In Situ X-Ray Characterization of Piezoelectric Ceramic Thin Films

bulletin cover story (Credit: Agresta; ANL.)

X-ray nanodiffraction instruments, such as this one at the Advanced Photon Source of Argonne National Laboratory, allow researchers to study the structure and functional prop- here has been rapid development in the erties of thin-film materials, including ceramics and the inte- Tprecision with which ferroelectric mate- grated circuit shown here, with spatial resolutions of tens to rial can be grown epitaxially on single-crystal hundreds of nanometers. substrates and in the range of physical phenomena exhibited by these materials. These developments have been chronicled regularly in the Bulletin.1,2 Ferroelectric thin-film materials belong to the broad category of electronic In situ X-ray ceramics, and they find applications in electronic and electromechanical devices rang- ing from tunable radio-frequency capacitors characterization to ultrasound transducers. The importance of these materials has motivated a new genera- of piezoelectric tion of materials synthesis processes, leading to the creation of thin films and superlattices with impressive control over the composi- ceramic thin films tion, symmetry, and resulting functionality. In By Paul G. Evans and Rebecca J. Sichel-Tissot turn, improved processing has led to smaller devices, with sizes far less than 1 micrometer, Advances in X-ray scattering characterization technology faster operating frequencies, and improved now allow piezoelectric thin-film materials to be studied in performance and new capabilities for devices. new and promising regimes of thinner layers, higher electric Important work continues to build on these fields, shorter times, and greater crystallographic complexity. advances to create materials that are lead-free and that incorporate other fundamental sources of new functionality, including magnetic order.

18 www.ceramics.org | American Ceramic Society Bulletin, Vol. 92, No. 1 The polarization of ferroelectric liant beams of X-rays materials can be changed by chang- with tunable photon ing the applied field. (See sidebar energy that are avail- “Piezoelectricity, crystal structure, and able at synchrotron symmetry.”) Polarization switching has light sources (see profound effects on the piezoelectric sidebar “Synchrotron distortion because the piezoelectric Radiation,” p. 23). The coefficients are effectively reoriented high brilliance of the when the polarization is changed. beam allows for focus-

