Anisotropic-strain-relaxation-induced crosshatch morphology in epitaxial SrTiO₃/NdGaO₃ thin films

Heteroepitaxial growth of thin films on lattice-mismatched substrates can give rise to various intriguing phenomena including the crosshatch surface morphology, which has been commonly observed for epitaxial semiconductor films such as Si_1−xGe_x/Si and In_xGa_1−xAs/GaAs and has been intensely investigated in the past decades.^1–3 Recently, the complex oxide heterostructures have emerged as an active research filed due to their versatile properties and application potential for the next generation electronic devices.^4,5 It has been found that the crosshatched pattern can also appear on perovskite oxide films of SrRuO₃, (Ca_1−xSr_x)(Zr_1−xRu_x)O₃/SrRuO₃, and La_0.5Ca_0.5MnO₃ epitaxially grown on SrTiO₃(001) [STO(001)] substrates.^6–8 Compared to the semiconductor heteroepitaxy, however, the crosshatch surface of the oxide films is for from being understood.

STO is one of the potential materials for tunable microwave devices due to its high nonlinear dielectric constants and low microwave loss at the cryogenic temperatures.⁹ The epitaxial strain has been shown to dramatically modify the structural and ferroelectric phase transitions of STO thin films.^10–12 Moreover, the two-dimensional electron gas (2DEG) has been reported for various interfaces between STO and LaAlO₃, GdTiO₃, and NdGaO₃ (NGO), with the mobility controllable via the epitaxial strain.^13–17 These observations suggest that the investigation of strain relaxation and surface morphology of STO films is important for the design of STO based devices. However, although the strain effect in STO films grown on MgO, LaAlO₃, (La_0.3Sr_0.7)(Al_0.65Ta_0.35)O₃ (LSAT), and DyScO₃ substrates has been investigated,^18–20 the strain relaxation on the surface morphology of STO films has rarely been explored.

In this paper, we report the first observation of the crosshatch surface morphology of epitaxial STO grown on orthorhombic NGO(001)_O and NGO(110)_O substrates (in Pbnm setting hereafter). Albeit with similar average lattice mismatches, the films on the cubic LSAT(001) substrates show a uniform surface. The crosshatched lines extend along the specific crystallographic direction(s) of the different substrates, and the density, width, and height of the lines enhance with the STO film thickness. According to the high resolution x-ray diffraction (XRD) measurements, the crosshatch surface morphologies could be ascribed to the different strain relaxation in the various epitaxial systems. Moreover, by using STO/NGO(110)_O plane with the crosshatched pattern as a template, the magnetotransport properties of epitaxial La_0.6Ca_0.4MnO₃ films can be dramatically changed. These observations could be significant for the designing and fabrication of multifunctional oxide devices using a bottom-up approach.

STO films of 16, 32 or 64 nm thick were grown simultaneously on orthorhombic NGO(001)_O and NGO(110)_O, and cubic LSAT(001) substrates by pulsed laser deposition, using a 248 nm KrF excimer laser with the laser energy of 2 J/cm² and repetition rate 5 Hz, resulting in a growth rate of ∼5 nm/min. During deposition, the temperature and oxygen pressure were set at 735 °C and 15 Pa, respectively. In order to optimize the oxygen content and to promote the strain relaxation, all the films were ex-situ annealed at 900 °C in a flowing O₂ gas atmosphere for 6 h. The structure and strain state of the films were analyzed by XRD using CuKα₁ (λ = 1.5406 Å, Panalytical X’ Pert) radiation, including the high-resolution x-ray reciprocal space mapping (RSM) around different zone reflections, and the surface morphology of the films was carefully characterized by atomic force microscopy using the tapping mode (AFM, Vecco, multimode V).

Bulk STO and LSAT have cubic structures with space group Pm3m and lattice constants of 3.905 Å and 3.868 Å, respectively.^11,21 NGO is orthorhombic with space group Pbnm and lattice parameters a_O = 5.4332 Å, b_O = 5.5034 Å and c_O = 7.7155 Å,²² corresponding to the pseudocubic lattices of $a pc = ( a O 2 + b O 2 ) 1 / 2 /2=3.8668Å$ and c_pc = c_O/2 = 3.8578 Å. Thus, the commensurate STO films on NGO(001)_O, NGO(110)_O, and LSAT(001) substrates suffer a comparable compressive strain ε = (a_substrate − a_film)/a_film × 100% of −0.978%, −1.093%, and −0.947%, respectively.

