3.1. Determination of the Growth Window
Initially, Nb
2O
5 films were grown on (100)
s SrTiO
3 substrates employing substrate temperatures between 400 °C and 750 °C with intervals of 50 °C in order to assess the growth window.
Figure 2a shows the wide-range HRXRD profiles of films grown at temperatures of 400 °C, 500 °C, 600 °C, and 700 °C that capture the most important observations. All diffraction patterns contain sharp peaks at approximately 0.255 Å
−1 and 0.51 Å
−1 that belong to the (100)
s and (200)
s diffraction peaks of the SrTiO
3 substrate, respectively (marked with an asterisk). The small peak observed at 0.46 Å
−1 is a measurement artifact caused by Cu Kß radiation. The other Bragg peaks, which are visible in
Figure 2a, are attributed to the niobium oxide films. Significant differences can be seen between the diffraction profiles of films grown at different temperatures.
No diffraction peaks are observed for the film grown at 400 °C, indicating an amorphous film structure. With increasing substrate temperature, the occurrence of Bragg peaks indicates the formation of a crystalline phase. However, depending on temperature, differences in the diffraction pattern are visible: (1) The diffraction patterns of the films grown between 450 °C and 650 °C exhibit a strong peak at q
z ≈ 0.316 Å
−1 corresponding to a lattice spacing of about 3.165 Å. This spacing is in reasonable agreement with the (180)
f lattice spacing of T-Nb
2O
5 (3.15 Å) [PDF 00-027-1313]. A higher magnification in the q
z range between 0.3 Å
−1 and 0.34 Å
−1 (
Figure 2b) shows that, additionally, a minor contribution at q
z ≈ 0.322 Å
−1 occurs that is attributed to the (200)
f reflection of T-Nb
2O
5. The intensity of the (200)
f reflection is approximately 1% of the (180)
f diffraction peak for a deposition temperature of 600 °C and decreases with decreasing deposition temperature. The overall shift of the film peak to lower q
z values with increasing deposition temperature indicates that the lattice parameter increases, as shown in
Figure 2c. This might be simply explained by an increase in the build-up of compressive strain when cooling the sample to room temperature after growth that is induced by the difference in the thermal expansion coefficient between Nb
2O
5 (1.3 × 10
−5 K
−1 [
14]) and the SrTiO
3 substrate (3.23 × 10
−5 K
−1 [
15]). AFM investigations (see
Figure 3) show that on (100)
s SrTiO
3 substrates, T-Nb
2O
5 grows with a fourfold rotational symmetry with needle-like grains aligned along the [010]s and [001]s directions of the substrate (in the following, the indices “f” and “s” denote the film and the substrate directions, respectively). Moreover, it can be seen that the grain size increases with increasing growth temperature. Such a change in grain size can result in the development of a tensile strain in the thin film that originates during the grain boundary formation [
16], which would result in a shift of the (180)
f diffraction peak to higher q
z values with increasing growth temperature. This is observed for temperatures above 600 °C, suggesting that both the difference in thermal expansion and the domain size contribute to the strain state of the T-Nb
2O
5 film.
For the film grown at 700 °C, the T-Nb
2O
5 (180)
f and (200)
f peaks in the HRXRD θ/2θ scan are no longer visible. Instead, three Bragg reflections at 0.197 Å
−1, 0.287 Å
−1, and 0.481 Å
−1 (marked by black circles in
Figure 2a) are observed. These three peaks belong to the (301)
f, (402)
f, and (703)
f diffraction peaks of the high-temperature phase of Nb
2O
5 (H-Nb
2O
5), respectively [pdf 00-037-1468]. In general, it is observed that the amount of H-Nb
2O
5 gradually increases with the deposition temperature: for deposition temperatures of 550 °C and below, no significant contribution of the H-Nb
2O
5 phase is observed (for clarity, the diffraction profile of the film grown at 550 °C is not shown in
Figure 2a). For films grown between 600 °C and 650 °C, the main phase is T-Nb
2O
5, but a small fraction of about 1% of the H-Nb
2O
5 phase is already present. Finally, the deposition rate decreases with increasing deposition temperature, as shown in
Figure 2c. This is likely caused by thermal desorption. By fitting the data, an activation energy of 0.67 ± 0.1 eV is determined.
Besides the temperature, it was also found that the occurrence of T-Nb
2O
5 and H-Nb
2O
5 depends on the growth rate. The diffraction profiles of two films grown at 600 °C with different growth rates (controlled by the concentration of niobium ethoxide precursor in toluene) reveals that the peaks corresponding to the H-Nb
2O
5 phase are absent and pure T-Nb
2O
5 is deposited when a higher growth rate is used, whereas the H-Nb
2O
5 polymorph is clearly present for a reduced growth rate (
Figure 2d). These observations indicate that the transformation from T-Nb
2O
5 to H-Nb
2O
5 is a thermally activated process. The transformation thus depends on both the deposition rate and the temperature. The presented results demonstrate that pure T-Nb
2O
5 and H-Nb
2O
5 phases can be obtained by choosing the appropriate deposition temperatures and growth rates.