Piezoelectricity is thus an excellent ing it to small spot (Credit: Chen, et al.; American Institute of Physics. Reprinted with permission.) marker for the interplay of mechanical sizes. The important Figure 1. Piezoelectric shift in the wavevector of the 002 Bragg reflection of an [001]-oriented BiFeO thin film during and electronic phenomena responsible aspect of X-ray scatter- 3 an electric-field pulse lasting 12 ns. The wavevector shift cor- for polarization switching. ing studies is that the responds to a piezoelectric strain of 0.5%.11 The thinness, faster operating tim- intensity and location ~ escales, and novel structural degrees of in reciprocal space of the reflections reflections appear) provide the lattice freedom available in epitaxial ferroelec- provide key information about the constant, and the variations of these tric thin films pose difficult challenges functional properties of piezoelectrics. positions as a function of the applied for characterization using conventional The positions in reciprocal space electric field determine the piezoelec- experimental methods. Researchers (derived from the angles at which X-ray tric coefficients. The strain and diffrac- have developed a series of powerful— now standard—characterization tech- Piezoelectricity, crystal structure, and symmetry—The piezoelectric niques based on measuring the displace- coefficients ment of the surface of the thin film using piezoelectric force microscopy or Piezoelectricity results from the polarization of crystals lacking inversion symmetry. In these materi- 3 als, an applied stress leads to a change in the electrical polarization, and, conversely, applied electric interferometry. Alternatively, the stress fields lead to a change in the lattice constants, referred to as the piezoelectric strain. In the limit of imparted by the piezoelectric material small strains, fields, and stresses, the piezoelectric strain is proportional to the applied electric field, can be quantified using the curvature of and the strain tensor and electric field are related by εjk = dijk∙Ei, where is the strain tensor, d is the the substrate or a cantilever.4 Another piezoelectric coefficient, and E is the applied electric field vector.20 Note that the piezoelectric tensor approach is to use focused ion-beam can lead to strains and shears along directions that are orthogonal to the applied field. The units of d, milling or selective etching to create more properly referred to as the converse piezoelectric coefficient, are distance divided by potential a bridge structure or cantilever into difference, often given in picometers per volt. The three-index notation for the piezoelectric coefficient can be reduced to a two-index notation, d , where the index i refers to the electric field direction the film by removing a section of the ij in the conventional manner where 1, 2, and 3 refer to the x, y, and z directions, respectively. The underlying substrate and to observe the second index j refers to elements of the strain tensor using Voigt notation.20 The tensor of converse distortion of the shape of this struc- piezoelectric coefficients dij relates the piezoelectric strain εj to the electric field Ei: ture.5 These approaches have proved d d d d d d to be phenomenally successful, but face ε1 ε6 ε5 11 12 13 14 15 16 E1 d d d d d d important limits, particularly regarding ε6 ε2 ε4 = 21 22 23 24 25 26 E2 time resolution and the precision with ε ε ε ] d31 d32 d33 d34 d35 d36 E [ 3 5 4 3 [ ] ][ which the relationship between atomic- scale effects and the overall electrome- The symmetry of thin films and ceramics is such a strong effect that a second, engineering notation, chanical distortion of the sample can be is widely used in describing the piezoelectric coefficients. The notation and units are identical to the ones described above, which can lead to some confusion about which definition is in use. In the determined. Understanding the atomic engineering notation, piezoelectric coefficients are defined so that the z direction, corresponding to origins of piezoelectricity, particularly subscript 3, is always in the direction of the applied electric field. Thus, the expansion along the field at nanosecond time scales, has proved direction is determined by the piezoelectric coefficient d33 in the engineering notation. The symmetry challenging, but new techniques based of the piezoelectric tensor also is different between the two definitions. In the crystallographic defini- on X-ray scattering address this void. tion, the piezoelectric tensor has the symmetry of the crystallographic unit cell. In the engineering definition, the tensor has the same symmetry as the overall shape of the piezoelectric thin film or X-ray diffraction ceramic solid, which is quite different from the crystallographic symmetry.

X-ray diffractometry techniques pro- The multiferroic complex oxide bismuth ferrite BiFeO3 is an excellent example of the difference between the crystallographic and engineering definitions of piezoelectricity. Although BiFeO has vide direct insight into the piezoelec- 3 rhombohedral symmetry in bulk crystals, a pseudocubic notation for the BiFeO piezoelectric tensor tricity of ceramics and epitaxial oxides. 3 and X-ray reflections are often used to emphasize the epitaxial relationship between the BiFeO thin Several experimental approaches do 3 film and its cubic substrate. The rhombohedral symmetry of BiFeO3 is not apparent from this notation, this by taking advantage of time- which has the side effect of complicating the expression for the piezoelectric tensor. Projecting the resolved scattering techniques.6–9 For piezoelectric tensor onto the [100], [010], and [001] directions of a tetragonal material forces most of example, X-ray scattering experiments the terms to be zero and makes many of the remaining coefficients identical.20 n take advantage of the highly bril-

American Ceramic Society Bulletin, Vol. 92, No. 1 | www.ceramics.org 19 In situ X-ray characterization of piezoelectric ceramic thin films

probe piezoelectric- variation of the lattice constant during ity. For example, the pulse. Figure 1 shows the Systematic measurements of the structural changes piezoelectric properties of thin-film induced in an epi- capacitors can be made by either apply- taxial thin film ing voltage pulses of various magnitudes

of BiFeO3 by an or by sweeping the voltage and record- electric field pulse ing the diffraction pattern as a function lasting 12 nanosec- of time. The latter approach is shown onds.11 The piezo- in Figures 2(a) and (b) and shows the electric expansion distortion resulting from positive and during the electric- negative pulses applied to the bot-

