이학박사학위논문 Flexoelectric Control of Ferroelectric Properties and Electronic Functions in Epitaxial BiFeO 3 Thin Films 켜쌓기성장시킨비스무스페라이트박막에서 강유전성과전기기능성의변전제

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1 저작자표시 - 동일조건변경허락 2.0 대한민국 이용자는아래의조건을따르는경우에한하여자유롭게 이저작물을복제, 배포, 전송, 전시, 공연및방송할수있습니다. 이차적저작물을작성할수있습니다. 이저작물을영리목적으로이용할수있습니다. 다음과같은조건을따라야합니다 : 저작자표시. 귀하는원저작자를표시하여야합니다. 동일조건변경허락. 귀하가이저작물을개작, 변형또는가공했을경우에는, 이저작물과동일한이용허락조건하에서만배포할수있습니다. 귀하는, 이저작물의재이용이나배포의경우, 이저작물에적용된이용허락조건을명확하게나타내어야합니다. 저작권자로부터별도의허가를받으면이러한조건들은적용되지않습니다. 저작권법에따른이용자의권리는위의내용에의하여영향을받지않습니다. 이것은이용허락규약 (Legal Code) 을이해하기쉽게요약한것입니다. Disclaimer

2 이학박사학위논문 Flexoelectric Control of Ferroelectric Properties and Electronic Functions in Epitaxial BiFeO 3 Thin Films 켜쌓기성장시킨비스무스페라이트박막에서 강유전성과전기기능성의변전제어연구 2014 년 2 월 서울대학교대학원 물리천문학부 전병철

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4 Flexoelectric Control of Ferroelectric Properties and Electronic Functions in Epitaxial BiFeO 3 Thin Films Byung Chul Jeon Supervised by Professor Tae Won Noh A Dissertation submitted to the Faculty of Seoul National University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy February 2014 Department of Physics and Astronomy Graduate School Seoul National University

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6 Flexoelectric Control of Ferroelectric Properties and Electronic Functions in Epitaxial BiFeO 3 Thin Films 켜쌓기성장시킨비스무스페라이트박막에서 강유전성과전기기능성의변전제어연구 지도교수노태원 이논문을이학박사학위논문으로제출함 2013 년 11 월서울대학교대학원물리 천문학부전병철 전병철의박사학위논문을인준함 2013 년 11 월 위원장 유재준 ( 인 ) 부위원장 노태원 ( 인 ) 위원 박제근 ( 인 ) 위원 최석봉 ( 인 ) 위원 부상돈 ( 인 )

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8 Abstract Abstract Flexoelectricity is the generation of an electric field by a strain gradient via electromechanical coupling. Although it was first theoretically reported by Kogan in the 1968, there have been few studies on flexoelectricity in bulk solid materials. It is because the flexoelectric effects are expected to be quite small in the rigid bulk solids. Recently, however it was reported that the strain gradient in epitaxial oxide thin films could be 6 or 7 orders of magnitude larger than the corresponding bulk values. As a result, flexoelectric effect has been emerging as a fascinating means for exploring the physical properties in epitaxial ferroelectric thin films. In this dissertation, I will report the effect of deposition temperature to the defect evolution and ferroelectric properties in BiFeO 3 thin films. I could successfully control the strain evolution of the BiFeO 3 films by varying the deposition temperature and the film thickness. I will show that the flexoelectric effect can reverse the as-grown polarization direction and associated changes in the electronic functional properties of BiFeO 3 thin films. Finally, I will show that the unusual coupling between internal electric field and defect formation in BiFeO 3 epitaxial thin films. By tailoring the internal electric field via flexoelectricity, I control the defect formation and achieve a nearly defect-free BiFeO 3 film that exhibits perfectly functional performances. Ferroelectric materials promise a broad range of functional electronic properties, which are generally governed by various defects. Critical to practical applications of ferroelectric properties is our ability for understanding and controlling the defect formation. To investigate the effects of deposition temperature to the defect evolution and i

9 Abstract the ferroelectric properties of the BiFeO 3 thin films, I grew BiFeO 3 thin films on (001) SrTiO 3 substrates using pulsed laser deposition at temperatures in the range of C at intervals of 10 C. Interestingly, I found that defects appeared at temperatures greater than 590 C and threshold temperature is between 580 C and 590 C. The defects led to significant changes in the optical absorption and impurity peaks in X-ray diffraction data. Analysis of the X-ray diffraction data indicates that the defects are Fe 2 O 3. Atomic force microscopy measurements showed that the appearance of defects accompanied an abrupt increase in the surface roughness. Furthermore, the presence of the defects significantly affected ferroelectric hysteresis. Our results suggest that the evolution of defects in BiFeO 3 thin films depends strongly on the deposition temperature. The flexoelectric effect can play an important role in determining the domain configurations and electronic transport properties in ferroelectric epitaxial thin films, due to its intrinsic and universal existence in every dielectric material. In BiFeO 3 epitaxial films with a large strain gradient, the flexoelectric and interfacial effects compete with each other in establishing the self-polarization state. The competing effects in the films were introduced by fabricating BiFeO 3 thin films of two different strain states, varying the deposition temperature and/or the film thickness. We found that uniaxially, fully strained BiFeO 3 films were self-poled, having a downward polarization; this indicated that the interfacial effect was dominant. In contrast, the relaxed films had upward selfpolarization, indicating that the flexoelectric effect was dominant. Interestingly enough, the two kinds of films also exhibited different unidirectional current flows, referred to as the diode effect. By understanding the self-poling mechanisms in BiFeO 3 films, such as ii

10 Abstract ferroelectric hysteresis and electronic transport characteristics, the configuration of the asgrown films can be optimized to allow full utilization of the ferroelectric functional device. Finally, internal fields (E int ) can be induced in ferroelectric thin film during the growth. Numerous origins have been proposed for the built-in electric field, namely, interfacial effects, flexoelectricity, defects, and piezoelectricity, and so on. I demonstrate that the defect formation in BiFeO 3 thin films critically depends on the internal electric field in the films. The large, systematic control of internal electric field is achieved via flexoelectricity, which can thereby modify the defect formation and associated electronic functions of the films. Such a flexoelectric control can be utilized to achieve a nearly defect-free BiFeO 3 film that exhibits perfectly functional performances, such as imprintfree polarization switching and switchable diode effect. This results highlight that flexoelectricity can dramatically modify the defect formation even with a small variation of growth parameters, emphasizing its potential key role in defect engineering. Our study provides novel insight into defect engineering, as well as a foundation for fully utilizing functional materials. Keywords: BiFeO 3, ferroelectric, strain gradient, flexoelectric effect, epitaxial thin film, self-polarization, defects, internal field. Student number: iii

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12 Contents Abstracts (English).i List of Figures...ix 1 Introduction BiFeO Flexoelectric effect in ferroelectrics Defect formation via internal electric field Experimental detail Pulsed laser deposition Williamson-Hall plot by high-resolution X-ray diffraction Piezoelectric force microscopy The effect of the deposition temperature on the formation of defects in BiFeO 3 thin films Introduction Experiments Fabrication of BiFeO 3 thin films Experimental setup and methods for characterizations Results and discussions Investigation of defects High-resolution X-ray diffraction Optical spectroscopy Atomic force microsopy 26 v

13 Contents Ferroelectric properties Conclusion Flexoelectric effect in the reversal of self-polarization and electronic functionalities of epitaxial ferroelectric thin films Introduction Flexoelectric effect Domain engineering in ferroelectrics Self-polarization in ferroelectric thin films Experiments Sample preparation Characterization of crystal structures Piezoresponse force microscopy Electrical measurements T D effect in BiFeO 3 thin films Uniaxially strain and relaxed BiFeO 3 thin films Thickness & T D -dependent lattice relaxation Mechanism of self-polarization As-grown domain state in BiFeO 3 thin films Reversal of self-polarization in BiFeO 3 thin films Estimation of flexoelectric field Williamson-Hall plot Estimation of strain gradient and flexoelectric field...53 vi

14 Contents 4.6 Control of electronic functional properties Configuration of defects P V hysteresis loops Electronic transport characteristics Conclusion Flexoelectric control of defect formation and electronic functions in ferroelectric thin films Introduction Results Experiments Thin films fabrication Structural analysis Electrical measurements Large dependence of strain gradient on T D Functional properties of BiFeO 3 films according to T D Defect configurations in BiFeO 3 films according to T D Large, systematic control of E int via flexoelectricity Demonstration of the E int effect on defect formation Discussion Conclusion Conclusion 93 vii

15 Contents Appendix.. 97 Publication List 국문초록 (Abstract in Korean) 감사의글 (Acknowledgements) viii

16 List of Figres List of Figures Figure 1.1 Phase control in ferroics and multiferroics. The stress σ, electric field E, and magnetic field H control the strain ε, electric polarization P, and magnetization M, respectively. For example, in a multiferroic material, H may control P and ε, or E may control ε and M, or σ may control P and M [1]. Figure 1.2 (a) Polarization hysteresis loop of an epitaxial BFO film grown on STO(111) with remnant polarization P r ~ 100 μc cm 2. (b) Four possible ferroelectric polarization variants in BFO [3]. Figure 1.3 I V curves taken both on the domain wall (black) and off the domain wall (red) reveal Schottky-like behaviour. Inset indicates the out-of-plane PFM image of a written 180 domain in a monodomain BFO(110) film [9]. Figure 1.4 (a) J E curves of bulk BFO after +150 V, 150 V. and +150 V pulses, in sequence. The diode forward and reverse directions switch when the direction of out-ofplane polarization is reversed by ±150 V pulses. The diode forward direction turns out to be the same as the direction of electric pulses used for polarization flipping [10]. (b) The zero-bias photocurrent density as a function of time with (top) green light (λ = 532 nm) or (bottom) red light (λ = 650 nm) on or off, shining on the different sides of bulk BFO (a sketch is shown in the inset). (c) and (d) Atomic resolution STEM images of the T phase and the R phase, respectively. Insets show schematic illustration of the unit cell [11]. Figure. 1.5 Schematic description of the evolution of the strain relaxation in epitaxial thin films. ix

17 List of Figres Figure 2.1 Schematic diagram of a pulsed laser deposition chamber. Figure 2.2 (a) Fitting results of (001), (002), (003), and (004) diffraction peaks; peak shapes are well fitted using Pearson VII function. (b) W-H plots for the inhomogeneous strain ε I. The numerical values of ε I were determined from the slope of the fit equation [6-8]. Figure 2.3 Sketch of domain nucleation in PFM. The dashed arrows indicate the electric field (denoted E field) lines. The solid needlelike (blue) figures show reversed domains (i.e., nuclei). The BE indicates the bottom electrode. Adapted from Yang et al. [10]. Figure 2.4 From left to right, topography, out-of-plane (OP) amplitude, OP phase, inplane (IP) amplitude, and IP phase images of epitaxial BiFeO 3 thin film. Figure 3.1 XRD θ 2θ scans of the BFO films grown at various T D (from bottom to top T D = 570 C, 580 C, 590 C, and 600 C). The peaks are indexed with the following symbols: B: BFO, S: STO, : Fe 2 O 3. Figure 3.2 (a) The imaginary part of the dielectric function of the BFO films. (b) Schematic band diagram of the BFO thin films. The yellow band indicates the defect level. Peaks indicated by the blue and red arrows correspond to the optical transition from O 2p to defect and Fe 3d levels, respectively. Figure 3.3 Surface roughness of the BFO films. The inset shows AFM images of the BFO films grown at various T D. Figure 3.4 P E hysteresis loops of the BFO films grown at various T D. The inset shows x

18 List of Figres P E hysteresis loops of the BFO film grown at 600 C. Figure 4.1 XRD θ 2θ scans of the 250-nm-thick BFO films grown at 570 C (solid red line) and 550 C (solid black line) on vicinal STO (001) substrates. The gray short-dashed and solid vertical lines indicate the (002) diffraction peak positions of the fully strained and relaxed BFO films on STO substrates, respectively. Figure 4.2 RSMs around the {103} STO Bragg family of peaks with various angles for 250-nm-thick US- and R-BFO films. The (103), (103), (013), and (013) peaks can be distinguished from each other in the RSM data, due to the large rhombohedral distortion of the BFO unit cell [22]. Figure 4.3 (a) HRXRD θ 2θ scans of BFO films grown at 570 C between 50 and 250 nm thick. The closed blue triangles, black circles, and open-inverted triangles indicate the (002) peaks of BFO, SRO, and STO, respectively. The gray dash-dotted and solid lines indicate the (002) diffraction peak positions of the fully strained and relaxed BFO films on STO substrates, respectively. The θ 2θ scans show that the 50-nm-thick film is fully strained in the [001] direction. However, above a critical thickness, the strain should start to relax. As the film thickness increased, the 2θ peak position moved to larger angles, indicating that the average c-axis lattice constant became smaller. (b) (e) RSM images around the (013) STO Bragg peaks of BFO films grown at 570 C between 50 and 250 nm thick. As displayed in the RSM data, all of these films were fully strained along the [010] direction; i.e., they should be US-BFO films. Figure 4.4 (a) and (b) Pseudocubic lattice parameters as a function of the film thickness xi

19 List of Figres for US- and R-BFO films, respectively. The solid and dotted gray lines represent the lattice parameter of bulk BFO and STO, respectively. Figure 4.5 Schematic representation of the direction of the strain relaxation for US-BFO films. The dark and pale gray areas represent strongly strained and relaxed BFO regions, respectively. (a), (b), and (c) indicate the schematic diagram top, side, and front views of the US-BFO film, respectively. The large blue arrow indicates the direction of vertical flexoelectric field (E F,3 ). The green-dotted and black solid-line arrows indicate the direction of ferroelectric polarization, P 1 and P 4, respectively. (d) Possible orientations of the polarization for US-BFO films on vicinal STO substrates. The stepbunching process and lattice dislocations (higher-order terms) are neglected in this representation. Recently, we demonstrated that in BFO films grown on vicinal STO substrates, some structural relaxation can occur through the step-bunching process and lattice dislocations [38]. However, because the resulting crystallographic tilt angle and the c-axis lattice constant should be higher-order variations, we neglected such effects in the schematic diagram [38]. To make the strain gradient more visible, we exaggerated the difference in the length scale of the BFO unit cells. Figure 4.6 (a) XRD θ 2θ scans of BFO films grown at 550 C between 50 and 250 nm thick. The closed blue triangles, black circles, and open-inverted triangles indicate the (002) peaks of BFO, SRO, and STO, respectively. The gray dash-dotted and solid lines indicate the (002) diffraction peak positions of the fully strained and relaxed BFO films on STO substrates, respectively. The θ 2θ scans show that the 50-nm-thick film is fully strained. However, above a critical thickness, the strain should start to relax. As the film xii