3.2. Domain Formation of T-Nb2O5 on (100)s- and (110)s-Oriented SrTiO3
In the following, we investigate the effect of lattice parameter mismatch and the symmetry of the substrate on the film growth and domain formation. We first concentrate on the T-Nb
2O
5 films on (100)
s-oriented SrTiO
3 and analyze the epitaxial relationship in more detail.
Figure 4a shows ω-scans of the (180)
f diffraction peaks of a T-Nb
2O
5 film grown at 600 °C. The shape of the ω-scan depends on the in-plane orientation of the substrate relative to the incident X-ray beam. When the X-ray beam is parallel to the [011]s in-plane direction of the substrate, two peaks are observed at ±0.7°. In the case of X-rays parallel to the [010]s or [001]s in-plane directions of the (100)s SrTiO3 substrate, a maximum at ω = 0° and two shoulders at ω = ±1.0° are observed. The peak splitting points to the formation of domains which are tilted by ±ω = 1.0° with respect to the surface normal toward the [010]s and [001]s directions. In addition, φ-scans were performed in order to study the number of domains in more detail. The φ-scan, presented in
Figure 4b, reveals the presence of four (0 16 0)
f T-Nb
2O
5 peaks aligned with the SrTiO
3 substrate, indicating that four T-Nb
2O
5 domain orientations are present in the film.
In order to understand these observations, the lattice mismatch between the T-Nb
2O
5 structure and (100)
s SrTiO
3 surface has to be considered. While the dimensions of the surface unit cell of (100)
s SrTiO
3 is given by 3.905 Å × 3.905 Å, the bulk lattice parameters of the orthorhombic T-Nb
2O
5 polymorph amount to
a = 6.168 Å,
b = 29.312 Å, and
c = 3.938 Å [
2]. According to the XRD data (
Figure 2b), the films contain (200)
f- and (180)
f-oriented domains. For both orientations, the
c-lattice parameter of T-Nb
2O
5 can be aligned with one in-plane direction of the (100)
s SrTiO
3 substrate, either along ±[010]s or ±[001]s. A schematic displaying both configurations of the crystallographic arrangement is given in
Figure 4c,d. This epitaxial alignment results in a lattice mismatch of only −0.8% in the
c-direction and is, therefore, expected to be energetically favorable. Since all in-plane variants are equivalent, there are four different in-plane orientations for the domains. This theoretical assumption of the presence of four different in-plane variants with (180)
f orientation is in good agreement with the ω- and φ-scans that were performed on the (180)
f and (0 16 0)
f diffraction peaks, i.e.,
Figure 4a,b.
The in-plane lattice alignment of the (180)
f-oriented domains in the direction orthogonal to the
c-axis cannot be guessed intuitively, because there exists no low-indexed/highly symmetric lattice plane that is both orthogonal to the (001)
f and (180)
f planes. Instead, it is found that the (3−80)
f plane makes an angle of 88.9° with the (180)
f plane. Assuming that (3−80)
f is parallel with the (001)
s plane, the (180)
f plane is tilted by α = −1.1° from the [001]s direction of the substrate, as shown schematically in
Figure 4c. This tilt angle is in good agreement with the tilt angle determined from the ω-scans in
Figure 2a (peak splitting by ∆ω ≈ 2°). Therefore, we conclude that the (3−80)
f plane is indeed lying parallel to the (100)
s plane of the SrTiO
3 substrate. Finally, it is noted that the lattice mismatch in the direction orthogonal to the
c-axis amounts to several percent and leads to a strong lattice relaxation in this direction.
In contrast to the (100)
s SrTiO
3 surface, the (110)
s SrTiO
3 surface does not exhibit a fourfold rotational symmetry but only a twofold one. The surface unit cell amounts to d
001 = 3.905 Å and d
1–10 = 5.522 Å. Similar to the film growth on (100)
s SrTiO
3, only the unit cell dimension of (110)
s SrTiO
3 along the [001]s direction (d
001 = 3.905 Å) fits to one of the lattice parameters of T-Nb
2O
5, namely the
c-axis (
c = 3.938 Å). Therefore, the number of domain orientations on SrTiO
3 (110)
s is expected to be reduced with respect to the SrTiO
3 (100)
s surface.
Figure 5a shows that a pure T-Nb
2O
5 phase was grown on (110)
s SrTiO
3 at 600 °C. A comparison of the films grown on (100)
s and (110)
s SrTiO
3 at 600 °C reveals that (i) on SrTiO
3 (110)
s, no H-Nb
2O
5 phase was additionally observed, and (ii) both films have a preferential (180)
f out-of-plane direction, suggesting that this is the preferred growth direction. Furthermore, the (200)
f out-of-plane orientation was not observed for films grown on SrTiO
3(110)
s within the experimental resolution. Again, the orientation of the domains in the film was studied by performing XRD ω-scans with the X-ray beam along different in-plane directions of the substrate, as indicated in
Figure 5b. The data clearly differ from the case of growth on (100)
s SrTiO
3 substrates, because only a single peak is observed when the X-ray beam is parallel with the [001]s direction. This peak is—however—split for the scans in the [1−11]
s and [1−10]
s directions, indicating that there are two domain orientations present in films grown on (110)
s SrTiO
3 that have (180)
f lattice planes that are tilted by approximately ±1° with respect to the [110]s orientation of the substrate. This tilt angle is the same as that in the case for T-Nb
2O
5 grown on (100)
s SrTiO
3. Therefore it is concluded that the (3−80)
f plane is parallel with the (1−10)
s plane of the SrTiO
3 substrate. In addition, it was found that the reduction of the number of domain orientations results in a significant change of the surface morphology. Instead of the rough surface with fourfold rotational symmetry that is observed on (100)
s-oriented substrates, the surface of the film grown on the (110)
s-oriented SrTiO
3 reflects the twofold symmetry, as observed by XRD, and has a root mean square surface roughness of 0.7 nm, as can be deduced from the data presented in
Figure 5c.
