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In Situ X-Ray Characterization of Piezoelectric Ceramic Thin Films

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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 phe- nomena exhibited by these materials. These developments have been chronicled regularly in the Bulletin.1,2 Ferroelectric thin-film materi- als belong to the broad category of electronic In situ X-ray ceramics, and they find applications in elec- tronic 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
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