20 List of Figres thickness increased, the 2θ peak position moved to larger angles, indicating that the average c-axis lattice constant became smaller. (b) (e) RSM images around the (013) STO Bragg peaks of BFO films grown at 550 C between 50 and 250 nm-thick. As displayed in the RSM data, the 50-nm-thick BFO film is fully strained. Above the critical thickness, the films were relaxed; i.e., they should be R-BFO films. Figure 4.7 Schematic diagram of the direction of the strain relaxation for R-BFO films. The dark and pale gray areas represent strongly strained and relaxed regions, respectively. (a), (b), and (c) Schematic diagram top, side, and front views, respectively. The large red and blue arrows indicate the direction of the horizontal (E F,1 ) and vertical (E F,3 ) flexoelectric fields, respectively. (d) Possible polarization orientation for R-BFO films. The green-dotted and black solid-line arrows indicate the direction of ferroelectric polarization, P 1 and P 4, respectively. The step-bunching process and lattice dislocations (higher-order terms) are neglected in this representation [38]. Figure 4.8 (a) and (b) Out-of-plane PFM images with 50-, 120-, 180-, and 250-nm-thick BFO films. The bright yellow and dark regions indicate the up- and down-polarization states, respectively. Figures 4.9 P V loops for (a) 50-, (b) 120-, (c) 180-, and (d) 250-nm-thick BFO films grown at 570 C; (e) 50-, (f) 120-, (g) 180-, and (h) 250-nm-thick BFO films grown at 550 C. The 50-nm-thick BFO films exhibited a leaky behavior. The 120-, 180-, and 250- nm-thick US-BFO (R-BFO) films showed negative (positive) imprint characteristics. These imprint behaviors were nearly consistent with thickness dependence of selfpolarization direction, as shown in the PFM images of Figures 4.8a and 4.8b. xiii

21 List of Figres Figure 4.10 Magnitude of the flexoelectric and interfacial effects as a function of film thickness. The red and black-dashed curves indicate the flexoelectric and interfacial effects, respectively. The right and left insets indicate the fully strained and relaxed BFO films, respectively. Figure 4.11 (a) Out-of-plane and (b) in-plane W-H plots for the inhomogeneous strain of the BFO films. Figure 4.12 (a) and (b) Schematic diagram of the location of the V O -rich defect layer in US- and R-BFO films, respectively. The large white arrows represent the as-grown polarization direction. Figure 4.13 (a) and (b) P V hysteresis loops of the US-and R-BFO films, respectively. Vertical gray-dashed lines indicate the voltage center of hysteresis loops. Figure 4.14 (a) and (b) J V curves of US- and R-BFO films, respectively. Figure 5.1 Structural analysis. (a) XRD θ 2θ scans of 250-nm-thick BiFeO 3 films gr own at T D = 550, 560, 570 and 580 C on vicinal SrTiO 3 (001) substrates. The gray s hort-dashed and solid vertical lines indicate the (002) diffraction peak positions of t he fully strained and relaxed BiFeO 3 films on SrTiO 3 substrates, respectively. (b) RSM images around the (013) SrTiO 3 Bragg peaks for 250-nm-thick BiFeO 3 films grown at T D = 550, 560, 570 and 580 C. Figure 5.2 Large, systematic variation of strain gradient, according to T D. (a) Expected surface mobility of adatoms at the T D range of 550 to 580 C. The inset schematically depicts the mobility of adatoms at each T D. (b) The measured strain gradients in 250-nm- xiv

22 List of Figres thick BiFeO 3 films for different T D. These values, estimated at room temperature, are believed to remain almost unchanged at high temperatures (during film-growth process), due to similar thermal lattice expansion of perovskite materials. Solid lines are the guide to eyes. Figure 5.3 Large dependence of strain gradient on T D. (a,b) Upper panels show atomic force microscopy images of 250-nm-thick BiFeO 3 films for (a) T D = 550 C and (b) 580 C. The film surface for T D = 580 C has a typical morphology of the step-flow growth mode. On the other hand, for T D = 550 C, the lateral length of BiFeO 3 grains became much shorter, possibly due to the limited mobility of adatoms at lower T D. Lower panels schematically describe the expected strain profile for (a) T D = 550 C and (b) 580 C. Considering the relationship bewteen the grain shape (e.g., aspect ratio) and strain relaxation, we can expect a larger strain gradient for lower T D. (c) Rough estimation of inplane strain gradient. According to a general model for the strain profile [23,24], independent of the actual relaxation mechanism, the in-plane strain ε can be expressed as follows: ε(x) = ε 0 e x/δ (2) where ε 0 and δ are constants, and x is the distance from the step edge. Typically, a film can be fully strained near the step edge (i.e., x = 0), due to a strong clamping effect. Also, we know the average in-plane strain values from the RSM results. Thus, using these information and Eq. (2), we can roughly estimate the profile of in-plane strain gradient. We here assumed the width of step terraces as 100 nm. The estimated values were found to be quite comparable with those obtained by W-H plots (Fig. 2b). xv

23 List of Figres Figure 5.4 Electronic functions of BiFeO 3 films, according to T D. (a) P E hysteresis loops for 250-nm-thick BiFeO 3 films deposited at four different T D of 550, 560, 570 and 580 C. (b) J E curves measured for 250-nm-thick BiFeO 3 films deposited at four different T D. Figure 5.5 The shift of P E loops. (a,b) P E hysteresis loops of 250-nm-thick BiFeO 3 films for (a) T D = 550 C and (b) 570 C. We recently demonstrated that the shift of P E loops is mainly due to the pinning field (E dd ) by defect dipoles (D defect ) [27]. We also found that the D defect alignmnent (and associated E dd direction) can be reversed by the polarization switching and subsequent annealing, which modifies the P E hysteresis loops (i.e., the direction of shift). (Details of the annealing procedure are explained in ref. 27.) (c,d) Schematic illustrations describing the D defect and E int (= E if + E flexo ) direction of the as-grown (left) and annealed state (right), for (c) T D = 550 C and (d) 570 C. (e) The direction of E dd (by D defect ) can be reversed after the annealing precedure, whereas the E int direction should be nearly unchanged. This means that the shifted value (E shift ) of P E loops can be expressed as E shift = ±E dd + E int (+: for as-grown state, : for annealed state) (3). Thus, using the E shift values (obtained from P E loops), we can estimate the values of E dd and E int, as shown in (e). The estimated values indicate that the shift of P E loops is mainly due to E dd (by D defect ), with small contribution from E int. Referring to the straingradient values (Fig. 5.2) for T D = 550 C and 570 C, we also determined the values of E if and E flexo, which are comparable with the calculated E if (ref. 28) and estimated E flexo values (Fig. 5.8). xvi

24 List of Figres Figure 5.6 Defect configurations in BiFeO 3 films, according to T D. (a) The schematic configurations of D defect and V O -rich layer in BiFeO 3 films according to T D, determined from the measurements of P E loops and J E curves. (b) The shift in P E loops of 250- nm-thick BiFeO 3 films, as a function of T D. We normalized the shifted values (E shift ) of P E loops by the coercive field (i.e., E c = (E c,+ E c, )/2). (c) Unit-cell volume (black closed squares) and estimated V O concentration (red closed circles) of 250-nm-thick BiFeO 3 films, as a function of T D. Figure 5.7 Two competing, intrinsic sources of E int in BiFeO 3 films on SrRuO 3 /SrTiO 3. (a) Interfacial charge discontinuity can generate the downward internal electric field (E if ) in BiFeO 3 films on SrRuO 3 /SrTiO 3 substrate [28]. Note that SrRuO 3 is self-terminated with SrO surface, since the RuO 2 -layer is highly volatile. (b) Relaxation of compressive misfit strain can generate the upward internal electric field (E flexo ) via flexoelectricity in BiFeO 3 films on SrRuO 3 /SrTiO 3 substrate. Figure 5.8 Large, systematic control of E int via flexoelectricity. The estimated E int for 250-nm-thick BiFeO 3 films, as a function of T D. Using the measured values of strain gradient, we estimated E flexo, projected onto the ferroelectric polarization direction (i.e., [111] or its equivalent ones). Red open and closed squares correspond to E flexo for the flexoelectric coefficient λ = 1.0 and 0.25, respectively. Red dashed line represents the averaged values of E flexo for λ = 1.0 and Blue open triangles represent E if, obtained by referring to the calculated values (ref. 9) and projecting them onto the polarization direction. Black solid line represents E int (= E flexo + E if ) according to T D, obtained by summing E flexo and E if. The positive (or negative) E int indicates the upward (or downward) xvii

25 List of Figres field direction. Figure 5.9 Demonstration of the E int effect on defect formation. (a,b) Schematics of the E int variation according to the film thickness t, for (a) T D = 550 and (b) 570 C. Red, blue and black arrows represent E flexo, E if and E int, respectively. The length o f arrows indicates the magnitude of the associated electric field. (c,d) The measure d shift of P E loops (black closed circles) and unit-cell volume (red open squares) as a function of t, for (c) T D = 550 and (d) 570 C. Solid lines are the guide to eyes. Figure 5.10 Effect of E int on polarization-mediated defect formation. (a) Schematic illus tration of the defect formation in ferroelectrics. Defect dipoles (D defect ) acquire the energy gain for their formation by the interaction with ferroelectric polarization P (ref. 27,35,36). Usually, cation vacancy (V cation ) or impurity forms D defect together w ith oxygen vacancy (V O ). Also, the interfacial accumulation of positively charged V O can have the energy gain by compensating the negative polarization charge, res ulting in the formation of V O -rich layer [37,38]. (b) Expectation of polarization profile at high temperatures during film growth, according to E int. For E int 0, the inter action between charged point defects and polarization can be weakened due to the rmal fluctuation (~k B T) of polarization, inhibiting the polarization-mediated defect fo rmation. On the other hand, if a large E int exists, it can induce a noticeable magnitude of polarization, as well as stabillize the ferroelectric polarization against thermal fluctuation. (c) The polarization-mediated defect formation can be promoted under a large E int. Figure 5.11 Possible effect of E int on the formation of point defects. (a) A large E int ca n cause the lattice volume expansion by piezoelectric effect in ferroelectrics. [Note xviii

26 List of Figres that E int can also cause the crystal volume expansion (as large as ~1.0 % locally) by electrostrictive effect in polar materials, already reported in ref. 39.] (b) The formation of point defects is accompanied with the increase of unit-cell volume, requiring an energy cost (e.g., from elastic energy). If the unit-cell volume is already large, the energy cost for the defect formation can be reduced. Referring to a recent theoretical work [40], we can expect that the formation of point defects can be mo re promoted for the enlarged unit cell under a large E int, increasing the equilibriu m defect concentration in our BiFeO 3 films. (c) In order to quantitatively explore a possible crystal volume expansion by E int, we consider the E flexo contribution. Th e strain relaxation and associated E flexo follow the exponential decay as a function of distance (d) from the bottom interface (i.e., e d / ). We assumed the averaged E flexo value of V m 1 and the δ value of 40 nm. We also used three differe nt values (d 33 = 100, 150, and 200 pm V 1 ) for converse piezoelectric coefficient. The d 33 value of BiFeO 3 is around pm V 1 at room temperature. Note that the d 33 is roughly proportional to the dielectric permittivity and polarization (i.e., P ), and thus can show the increasing trend as the temperature increases and approaches to the Curie temperature. In spite of the parameter dependence, our res ult evidently shows that the E int can lead to a lattice-volume expansion (as large a s locally %) at high temperatures during film growth. Figure A.1 (a) BFO/SRO/STO 박막의 θ-2θ 를 (001), (002), (003), 그리고 (004) 까 지측정한데이터. (b) BFO 박막 peak 을 Pearson VII 식을이용한 fitting. 여기서 xix

27 List of Figres β BFO 는 BFO 박막의 FWHM 값. Figure A.2 Out-of-plane WHP. 기울기는 inhomogeneous strain, ε I 를나타낸다. Figure A.3 BFO/SRO/STO 박막의 (013), (023), 그리고 (033) 까지측정한 RSM 데이터. I used the line width in the k-direction of the RSM peaks (013), (023), and (033) of BFO films. xx

28 Chapter 1 Chapter 1 Introduction 1.1 BiFeO 3 BiFeO 3 (BFO) is one of the most interesting multiferroic materials [1,2]. It simultaneously has at least two order parameters, i.e., ferroelectricity [2], ferroelasticity [3], and antiferromagnetism [1,2]. It has been explored for several decades, since they offered the possibility of manipulating the magnetic polarization by an electric field or vice versa, as shown in Figure 1.1. Magnetoelectric multiferroics are technologically and scientifically promising because of their potential applications in data storage, spintronics, sensor applications, etc. The ferroelectric and antiferromagnetic ordering temperatures are far above room temperature; the Curie and Néel temperatures are 1103 and 643 K, respectively [2]. Moreover, among all known ferroelectrics, BFO has the largest remnant polarization of 100 μc cm 2 along [111] direction, as shown in Figure 1.2(a). The bulk BFO shows rhombohedral (a=5.58 Å and α=89.5 ) crystal structure at room temperature with the space group R3c and G-type antiferromagnetism. There are four possible polarization variants, r 1, r 2, r 3, and r 4 in BFO, as shown in Figure 1.2(b) [3]. These properties make BFO be a promising ferroelectric material for applications, such as 1

29 Chapter 1 magnetoelectrics [4,5], ferroelectric random-access memory [7], photovoltaics [8], etc. Figure 1.1 Phase control in ferroics and multiferroics. The stress σ, electric field E, and magnetic field H control the strain ε, electric polarization P, and magnetization M, respectively. For example, in a multiferroic material, H may control P and ε, or E may control ε and M, or σ may control P and M [1]. (a) P ( C/cm 2 ) (b) -100 BFO/SRO/STO(111) Voltage (V) Figure 1.2 (a) Polarization hysteresis loop of an epitaxial BFO film grown on STO(111) with remnant polarization P r ~ 100 μc cm 2. (b) Four possible 2