Figure 1 shows XRD linear scans from STO/NGO(001)_O films with thicknesses (t) of 16, 32 and 64 nm, and a 64 nm STO/LSAT(001) film. The rocking curve (RC) on STO(002) reflection for each sample is shown correspondingly in the right column. For STO/NGO(001)_O the out-of-plane lattice constants of the films (3.941–3.937 Å) show little change with the film thicknesses. They are larger than the bulk value of 3.905 Å, confirming that the films suffer a compressive strain in the epitaxial plane. The thinner STO/NGO(001)_O films show sharper Laue fringes, indicating that as t increases the epitaxial quality may degrade. Also, for the 32 and 64 nm films a shoulder-like diffusive reflection emerges on both sides of STO(002) in the RCs. In contrast, the shape of the RC of STO/LSAT(001) film exhibits a Gaussian distribution. These imply that the strain relaxation mechanism or the distribution (or type) of misfit dislocations (MDs) in STO/LSAT films may be different from those in STO/NGO films,^23,24 which will be discussed later.

In order to further analyze the strain state of the samples, high resolution x-ray RSM has been performed around the NGO(116)_O and LSAT(103) reflections. For STO/NGO(001)_O, as shown in Figs. 2(a)–2(c), at t = 16 nm the sharp STO(103) reflection with exactly the same in-plane Q_[110]O as the NGO(116)_O indicates that the film is fully strained. As t is increased to 32 and then to 64 nm, strain relaxation occurs, leading to more diffusive reflections on both sides of the STO(103) peaks. Note that the central STO(103) reflection keeps nearly the same in-plane lattice constant as the substrate (d_[100] = λ/2Q_[110]O ≈ 3.873 Å), and the out-of-plane lattice constants also show a negligible change (d_[001] = 3λ/2Q_[001] ≈ 3.933 Å). By contrast, STO(103) reflection of the 64 nm STO/LSAT(001) film [Fig. 2(d)] is even more diffusive. It shifts towards smaller Q_[100] implying an elongated in-plane lattice constant of the film. This further indicates that the strain relaxation in STO/LSAT(001) films may be quite different from that in STO/NGO(001)_O films.

Along with the strain relaxation as aforementioned, the surface morphology of the STO films shows intriguingly different patterns dependent upon the substrates. Figures 3(a) and 3(b) show the typical AFM images scanned from the 64 nm STO films grown on NGO(001)_O and LSAT(001), respectively. It is seen that the former exhibits a striking crosshatched pattern with periodic ridges and trenches extending along the [110]_O and [−110]_O directions of the substrate. In contrast, a uniform smooth surface embedded with three-dimensional (3D) islands of 1∼2 unit-cells height is observed for the STO/LSAT(001) films. We also show the AFM surface morphology of a 64 nm STO/STO(001) film [Fig. 3(c)] and a 32 nm STO/LSAT(001) film [Fig. 3(d)]. It is seen that these films also have smooth surface with atomic steps and terraces, but no the crosshatched lines. These observations strongly suggest that the formation of a crosshatched surface could be linked closely to the symmetry mismatch between the STO films and the various substrates.

In Fig. 4, the AFM images show the evolution of the crosshatched surface morphology of STO/NGO(001)_O films at various thicknesses. In the right column, the height profiles are extracted along the lines marked on the AFM images, with the arrows denoting the scan directions. For t = 16 nm, one crosshatched line with just one unit cell height appear in [110]_O direction, and with t increasing (16 → 32 → 64 nm), more and more lines emerge and bunch up together to increase the width (0.1 → 0.4 μm) and height (1 → 3 unit cells). The lines along the [−110]_O direction also show up at t = 64 nm to form a crosshatched pattern. The observation of well-defined atomic steps and terraces at small t indicates that the films adopt a layer by layer or step-flow growth mode. With t increasing, the root-mean-square (RMS) roughness of the surface enhances at the same time (0.162 → 0.203 → 0.274 nm). Apparently, the crosshatched lines are closely linked to the surface atomic steps and terraces, for example, for the 32 nm film the crosshatched line along the [110]_O direction is consisted of periodic atomic terraces with one unit-cell height at a period of ∼0.33 μm. These atomic terraces along with the crosshatched lines in the two orthogonal directions merged together, leading to a greatly enhanced surface undulation of the 64 nm film.

