}_{\mathrm{o}}$ reflection peak of the $\mathrm{NdGa}{\mathrm{O}}_3$ substrate after heating to 400 K (black curve) and after cooling to 80 K (red curve). (b) Temperature dependence of the vertical lattice parameter of the $\mathrm{NaNb}{\mathrm{O}}_3$ phase for a reference sample and for the film grown from the $\mathrm{N}{\mathrm{a}}_{1.17}\mathrm{Nb}{\mathrm{O}}_{3+\delta }$ target for cooling (open blue symbols) and heating (solid red symbols).The orange dashed-dotted line in (b) represents the simulated out-of-plane lattice parameter for unstrained bulk $\mathrm{NaNb}{\mathrm{O}}_3$ [28]. The dashed lines in (b) mark the temperature of the hysteretic ferroelectric phase transition (see Fig. 4). (c) Vertical lattice parameter of the $\mathrm{NaNb}{\mathrm{O}}_3$ phase of epitaxial $\mathrm{N}{\mathrm{a}}_{1+x}\mathrm{Nb}{\mathrm{O}}_{3+\delta }$ films on (110) $\mathrm{NdGa}{\mathrm{O}}_3$ grown from targets with Na excess $x$.

Figure 4

Cross-sectional (S)TEM images of an epitaxial $\mathrm{NaNb}{\mathrm{O}}_3$ film on a $\mathrm{NdGa}{\mathrm{O}}_3$ substrate grown from a Na excess target: (a) dark-field TEM micrograph recorded under $g={110}_{\mathrm{NdGa}{\mathrm{O}}_3}$ two-beam conditions; (b) STEM $Z$-contrast image; (c) magnified view from (b) with a model of the pseudocubic unit cell of $\mathrm{NaNb}{\mathrm{O}}_3$ where green, yellow, and red balls represent Nb, Na, and O atoms, respectively.

Figure 5

Comparison of the temperature dependence of (a) the nonstoichiometric film $\mathrm{N}{\mathrm{a}}_{1.17}\mathrm{Nb}{\mathrm{O}}_{3+\delta }$ on (110)$\mathrm{NdGa}{\mathrm{O}}_3$, (b) polycrystalline $\mathrm{NaNb}{\mathrm{O}}_3$ (adapted from [8]), and (c) nominally stoichiometric $\mathrm{NaNb}{\mathrm{O}}_3$ on (110)$\mathrm{NdGa}{\mathrm{O}}_3$. The insets in (a) show the current-voltage characteristics for sample $\mathrm{N}{\mathrm{a}}_{1.17}\mathrm{Nb}{\mathrm{O}}_{3+\delta }$ recorded at 320 K for cooling (red) and heating (black). The films in (a) and (c) are $\sim 27\mathrm{nm}$ thick; the direction of the thermal cycling in (a) and (b) are indicated by the arrows; the red dashed lines in (a) and (c) show the Curie-Weiss fit with a Curie-Weiss temperature $T_{\mathrm{CW}}$ and Burns temperature $T_{\mathrm{Burns}}$. In (c) data sets for different frequencies are given. The frequency increases as indicated by the arrow from 15 kHz (highest permittivity) to 1.5 MHz (lowest permittivity).

Figure 6

Lorentz fit of the ferroelectric transition for the stoichiometric $\mathrm{NaNb}{\mathrm{O}}_3$ film (blue open symbols for heating and cooling) and the nonstoichiometric $\mathrm{N}{\mathrm{a}}_{1.17}\mathrm{Nb}{\mathrm{O}}_{3+\delta }$ film (red solid squares for heating and black solid triangles for cooling) according to Eq. (1). The solid lines represent the slope γ, the values of γ are given in the figure, and the standard deviation of the fits is smaller than 0.003.