In-situ observation of ultrafast 90° domain switching under application of an electric field in (100)/(001)-oriented tetragonal epitaxial Pb(Zr0.4Ti0.6)O3 thin films

Ferroelastic domain switching significantly affects piezoelectric properties in ferroelectric materials. The ferroelastic domain switching and the lattice deformation of both a-domains and c-domains under an applied electric field were investigated using in-situ synchrotron X-ray diffraction in conjunction with a high-speed pulse generator set up for epitaxial (100)/(001)-oriented tetragonal Pb(Zr0.4Ti0.6)O3 (PZT) films grown on (100)cSrRuO3//(100)KTaO3 substrates. The 004 peak (c-domain) position shifts to a lower 2θ angle, which demonstrates the elongation of the c-axis lattice parameter of the c-domain under an applied electric field. In contrast, the 400 peak (a-domain) shifts in the opposite direction (higher angle), thus indicating a decrease in the a-axis lattice parameter of the a-domain. 90° domain switching from (100) to (001) orientations (from a-domain to c-domain) was observed by a change in the intensities of the 400 and 004 diffraction peaks by applying a high-speed pulsed electric field 200 ns in width. This change also accompanied a tilt in the angles of each domain from the substrate surface normal direction. This behaviour proved that the 90° domain switched within 40 ns under a high-speed pulsed electric field. Direct observation of such high-speed switching opens the way to design piezo-MEMS devices for high-frequency operation.

significant feature and is required for the design of high-performance piezoelectric devises for MEMS applications. Much efforts have been devoted to clarify the dynamics of the non-180° ferroelastic domain in epitaxial Pb(Zr 1−x Ti x )O 3 films [4][5][6][7][8][9] . The change in the non-180° ferroelastic domain structure with the application of an electric field has been investigated using various techniques, such as transmission electron microscopy (TEM) 6,9 , piezoresponse force microscopy (PFM) 4,7,8 , and X-ray diffraction (XRD) 5 for polydomain (100)/(001)-oriented epitaxial tetragonal Pb(Zr 1−x Ti x )O 3 films. The domain structures strongly depend on the film thickness and substrate [10][11][12] , and the Zr/(Zr + Ti) ratio in the films 13 , as well as the poling treatment.
The dynamics of the crystal lattice while applying an electric field in Pb(Zr 1−x Ti x )O 3 films have been measured by in-situ XRD measurement [14][15][16][17] . Lattice elongation and 180° domain wall motion were observed at sub-nanosecond timescales for (001)-oriented Pb(Zr 1−x Ti x )O 3 thin films 14,15 , and it has been reported that non-180° ferroelastic domains can be switched by application of an electric field on the order of hundreds of nanoseconds 16,17 in ferroelectric films. However, it has not been clarified yet how fast does the 90° domain switching proceed -in particular, the relationship between the lattice elongation and geometrical domain structure deformation in tetragonal Pb(Zr 1−x Ti x )O 3 thin films has not been determined from a response speed point of view.
In the present study, we investigated the change in lattice parameters and domain structure for 600-nm thick (100)/(001)-oriented epitaxial tetragonal Pb(Zr 0.4 Ti 0.6 )O 3 films, which were subjected to an applied rectangular electric field pulses of 200-ns and rest time of 800 ns. The average lattice parameters and domain structure of the films under this electric field was then determined using a time-resolved in-situ synchrotron X-ray diffraction system in conjunction with a high-speed pulse generator. We show that in contrast to conventionally accepted scenario of sluggish nature of ferroelastic domain switching as pointed out in ceramics 18 , simultaneous lattice deformation (c-axis and a-axis) and ferroelastic domain switching (c-domain volume fraction and geometrical twin 90° domain structure) occurs on the order of sub-microseconds.