For STO/NGO(110)_O films, the crosshatch shows a characteristic of strong anisotropy. As shown in Fig. 5, at 16 nm aside from the clear atomic steps and terraces, a series of slim lines just appear along [1–10]_O of the NGO(110)_O substrate. Even at t = 64 nm, the crosshatched [1–10]_O lines bunch up together, with just a few lines emerged in the [001]_O direction. The RMS roughness also shows weak thickness-dependence, from 0.198 Å (t = 16 nm) to 0.2 Å (t = 64 nm).

Now, we try to discuss the origin of the crosshatched pattern on the films. A plausible model associated with surface atomic steps flow has been used to explain the crosshatch morphology of the semiconductor and oxide films.^25,26 With clear atomic steps and their flow at enhanced t as observed for our STO/NGO films, this model seems also suitable for the present results. As shown schematically in Figs. 6(a)–6(c), when t is less than the critical film thickness h_C (t < h_C), the film is fully strained, as t > h_C the strain is relaxed by formation of the 60° MDs, whose glides introduce surface steps flow on the films, and as t further increases (t ≫ h_C), more and more surface steps emerge and bunch up together via step flow during the growth or post-annealing process, thus leading to a crosshatch morphology of the films.

This statement could be confirmed by comparing the RSMs on STO(002) reflections from the same series of samples. As shown in Fig. 7, the 16 nm STO/NGO(001)_O film shows a sharp peak with very weak diffusive reflections, while for the 32 and 64 nm films two satellites appear on both sides of the STO(002) main reflection along the horizontal [110]_O direction, consistent with the linear scans shown in Fig. 1. Similarly, the STO/NGO(110)_O film at 64 nm also shows two satellites along the in-plane [001]_O direction [Fig. 7(d)]. However, for the 64 nm STO/LSAT(001) film an isotropic Gaussian distribution in both the horizontal and vertical directions can be found for the STO(002) peak. It has been revealed that the formation of 60° MD arrays, of which the Burgers vector has the tilt component ±b_z (normal to the interface), can give rise to the satellites around the main reflection. However, the satellites will be absent for edge MD with Burge vector lying in the interface.^23,27,28 Therefore, it can be argued that the 60° MDs may be formed by strain relaxation in STO/NGO films, in contrast to edge MDs [Fig. 3(b)] in STO/LSAT films.

The crosshatched patterns on the STO/NGO(001)_O [NGO(110)_O] films could be intrinsically ascribed to the anisotropic strain relaxation. As shown in Figs. 6(d)–6(f), due to the symmetry mismatch of cubic/orthorhombic STO/NGO interfaces, assuming a “cube-on-cube” growth mode the films grown on the (001)_O [(110)_O] planes of NGO substrates will suffer an anisotropic strain: −1.64% (−1.23%) and −0.35% (0.99%) along the in-plane [100]_O{[001]_O} and [010]_O{[1-10)_O]} directions. The induced crosshatched lines also show strong anisotropy, which is more pronounced for the STO/NGO(110)_O films. The much denser crosshatched lines in [1-10]_O direction (Fig. 5) may be attributed to the larger epitaxial strain of −1.23% along the orthogonal [001]_O direction. By contrast, an isotropic compressive strain of −0.96% is exerted on the STO films by LSAT(001), and the uniform surface of STO/LSAT(001) films might arise from the isotropic strain relief. Note that, this is also consistent with the previous reports, where the (Ca_1−xSr_x)(Zr_1−xRu_x)O₃/SrRuO₃/STO or SrRuO₃/STO films have the orthorhombic/cubic interfaces and crosshatch surface morphology.^6,7 On the other hand, for the isotropically strained BaTiO₃/STO (tetragonal/cubic) films, the strain is relaxed by forming edge MDs arrays and no crosshatch surface was observed.²⁹ Also, for our STO(64 nm)/STO(001) films no crosshatch was observed [Fig. 3(c)]. Thus, the symmetry mismatch and/or the anisotropic strain relaxation could be very relevant to the appearance of crosshatch surface morphology in the complex oxide films.