field pulse—a strain tom electrode of a Pb(Zr,Ti)O3 (PZT) of approximately thin-film capacitor.12 The measure- 0.5 percent—shifts ments required a series of thousands of the diffraction peak electric-field pulses to allow acquisition to a smaller wave- of the diffraction pattern over the full

vector, qz. For this range of relevant angles. In this case, measurement, the positive and negative pulses produce (Credit: Do, et al., Taylor & Francis Ltd. Reprinted with permission.) electric fields were piezoelectric expansion because the first Figure 2. Shift in the 002 Bragg reflection of a Pb(Zr,Ti)O3 thin film in which the top electrode is grounded and (a) positive or synchronized with few pulses are enough to switch the sign (b) negative polarity voltage pulses are applied to the bottom X-rays generated by of the polarization of the PZT capaci- electrode. The reflection shifts to smaller angles, corresponding individual bunches tor. Combining the strains measured to larger lattice constants, in both cases because the measure- of stored electrons from the shift of the diffraction pattern ments require many electric-field pulses and the remnant polar- at the Advanced with the time dependence of the volt- ization rapidly switches to the direction favored by the sign of Photon Source age leads to the plots of strain as a func- the applied field. (c) Field-dependent strain measured from (a) facility (Argonne tion of voltage shown in Figure 2(c). and (b), plotted as a function of the applied voltage. The strain National Laboratory, The slopes of these lines give piezoelec- is proportional to the voltage in both cases, with piezoelectric Argonne, Ill.). Thus, tric coefficients that are consistent with coefficients of 53 pm/V and 54 pm/V for positive and negative voltage pulses, respectively.12 the time resolu- previous measurements in the same tion is limited only material.12 tion angle are related through the Bragg by the duration of the X-ray bunches Alternating the sign of applied equation λ = 2dsin θ. Reciprocal space and by the electrical bandwidth of voltage pulses switches the capacitor is spanned by wavevectors so that the the equipment generating the voltage between two polarization states in each Bragg reflections occur at wavevectors pulses. The characteristic rise-and-fall repetition of the pulse sequence. The with magnitude q = 2π/d. The intensity times of the shift in the diffraction peak diffraction patterns and strain observed of X-ray reflections depends on the shown in Figure 1 are 1.4 nanoseconds in this case are shown in Figures 3(a) direction of the polarization, an effect and correspond to the charging time and (b). As was the case in Figure 2, that can be combined with nanofocused constant of the capacitor. In addi- large pulses of either sign lead to large X-ray beams to produce maps of the tion, the shift of the diffraction peak piezoelectric expansions. When the direction of the remnant polarization.10 provides a quantitative measure of the voltages switch signs, however, the Because X-ray diffractometry allows for precise measurement of lattice parameters, the piezoelectric coefficients can be determined in situ, that is, while the sample is subject to either constant or varying electric fields. Consequently, in situ X-ray diffractometry provides a means to begin understanding the fundamental source of piezoelectric phenomena. (Credit: Do, et al., Taylor & Francis Ltd. Reprinted with permission.) Measuring lattice constants of Figure 3. (a) Piezoelectricity-induced angular shift of the 002 Bragg X-ray reflection of piezoelectric thin films a Pb(Zr,Ti)O3 thin film in a bipolar applied electric field. (b) Piezoelectric hysteresis loop Epitaxial thin-film capacitors are an derived from (a). These measurements allow the local coercive electric field and piezeo- excellent system for testing new ways to electric coefficients to be measured.12