30 Chapter 1 ferroelectric polarization variants in BFO [3]. There have been many issues in BFO material due to the intriguing physical properties from the last decade. Seidel et al. reported the observation of roomtemperature electronic conductivity at ferroelectric domain walls in the insulating BFO thin film [9]. Figure 1.3 shows the current voltage (I V) curves at the domain (red solid line) and domain wall (black solid line), respectively. They observed Schottky-like conduction behavior at the domain wall. Choi et al. reported a switchable diode and photovoltaic effects in BFO single crystal, as shown in Figure 1.4a and 4b [10]. Using a combination of epitaxial growth techniques in conjunction with theoretical approaches, Zeches et al. showed the formation of a morphotropic phase boundary through epitaxial constraint in lead-free piezoelectric bismuth ferrite films (show Figure 1.4c and 4d) [11]. Figure 1.3 I V curves taken both on the domain wall (black) and off the domain wall (red) reveal Schottky-like behaviour. Inset indicates the out-of-plane PFM image of 3

31 Chapter 1 a written 180 domain in a monodomain BFO(110) film [9]. 1.2 Flexoelectric effect in ferroelectrics Flexoelectricity is the generation of an electric field by a strain gradient via electromechanical coupling. This effect was predicted theoretically by Kogan in 1964 [12] and experimentally observed by Bursian and Zaikovskii in 1968 [13]. The phenomenon was given the name flexoelectricity by Indenbom et al. in 1981 [14]. Despite its long history, there has been little research on flexoelectricity of bulk solid materials [14-24], because its effects had been widely accepted to be quite small. Namely, the flexoelectric coefficients are small ( C m 1 ) [23], and the strain gradients generated by mechanical bending are quite small, typically on the order of 0.1 m 1 [24]. Recently, there has been much interest in flexoelectricity, especially regarding epitaxial thin films [25-31]. Inside these material systems, a strain gradient as large as m 1 can be produced [25,26]. Note that this value of the strain gradient is 6 or 7 orders of magnitude larger than the corresponding bulk values. Figure 1.5 indicates the strain gradient by relaxation of strain in epitaxial thin film. Using numerous epitaxial ferroelectric thin films, experimental studies showed that flexoelectricity can affect the domain configuration and imprint [26], dielectric constant [27,28], continuous rotation of the spontaneous polarization direction [29], polarization switching by mechanical force [30], and unusual coupling between electronic transport and the mechanical strain gradient [31]. 4

32 Chapter 1 a b c d Figure 1.4 (a) J E curves of bulk BFO after +150 V, 150 V. and +150 V pulses, in sequence. The diode forward and reverse directions switch when the direction of out-of-plane polarization is reversed by ±150 V pulses. The diode forward direction turns out to be the same as the direction of electric pulses used for polarization flipping [10]. (b) The zero-bias photocurrent density as a function of time with (top) green light (λ = 532 nm) or (bottom) red light (λ = 650 nm) on or off, shining on the different sides of bulk BFO (a sketch is shown in the inset). (c) and (d) Atomic resolution STEM images of the T phase and the R phase, respectively. Insets show schematic illustration of the unit cell [11]. 5

33 Chapter 1 relaxation of strain within tens of nm Fully relaxed Relaxation region Fully strained Substrate O B A E flexo Figure 1.5 Schematic description of the evolution of the strain relaxation in epitaxial thin films. 1.3 Defect formation via internal electric field The advancement of materials science relies on our ability to modify and optimize a wide range of functional properties. These properties, including electronic, magnetic, and optical properties, critically depend on the type and concentration of defects, which exist in every material. Particularly in ferroelectrics, defects play a governing role in the control and optimization of these materials [32,33]. Typical ferroelectric materials allow for a diversity of point defects and extended defects, which sometimes seem unavoidable even with the well-chosen fabrication conditions. These defects are usually detrimental to a functional ferroelectric property [32], but can be desirable for some functions, such as giant electromechanical response [34] and multilevel data storage [35]. This makes it necessary to fully understand the mechanism of defect formation, for relevantly controlling defects and their effect. While our understanding still continues to evolve, the exact mechanism of defect formation remains unclear, with many important factors 6

34 Chapter 1 unresolved. The interaction between polarization and charged point defects is one of the wellknown mechanisms for defect formation in ferroelectrics [34-38]. It has been widely accepted that ferroelectric polarization drives charged point defects (e.g., vacancies) to migrate towards the energetically preferred sites, facilitating the defect formation during fabrication process. However, it has been overlooked that such polarization-mediated defect formation can be more promoted by other intrinsic polarizations, which have a different origin from the ferroelectric polarization. Recent studies reported that in epitaxial thin films, a huge internal electric field (E int ) can emerge intrinsically by various sources, such as interfacial charge discontinuity [39,40] and strain gradient [26,29], generating a considerable magnitude of polarization. Its magnitude can be around E int = 10 6 V m 1 on the average and even as large as V m 1 locally, which can induce the polarization of 1 10 μc cm 2 and seems large enough to affect the defect formation at high temperatures. Therefore, although overlooked so far, it would be critical to explore how such E int and induced polarization influence the defect formation in thin films. Particularly, flexoelectricity (i.e., generation of E int by strain gradient) [24,26,40-43] has recently gained much attention. The strain gradient naturally breaks the inversion symmetry and thus can induce an electric response and intriguing phenomena in all dielectric materials. Especially regarding epitaxial thin films, in which the lattice mismatch can give rise to very steep elastic strain relaxation, the strain gradient becomes huge and the associated flexoelectric field can be as large as 10 7 V m 1. This flexoelectric field has played an important role in novel electronic functions, such as 7

35 Chapter 1 domain control [26], flexoelectric rotation of polarization [40], mechanical writing of polarization [30], and flexoelectric diode [31]. Despite such universal, strong nature of flexoelectricity, however, its possible influence on the defect formation during thin-film epitaxy has received little consideration. The exploitation of such an effect would allow the design of defect configuration and associated electronic functions, as well as provide a pathway to unravelling the fundamental physics of defect formation. 8

36 Chapter 1 References 1. N. A. Spaldin and M. Fiebig, Science 309, 391 (2005). 2. J. Wang et al., Science 299, 1719 (2003). 3. S. H. Baek et al., Nat. Mater. 9, 309 (2010). 4. T. Zhao et al., Nature Mat. 5, 823 (2006). 5. M. Fiebig et al., Nature 419, 818 (2002). 6. N. A. Hill and K. M. Rabe, Phys. Rev. B 59, 8759 (1999). 7. D. Lee et al., Adv. Mater. 24, 402 (2012). 8. W. Ji et al., Adv. Mater. 22, 1763 (2010). 9. J. Seidel et al., Nature Mat. 25, 229 (2009). 10. T. Choi et al., Science 324, 63 (2009). 11. R. J. Zeches et al., Science 326, 977 (2009). 12. S. M. Kogan, Sov. Phys. Solid State, 5, 2069 (1964). 13. E. V. Bursian et al., Sov. Phys. Solid State 10, 1121 (1968). 14. V. L. Indenbom et al., Kristallografiya 26, 1157 (1981). 15. A. K. Tagantsev, Phys. Rev. B 34, 5883 (1986). 16. W. Ma, L. E. Cross, Appl. Phys Lett. 78, 2920 (2001). 17. R. Resta, Phys. Rev. Lett. 105, (2010). 18. R. Maranganti, and P. Sharma, Phys. Rev. B 80, (2009). 19. A. K. Tagantsev, V. Meunier, P. Sharma, MRS Bulletin, 34, 643 (2009). 20. A. Gruverman et al., Appl. Phys. Lett. 83, 728 (2003). 21. W. Ma and L. E. Cross, Appl. Phys. Lett. 86, (2005). 9

37 Chapter W. Ma, L. E. Cross, Appl. Phys. Lett. 88, (2006). 23. L. E. Cross, J. Mater. Sci. 41, 53 (2006). 24. P. Zubko et al., Phys. Rev. Lett. 99, (2007). 25. D. Lee, T. W. Noh, Philos. Transact. A. Math. Phys. Eng. Sci. 370, 4944 (2012). 26. D. Lee, et al., Phys. Rev. Lett. 107, (2011). 27. G. Catalan et al., J. Phys.: Condens. Matter 16, 2253 (2004). 28. G. Catalan et al., Phys. Rev. B 72, (R) (2005). 29. G. Catalan et al., Nature Mater. 16, 963 (2011). 30. H. Lu et al., Science 336, 59 (2012). 31. D. Lee et al., Nano Lett. 12, 6436 (2012). 32. M. E. Lines, A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials, Clarendon, Oxford M. Dawber, K. M. Rabe, J. F. Scott, Rev. Mod. Phys. 77, 1083 (2005). 34. X. Ren, Nat. Mater. 3, 91 (2004). 35. D. Lee et al., Adv. Mater. 24, 6490 (2012). 36. D. Lee et al., Phys. Rev. B 84, (2011). 37. M. F. Chisholm et al., Phys. Rev. Lett. 105, (2010). 38. D. Lee et al., Phys. Rev. B 81, (2010). 39. A. Ohtomo, H. Y. Hwang, Nature 427, 423 (2004). 40. P. Yu et al., Proc. Natl. Acad. Sci. 109, 9710 (2012). 41. S. M. Kogan, Sov. Phys. Solid State 5, 2069 (1964). 42. G. Catalan et al., Phys. Rev. B 72, (R) (2005). 10

38 Chapter P. Zubko et al., Annu. Rev. Mater. Res. 43, 387 (2013). 11

39

40 Chapter 2 Chapter 2 Experimental detail 2.1 Pulsed laser deposition The choice of deposition method has a significant impact on the properties of oxide thin films [1-4]. Each deposition method has its own unique advantage and disadvantage that affects microstructure and physical property of films. Pulsed Laser Deposition (PLD) method offers a very wide range of deposition parameters, which makes it an attractive tool for investigating the effects of the deposition parameters.[5] For example, PLD has flexibility in controlling parameters like deposition temperature, deposition pressure, target material composition, growth rate. Figure 2.1 shows a schematic diagram of an experimental setup. It consists of a target holder and a substrate holder housed in a vacuum chamber. A high power laser is used as an external energy source to vaporize materials and to deposit thin films. A set of optical components is used to focus the laser beam over the target surface. 13

41 Target rotator Chapter 2 Window Focusing lens Target Plume Substrate Substrate Heater Reactive gas Figure 2.1 Schematic diagram of a pulsed laser deposition chamber. The decoupling of the vacuum chambers and the evaporation power source makes PLD more simple and flexible than with the constraints imposed by the use of internally powered evaporation sources. Because of the fast and very directional plume, attenuation due to trajectory change as a result of collisions with the background gas is small. Main advantages of PLD are listed as follows: Ability of using high pressures as well as ultra high vacuum (UHV) conditions. Flexibility and good control of substrate temperature by allowing heater designs in 14

42 Chapter 2 different complexity. High energy particles in plasma increased reactivity by using a large variety of process gases. Stoichiometric transfer from target to substrate Highly controllable deposition rate Multiple target usage for multilayer depositions Reduced deposition chamber size by placing the power source outside of the chamber, which eases the pumping operations. However, there are two major drawbacks of PLD. One is the lack of uniformity over a large area due to narrow angular distribution of the plume. It may be solved by rotation or translation of substrates. The other one, splashing which means, the deposition of particulates onto the substrates is an intrinsic problem, much more difficult to overcome. The occurrence of splashing has many origins. For example, surface boiling, exfoliation of target, etc. The solutions to avoid splashing are lowering the laser power density, using mechanical particle filter, which actually lowers the deposition rate. The parameters for the optimization of PLD conditions are listed as follows: Substrate temperature Growth rate Laser energy density Ambient gas pressure 15

43 Chapter 2 Laser beam intensity profile, which is determined by laser path and voltage. Annealing (Treatment after film deposition) Substrate pre-treatment 2.2 Williamson-Hall plot by high-resolution X-ray diffraction The crystal structure of thin films can be usually obtained from the high-resolution X- ray diffraction (HRXRD). Through HRXRD measurement combined with x-ray reflectometry (XRR) measurements, the lattice constants of the global film can be obtained along with the film thickness. On the other hand, θ-2θ scan shows the c-axis lattice constant of the film along with the thickness of the film. When a superlattice is deposited instead of thin film, satellite peaks can be observed due to the multiplied unit cell of the superlattice structure. By analyzing them we can confirm the period of the superlattices. In addition, by analyzing the reciprocal space mapping (RSM), we can obtain the information on the in-plane lattice constant. The x- and y-axis in the map corresponds to the reciprocal of the a- and c-axis, respectively. In order to calculate the vertical inhomogeneous strain (ε I ), four peaks (001), (002), (003), and (004) are selected from the XRD θ 2θ data, as-shown in Figure 2.2a. The following equation was used for the fit [6-8]. cos K / D 4 sin, where β is defined by sample substrate, and β sample and β substrate indicate the full-width at half maximum (FWHM) values of sample and substrate peaks, respectively [5], λ I 16

44 Chapter 2 = Ǻ, D is the coherence length along the scattering vector, K is a geometrical constant which was taken as 1. We adopted the Pearson VII function, 2 I( x) I(0) /(1 Cx ) m for fitting to obtain the more accurate line widths [8]. There are many approaches to the modeling of diffraction lines, but one of the most commonly used functions is the Pearson VII. The Pearson VII clearly includes the Lorentzian (m = 1) and it tends to a Gaussian as m. The solid lines are fitted results, as shown in Figure 2.2b. Similarly, we estimated the in-plane ε I of the films. To obtain the in-plane ε I, we used the line width in the k-direction of the RSM peaks (013), (023), and (033) of film and substrate. (I will explain the W-H plot method more detail in Appendix) (a) BFO(003) BFO(002) BFO(001) BFO(004) (b) 15 Intensity (arb. units) Δ2θ β BiFeO 3 thin film cos (10 3 ) sin Figure 2.2 (a) Fitting results of (001), (002), (003), and (004) diffraction peaks; peak shapes are well fitted using Pearson VII function. (b) W-H plots for the inhomogeneous strain ε I. The numerical values of ε I were determined from the slope of the fit equation [6-8]. 17