At last, we try to use the crosshatched pattern to modify the properties of epitaxial manganite films. La_0.6Ca_0.4MnO₃ (LCMO) films at 16 nm were grown directly on NGO(110)_O substrate, and for comparison on the STO(30 nm)/NGO(110)_O film with crosshatched pattern, as shown in Fig. 8(a). After a close inspection, it is seen that the LCMO thin film can copy the crosshatched pattern of the underlying STO/NGO film [Fig. 8(b)]. According to Fig. 8(c), both the LCMO films (and the STO layer as well) are coherently strained on NGO(110)_O substrates, however, their transport properties are quite different. Figure 8(d) shows the temperature-dependent resistivity (ρ-T) curves measured at magnetic field (H) of 0 and 1 T, and the magnetoresistance {MR = [ρ(H)-ρ(0)]/ρ(0)} in the bottom panel. Both the films show a bulklike ferromagnetic-metallic transition at T_C of about 250 K,³⁰ but the LCMO/STO/NGO film has a larger residual resistance at 10 K and a strikingly enhanced MR in the temperature range of 10∼230 K. This could be ascribed to the crosshatched lines in LCMO films, which serve as spin scattering centers to cause disordered spins around the lines. The dense crosshatched lines may be regarded as the patterned grain boundaries giving rise to a large low-field MR in a wide temperature range.^31–34 Similarly, the crosshatched pattern has been found to enhance the MR of epitaxial La_0.5Ca_0.5MnO₃ films.⁸ 

Another possibility for the induced low-field MR in LCMO(16 nm)/STO(30 nm)/NGO(110)_O films may lie on the changed strain state due to the insertion of the STO buffer layer. Although the in-plane lattice constants of the STO buffer can hardly relax due to the buckling of the underlying NGO(110)_O substrate, as confirmed by the RSM shown in Fig. 8(c), the partial relaxation can still exist given that the crosshatched lines are indication of the strain relaxation as aforementioned (Figs. 5 and 7). Moreover, the interfacial octahedral connectivity and proximity effect between MnO₆/TiO₆ and MnO₆/GaO₆ should also be essentially different.³⁵ In order to further examine the strain effect, we grow the 16 nm LCMO films on pure STO(001) and STO(30 nm)/LSAT(001) substrates. As shown in Fig. 9, all the films [with the LCMO/NGO(110)_O and LCMO/STO/NGO(110)_O films put together for comparison] are epitaxially strained, showing clear thickness fringes [Figs. 9(a) and 9(b)], but their transport properties are very sensitive to the strain states supplied by the different (buffered) substrates. The LCMO/STO(001) films show a strong antiferromagnetic insulating state with the MR pronounced only at low temperatures and under a high magnetic field [Fig. 9(c)], which is in good agreement with many previous reports.^36,37 For the LCMO/STO(30 nm)/LSAT(001) film, however, the insulating state becomes weaker, showing the MR onset at a higher temperature [Fig. 9(d)]. Along this line, the induced large low-field MR in a wide temperature range observed for LCMO(16 nm)/STO(30 nm)/NGO(110)_O films could also be attributed to the possible enhancement of strain state due to the (partial) relaxation of the STO buffer (as manifested by the appearance of the crosshatched lines). Clearly, this buffer layer effect could be beneficial to the practical applications.

In summary, the crosshatch morphology has been observed for the symmetry mismatched epitaxy of STO/NGO(001)_O and STO/NGO(110)_O, and it is absent for the symmetry matched STO/LSAT(001) and STO/STO(001) films. The crosshatched lines appear anisotropically and extend parallel to specific crystallographic axes of the substrates. The density, width, and height of the crosshatched lines enhance with the film thicknesses. According to the high-resolution XRD measurements, the crosshatch morphology could be ascribed to the anisotropic strain relaxation with possibly the 60° misfit dislocation arrays in STO/NGO films. We argue that the symmetry mismatch induced anisotropic strain relaxation could be very relevant to the crosshatch surface morphology in complex oxide films. Using the crosshatched STO/NGO(110)_O films as a template, the magnetotransport properties of LCMO films can be dramatically modified. The results indicate that not only the lattice but the symmetry of the substrate plays a crucial role in determining the strain relaxation and surface morphology of the perovskite oxide films, and offer a new route for the design and fabrication of the perovskite oxide devices.

This work was supported by the NSF of China (Grant Nos. 11274287, 11204313, 11474263, and U1432251), the National Basic Research Program of China (Grant Nos. 2012CB927402 and 2015CB921201), and the Fundamental Research Funds for the Central Universities (Grant No. WK2340000052).