20 www.ceramics.org | American Ceramic Society Bulletin, Vol. 92, No. 1 lattice first contracts, producing the comes from two characteristic electromechanical hyster- closely related esis shown in Figure 3(b). The results effects. The first in Figure 3 correspond to a structural is the piezoelec- observation of the hysteresis of fer- tric expansion of roelectric capacitors, an effect that is the lattice. A sec- useful for decoupling the fundamental ond, more subtle origin of hysteresis from artifacts associ- effect, is the rota- ated with electrical measurements. tion of the {103} planes as the c Piezoelectricity in thin films with lattice constant complex microstructures increases, which In Figures 2 and 3, the direction rotates the peak along which the X-ray experiments position around probed the piezoelectric strain was the origin in

parallel to the direction of the applied reciprocal space. (Credit: R. Sichel, U. Wisconsin-Madison.) Figure 4. Field-dependent projections of the three-dimensional dif- electric field. Thus, the piezoelectric The values of d33 fraction pattern of a BiFeO thin film onto the q –q plane. The BiFeO coefficients measured in this case cor- and d31 for each 3 x z 3 respond to the d component of the distinct structural layer exhibits four {103} diffraction peaks, resulting from structural 33 variants with various crystallographic orientation within the X-ray piezoelectric tensor. In the thin-film volume, shown spot. Arrows indicate the directions of the shifts of these reflections next to the reflec- case, only E3 is nonzero, and the piezo- in electric fields from 0 to 250 kV/cm. The SrRuO3 reflection is not electric coefficients that determine the tions in Figure 4, displaced by the applied field because there is no piezoelectric strain do not account 14 tensile or compressive strain are d31, d32, in the bottom electrode. for rotations of and d33. Shear strains are determined the atomic planes and represent only be in the more relaxed regions than in by coefficients, d34, d35, and d36. Time- resolved microdiffractometry probes the the apparent change in lattice con- regions with no in-plane piezoelectric out-of-plane and the in-plane piezoelec- stant. Nevertheless, it is clear that the response. These effects are even more piezoelectric response varies for each pronounced in ceramics, where in situ tric response, measuring the strains ε1, domain. The apparent value of d diffractometry studies have shown that ε2, and ε3 from changes to the in-plane 31 lattice constants and the out-of-plane domains at this location on the sample the fraction of the overall piezoelectric c-axis lattice constants, respectively. ranges from –37 picometers per volt to distortion that directly results from the The full piezoelectric tensor is par- +0.69 picometers per volt. The nonzero expansion of the lattice is small com- pared with the motion of domain walls ticularly important for BiFeO because values of d31 occur because the in-plane 3 7 the bulk rhombohedral unit cell is dis- lattice constant within the domains and other long-range elastic effects. torted during epitaxial growth, leading is not completely clamped by the sub- to a complex thin-film microstructure.13 strate, and each domain is in a different High fields, ultrafast dynamics, Instead of a single intense peak, the stress states because of the incomplete and complex domains relaxation of the film. A domain near The precision and high resolution of {103} reflections of BiFeO3 are split because the film has regions with the the edge of a mosaic block or any other in situ diffractometry probes provide a four possible orientations of its rhom- type of defect, for example, is under way to study electromechanical materi- bohedral distortion relative to the cubic mechanical constraints very different als in new regimes, such as ultrashort substrate, as well as varying degrees of from one in a perfectly epitaxial region plastic relaxation and tilt. Applying a of the film. voltage in this case results in a piezo- The in-plane piezoelectric response electric response that depends on the of the partially relaxed BiFeO3 lies local structure of the thin film. Figure between the polycrystalline and epi- 4 shows the piezoelectric response by taxial regimes. A completely clamped plotting positions in reciprocal space film would have an effective d31 of zero. Wafer flexure studies have shown that of the BiFeO3 pseudocubic {103} reflec- 14 tions for several electric fields. The polycrystalline Pb(Zr,Ti)O3 thin films arrows in Figure 4 indicate the change grown by the sol–gel method have val- (Credit: Chen, et al.; American Institute of Physics. Reprinted with permission.) Figure 5. Electric-field dependence of the in reflection positions as E increases ues of d that increase with increasing 31 piezoelectric strain in BiFeO thin films film thickness, probably because the 3 from 0 to 250 kilovolts per centimeter. at very high electric fields. The low-field There is no distortion of the electrode substrate clamps the film less effec- piezoelectric coefficient of 55 pm/V does tively as the film gets thicker.4 BiFeO material, SrRuO3. 3 not provide a good fit to strains observed domains with nonzero d are likely to 11 The distortion evident in Figure 4 31 at fields above ~150 MV/m.