45 Chapter Piezoelectric force microscopy Piezoresponse force microscopy (PFM), a specialized atomic force microscopy (AFM) technique, is a very powerful method for direct visualization of ferroelectric (FE) static domain configurations and their dynamic behaviors at nanoscale [9-13]. All FEs should exhibit the piezoelectric effect, a linear coupling between mechanical strains and electric fields. When a stress is applied to FE materials, a mechanical displacement will be induced, leading to the generation of an electric field: we call this phenomenon as piezoelectric effect. PFM detect the converse piezoelectric response of FE materials, i.e., local mechanical vibrations induced by an applied external ac field. Figure 2.3 Sketch of domain nucleation in PFM. The dashed arrows indicate the electric field (denoted E field) lines. The solid needlelike (blue) figures show reversed domains (i.e., nuclei). The BE indicates the bottom electrode. Adapted from Yang et al. [10]. In conventional PFM, an ac bias, V tip = V 0 sinωt, is applied to a conductive tip of AFM 18

46 Chapter 2 in contact with a bare surface of the sample (Figure 2.3). Here, the amplitude of V 0 should be smaller than the coercive voltage of FE materials. Then, the local piezoelectric strain s caused by V tip is that s = s 0 sin(ωt + ϕ). The amplitude s 0 and phase difference ϕ yield the information on the magnitude of piezoresponse and the orientation of polarization in FE domains, respectively. We used the piezoelectric force microscopy (PFM) to image the ferroelectric domains. The operation of PFM is usually based on the fact that when an external electric field is applied to a ferroelectric material, the z-deformation (i.e., vertical strain of the material) depends on the polarization direction. If the domain with upward polarization is vertically stretched for a applied electric field, then the domain with downward polarization is vertically squeezed. Thus, by using the PFM, we can clearly image the ferroelectric domains. Figure 2.4 shows the domain pattern in epitaxial BiFeO 3 /SrRuO 3 on vicinal SrTiO 3 substrate, obtained with our PFM setup. Domains and domain wall are seen clearly in Figure μm 2 Figure 2.4 From left to right, topography, out-of-plane (OP) amplitude, OP phase, in-plane (IP) amplitude, and IP phase images of epitaxial BiFeO 3 thin film. 19

47 Chapter 2 References 1. H. Kitahata, K. Tadanaga, T. Minami, N. Fujimura, and T. Ito, Japanese J. Appl. Phys. Part 1-Regular Papers Short Notes & Review Papers 38 (1999) Y. Chye, T. Liu, D. Li, K. Lee, D. Lederman, and T. H. Myers, Appl. Phys. Lett. 88 (2006) W. C. Yi, J. S. Choe, C. R. Moon, S. I. Kwun, and J. G. Yoon, Appl. Phys. Lett. 73 (1998) T. Yoshimura, N. Fujimura, N. Aoki, K. Hokayama, S. Tsukui, K. Kawabata, and T. Ito, Japanese Journal of Applied Physics Part 1-Regular Papers Short Notes & Review Papers 36 (1997) D. B. Chrisey and G. K. Hubler, eds., Pulsed laser deposition of thin films, 6. G. K. Williamson, and W. H. Hall, Acta Metall. 1953, 1, J. I. Langford, D Louër, Rep. Prog. Phys. 1996, 59, G. Catalan, B. Noheda, J. McAneney, L. J. Sinnamon, J. M. Gregg, Phys. Rev. B 2005, 72, (R). 9. M. Alexe and A. Gruverman, Ferroelectrics at Nanoscale: Scanning Probe Microscopy Approach (Springer, New York, 2004). 10. S. M. Yang, J.-G. Yoon, and T. W. Noh, Curr. Appl. Phys. 11, 1111 (2011). 11. A. Gruverman, O. Auciello, and H. Tokumoto, Annu. Rev. Mater. Sci. 28, 101 (1998). 12. S. Hong et al., J. Appl. Phys. 89, 1377 (2001). 13. S. V. Kalinin and D. A. Bonnell, Phys. Rev. B 65, (2002). 20

48 Chapter 3 Chapter 3 The effect of the deposition temperature on the formation of defects in BiFeO 3 thin films 3.1 Introduction BiFeO 3 (BFO) is a particularly interesting multiferroic material [1] and has two order parameters, ferroelectricity and antiferromagnetism. The ferroelectric and antiferromagnetic ordering temperatures are significantly greater than room temperature; the Curie temperature is 1103 K and the Néel temperature is 643 K [2,3]. Moreover, BFO has the largest remnant polarization of all known ferroelectrics of 100 μc cm 2 along the [111] direction [4]. These properties make BFO a promising ferroelectric material for applications including ferroelectric random-access memory [5], photovoltaics [6], and magnetoelectrics [7]. Recent studies of ferroelectric materials have shown that control over defects is important for tuning the physical and functional properties of ferroelectric devices. Lee et al. reported that multilevel data storage could be realized using BFO thin films via defect dipole engineering [5]. They further demonstrated active control of irreversible defect dipoles in BFO thin film without compromising the ferroelectricity [8]. More 21

49 Chapter 3 recently, through site-specific substitutional alloying, Choi et al. showed that the bandgap of ferroelectric Bi 4 Ti 3 O 12 could be controlled without deterioration of the ferroelectric properties [9]. To obtain desired functionality using defect engineering in BFO thin films, an effective method to control the defect states is required. The site-engineering concept [10], which exploits the non-stoichiometric BFO target [11], and adjustment of the oxygen partial pressure [12] are useful techniques to control the defects in BFO thin films. It is also known that the deposition temperature, T D, significantly affects defect formation in BFO films [13]. However, the evolution of defects depending on the small ranges of T D in BFO films has not yet been carefully investigated. Moreover, the effects of defects on the functional properties of BFO films have been rarely studied. Therefore, a detailed investigation is required to understand the effects of T D on the defect evolution in BFO thin films. In this chapter, we investigated the evolution of defects in BFO films grown on (001) SrTiO 3 (STO) substrates as a function of T D, which was varied over a narrow range of C in intervals of 10 C. X-ray diffraction (XRD) data of the BFO films grown at T D 590 C exhibited Fe 2 O 3 defect peaks, whereas those grown at T D 580 C did not show any defect peaks. The presence of the defects in the BFO films grown at T D 590 C was also investigated using optical spectroscopy. We found that the presence of defects was strongly correlated with changes in the surface morphology and ferroelectric properties of the BFO films. Well-aligned stripe patterns and nearly rectangular polarization electric field (P E) hysteresis loops were observed in the BFO 22

50 Chapter 3 films grown at T D 580 C. However, the surface roughness abruptly increased and the P E hysteresis loops showed leaky behavior in the films grown at T D 590 C. These results indicated that T D ~ 590 C was threshold temperature. 3.2 Experiments Fabrication of BiFeO 3 thin films We grew BFO thin films using pulsed laser deposition (PLD) [13]. The films were sandwiched between a Pt top electrode and a SrRuO 3 (SRO) bottom electrode. BFO/SRO thin-film layers were fabricated on STO substrates with a 4 miscut toward the [100] direction. To form the bottom electrode, the 20-nm-thick SRO layer was deposited at 650 C, the laser fluence was 2 J cm 2, and the repetition rate was 2 Hz. The BFO thin films were deposited on top of the SRO bottom electrode at T D = 570 C, 580 C, 590 C, and 600 C. For the top electrode, the Pt layer was photolithographically patterned to form the BFO capacitors Experimental setup and methods for characterization The crystal structure of the BFO films was analyzed using high-resolution XRD (Bruker AXS D8 Advanced X-ray Diffractometer). Optical spectra were obtained using a VASE (J. A. Woollam) ellipsometer. The angle of incidence of the polarized light was 65, 70, and 75. Ferroelectric P E hysteresis loops were measured using a TF analyzer 2000 (AixACCT) at room temperature. The surface state of the BFO films was 23

51 Intensity (arb. units) Chapter 3 measured using an atomic force microscope (AFM) (XE-100, Park systems). 3.3 Results and discussions Investigation of defects High-resolution X-ray diffraction Figure 3.1 shows XRD θ 2θ scans of the BFO films grown at various T D. For BFO films grown at 570 C and 580 C, only the BFO (00l) peaks were present, indicating that the crystalline axes of the films were well-aligned and without impurities. In the BFO film grown at 590 C, an Fe 2 O 3 peak at 2θ 49 appeared. The Fe 2 O 3 peaks were more clearly identified at 2θ = 24.2 and 2θ = 49.4 in the BFO film grown at 600 C [12] S S 10 7 B B C 590 C 580 C 570 C θ (deg.) Figure 3.1 XRD θ 2θ scans of the BFO films grown at various T D (from bottom to top T D = 570 C, 580 C, 590 C, and 600 C). The peaks are indexed with the 24

52 Chapter 3 following symbols: B: BFO, S: STO, : Fe 2 O 3. a b C 580 C 590 C C Defect level E F Fe 3d Photon Energy (ev) O 2p Figure 3.2 (a) The imaginary part of the dielectric function of the BFO films. (b) Schematic band diagram of the BFO thin films. The yellow band indicates the defect level. Peaks indicated by the blue and red arrows correspond to the optical transition from O 2p to defect and Fe 3d levels, respectively Optical spectroscopy The appearance of defects can also be identified by optical spectroscopy experiments. For example, the defects states in STO thin films manifest as finite optical absorption below the fundamental band gap of STO [14]. Figure 3.2a shows the imaginary part of the dielectric function, ε 2, of the BFO films. The data were analyzed by considering 25

53 Chapter 3 homogeneous BFO+Fe 2 O 3 mixed layers. The overall spectral shapes of the dielectric functions for the BFO films grown at 570 C and 580 C were almost identical. The band gap estimated from the ε 2 data was 2.5 ± 0.2 ev. Pronounced peaks above 2.2 ev are attributed to dipole-allowed excitations from O 2p to Fe 3d bands (indicated by the red arrow in Fig. 3.2b), which is consistent with the results of both first-principles calculations and experiments [15 18]. We note that the spectral shape of ε 2 for the films grown at T D 590 C were significantly different from those of the films grown at T D 580 C. Suppression of ε 2 at photon energies greater than 3.5 ev was observed, as shown in Fig. 3.3, which may be due to the increased surface roughness of these films. In addition, a weak absorption peak appeared around 2.0 ev, which is below the optical band gap of BFO. The weak absorption may result from optical transitions from the O 2p to localized defect levels, as depicted in Fig. 3.2b [19]. These optical data indicate that the defects appeared abruptly at T D = 590 C, which is consistent with the XRD data, as shown in Fig Atomic force microscopy The presence of the defects affected the surface morphology of the BFO thin films. AFM measurements show that the surface roughness significantly increased with the appearance of the defects, as shown in Fig The surface of the BFO films grown at T D 580 C exhibited well-ordered stripe patterns, which were nearly consistent with the pattern of the BFO film grown on the 4 miscut [100] SrTiO 3 substrate [20]. The films grown at T D 590 C exhibited mosaic patterns and also exhibited a considerably larger 26

54 Chapter 3 surface roughness than those grown at lower temperatures. Thus, we believe that important role of T D includes robustness of sample stoichiometry by decreasing the propensity for volatile species to desorb and to maintain the step-flow growth up to threshold temperature ºC 580ºC 590ºC 600ºC Roughness (nm) μm Deposition temperature ( C) Figure 3.3 Surface roughness of the BFO films. The inset shows AFM images of the BFO films grown at various T D Ferroelectric properties The ferroelectric properties were also affected by the presence of the defects. Figure 3.4 shows P E hysteresis loops of the BFO films. Note that the hysteresis loops of the BFO films grown at T D 580 C were almost rectangular, indicating that the leakage currents were very small and that the polarization relaxation was not likely to occur. The BFO film grown at 590 C was somewhat leaky, but the remnant polarization of the 27

55 Chapter 3 film grown at 590 C was almost the same as that of the films grown at T D 580 C. The BFO film grown at 600 C exhibited a very large leakage current and the hysteresis loop lost the rectangular shape, as shown in the inset of Fig Polarization (μc cm 2 ) k 20k k C 40k C 580 C 590 C Electric field (kv cm 1 ) Figure 3.4 P E hysteresis loops of the BFO films grown at various T D. The inset shows P E hysteresis loops of the BFO film grown at 600 C. 3.3 Conclusion We controlled the formation of defects in BFO films by varying the substrate temperature during epitaxial growth over a narrow range of 570 C 600 C. We found that the presence of defects significantly affects the optical and ferroelectric properties. The BFO films grown at T D 580 C had a band gap of 2.5 ± 0.2 ev and showed rectangular P E hysteresis loops. Fe 2 O 3 impurities appeared in the BFO films grown at T D 590 C, leading to weak absorption below the band gap and leaky P E hysteresis 28

56 Chapter 3 loops. Our work suggests that the defect evolution in BFO films critically depends on the deposition temperature. 29

57 Chapter 3 References [1] Wang J, Neaton JB, Zheng H, Nagarajan V, Ogale SB, Liu B, et al. Science 2003;299: [2] Smolenskii GA, Isupov, V, Agranovskaya A, Kranik N, Sov. Phys. Solid State 1961;2:2651. [3] Fischer P, Polomska M, Sosnowska I, Szymanski M, J. Phys. C 1980;13:1931. [4] Ederer C, Spaldin NA, Phys. Rev. Lett. 2005, 95, [5] Lee D, Yang SM, Kim TH, Jeon BC, Kim YS, Yoon JG. Adv. Mater. 2012; 24: 402. [6] Ji W, Yao K, Liang YC, Adv. Mater. 2010;22:1763. [7] Baek SH, Jang HW, Folkman CM, Li YL, Winchester B, Zhang JX, et al. Mater. 2010;9:309. [8] Lee D, Jeon BC, Baek SH, Yang SM, Shin YJ, Kim TH, et al. Adv. Mater. 2012; 24: [9] Choi WS, Chisholm MF, Singh DJ, Choi T, Jellison Jr GE, Lee HN, Nature Communications 2012;3:689. [10] Qi X, Dho J, Tomov R, Blamire MG, MacManus-Driscoll JL, Appl. Phys. Lett. 2005;86: [11] Das RR, Kim DM, Baek SH, Eom CB, Zavaliche F, Yang SY, et al. Appl. Phys. Lett. 2006;88: [12] Béa H, Bibes M, Barthélémy A, Bouzehouane K, Jacquet E, Khodan A, et al. Appl. Phys. Lett. 2005;87:

58 Chapter 3 [13] Jeon BC, Lee D, Lee MH, Yang SM, Chae SC, Song TK, et al. Adv. Mater., 2013;25:5643. [14] Kim YS, Kim J, Moon SJ, Choi WS, Chang YJ, Yoon JG, et al. Appl. Phys. Lett. 2009;94: [15] Neaton JB, Ederer C, Waghmare UV, Spaldin NA, and Rabe KM, Phys. Rev. B 2005;71: [16] Chen P, Podraza NJ, Xu XS, Melville A, Vlahos E, Gopalan V, et al. Appl. Phys. Lett. 2010;96: [17] Ihlefeld JF, Podraza NJ, Liu ZK, Rai RC, Xu X, Heeg T, et al. Appl. Phys. Lett. 2008;92: [18] Pisarev RV, Moskvin AS, Kalashnikova AM, Rasing Th, Phys. Rev. B 2009;79: [19] Yang CH, Seidel J, Kim SY, Rossen PB, Yu P, Gajek M, et al. Nature Mater. 2009;8:485. [20] Jang HW, Ortiz D, Baek SH, Folkman CM, Das RR, Shafer P, et al. Adv. Mater. 2009;21:

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60 Chapter 4 Chapter 4 Flexoelectric effect in the reversal of self-polarization and associated changes in the electronic functional properties of epitaxial ferroelectric thin films 4.1 Introduction Flexoelectric effect Flexoelectric effect is the generation of an electric field by a strain gradient via electromechanical coupling. This effect was predicted theoretically by Kogan in 1964 [1] and experimentally observed by Bursian and Zaikovskii in 1968 [2]. The phenomenon was given the name flexoelectricity by Indenbom et al. in 1981 [3]. Despite its long history, there has been little research on flexoelectricity of bulk solid materials [3-13], because its effects had been widely accepted to be quite small. Namely, the flexoelectric coefficients are small ( C m 1 ) [12], and also the strain gradients generated by mechanical bending are quite small, typically on the order of 0.1 m 1 [13]. Recently, there has been much interest in flexoelectricity, especially regarding epitaxial thin films [14-20]. Inside these material systems, a strain gradient as large as m 1 can be produced [14,15]. Note that this value of the strain gradient is 6 or 7 33

61 Chapter 4 orders of magnitude larger than the corresponding bulk values. Using numerous epitaxial ferroelectric thin films, experimental studies showed that flexoelectricity can affect the domain configuration and imprint [15], dielectric constant [16,17], continuous rotation of the spontaneous polarization direction [18], polarization switching by mechanical force [19], and unusual coupling between electronic transport and the mechanical strain gradient [20], Domain engineering in ferroelectrics Domain engineering in ferroelectrics, ferromagnetics, and multiferroics, has been attracting worldwide attention recently, due to its functionality and ease of control [21-23]. Ferroelectric materials, in particular, are important due to their promising application [24-27] in such devices as ferroelectric random-access memory, photovoltaics [24], magnetoelectrics [25], and optoelectronic devices [27]. Since most of the functional properties of ferroelectrics are directly related to the electrically switchable polarization and domain configurations, the control of ferroelectric polarization states has been the main concern in ferroelectric community [28,29]. Especially, BiFeO 3 (BFO) is more interesting than any other ferroelectrics, due to its room temperature multiferroics and large Pb-free piezoelectrics [30]. By controlling the domain structure in BFO films, for example, Yang and co-workers reported photovoltages that were significantly higher than the electronic band-gap [24]. Observation of the domain wall conductivity in BFO thin films has emphasized the importance of controlling domain configuration and polarization state, which can lead to a new device concept using ferroelectrics [26]. 34

62 Chapter 4 Unfortunately, BFO films can have very complicated domain structures, depending on the substrates [31]. Recently, several studies have tried to control the ferroelectric domain structures of BFO films by varying the substrates [21], miscut directions [32], and orientations [23]. In particular, as-grown ferroelectrics thin films (including BFO) have a self-poled domain state (i.e., self-polarization) when deposited on oxide electrodes, such as SrRuO 3 (SRO) and doped manganites [22,23,33]. The determination of the as-grown polarization state is critical for full utilization of the BFO thin films, because the polarization state affects the defect configuration, and, in turn, the ferroelectric hysteresis and electronic transport Self-polarization in ferroelectric thin films Many ferroelectric films were reported to have one preferred polarization direction just after deposition [21-23,33-37]. This phenomenon, known as a self-polarization, has been attributed to a built-in electric field. Numerous origins have been proposed for the built-in electric field, namely, defects [34], piezoelectricity [35], interfacial electrode effects [22,33], and so on. Specifically for BFO thin films, most of the earlier research showed that the as-grown films usually exhibited downward self-polarization [22,23,33]. Here, I show how flexoelectricity can reverse the direction of the as-grown polarization in epitaxial BFO thin films grown on a vicinal SrTiO 3 (STO) substrate with an SRO bottom electrode. Additionally, the change in the self-polarization could result in large variations of the functional properties of the as-grown BFO films, including ferroelectric hysteresis and diode behavior. 35

63 Chapter Experiments Sample perperation We used high-quality BFO epitaxial thin films with thicknesses varying from 50 to 250 nm. The films were sandwiched between a Pt top electrode and a single crystal SRO bottom electrode. BFO/SRO thin-film layers were fabricated using pulsed laser deposition (PLD) onto STO (001) single-crystal substrates, with a 4 miscut toward the [100] direction. To form the bottom electrode, an SRO layer (20-nm-thick) was deposited onto an STO substrate by PLD at 650 C. The target-substrate separation was 2 inches. An oxygen pressure of 100 mtorr was maintained. The laser fluence and repetition rate were 2 J cm 2 and 2 Hz, respectively. The BFO thin film was grown on top of the SRO bottom electrode by PLD over a temperature range of 550 to 600 C. A stoichiometric BFO ceramic target was used. The deposited BFO film was postannealed in situ inside the PLD chamber at the deposition temperature for 1 hour under an oxygen atmosphere of 760 Torr. For the top electrode, a Pt layer (40-nm-thick) was deposited at room temperature by sputter deposition. After the deposition, the Pt layer was photolithographically patterned to form the BFO capacitors. Pt top electrodes consisted of 10 to 200-μm square patterns Characterization of crystal structures The crystal structures of the BFO films were analyzed using high-resolution X-ray 36

64 Chapter 4 diffraction (D8 Advanced, Bruker AXS). To evaluate the in-plane strain states, we used reciprocal space mapping analysis of {103} family peaks with various phi angles (0, 90, 180, and 270 ). The average a-axis lattice constant was calculated from the average value of the BFO (103) and (103) peak. The average b-axis lattice constant was determined from the BFO (013) peak value for = 90. The average c-axis lattice constant was obtained from the θ 2θ data Piezoresponse force microscopy The piezoresponse force microscopy (PFM) measurements were performed using an XE-100 (Park systems) with commercially available Pt/Ir-coated Si tips (PPP-EFM, Nanosensors). For PFM imaging, we applied an AC voltage of 1.0 Vrms at 17.1 khz to the bottom electrode (i.e., sample bias). We measured the amplitude and phase signals of the converse piezoelectric responses with a lock-in amplifier (SR830, Stanford Research Systems) Electrical measurements Ferroelectric polarization voltage (P V) hysteresis loops were measured using a TF analyzer 2000 (AixACCT) at room temperature. We performed current density voltage measurements at room temperature using a low-noise probe station and a picoampere meter (Keithley 236). A +12 V ( 12 V) external-poling voltage was applied to the uniaxially strained (relaxed) BFO capacitor to obtain the downward (upward) polarization state; a 12 V (+12 V) external-poling voltage resulted in upward (downward) 37

65 Chapter 4 polarization Intensity (arb. units) T D = 570 C T D = 550 C Fully strained BFO Bulk BFO : BFO (002) : SRO (002) : STO (002) θ (degree) Figure 4.1 XRD θ 2θ scans of the 250-nm-thick BFO films grown at 570 C (solid red line) and 550 C (solid black line) on vicinal STO (001) substrates. The gray shortdashed and solid vertical lines indicate the (002) diffraction peak positions of the fully strained and relaxed BFO films on STO substrates, respectively. 4.3 T D effect in BiFeO 3 thin films Uniaxially strain and relaxed BiFeO 3 thin films Figure 4.1 shows the XRD θ 2θ scan for 250-nm-thick BFO films grown at 570 C and 550 C. For these films, only the BFO (00l) peaks appear, indicating that the crystalline axes of the films were well-aligned. The BFO (002) peaks for both the films 38

66 Chapter 4 were located between the predicted positions for the fully strained BFO film and bulk BFO, shown as the dotted and solid lines, respectively. This indicated that some structural relaxation occurred for both the films. Additionally, the BFO (002) peak position of the film grown at 550 C was closer to the bulk BFO value, indicating that this film became more relaxed along the [001] direction than that grown at 570 C US-BFO STO a b c d (0 0 L) (r.l.u.) 2.96 SRO 2.92 (103) (013) (103) (013) BFO 2.88 ϕ = 0 T D = 570 C ϕ = 90 T D = 570 C ϕ = 180 T D = 570 C (H 0 0) (r.l.u.) (0 K 0) (r.l.u.) (H 0 0) (r.l.u.) ϕ = 270 T D = 570 C (0 K 0) (r.l.u.) R-BFO STO e f g h (0 0 L) (r.l.u.) 2.96 SRO 2.92 (103) (013) (103) (013) BFO 2.88 ϕ = 0 T D = 550 C ϕ = 90 T D = 550 C ϕ = 180 T D = 550 C ϕ = 270 T D = 570 C (H 0 0) (r.l.u.) (0 K 0) (r.l.u.) (H 0 0) (r.l.u.) (0 K 0) (r.l.u.) Figure 4.2 RSMs around the {103} STO Bragg family of peaks with various angles for 250-nm-thick US- and R-BFO films. The (103), (103), (013), and (013) peaks can be distinguished from each other in the RSM data, due to the large rhombohedral distortion of the BFO unit cell [22]. 39

67 (0 0 L) (r.l.u.) Intensity (arb. units) Fully strained BFO Bulk BFO Chapter a nm : BFO (002) : SRO (002) : STO (002) nm 120 nm 50 nm θ (degree) b STO SRO c d e (0 13) BFO nm 120 nm 180 nm 250 nm (0 K 0) (r.l.u.) Figure 4.3 (a) HRXRD θ 2θ scans of BFO films grown at 570 C between 50 and 250 nm thick. The closed blue triangles, black circles, and open-inverted triangles indicate the (002) peaks of BFO, SRO, and STO, respectively. The gray dash-dotted and solid lines indicate the (002) diffraction peak positions of the fully strained and 40

68 Chapter 4 relaxed BFO films on STO substrates, respectively. The θ 2θ scans show that the 50- nm-thick film is fully strained in the [001] direction. However, above a critical thickness, the strain should start to relax. As the film thickness increased, the 2θ peak position moved to larger angles, indicating that the average c-axis lattice constant became smaller. (b) (e) RSM images around the (013) STO Bragg peaks of BFO films grown at 570 C between 50 and 250 nm thick. As displayed in the RSM data, all of these films were fully strained along the [010] direction; i.e., they should be US-BFO films. Although deposition temperature (T D ) differed by only 20 C, we found that our BFO thin films had different strain relaxation behaviors. To obtain information on the in-plane strain state, we used reciprocal space mapping (RSM) analysis of the {103} family of BFO peaks with various angles for the 250-nm-thick BFO films, as shown in Figure 4.2 [22]. The (013) and (013) BFO Bragg peaks for the film grown at 570 C are located near the vertically dotted line, indicating that this film was almost fully strained along the [010] direction, while the (103) and (103) BFO Bragg peaks were located outside of the vertically dotted line, as shown in Figures 4.2(a)-(d), indicating that this film was relaxed along the [100] direction. From here on, the films grown at 570 C will be referred to as uniaxially strained BFO (US-BFO) films. Figures 4.2(e)-(f) show the RSM results for the film grown at 550 C. Note that the {103} family of peaks are located outside of the vertically dotted line, indicating that the film was relaxed in all directions; these films will be referred to as relaxed BFO (R-BFO) films. 41

69 Chapter 4 Lattice parameter (Å ) a T D = 570 C a T D = 550 C b c US-BFO b Bulk BFO a b c STO R-BFO Thickness (nm) Thickness (nm) Figure 4.4 (a) and (b) Pseudocubic lattice parameters as a function of the film thickness for US- and R-BFO films, respectively. The solid and dotted gray lines represent the lattice parameter of bulk BFO and STO, respectively Thickness & T D -dependent lattice relaxation To obtain further information on how strain developed in the US-BFO films, we deposited four BFO films at 570 C with four different thicknesses of 50, 120, 180, and 250 nm. The 50-nm-thick film is fully strained in the ab-plane. As the film thickness increased, the average value of the c-axis lattice constant decreased, but the b-axis lattice constant remained constant, as shown in Figure 4.3. We determined the average values of all the lattice constants from the θ 2θ and RSM data. The results are shown in Figure 4.5(a). Note that the average value of the b-axis lattice constant was independent of the film thickness and nearly the same as that of the STO substrate. Because the b-axis 42

70 [001] [001] [010] [001] Chapter 4 corresponds to the direction of step edges in STO substrates, the uniaxially strained growth behaviors should originate from clamping effects of the US-BFO films at the STO step edges. a Top view d P 1 P 4 [100] b [100] Side view c Front view Relaxed E F,3 strained SRO/STO [100] [010] Figure 4.5 Schematic representation of the direction of the strain relaxation for US- BFO films. The dark and pale gray areas represent strongly strained and relaxed BFO regions, respectively. (a), (b), and (c) indicate the schematic diagram top, side, and front views of the US-BFO film, respectively. The large blue arrow indicates the 43