Results and Discussion
High-resolution X-ray diffraction (HRXRD) 2θ-ω mappings around the PZT 400 and 004 diffraction peaks of (100)/(001)-oriented epitaxial PZT films grown on (100) c SrRuO 3 //(100)KTaO 3 substrates are shown in Fig. 1(a) and (b), respectively. Split PZT 400 diffractions as twin peaks (a-domains) are observed in Fig. 1(a), together with SrRuO 3 400 c and KTaO 3 400 diffraction peaks, while split PZT 004 diffractions as twin peaks (c-domains) are observed in Fig. 1(b). This tilted domain structure has been examined in a number of reports using cross-sectional TEM or X-ray rocking curve analysis [10][11][12][13][19][20][21][22][23][24] . The twin peaks split in the rocking curve direction (ω-axis), the horizontal axis in Fig. 1(a) and (b), are observed because of the tetragonality of the film structure 10,12 . The tilting angles of c-domains (β angle) and a-domains (α angle) can be interpreted by considering that the films are required to be attached to a flat surface substrate, as illustrated in Fig. 1 (c). Angles of α = 0.41° and β = 1.96° were obtained from the 2θ-ω mappings shown in Fig. 1(a) and (b), respectively. It must be mentioned that the disoriented angles from the substrate surface have been ascertained to depend on the volume fraction of the c-domain (V c ) 22 and the tetragonality (c/a ratio), as described in supplementary materials 12 .  Fig. 1(a)] measured by the application of a 200-ns pulsed electric field with an amplitude of 170 kV/cm and zero field. The PZT 004 peak shifted to a lower 2θ angle, which demonstrates the elongation of the surface normal c-axis lattice parameter of the c-domain, with an applied electric field. On the other hand, the PZT 400 peaks shifted in the opposite direction (higher 2θ angle), as shown in Fig. 2(b), indicating a decrease in the surface normal a-axis lattice parameter of the a-domain under an applied electric field. This elongation of the surface normal c-axis lattice parameter of the c-domain and decrease in the surface normal a-axis lattice parameter of the a-domain occurs simultaneously. Moreover, a clear difference in the intensities of both PZT 004 and PZT 400 diffraction peaks between 0 V (before applying an electric field) and 170 kV/cm (under applying an electric field) is found. This result is direct evidence of 90° domain switching from (100) to (001) orientation, as is the increase in V c during a 200-ns-wide pulsed electric field. The application of an electric field forces ferroelectric/ferroelastic domains to move towards the direction parallel to the electric field to minimise the total energy in the film. It must be noted that the decrease in the lattice spacing along the a-axis of a-domain that is perpendicular to the polarization direction can be understood by the shear deformation owing to none-zero piezoelectric tensor d 15 25 .
The appreciable d 15 response in the a-domain may be also associated with the change of domain fraction by the electric field. Full understanding of the geometrical correlation between a-and c-domains under the electric field will be reported in the future. Figure 3 shows the change in the rocking curve scans (ω scans) for the c-domain [scan V in Fig. 1(b)] and a-domain [scans III and IV in Fig. 1(a)] under an applied 200-ns-wide pulsed electric field. The tilting angle of the PZT 004 twin peaks decreased, as shown in the Fig. 3(a). This motion indicates decreasing α angles of the c-domains (Δα), which is accompanied by an increase in V c under the applied electric field, in agreement with Fig. 2. On the other hand, as shown in Fig. 3(b) and (c), the PZT 400 peaks were shifted to lower and higher angles, respectively, which indicate an increase in the β angle of the a-domains (Δβ) under the application of an electric field. Thus the time-resolved in-situ XRD measurements show direct evidence of a dynamic increase of the V c and lattice parameters as well as changing tilting angle of each domain with the application of an electric field.
We now discuss the time response of the changes in the lattice parameters, V c , and the tilting angle of the domains with respect to an electric field. Figure 4 shows the electric charge ( Fig. 4(a)), the lattice strains ( Fig. 4(b)), the tilting angles (Fig. 4(c)), and the peak intensity of each domain (Fig. 4(d)) as a function of time. The electrical charges were plotted every 2 ns, while others were every 20 ns to obtain sufficient intensity for analysis. These data were obtained by fitting with Gaussian functions except for Fig. 4(a). An imperfect rectangular shape of the charge with respect to an applied electric pulse is shown in Fig. 4(a)  derivative for the charge, which is the current flowing through the electric circuit, is shown in Fig. 4(e). Two peaks correspond to the current associated with applying and removing an electric field. The transition duration, which is defined as the time over which a current with an absolute value larger than the noise level of 0.002 mA flows, is approximately 40 ns for both application and removal. This duration time includes both rise time, determined by the limitation of the current pulse generator, and transient time, determined by impedance of the electric circuit. Conversely, Fig. 4(b)-(d) show that the elastic deformation, tilting motion, and ferroelastic domain switching seem to have been completed within 40 ns because each spectrum has only one single data point during the change in electric field that corresponds to these transition states. As previous studies reported 13  domain structures. But the increase and decrease in integrated intensities of 004 and 400 peaks, respectively, strongly support the domain switching from a-domain to c-domain. When the field was removed, tilt angles and intensities return back to their original positions at zero field at less than 40 ns as well. These data were acquired during the repetitive application of electric pulses of 800-ns duration confirming that the observed changes in tilt angles and intensities and hence a ferroelastic domain wall motions is perfectly repeatable. More importantly all these motions (charge, lattice strain, domain switching, and change in tilting angle) occur simultaneously without delay when the electric field across the PZT film changed. This means that the 90° domain switching from (100) to (001) can be exploited to enhance the piezoresponse response even on the order of several tens of nanoseconds.
It should be noted that the response time in this study is less than that of previously reported data, which is on the order of hundreds of nanoseconds 16,17 . Moreover, the non-180° ferroelastic domain motion for thin films does not suffer from frequency dispersion as seen in bulk ceramics 18 , where it becomes inactive for short such ns pulse time. One possible explanation could be that the electric fields applied to the film are one order higher than those applied to the ceramics, which may have enabled us to achieve high-speed non-180° domain switching. Additionally non-180° domain switching by an electric field can be also influenced by strains of the grain that are accumulated in polycrystalline ceramic bodies. These are changed by grain size, grain shape, and grain-to-grain disorientation in neighbour grains 26 . Finally, it is worth noting to compare the strain evaluated from the present in-situ XRD and strain-electric-field measurement (see Fig. S3) by applying unipolar electric field with 5 Hz. The figure shows that the almost linear response of strain with respect to electric field, indicating piezoelectric coefficient (d 33obs. ) of around 100 pC/N. The volume fraction change in c-domain calculated from tilting angle and total strain as a function of time during in-situ XRD measurements are plotted in Fig. 4(f) and (b), respectively. The piezoelectric coefficient (d 33XRD ) obtained from the XRD measurement is around 86 pC/N, showing reasonable agreement with the value obtained by strain -electric field measurements. This consistency between them again confirms that the ferroelastic domain switching here does not suffer from strong frequency dispersion previously observed for 90° domain switching 18 .
Note that the intrinsic component, which indicates the lattice deformation of c-domain by electric field, is only 17 pC/N, of which contribution for total d 33XRD is around 20%. That is domain switching from a-domain to c-domain dominates the total piezoelectric response. Our observation of fast 90° domain switching opens up exciting new possibilities for ultrafast electromechanical switches and sensors that including piezoelectric transistor applications that rely on 90° domain wall motion 27 .