American Ceramic Society Bulletin, Vol. 92, No. 1 | www.ceramics.org 21 In situ X-ray characterization of piezoelectric ceramic thin films

ing the intrinsic time Outlook scales of the processes In situ diffractometry studies offer responsible for the a quantitative way to characterize the electronic properties properties of piezoelectric materials and of ferroelectrics. In to begin to understand the fundamental epitaxial ferroelec- origin of these properties. The precision trics, polarization with which lattice parameters can be switching occurs by measured in X-ray studies allows piezo- a process in which electric coefficients to be extracted domains of the polar- quantitatively for thin-film materials, ization favored by the in the conventional case where the field nucleate and films expands normal to the surface and grow across the film. when adjacent areas cooperatively vary This process can be their in-plane structures. In more com- imaged stroboscopi- plex systems, in situ probes allow the cally by using the properties of piezoelectrics to be studied large piezoelectric at high electric fields, very short pulse expansion that occurs times, and in systems with unusual when the polarization domain patterns. Further applications (Credit: Evans; U. Wisconsin-Madison.) Figure 6. Disappearance of domain satellite reflections at switches as a marker of this approach will allow researchers –1 for the transition. to better understand the relationship Qy = 0.08 Å in a PbTiO3/SrTiO3 superlattice in an applied electric field. The decrease in the intensity of these satellites The images reveal between piezoelectric properties and occurs because the applied field drives the system out of the that domains in a crystallographic symmetry, for example, striped domain state and into a configuration with uniform PZT thin film nucle- in testing theoretical predictions of the polarization in the SrTiO and PbTiO layers. 3 3 ate with character- role of distortions of oxygen octahedra pulses or very large electric fields. The istic spacings of several micrometers in superlattice materials.19 Advances ability to apply short-duration electric- and subsequently propagate into the in X-ray technology will allow these field pulses allows materials to be stud- unswitched material at a velocity of 40 studies to extend to shorter picosecond- ied in electric fields with magnitudes meters per second under electric fields scale times, and with improvements 6 far larger than fields at which the film of 230 kilovolts per centimeter. in X-ray detectors, to probe less-well- would exhibit dielectric breakdown in Diffractometry probes are particu- ordered systems including polymers and steady state. These high fields can reach larly useful when the thin film has a other organic piezoelectrics. 2 to 3 megavolts per centimeter and lead complex domain pattern. For example, epitaxial superlattices consisting of Acknowledgments to strains of 2.0 percent in BiFeO3 and 11, 15 alternating layers of dielectric and fer- The authors gratefully acknowledge up to 2.7 percent in Pb(Zr,Ti)O3. These fields can be large enough that roelectric materials spontaneously form support from the Ceramics Program of the approximations that the strain and a nanometer-scale striped domain pat- the NSF Division of Materials Research electric field are small no longer apply. tern that results because of the weak through grants DMR-0705370 and For BiFeO , in particular, the effects interaction between adjacent ferroelec- DMR-1106050. The authors also thank 3 17 that result from high fields are particu- tric layers. An applied electric field Pice Chen, Alexei Grigoriev, Ji Young larly large, as shown in Figure 5.11 In can favor stronger coupling, enough to Jo, and Dal-Hyun Do for collaborations this case, the electric field is applied drive the system into a single-polariza- and insightful discussions. along the pseudocubic [001] direction tion state. In this situation, diffraction information comes from the domains About the authors of a BiFeO3 thin film, leading to a large strain consistent with the rotation of themselves and from the piezoelectric Paul Evans is a professor at the the polarization and the possibility that strain induced by applied electric fields, University of Wisconsin–Madison. 19 the system is approaching a structural as shown in Figure 6. Insight into the Rebecca Sichel-Tissot earned her rhombohedral-to-tetragonal phase mechanism of the electric-field-induced PhD in 2011 from the University of transition. Such phase transitions have transformation from the striped-domain Wisconsin–Madison and is presently been reported in thin films grown with state to the eventual uniform polariza- a postdoctoral researcher at Drexel varying degrees of epitaxial mismatch,16 tion state can be obtained either at University. Contact: [email protected]. but diffractometry probes have not yet long timescales using laboratory X-ray edu, [email protected]. 17 been able to capture the transitions or diffractometry or at nanosecond their dynamics in situ. elapsed times using synchrotron-based References 18 A further use of the time resolution techniques. 1L.M. Shepard, “Advances in Processing of of in situ techniques is in understand- Ferroelectric Thin Films,” Am. Ceram. Soc.