The presented data thus show that the symmetry mismatch between T-Nb2O5 and SrTiO3 result in the formation of domains with different crystallographic orientations. Interestingly, the in-plane orientation is determined by the alignment of the T-Nb2O5 c-axis with the <001> directions of the substrate, whereas the out-of-plane direction is the same for thin films grown on (100)s- and (110)s-oriented SrTiO3. The latter could be due to a preferred growth direction and suggest that the structural coupling across the interface is weak, because, in the case of a strong coupling, the film orientation would be determined by the substrate orientation and would thus change when the substrate orientation changes.
3.3. TEM Investigations of the Microstructure
Up to now, we can summarize that the use of (110)
s-oriented SrTiO
3 substrates leads to a reduction in the number of in-plane rotational domain variants in T-Nb
2O
5 thin films from four to two. The domains have (180)
f out-of-plane orientation with a tilt angle of about ±1° from the [110]s substrate surface normal. In the following, the structural properties of these films are analyzed in greater detail using transmission electron microscopy (TEM).
Figure 6 shows cross-sectional TEM images of T-Nb
2O
5 films grown on (110)
s- and (100)
s-oriented SrTiO
3 substrates, respectively. In agreement with our XRD measurements, electron diffraction (
Figure 6c,d) and HRTEM imaging (
Figure 6e,f) reveal that, in both cases, the film grows with (180)
f orientation. Abrupt intensity variations within the T-Nb
2O
5 film for both substrate orientations in dark-field TEM images recorded close to the [001]s zone axis (see
Figure 5a,b) point toward the presence of domains having a lateral size between 10 and 100 nm. The nature of these domains can be deduced by analyzing the electron diffraction and HRTEM data more carefully. In the case of the growth on a (100)
s-oriented SrTiO
3 substrate, two different HRTEM contrast patterns, i.e., domain types of the T-Nb
2O
5 film, were observed in images recorded in the [001]s zone axis. Since the HRTEM image shown in
Figure 6e was recorded with a small underfocus of Δf ≈ −6 nm and a thickness of the TEM specimen of t ≈ 6 nm, the dark intensity minima in the film correspond to Nb-atomic columns. One type of domain appears in the HRTEM micrograph with a quasi-hexagonal pattern (see right part of
Figure 6e). A simplified model of T-Nb
2O
5 adapted from Lee et al. [
12] (
Figure 1c) in the [001]f projection matches the HRTEM pattern very well. This type of domain thus grows with the epitaxial relationship [001]f parallel to [001]s. The second type of domain is characterized by a rectangular HRTEM pattern (see left part of
Figure 6e), which matches very well to a model of T-Nb
2O
5 being rotated in-plane by 90° with respect to the first type of domain, i.e., the epitaxial relationship of these domains is [001]f perpendicular to [001]s. In the case of growth on (110)s-oriented substrates, only one type of domain was observed, namely, the one with the epitaxial relationship [001]f parallel to [001]s (see
Figure 6f). Analyzing the Fourier transformation (not shown here) of that HRTEM image, we found that while the pure in-plane Fourier components of the neighboring domains (left and right side in
Figure 6f) match with each other, their out-of-plane Fourier components are separated. This can be explained by a 180° in-plane rotation between the domains. The observed separation of the out-of-plane Fourier components corresponds to a tilt of the (180)
f planes of the neighboring domains by approximately 2° with respect to each other. This, in fact, agrees very well with the results of the XRD measurements. The presence of variants of each domain type that are rotated in-plane by 180° leads finally to four and two possible differently oriented domains for T-Nb
2O
5 films grown on (100)
s and (110)
s SrTiO
3 substrates, respectively.
These findings from the HRTEM analysis are also confirmed on a macroscopic scale by electron diffraction data recorded close to the [001]s zone axis. In the case of a (110)
s SrTiO
3 substrate, the diffraction image of the T-Nb
2O
5 film (see
Figure 6c) shows only a quasi-hexagonal pattern. For the film grown on a (100)
s-oriented substrate, there are additional reflections arranged in a rectangular way (mark by red arrows in
Figure 6d) in the diffraction image. The weaker spots that appear in both diffraction images and that are split correspond to a periodic superstructure of approx. 3 nm in the films, which is consistent with previous observations [
7].