71 Chapter 4 direction of vertical flexoelectric field (E F,3 ). The green-dotted and black solid-line arrows indicate the direction of ferroelectric polarization, P 1 and P 4, respectively. (d) Possible orientations of the polarization for US-BFO films on vicinal STO substrates. The step-bunching process and lattice dislocations (higher-order terms) are neglected in this representation. Recently, we demonstrated that in BFO films grown on vicinal STO substrates, some structural relaxation can occur through the step-bunching process and lattice dislocations [38]. However, because the resulting crystallographic tilt angle and the c-axis lattice constant should be higher-order variations, we neglected such effects in the schematic diagram [38]. To make the strain gradient more visible, we exaggerated the difference in the length scale of the BFO unit cells. Based on the structural data, we proposed a schematic diagram of the US-BFO films, as shown in Figure 4.5. According to our RSM analysis, the US-BFO films were strongly clamped along the [010] direction. Along that direction, the lattice constant of the inplane BFO near the substrate might be the same as that of the substrate. Experimentally, we found that this as-grown film should have a downward polarization. With the preferential distortion of the BFO unit cells on the miscut STO substrate, only two polarization variants, P 1 and P 4 are possible [32]. 44

72 Chapter 4 Intensity (arb. units) a 250 nm 180 nm 120 nm Fully strained BFO Bulk BFO : BFO (002) : SRO (002) : STO (002) nm θ (degree) (0 0 L) (r.l.u.) b STO c d e SRO BFO (013) nm 120 nm 180 nm 250 nm (0 K 0) (r.l.u.) Figure 4.6 (a) XRD θ 2θ scans of BFO films grown at 550 C between 50 and 250 nm thick. The closed blue triangles, black circles, and open-inverted triangles indicate the (002) peaks of BFO, SRO, and STO, respectively. The gray dash-dotted and solid lines indicate the (002) diffraction peak positions of the fully strained and relaxed 45

73 Chapter 4 BFO films on STO substrates, respectively. The θ 2θ scans show that the 50-nmthick film is fully strained. However, above a critical thickness, the strain should start to relax. As the film thickness increased, the 2θ peak position moved to larger angles, indicating that the average c-axis lattice constant became smaller. (b) (e) RSM images around the (013) STO Bragg peaks of BFO films grown at 550 C between 50 and 250 nm-thick. As displayed in the RSM data, the 50-nm-thick BFO film is fully strained. Above the critical thickness, the films were relaxed; i.e., they should be R-BFO films. To obtain information on the strain evolution of R-BFO films, we also deposited four BFO films at 550 C with thicknesses of 50, 120, 180, and 250 nm. Their XRD θ 2θ and RMS data are shown in Figure 4.6. Similar to the US-BFO case, this 50-nm-thick film was fully strained in the ab-plane. However, above a critical thickness, all of the thicker films became relaxed along the b-axis as well as along the a-axis, contrary to the US- BFO films. Figure 4.4(b) shows the average values of their lattice constants, evaluated from XRD data. ogressively in all directions. Although T D was lower by only 20 C, compared with that of the US-BFO films, the step edges of the STO substrate could not clamp the BFO layer effectively in the R-BFO films. 46

74 Chapter 4 a Top view d [001] P 1 P 4 [010] [100] b [100] Side view E F,1 c Front view Relaxed E F,3 strained [001] SRO/STO [001] [100] [010] Figure 4.7 Schematic diagram of the direction of the strain relaxation for R-BFO films. The dark and pale gray areas represent strongly strained and relaxed regions, respectively. (a), (b), and (c) Schematic diagram top, side, and front views, respectively. The large red and blue arrows indicate the direction of the horizontal (E F,1 ) and vertical (E F,3 ) flexoelectric fields, respectively. (d) Possible polarization orientation for R-BFO films. The green-dotted and black solid-line arrows indicate 47

75 Chapter 4 the direction of ferroelectric polarization, P 1 and P 4, respectively. The stepbunching process and lattice dislocations (higher-order terms) are neglected in this representation [38]. Figure 4.7 shows our proposed schematic diagram of the strain states of R-BFO films. Near the substrate, the BFO layers were fully strained. However, above the critical thickness, strain relaxation should occur in all directions. It should be noted that the b- axis lattice near the step edge could be somewhat more strained than those far from the step edge due to the clamping effect, as shown in Figure 4.7a. As a result, there should be an expansion of the b-axis lattice constant along the [100] direction. This strain gradient, u 22 / x 1, will generate a horizontal electric field by flexoelectricity (large red arrow in Figure 4.7a). Note that u jk and x i are the strain and spatial coordinates of the film (i, j, and k = 1, 2, and 3) [4,7]. Additionally, there should be vertical electric fields due to u 11 / x 3, u 22 / x 3, and u 33 / x 3 (large blue arrow in Figure 4.7c), which come from the relaxation of the a-, b-, and c-axis lattice constants along the [001] direction. Note that the u 22 / x 1 and u 22 / x 3 terms can appear only for the R-BFO films. We argue that these new strain gradient terms could reverse the downward self-polarization direction of R-BFO films to an upward self-polarization. 4.4 Mechanism of self-polarization As-grown domain state in BiFeO 3 thin films 48

76 Chapter 4 a T D = 570 C As-grown As-grown As-grown As-grown +10 V +10 V +10 V +10 V 50 nm 120 nm 180 nm 250 nm b T D = 550 C As-grown As-grown As-grown As-grown +10 V 10 V 10 V 10 V 50 nm 120 nm 180 nm 250 nm Figure 4.8 (a) and (b) Out-of-plane PFM images with 50-, 120-, 180-, and 250-nmthick BFO films. The bright yellow and dark regions indicate the up- and downpolarization states, respectively. To measure the self-polarization direction, we performed piezoresponse force microscopy (PFM) experiments. The as-grown BFO films deposited at 570 C always had downward self-polarization, irrespective of whether they were fully or uniaxially strained (Figure 4.8a). In contrast, the film deposited at 550 C with a thickness of 50 nm, was fully strained and had downward self-polarization (the first picture of Figure 4.8b). However, as the film thickness increased, the self-polarization direction changed from down to up (Figure 4.8b). These results indicate that the polarization direction of the asgrown films is not determined by particular defects, but depends on the film thickness and strain relaxation. Note that the structural change from fully strained to the relaxed state also occurred for thicknesses in the range of 50 to 120 nm, as shown in Figures 4.4a and 49

77 Polarization (μc cm -2 ) Chapter 4 4.4b. Namely, the change in the self-polarization direction seems to be closely related to change of the strain state for R-BFO films. Moreover, we measured polarization voltage (P V) hysteresis loops and found that the imprints of the R-BFO films with thickness larger than 100 nm were opposite to those of the US-BFO films, as shown in Figure 4.9, in consistent with changes in the self-polarization direction nm T D = 570 C 120 nm US-BFO 180 nm US-BFO 250 nm US-BFO a b c d 80 T D = 570 C 80 T D = 570 C 80 T D = 570 C nm T D = 550 C 120 nm R-BFO 180 nm R-BFO 250 nm R-BFO T D = 550 C 80 T D = 550 C 80 T D = 550 C Voltage (V) Voltage (V) Voltage (V) Voltage (V) 0 40 e f g h Figures 4.9 P V loops for (a) 50-, (b) 120-, (c) 180-, and (d) 250-nm-thick BFO films grown at 570 C; (e) 50-, (f) 120-, (g) 180-, and (h) 250-nm-thick BFO films grown at 550 C. The 50-nm-thick BFO films exhibited a leaky behavior. The 120-, 180-, and 250-nm-thick US-BFO (R-BFO) films showed negative (positive) imprint characteristics. These imprint behaviors were nearly consistent with thickness dependence of self-polarization direction, as shown in the PFM images of Figures 4.8a and 4.8b Reversal of self-polarization in BiFeO 3 thin films 50

78 Chapter 4 Magnitude BFO SRO STO Region I Fully strained BFO SRO STO Region II Strain relaxed 0 Film Thickness Figure 4.10 Magnitude of the flexoelectric and interfacial effects as a function of film thickness. The red and black-dashed curves indicate the flexoelectric and interfacial effects, respectively. The right and left insets indicate the fully strained and relaxed BFO films, respectively. To explain the reversal of the self-polarization mechanism, we suggested a schematic diagram, as shown in Figure Recently, Yu et al. demonstrated that the selfpolarization direction could be engineered by varying the termination layer of the bottom electrode [33]. Balke et al. reported that the self-polarization direction is determined by the internal field produced by the different interface charges [37]. Note that both the fully strained and US-BFO films always had downward self-polarization because of the dominant interfacial electrode effect, in agreement with earlier reports [22,23,33]. 51

79 Chapter 4 However, for our R-BFO films, we propose that the above-mentioned additional strain gradient terms, i.e., u 22 / x 1 and u 22 / x 3, can generate the electric fields by flexoelectricity. With an increase in the film thickness, this flexoelectric effect should compete with the interfacial effects. 4.5 Estimation of flexoelectric field Williamson-Hall plot To obtain more quantitative information, we estimated the values of the out-of-plane and in-plane strain gradients using Williamson-Hall (W-H) plot [17,39]. The W-H plots of BFO films were obtained from the XRD θ 2θ and RSM peak widths [39], as shown in Figure To obtain the out-of-plane gradual change of strain, four peaks (001), (002), (003), and (004) were selected from the XRD θ 2θ data. The numerical values of ε I were determined from the slope of the fit equation [17,39,40]. K w cos 4 I sin D where measured instrument, and β measured is the measured line width of the diffraction peaks of the samples, β instrument is estimated from the peak width β substrate of a nearby substrate peak, [S4] λ w = Å is the x-ray wavelength, D is the coherence length along the scattering vector, K is a geometrical constant which was taken as 1. Figure 4.11 shows the plots of 4sin vs cos. Out-of-plane ε I for the US- and R-BFO films are 0.37 % and 0.46 %, respectively. From the out-of-plane ε I values, we estimated the out- 52

80 Chapter 4 of-plane strain gradients as m 1 and m 1 for the US- and R-BFO films, respectively. cos (10 3 ) US-BFO R-BFO a US-BFO R-BFO b 0 Out-of-plane In-plane sin 4sin Figure 4.11 (a) Out-of-plane and (b) in-plane W-H plots for the inhomogeneous strain of the BFO films. Similarly, we estimated the in-plane ε I of the BFO films (Figure. 4.11b). To obtain the in-plane ε I, we used the line width in the k-direction of the RSM peaks (013), (023), and (033) of BFO and STO for US- and R-BFO films. From the W-H plots for the width of those peaks, the in-plane ε I was estimated to be 0.15 % and 0.74 % for the US- and R- BFO films, respectively. From these in-plane ε I values, we determined the in-plane strain gradients as m 1 and m 1 for the US- and R-BFO films, respectively Estimation of strain gradient and flexoelectric field We estimated the out-of-plane strain gradient along [001], which correspond to u 33 / x 3, as m 1 and m 1 for the US- and R-BFO films, respectively. 53

81 Chapter 4 We also estimated the in-plane strain gradients to be m 1 and m 1 for the US- and R-BFO films, respectively. With the experimentally obtained values of strain gradient, we could estimate the flexoelectric fields, E F,i (i = 1, 2, and 3), using[15,19,20] E F, i e u a x 0 j jk i (a) where λ is a scaling factor, e is the electronic charge, a j is the lattice constant, and 0 is the permittivity of free space. Usually, in perovskite oxide systems, λ is known to have a value on the order of 10 0 or 10 1 (e.g., λ = and 14.5 for PbMg 1/3 Nb 2/3 O 3 and Ba 0.67 Sr 0.33 TiO 3, respectively) [41]. To the best of our knowledge, the precise value of λ is not known yet for BFO. By assuming λ = 1, we estimated E F,1 for R-BFO to be ~ 8.7 MV m 1, while E F,1 for US-BFO was estimated to be one order of magnitude weaker than that of the R-BFO. Similarly, we could estimate the vertical magnitude of the flexoelectric field, E F,3 to be 2.3 MV m 1 and 3.2 MV m 1 for US-BFO and R-BFO, respectively. The ferroelectric polarization in BFO is [111]-oriented; thus, the effect of both the vertical and horizontal components of the flexoelectric field should be considered with regard to polarization reversal. As a result, the flexoelectric field in R-BFO is much higher, compared with that of the US-BFO film. Additionally, the estimated magnitude of the flexoelectric field in R-BFO gradually became comparable to that of the coercive field for BFO at high temperatures, during the growth [41]. Therefore, the flexoelectric effect should play an important role in reversing the self-polarization direction in R-BFO films. 54

82 Chapter Control of electronic functional properties Configuration of defects a b Pt US-BFO SRO STO V O defect layers Pt R-BFO SRO STO Figure 4.12 (a) and (b) Schematic diagram of the location of the V O -rich defect layer in US- and R-BFO films, respectively. The large white arrows represent the asgrown polarization direction. It is well known that the configuration of defects, such as oxygen vacancies, V O, in ferroelectric films can be determined by the polarization state, especially at high growth temperatures [29,42,43]. Because BFO has a very high Curie temperature of 830 C, our BFO films should be in a ferroelectric state during the growth process. Thus, the generated self-polarization will drive V O to one of the interfacial regions to compensate for the negative polarization charge during the growth [42]. For US- and R-BFO films, an interfacial V O -rich defect layer formed at the top and bottom interfaces, respectively, as shown in Figure 4.12a and 4.12b. Additionally, to satisfy the lowest energy configuration 55

83 Chapter 4 in the ferroelectric material, the defect dipoles (D defect ) should be aligned along the spontaneous polarization direction during the growth, resulting in imprint [29,43]. The different location of the V O -rich defect layer and alignment of D defect can result in changes of diode characteristics and ferroelectric hysteresis, respectively. Polarization (μc cm -2 ) a US-BFO Voltage 2 khz Polarization (μc cm -2 ) b R-BFO Voltage 2 khz Figure 4.13 (a) and (b) P V hysteresis loops of the US-and R-BFO films, respectively. Vertical gray-dashed lines indicate the voltage center of hysteresis loops P V hysteresis loops To confirm the configuration of the D defect alignment to the imprint, we measured the P V hysteresis loops for 250-nm-thick US- and R-BFO films, as shown in Figure 4.13a and 4.13b. The remnant polarization values along the [001] pseudocubic direction were nearly the same, i.e., approximately 65 and 60 μc cm 2, respectively [21,32]. Figure 4.13a shows a US-BFO film with a negative imprint; namely, its coercive voltages are +1.9 V for a positive bias and 4.0 V for a negative bias. In contrast, the R-BFO film 56

