Effect of substrate orientation on lattice relaxation of epitaxial ...

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014104-4 D. Kan and I. Takeuchi J. Appl. Phys. 108, 014104 2010 FIG. 4. Color online a Semilogarithmic contour plots <strong>of</strong> the x-ray reciprocal space mapping for the 1 m-thick 001-oriented BiFeO 3 thin film. The mapping was measured around the 003 SrTiO 3 Bragg reflection with incident x-ray parallel to the 100 =0 and 110 direction =45°. For clarity, the thick black ellipses are drawn to indicate the reflections from the BiFeO 3 layer. b Schematics describing the tilting <strong>of</strong> the domain structures in the 001 film. c Tilt angle the angle in blue in b plotted as a function <strong>of</strong> thickness. Based on the monoclinic cell drawn in Fig. 1c, the appearance <strong>of</strong> the two BFO reflections in the 220 RSM can be understood as the existence <strong>of</strong> two crystallographic domain structures where one <strong>of</strong> the BFO domain structure is distorted along either the 001 or 001¯ direction and that the 110 plane is tilted up or down with respect to the 110 <strong>substrate</strong> surface. The thickness dependence <strong>of</strong> the lattice parameters and FIG. 5. Color online a Semilogarithmic contour plots <strong>of</strong> the x-ray RSM for the 400 nm-thick 110oriented BiFeO 3 thin film. The mappings were measured around the 220, 222, and 310 SrTiO 3 Bragg reflection. b–d Thickness dependence <strong>of</strong> the lattice constants b, angle c and the saturated polarization value d. Inb, the dotted line shows the lattice parameters <strong>of</strong> the STO <strong>substrate</strong>. In d, the tetragonality is defined to be 2c m / am 2 +b m 2 . Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
014104-5 D. Kan and I. Takeuchi J. Appl. Phys. 108, 014104 2010 FIG. 6. Color online a L scans <strong>of</strong> the 220 BiFeO 3 reflection for the 110-oriented film with thickness up to 1 m. The scans were performed along the 001 SrTiO 3 direction. b Evolution <strong>of</strong> the distortion green circle, tilting blue square and rotation angle red triangle for the domain structure in 110 film with thickness. c Schematics describing the evolution <strong>of</strong> the tilting <strong>of</strong> domain structures in 110 films as a function <strong>of</strong> thickness. the distortion angle determined using the monoclinic cell are plotted in Figs. 5b and 5c, respectively. Due to the anisotropic strain from the 110 <strong>substrate</strong>, the lattice constants along the 001 c m and 11¯0 b m STO direction show different behaviors. In the thickness less than 100 nm, c m is locked to the same lattice constant as the <strong>substrate</strong>, while b m has the larger value than the one for the <strong>substrate</strong>. This reveals that the negligible strain along the 11¯0 STO direction and the contraction in c m result in the expansion in b m . As the thickness is increased up to 200 nm, the relaxation takes place exhibiting the distinct change in the lattice constants and . Beyond this thickness, b m and remain constant while c m shows gradual increase with thickness. This behavior indicates that, for the 110-oriented film, the stored elastic energy is relieved through the change in not only the lattice constants but also the distortion angle. The uniaxial strain along the 001 direction allows the relaxation in the angle while the biaxial strain for the 001-oriented BFO thin film keeps the lattice constant fixed, suppressing the angle relaxation process which is only seen in the larger thickness region. Combining our experimental results in Figs. 2, 3, and 5, we can conclude that compressive strain from <strong>substrate</strong> is mainly applied along the 100 axis and that the distortion angle is predominantly relaxed in the <strong>orientation</strong> where the compressive strain along the 100 axis is not involved. This is also confirmed by the fact that the thickness where the lattice constants begin to be fully relaxed become smaller as the number <strong>of</strong> the 100 axes on the <strong>substrate</strong> surface is decreased. In Fig. 5d, the tetragonality 2c m / 2 am +b 2 m and the saturated polarization value at room temperature are plotted against the thickness. Due to the uniaxial strain, the tetragonality becomes lower than 1, from which the slight decrease in the polarization is expected. The observed polarization, however, is 90 C/cm 2 which is consistent with the value estimated with the projection rule, 105/3/ 2 C/cm 2 . This indicates again that strain relaxation has little impact on the polarization value beyond 400 nm. Another interesting behavior is the tilting <strong>of</strong> the 110 plane associated with the lattice relaxation. Figure 6a shows a L scan at the 220 BFO peak along the 001 direction. When the lattice relaxation takes place in the film, the peak begins to split into two peaks 200 nm-thick sample, indicating that the relaxation induces the tilting <strong>of</strong> the 110 plane <strong>of</strong> the surface. Note that this tilting is essentially the same as the one observed for the 001 film, revealing that the tilting in connection with the strain relaxation is an intrinsic characteristic <strong>of</strong> the epitaxially-stabilized monoclinic phase in BFO. The key observation for the 110 film is that the tilt angle varies with thickness and that one <strong>of</strong> the tilted surfaces <strong>of</strong> the two domain structures becomes parallel to the <strong>substrate</strong> surface. The domain structure with the surface parallel to the <strong>substrate</strong> eventually becomes the dominant one with increasing thickness. This behavior is summarized in Figs. 6b and 6c. When the lattice relaxation occurs, the domains tilt in opposite directions with the angle in blue as shown in Fig. 6c. Judging from the intensity <strong>of</strong> the BFO 220 x-ray reflections Fig. 6a, the population <strong>of</strong> the domain structures tilted in the opposite directions are equally distributed. As the thickness is increased further, both <strong>of</strong> the domains are rotated in the same direction the angle in red in the Figs. 6b and 6c. This results in one <strong>of</strong> the 110 surfaces <strong>of</strong> the domain structures becoming parallel to the <strong>substrate</strong> surface. It should be noted that the domain with the surface parallel to the <strong>substrate</strong> surface shows the prominent x-ray diffraction peak, indicating that this is the major domain. The population <strong>of</strong> the other domain structure decreases with increasing thickness. This observation implies that the 100 twin boundary where the domain with the distortion in Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
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