22 www.ceramics.org | American Ceramic Society Bulletin, Vol. 92, No. 1 12D.-H. Do, A. Grigoriev, D.M. Kim, C.-B. Synchrotron radiation Eom, P.G. Evans, and E.M. Dufresne, “In Third-generation X-ray sources from synchrotron light sources, such as the Advanced Photon Source Situ X-ray Probes for Piezoelectricity in at Argonne National Laboratory (Argonne, Ill.), generate X-rays with very high intensity and small Epitaxial Ferroelectric Capacitors,” Integr. angular divergence, termed "brilliance." This brilliance, in turn, allows X-rays to focus to very small Ferroelectr., 101, 174 (2009). spot sizes, on the order of 100 nm or smaller. This spatial resolution is comparable to scanning 13R.J. Sichel, A. Grigoriev, D.-H. Do, S.-H. probe microscopy and makes the study of the functional properties of highly heterogeneous materi- Baek, H.-W. Jang, C.M. Folkman, C.-B. als possible. Eom, Z. Cai, and P.G. Evans, “Anisotropic X-ray wavelengths are selected to match the needs of the experiment. Wavelengths of ~1 Å, which Relaxation and Crystallographic Tilt in are required for diffractometry experiments, easily penetrate the top electrodes of device structures, BiFeO3 on Miscut SrTiO3 (001),” Appl. such as capacitors, which allows in situ studies to be performed in applied electric fields. Even with Phys. Lett., 96, 051901 (2010). the angular convergence introduced by focusing, synchrotron X-ray diffractometry experiments have 14R.J. Sichel-Tissot, “Structural and sufficient precision to observe piezoelectric strains on the order of 10–5. In these studies of piezo- Electromechanical Properties of Epitaxial electricity, the thin-film capacitor is positioned at the focus of the X-ray beam and the diffractometry BiFeO Thin Films,” PhD Thesis, University experiment is conducted in an electric field provided by a probe tip contacting the top electrode. 3 of Wisconsin–Madison, 2011. 15A. Grigoriev, R. Sichel, H.-N. Lee, E.C. Landahl, B. Adams, E.M. Dufresne, and P.G. Evans, “Nonlinear Piezoelectricity in Epitaxial Ferroelectrics at High Electric Fields,” Phys. Rev. Lett., 100, 027604 (2008). 16R.J. Zeches, M.D. Rossell, J.X. Zhang, A.Hatt, Q. He, C.H. Yang, A. Kumar, C.H. Wang, A. Melville, C. Adamo, G. Sheng, Y.H. Chu, J.F. Ihlefeld, R. Erni, C. Ederer, V. Gopalan, L.Q. Chen, D.G. Schlom,

(Credits: (a) Alexei Grigoriev, Univeristy of Tulsa; (b) Chen et al.; IOP. Reprinted with permission.) N. A. Spaldin, L.W. Martin, R. Ramesh, (a) Photograph and (b) schematic of in situ synchrotron X-ray diffractometry studies “A Strain-Driven Morphotropic Phase

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Switching Contribution to the Dynamic Field Piezoelectricity of Epitaxial BiFeO3

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