84 Chapter 4 shows a positive imprint; namely, its coercive voltages are +4.4 V for a positive bias and 2.5 V for a negative bias, as-shown in Figure 4.13b. The two BFO films exhibited different imprint characteristics, as expected. 50 a US-BFO 10 b R-BFO J (μa cm 2 ) 0 50 : Poled with +12 V J (μa cm 2 ) 5 0 : Poled with +12 V : Poled with 12 V 100 : Poled with 12 V Voltage (V) Voltage (V) Figure 4.14 (a) and (b) J V curves of US- and R-BFO films, respectively Electronic transport characteristics Additionally, it is already known that the defect layers at the interface can affect the transport properties such as diode behavior [42]. We measured the current density voltage (J V) curves for 250-nm-thick US- and R-BFO films. Figure 4.14a shows that the J V curves for the US-BFO film measured between 0.8 and +0.8 V, which were much smaller than the coercive voltages [42]. The small sweep voltage range ensured that no polarization switching occurred during the measurements. In the case of an ideal BFO capacitor, the hole carriers can be injected from the electrodes when a positive bias is applied. However, if the defective layer is located at the interface, it could disturb the carrier injection process. With a negative poling (i.e., a single domain of upward 57

85 Chapter 4 polarization), the J V curve exhibited reverse diode behavior. Conversely, with positive poling (i.e., a single domain of downward polarization), the J V curve did not show any diode behavior for the US-BFO film. On the other hand, for the R-BFO film, the J V curve should exhibit forward diode behavior with a positive poling. Conversely, with negative poling, the J V curve did not show any diode behavior. Such J V curves were actually observed, as shown in Figure 4.14b. 4.7 Conclusion In summary, we found that the flexoelectric effects can play an important role in determining the self-polarization direction in the BFO thin films. We could successfully control the strain evolution of the films by varying the deposition temperature and the film thickness. Then, due to flexoelectric effects, the different strain gradient states inside the BFO films could create different built-in electric fields, which resulted in changes in the self-polarization direction. In addition, the self-polarization field could also produce large variations in the imprint and diode characteristics of the as-grown BFO films by generating a defect layer and aligning the defect dipoles during the film deposition process. Thus, strain gradient engineering at the nanoscale can potentially provide exciting new opportunities to realize flexoelectricity-based devices. 58

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90 Chapter 5 Chapter 5 Flexoelectric control of defect formation and electronic functions in ferroelectric thin films 5.1 Introduction The advancement of materials science relies on our ability to modify and optimize a wide range of functional properties. These properties, including electronic, magnetic and optical properties, strongly depend on the type and concentration of defects, which exist in every material. Particularly in ferroelectrics, defects play an important role in the control and optimization of these materials [1,2]. Typical ferroelectric materials contain a diversity of point defects and extended defects, which sometimes seem unavoidable even in the well-controlled fabrication conditions. These defects are usually detrimental to a functional ferroelectric property [1], but can enable some desirable functions, such as giant electromechanical response [3] and multilevel data storage [4]. This makes it necessary to fully understand the mechanism of defect formation, which can provide a relevant way for tailoring defects and their effect. While our understanding still continues 63

91 Chapter 5 to evolve, the exact mechanism of defect formation remains unclear, with many important factors unresolved. The interaction between polarization and charged point defects is one of the wellknown mechanisms for determining the type and concentration of defects in ferroelectrics [3 7]. For example, it has been widely accepted that ferroelectric polarization drives charged point defects (e.g., vacancies) to migrate towards the energetically preferred sites, facilitating the formation of some defect compexes during fabrication process. However, it has been overlooked that such polarization-mediated defect formation can be more promoted by other intrinsic polarizations, which have a different origin from the ferroelecctric polarization. Recent studies reported that in epitaxial thin films, a huge internal electric field (E int ) can emerge intrinsically by various sources, such as interfacial charge discontinuity [8,9] and strain gradient [10,11], generating a consierable magnitude of polarization. Its magnitude can be around E int = 10 6 V m 1 on the average and even as large as V m 1 locally, which can induce the polarization of 1 10 μc cm 2 and seems large enough to affect the defect formation at high temperatures. Therefore, although overlooked so far, it would be critical to explore how such E int and induced polarization influence the defect formation in thin films. Particularly, flexoelectricity (i.e., generation of E int by strain gradient) has recently gained much attention [10 16]. The strain gradient naturally breaks the inversion symmetry and thus can induce an electric response and intriguing phenomena in all dielectric materials. Especially for epitaxial thin films, in which the lattice mismatch can give rise to very steep elastic strain relaxation, the strain gradient becomes huge and the 64

92 Chapter 5 associated flexoelectric field can be as large as 10 7 V m 1. This flexoelectric field has played an important role in novel electronic functions, such as domain control [10], flexoelectric rotation of polarization [11], mechanical writing of polarization [17] and flexoelectric diode [18]. Despite such universal, strong nature of flexoelectricity, however, its possible inflence on the defect formation during thin-film epitaxy has received little consideration. The exploitation of such an effect would allow the design of defect configuration and associated electronic functions, as well as provide a pathway to unravelling the fundamental physics of defect formation. Here, we demonstrate the intriguing effect of E int on defect formation in ferroelectric BiFeO 3 thin films. We show that flexoelectric effect can systematically control the E int and associated defect formation, emphasizing the key role of flexoelectricity in defect engineering. Finally, the flexoelectric control of defect formation allows a nearly defectfree film with fully functional electronic properties. For our study, we used a high-quality BiFeO 3 epitaxial thin film, grown on vicinal SrTiO 3 (001) substrate with a conductive SrRuO 3 buffer layer. Recent works demonstrated the possibility of a large E int in BiFeO 3 films [9,19]. Also, it has been shown that the defect effects in BiFeO 3 films can be clearly visualized by measuring their functional properties [4,5]. Therefore, this material system offers a great opportunity to investigate the effect of E int on defect formation. 5.2 Results Experiments 65

93 (0 0 L) (r.l.u.) Intensity (arb. units) Chapter Thin films fabrication a Fully strained BiFeO 3 Bulk BiFeO 3 : BiFeO 3 : SrRuO 3 : SrTiO 3 (002) T D = 580 C T D = 570 C T D = 560 C T D = 550 C θ (degree) b 3.05 T D = 550 C T D = 560 C T D = 570 C T D = 580 C 3.00 SrTiO 3 SrRuO BiFeO (0 K 0) (r.l.u.) (0 K 0) (r.l.u.) (0 K 0) (r.l.u.) (0 K 0) (r.l.u.) Figure 5.1 Structural analysis. (a) XRD θ 2θ scans of 250-nm-thick BiFeO 3 films grown at T D = 550, 560, 570 and 580 C on vicinal SrTiO 3 (001) substrates. The gray short-dashed and solid vertical lines indicate the (002) diffraction peak positions of the fully strained and relaxed BiFeO 3 films on SrTiO 3 substrates, respectively. (b) RSM images around the (013) SrTiO 3 Bragg peaks for 250-nm-thick BiFeO 3 films grown at T D = 550, 560, 570 and 580 C. We used high-quality BiFeO 3 epitaxial thin films with 250-nm-thickness. The films 66

94 Chapter 5 were sandwiched between a Pt top electrode and a single crystal SrRuO 3 bottom electrode. BiFeO 3 / SrRuO 3 thin-film layers were fabricated using pulsed laser deposition (PLD) onto SrTiO 3 (001) single-crystal substrates, with a 4 miscut toward the [100] direction. To form the bottom electrode, an SrRuO 3 layer (20-nm-thick) was deposited onto an SrTiO 3 substrate by PLD at 650 C. An oxygen pressure of 100 mtorr was maintained. The laser fluence and repetition rate were 2 J cm 2 and 2 Hz, respectively. The BiFeO 3 thin film was grown on top of the SrRuO 3 bottom electrode by PLD over a temperature range of 550 to 570 C. A stoichiometric BiFeO 3 ceramic target was used. The deposited BiFeO 3 film was postannealed in situ inside the PLD chamber at the deposition temperature for 1 hour under an oxygen atmosphere of 760 Torr. For the top electrode, a Pt layer (40-nm-thick) was deposited at room temperature by sputter deposition. After the deposition, the Pt layer was photolithographically patterned to form the BiFeO 3 capacitors. Pt top electrodes consisted of 10 to 200-μm square patterns Structural analysis In order to check the crystallography and estimate the strain and its relaxation of BiFeO 3 epitaxial thin films, we used a high-resolution X-ray diffraction (XRD). Figure 5.1a shows XRD θ 2θ scans for 250-nm-thick BiFeO 3 films grown at four different deposition temperatures, i.e., T D = 550, 560, 570 and 580 C. For these films, only the (00l) pseudocubic reflections could be seen along with the substrate peaks, indicating the formation of a single-crystalline BiFeO 3 phase with the well-oriented crystalline axes. If a BiFeO 3 film is fully strained under compression by a SrTiO 3 substrate, the in-plane lattice 67

95 Chapter 5 constant of the film should be the same as that of SrTiO 3 and the c-axis lattice should be elongated, due to the Poisson relation where the total volume is conserved. Using this relationship, we estimated that the (002) peak for the fully strained BiFeO 3 should be located at 2θ = 44.45, marked by the black-dashed vertical line. On the other hand, if the film becomes fully relaxed, then the (002) peak should be located at the 2θ position of bulk BiFeO 3, i.e., 2θ = 45.79, marked by the black-solid vertical line. Figure 5.1a shows that the out-of-plane strain (along the [001] direction) became more relaxed with the T D lowered. To obtain information about the in-plane strain state, we used a reciprocal space mapping (RSM) analysis for 250-nm-thick BiFeO 3 films. Figure 5.1b shows the RSM results around the (013) SrTiO 3 Bragg peak for several different T D. The (013) BiFeO 3 Bragg peak for T D = 580 C is located on the vertically dotted line, indicating that the film is fully strained along the [010] direction. On the other hand, the (013) BiFeO 3 peak for T D = 550 C is located on the left side of the vertical dotted line, indicating that the film is relaxed along the [010] direction. These RSM data show that the in-plane strain (along the [010] direction) became more relaxed with the T D lowered, similarly as the out-ofplane strain. Thus, our XRD θ 2θ and RSM data implies that even the small variation of T D can systematically modify the strain gradient in the films Electrical measurements We investigated the ferroelectric properties of BiFeO 3 films using a T-F analyzer 2000 (AixACCT) at room temperature. We measured polarization electric field (P E) 68

96 Chapter 5 hysteresis loops at 2 khz. We measured current density electric field (J E) curves at room temperature in the dark, using a low-noise probe station and a picoampere meter (Keithley 236). Before the J E curve measurements, a +12 V ( 12 V) external-poling voltage was applied to BiFeO 3 capacitors to obtain the downward (upward) polarization state. a Adatom mobility (a.u.) b Strain gradient (10 5 m 1 ) t = 250 nm Out-of-plane In-plane T D ( C) Figure 5.2 Large, systematic variation of strain gradient, according to T D. (a) Expected surface mobility of adatoms at the T D range of 550 to 580 C. The inset schematically depicts the mobility of adatoms at each T D. (b) The measured strain gradients in 250-nm-thick BiFeO 3 films for different T D. These values, estimated at 69

97 Chapter 5 room temperature, are believed to remain almost unchanged at high temperatures (during film-growth process), due to similar thermal lattice expansion of perovskite materials. Solid lines are the guide to eyes Large dependence of strain gradient on T D To explain how the strain and its relaxation in BiFeO 3 films depend on the T D variation, we consider the surface mobility of adatoms during film growth. It is natural that the surface mobility of adatoms can be enhanced with the T D increased (Fig. 2a), which is schematically depicted in the inset. Generally, the coherent thin-film growth depends on the mobility of adatoms [20]: a higher mobility of adatoms can lead to better coherent growth and more strained state. Specifically, we found that the lateral-growth behaviour of BiFeO 3, related to the adatom mobility, was changed according to T D (Fig. 5.3), which can influence the strain profile in the films. Thus, we expect that despite the slight T D variation (i.e., from 550 to 580 C), there can be a considerable change in a strain gradient, as well as an average strain of the films. In order to confirm this expectation, we estimated the strain gradient of 250-nmthick BiFeO 3 films, using Williamson-Hall (W-H) plot [13,21,22]. First, to obtain the outof-plane inhomogeneous strain (ε I ), four Bragg peaks (001), (002), (003) and (004) were selected from the XRD θ 2θ data. Then, ε I was extracted from the following fit equation: K w cos 4 I sin (1) D 70

98 Chapter 5 where measured instrument, β measured is the measured line width of the diffraction peaks of the samples, β instrument is estimated from the peak width β substrate of a nearby substrate peak, λ w = Å is the X-ray wavelength, D is the coherence length along the scattering vector, and K is a geometrical constant that was taken as 1. From the extracted out-of-plane ε I values, we estimated the out-of-plane strain gradients as , , and m 1, for BiFeO 3 films grown at T D = 550, 560, 570 and 580 C, respectively (Fig. 2b) [19]. a T D = 550 C b T D = 580 C c 6 Miscut direction BiFeO 3 1 μm In-plane strain gradient (10 5 m 1 ) T D ( C) Strained x (nm) x SrRuO 3 Relaxed Figure 5.3 Large dependence of strain gradient on T D. (a,b) Upper panels show atomic force microscopy images of 250-nm-thick BiFeO 3 films for (a) T D = 550 C and (b) 580 C. The film surface for T D = 580 C has a typical morphology of the stepflow growth mode. On the other hand, for T D = 550 C, the lateral length of BiFeO 3 grains became much shorter, possibly due to the limited mobility of adatoms at lower T D. Lower panels schematically describe the expected strain profile for (a) T D 71

99 Chapter 5 = 550 C and (b) 580 C. Considering the relationship bewteen the grain shape (e.g., aspect ratio) and strain relaxation, we can expect a larger strain gradient for lower T D. (c) Rough estimation of in-plane strain gradient. According to a general model for the strain profile [23,24], independent of the actual relaxation mechanism, the inplane strain ε can be expressed as follows: ε(x) = ε 0 e x/δ (2) where ε 0 and δ are constants, and x is the distance from the step edge. Typically, a film can be fully strained near the step edge (i.e., x = 0), due to a strong clamping effect. Also, we know the average in-plane strain values from the RSM results. Thus, using these information and Eq. (2), we can roughly estimate the profile of in-plane strain gradient. We here assumed the width of step terraces as 100 nm. The estimated values were found to be quite comparable with those obtained by W-H plots (Fig. 2b). Similarly, to obtain the in-plane ε I, we used the line width in the k-direction of the RSM peaks (013), (023) and (033) of BiFeO 3 and SrTiO 3 for BiFeO 3 films [19]. From the W-H plots for the width of those peaks, the in-plane ε I was calculated. Using these inplane ε I values, we determined the in-plane strain gradients as , m 1, and m 1, for BiFeO 3 films grown at T D = 550, 560, 570 and 580 C, respectively (Fig. 5.2b). These values are quite comparable with those obtained by following a general model for the strain relaxation (Fig. 5.3). Thus, our results evidently confirm the feasibility of a systematic, large variation of strain gradient, by the precise 72