Conclusion
In summary, we used time-resolved synchrotron XRD in conjunction with a high-speed pulse generator to demonstrate the average lattice and domain motions as well as the tilting angle of the domains. The 90° domain can be switched by a 200-ns-wide electric field. The change in tilt angles of Δα = 0.05° in the a-domain and Δβ = −0.03° in the c-domains were observed under an applied electric field, commensurate with a change in V c and tetragonality (c/a). Moreover, reversible 90° occurs within 40 ns, a limit set by our present electrical set up. This opens up exciting new possibilities for ultrafast electromechanical switches and sensors that rely on 90° domain wall motion.

Methods
Pb(Zr 0.4 Ti 0.6 )O 3 [PZT] films, 600 nm in thickness, grown on (100) c SrRuO 3 -coated (100) KTaO 3 substrates by pulsed-metal organic chemical vapour deposition (MOCVD) were used for measurements. Details of the sample preparation are given elsewhere 28 . SrRuO 3 , which was indexed by a pseudo-cubic notation like hkl pc here, was grown by a RF-magnetron sputtering method reported in our previous paper 29 . For applying an electric field to this film, Pt top electrodes 100 μm in diameter were fabricated on the PZT films by electron-beam evaporation.
To determine the structural characterisations of the PZT films before applying an electric field, high-resolution X-ray diffraction (HRXRD) and 2θ-ω mapping were performed with a 12.4-keV X-ray beam at the National Institute for Materials Science (NIMS) beam line, BL15XU, of SPring-8, Japan.
In-situ observation of the change in lattice parameters and domain structure with an applied electric field was carried out at the BL13XU at SPring-8 for Pt/PZT/SrRuO 3 capacitors. To acquire the electric field-induced changes in diffraction data, an incident beam with photon energy of 12.4 keV was focused down to a few micrometres in width and height using a two-dimensional focusing refractive lens and irradiated on the Pt top electrode with the help of a fluorescent X-ray detector. We applied pulse voltages with a magnitude of 10 V and monitored the changes in 400 and 004 diffraction peaks. A positive 10-V square pulsed voltage 200 ns in width was applied to the capacitor to obtain sufficient poling treatment prior to measurement. The 200-ns square pulsed electric field was applied using a pulse generator (Agilent, 8114 A) and FCE-HS3 (Toyo, 6321). Time-resolved X-ray diffraction was measured using a high-speed avalanche photodiode detector (APD). The pulse height generated by a time-to-amplitude converter (ORTEC 567), for which X-ray pulse measured by the APD detector was used as a start signal and pulse signal synchronized to the electric pulse applied to the PZT films was used as a stop signal, is canalized by a multi-channel analyser. This technique cannot detect more than one photon for one period, so that properly attenuated X-rays were irradiated. No remarkable fatigue was confirmed during measurements (see Fig. S4). Detailed description of the time-resolved synchrotron X-ray diffraction measurement is given elsewhere 30 .