100 Chapter 5 control of T D Functional properties of BiFeO 3 films according to T D a 80 T D = 550C 80 T D = 560C 80 T D = 570C 80 T D = 580C P (μc cm 2 ) E (MV m 1 ) E (MV m 1 ) E (MV m 1 ) E (MV m 1 ) b J (μa cm 2 ) T D = 550C : Poled with 12 V : Poled with +12 V T D = 560C T D = 570C T D = 580C E (MV m 1 ) E (MV m 1 ) E (MV m 1 ) E (MV m 1 ) Figure 5.4 Electronic functions of BiFeO 3 films, according to T D. (a) P E hysteresis loops for 250-nm-thick BiFeO 3 films deposited at four different T D of 550, 560, 570 and 580 C. (b) J E curves measured for 250-nm-thick BiFeO 3 films deposited at four different T D. Such tunability of strain gradient may lead to drastic change in defect configurations and functional properties of the films. We explored this possibility by measuring polarization electric field (P E) loops of BiFeO 3 films deposited at different T D (Fig. 5.4a). As demonstrated in our previous work (ref. 4; Fig. 5.5), defect dipoles (D defect ) can mainly cause the shift of P E loops, called the imprint, in BiFeO 3 and other ferroelectric 73

101 Chapter 5 films [4,25,26], whose amount depends on the D defect concentration. Figure 5.4a shows that every film exhibits a good P E hysteresis loop with a nearly rectangular shape, indicating no polarization relaxation. On the other hand, the shift of P E loop exhibits a strong dependence on T D : the film deposited at T D = 560 C shows almost no shift in P E loops, while those deposited at T D = 550, 570 and 580 C show an apparent shift. Thus, we can expect that the relatively large amount of D defect is accompanied with BiFeO 3 films for T D = 550, 570 and 580 C, while the nearly D defect -free film is achievable for T D = 560 C. a 80 As-grown Annealed T D = 550ºC b 80 As-grown Annealed T D = 570ºC P (μc cm 2 ) E (MV m 1 ) E (MV m 1 ) c d As-grown Annealed As-grown Annealed E int D defect T D = 550ºC T D = 570ºC e T D (ºC) E dd (MV m 1 ) E int (MV m 1 ) E if (MV m 1 ) E flexo (MV m 1 )

102 Chapter 5 Figure 5.5 The shift of P E loops. (a,b) P E hysteresis loops of 250-nm-thick BiFeO 3 films for (a) T D = 550 C and (b) 570 C. We recently demonstrated that the shift of P E loops is mainly due to the pinning field (E dd ) by defect dipoles (D defect ) [27]. We also found that the D defect alignmnent (and associated E dd direction) can be reversed by the polarization switching and subsequent annealing, which modifies the P E hysteresis loops (i.e., the direction of shift). (Details of the annealing procedure are explained in ref. 27.) (c,d) Schematic illustrations describing the D defect and E int (= E if + E flexo ) direction of the as-grown (left) and annealed state (right), for (c) T D = 550 C and (d) 570 C. (e) The direction of E dd (by D defect ) can be reversed after the annealing precedure, whereas the E int direction should be nearly unchanged. This means that the shifted value (E shift ) of P E loops can be expressed as E shift = ±E dd + E int (+: for as-grown state, : for annealed state) (3). Thus, using the E shift values (obtained from P E loops), we can estimate the values of E dd and E int, as shown in (e). The estimated values indicate that the shift of P E loops is mainly due to E dd (by D defect ), with small contribution from E int. Referring to the strain-gradient values (Fig. 5.2) for T D = 550 C and 570 C, we also determined the values of E if and E flexo, which are comparable with the calculated E if (ref. 28) and estimated E flexo values (Fig. 5.8). Additionally, we explored current J E curves for each polarization state of BiFeO 3 films (Fig. 5.4b). The small values of applied E ensures that little polarization switching occurs during the J E measurements. BiFeO 3 has shown rectifying diode and 75

103 Chapter 5 photovoltaic effects, whose polarity can be switched by the polarization reversal [29]. We recently found that in BiFeO 3 thin films, the diode effect was governed by interfacial carrier injection, and the switching of diode polarity could be inhibited by an interfacial defective layer (presumably, oxygen vancancy (V O )-rich layer) [5]. Similarly as in previous studies, the polarity of diode effect could not be switched in our BiFeO 3 films for T D = 550, 570 and 580 C (Fig. 5.4b), indicating the presence of V O -rich layer at the interface. Interestingly, however, the BiFeO 3 film for T D = 560 C clearly showed the polarity-switchable diode effect, implying a relatively perfect, much less defective interface of the film Defect configurations in BiFeO 3 films according to T D Figure 5.6a summarizes the defect configurations, determined from the measurements of P E loops and J E curves, in BiFeO 3 films according to T D. We also plot the shifted values of P E loops as a function of T D, as shown in Fig. 5.6b. Further information on the defect concentration can be obtained more easily by measuring the unit-cell volume of BiFeO 3 films. Since the formation of point defects usually results in the increase of unitcell volume [30], the measurement of unit-cell volume provides a simple, but effective, way for a relative comparison of the point-defect concentrations. Figure 5.6c shows the unit-cell volume of BiFeO 3 films as a function of T D, measured from a high-resolution XRD. The film for T D = 560 C shows the smallest unit-cell volume, which implies a fewer amount of defects, compared to those for T D = 550, 570 and 580 C, consistenly with our expectation from P E loops and J E curves. 76

104 Chapter 5 Unit-cell volume (Å 3 ) V O concentration (at.%) a T D = 550C T D = 560C T D = 570, 580C Pt BiFeO 3 D defect V O -rich layer SrRuO 3 SrTiO 3 b 0.4 E shift /E c 0.2 c t = 250 nm T D (C) t = 250 nm 0 Figure 5.6 Defect configurations in BiFeO 3 films, according to T D. (a) The schematic configurations of D defect and V O -rich layer in BiFeO 3 films according to T D, determined from the measurements of P E loops and J E curves. (b) The shift in P E loops of 250-nm-thick BiFeO 3 films, as a function of T D. We normalized the shifted 77

105 Chapter 5 values (E shift ) of P E loops by the coercive field (i.e., E c = (E c,+ E c, )/2). (c) Unit-cell volume (black closed squares) and estimated V O concentration (red closed circles) of 250-nm-thick BiFeO 3 films, as a function of T D. Furthermore, we tried to roughly estimate the V O concentration in the films from the measured unit-cell volume. According to the empirical model, the unit-cell volume V of perovskites can be expressed as below [31] V A ( r r ) (4) 3 3 B anion where r B and r anion are ionic radii of B-site cation and anion, respectively, and A is a constant close to 2. By assuming oxygen-deficient BiFeO 3 δ for the simplicity, we can define the effective cation and anion radii as [32] r B (1 2 ) r (2 ) r (5) 3 2 Fe Fe 3 (6) 3 3 ranion ( ) ro ( ) r v where r 3 Fe, r 2 Fe, r O and r v are the ionic radii of Fe 3+, Fe 2+, oxygen and V O, respectively. The values for these radii are all available, with the exception of those for V O, from the work of Shannon [33]. For our study, we chose the value of r v as 1.0 Å (ref. 32). Then, we determined the δ values (i.e., the concentration of V O ) from the measured unit-cell volume. Figure 5.6c shows that while the BiFeO 3 film for T D = 560 C is free of excessive V O, other films for different T D include a noticeable amount of V O. Thus, it seems clear that the defect formation is sensitive to T D, and even a very small deviation of T D (from 560 C) promotes the defect formation in our BiFeO 3 films. 78

106 Chapter 5 a b a bulk BiFeO 3 E if SrRuO 3 BiO +1 FeO 2 1 BiO +1 FeO 2 1 BiO +1 FeO 2 1 SrO 0 RuO 2 0 E flexo Figure 5.7 Two competing, intrinsic sources of E int in BiFeO 3 films on SrRuO 3 /SrTiO 3. (a) Interfacial charge discontinuity can generate the downward internal electric field (E if ) in BiFeO 3 films on SrRuO 3 /SrTiO 3 substrate [28]. Note that SrRuO 3 is self-terminated with SrO surface, since the RuO 2 -layer is highly volatile. (b) Relaxation of compressive misfit strain can generate the upward internal electric field (E flexo ) via flexoelectricity in BiFeO 3 films on SrRuO 3 /SrTiO 3 substrate Large, systematic control of E int via flexoelectricity. Our results in Fig. 5.4 and 5.6 revealed a couple of interesting features on the defect formation in BiFeO 3 films. First, the small T D variation (i.e., ±10 C) made a surprisingly large difference in defect concentration, and then significantly modified functional properties of BiFeO 3 films. Secondly, we found that only the film deposited at the intermediate T D (= 560 C) was free of excessive defects, although it is more natural that the defect concentration is monotonically varied according to the increased (or decreased) 79

107 Chapter 5 T D. These results highlight that there exists an unconventional mechanism of defect formation in our BiFeO 3 films. We propose that flexoelectricity can play an emerging role in defect formation via tailoring E int in the films. The BiFeO 3 film on SrRuO 3 /SrTiO 3 substrate has mainly two dominant sources for E int : one is flexoelectric effect by strain gradient that can generate upward electric field (E flexo ) [19], and another is the interfacial charge discontinuity that can generate downward electric field (E if ; Fig. 5.7) [9]. We estimated E flexo from the measured strain gradient, using the following equation [15,16]: E flexo e a x 0 (5) where e is the electronic charge, ε 0 is the permittivity of free space, a is the lattice constant, ε/ x is the strain gradient, and λ is a flexoelectirc coefficient close to unity. Importantly, we already showed that even a small variation of T D can greatly modify the strain gradient (Fig. 5.2). Thus, the associated E flexo can vary considerably according to T D, whereas E if is expected to remain nearly unchanged, which enables a large, systematic control of E int (= E flexo + E if ). Figure 5.8 shows that a subtle competition between E flexo and E if causes a drastic change in E int : even for the small T D variation from 550 to 580 C, E int can have a wide range of change (from E int V m 1 to 10 6 V m 1 through E int 0), which may also explain our observed drastic change in defect configurations. We should note that the nearly defect-free BiFeO 3 film (corresponding to T D = 560 C) was achievable in the case of a small E int (i.e., E int 0), while the relatively large amount of defects in the films 80

108 Chapter 5 (corresponding to T D = 550, 570 and 580 C) was accompanied with a large E int. Thus, it seems that a large E int might promote the defect formation in BiFeO 3 and, in other words, a small E int is essential for making a defect-free film. + 0 E int 6 t = 250 nm Electric field (MV m 1 ) 3 0 E flexo E int E if T D ( C) 580 Figure 5.8 Large, systematic control of E int via flexoelectricity. The estimated E int for 250-nm-thick BiFeO 3 films, as a function of T D. Using the measured values of strain gradient, we estimated E flexo, projected onto the ferroelectric polarization direction (i.e., [111] or its equivalent ones). Red open and closed squares correspond to E flexo for the flexoelectric coefficient λ = 1.0 and 0.25, respectively. Red dashed line represents the averaged values of E flexo for λ = 1.0 and Blue open triangles represent E if, obtained by referring to the calculated values (ref. 9) and projecting them onto the polarization direction. Black solid line represents E int (= E flexo + E if ) 81

109 Chapter 5 according to T D, obtained by summing E flexo and E if. The positive (or negative) E int indicates the upward (or downward) field direction Demonstration of the E int effect on defect formation. To confirm the effect of E int on defect formation, we controlled the E int by varying only the film thickness, with other growth parameters fixed. We first present the case of T D = 550 C. The fully strained 50-nm-thick BiFeO 3 film without any strain relaxation has no flexoelectric contribution (i.e., E flexo = 0), with the contribution only from E if. This causes the 50-nm-thick BiFeO 3 film to have a large downward E int, whereas 250-nm-thick film with a substantial E flexo contribution has a large upward E int, as schematically shown in Fig. 5.9a. This implies that at an intermediate thickness between 50 and 250 nm, E flexo and E if should be balanced with each other, making E int to be reduced. Due to this reduced E int, according to our prediction, the films with intermediate thicknesses should have a fewer amount of defects, compared to the thinnest or thickest films. Indeed, by measuring the unit-cell volume and shift of P E loops, we found that the films with intermediate thicknesses were less defective (Fig. 5.9c). For T D = 570 C, differently from the case of T D = 550 C, the strain gradient cannot be large enough to reverse the E int direction (Fig. 5.9b). Increasing t makes E int to vary from a large negative value to a small negative one, just without the directional change. In this case, according to our prediction, the defect concentration in the films would decrease monotonically with the t increased, which is verified by measuring the unit-cell volume 82

110 Chapter 5 and shift of P E loops (Fig. 5.9d). Thus, these results unambiguously demonstrate the important role of E int in defect formation. a T D = 550 C E int E int 0 E if E flexo D defect c E shift /E c T D = 550 C Unit-cell volume (Å 3 ) 50 nm 250 nm t b TD = 570 C d T D = 570 C 62.4 E shift /E c Unit-cell volume (Å 3 ) 50 nm 250 nm t t (nm) Figure 5.9 Demonstration of the E int effect on defect formation. (a,b) Schematics of the E int variation according to the film thickness t, for (a) T D = 550 and (b) 570 C. Red, blue and black arrows represent E flexo, E if and E int, respectively. The length of arrows indicates the magnitude of the associated electric field. (c,d) The measured shift of P E loops (black closed circles) and unit-cell volume (red open squares) as a function of t, for (c) T D = 550 and (d) 570 C. Solid lines are the guide to eyes. 5.3 Discussion 83

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