- Email: [email protected]
Size effects in nanoscale ferroelectrics
Journal of Alloys and Compounds 449 (2008) 2–6
Size effects in nanoscale ferroelectrics A. R¨udiger ∗ , R. Waser Center of Nanoelectronic Systems for Information Technology, Institute of Solid State Research, Research Center Jue¨oich, 52425 Juelich, Germany Received 8 November 2005; received in revised form 23 December 2005; accepted 30 December 2005 Available online 21 December 2006
Abstract Ferroelectrics are among the most advanced candidates of fast non-volatile memory materials. How do the properties of the commonly used perovskites such as PbTiO3 , Pb(Zrx Ti1−x )O3 (PZT) and BaTiO3 change with size? Is there a fundamental limit showing up below which ferroelectricity irrevocably ceases? While the operating voltage as the predominant driving force for commercial applications shifted the thickness down to a few unit cells, ferroelectrics are now on the verge of true nanoscale integration of laterally confined structures. Top-down, bottom-up approaches and their combination provide samples far below 100 nm and indicate that the interaction of electrode and ferroelectric becomes increasingly relevant in terms of strain, screening of the depolarization field and fatigue resistance. As the qualitative understanding of nanoscale ferroelectricity advances the ferroelectric limit appears to be below 10 nm thus paving the road for further miniaturization. © 2007 Published by Elsevier B.V. Keywords: Ferroelectric; Piezoelectric; Atomic force microscopy; FeRAM
1. Introduction Ferroelectrics make use of two thermodynamically equivalent groundstates of the spontaneous polarization that can be reversed by and external electric field. This type of memory is therefore non-volatile. As the structures are shrinking in thickness, the operation voltage has dropped below one volt, and the switching speed is only limited by the RC time constants of the circuit [1]. So we practically have a fast and energy-efficient nonvolatile but charge-based memory. How small can this device become and still provide a detectable amount of charge? The commonly used perovskites are wide-bandgap semiconductors so dc-conductivity can be omitted for bulk samples where the detected switching current is solely displacive. The polarization as expressed by a bound surface charge density (C/m2 ) is thickness independent but rapidly shrinks with area (see Fig. 1). For typical materials we are left with only 6000 electrons for a capacitor of 100 nm × 100 nm. A device of 10 nm × 10 nm will therefore have to operate with 60 electrons. Irrespective of all challenges to operate at these current levels, a fundamental question arose from the analogy to ferromag-
∗
Corresponding author. Tel.: +49 2461 61 4732; fax: +49 2461 61 2550. E-mail address: [email protected] (A. R¨udiger).
0925-8388/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.jallcom.2005.12.133
netism. How small can such a structure be made and still be ferroelectric [2]? The situation is fundamentally different from superparamagnetism as the coupling force has a very long interaction length as compared to magnetism. The unit cell dipoles are electrostatically coupled and strain also propagates several unit cells across the material. This is why the phenomenological mean-field Landau–Ginzburg–Devonshire theory was successfully employed to describe many features of ferroelectricity and its phase transitions on a macroscopic scale. But as the structures shrink down to the length-scales of ferroelectric coupling we should wonder to what extent the assumptions of mean-field theories still hold true. And indeed, in order to account for some size-driven effect, the polynomial description of the free-energy had to be expanded by two more terms: a surface energy term and a polarization gradient term both of which contain parameters that are not experimentally accessible [3–6]. Ab initio calculations are on the way together with a comprehensive survey on thin films provided by Dawber et al. [7]. The surface plays a major role as its volume fraction increases with decreasing overall volume: the polarization gradient is a direct consequence of a modified surface. There is plenty of experimental evidence that the surface behaves different from the bulk [8]. Talking about the surface it has to become clear that ferroelectricity in contrast to mere pyroelectricity does not only involve a structural prerequisite (polar axis) but the need for reversibility which
A. R¨udiger, R. Waser / Journal of Alloys and Compounds 449 (2008) 2–6
3
All the aforementioned three contributions: structure, composition and time will also depend on the shape of our structures as a dipole–dipole interaction is highly anisotropic and as strain can be used to intensify the tetragonality and therefore the polarization. 2. Structure
Fig. 1. Single shot hysteresis loop with in situ compensation (no averaging) in a stand-alone 300 nm × 300 nm PZT capacitor [19].
goes far beyond the structure. So the mere existence of a noncentrosymmetric phase with a polar axis is necessary, but not sufficient to pinpoint ferroelectricity. A pyroelectric in that sense is a ferroelectric where the breakdown-voltage is smaller than the coercive field. Once we want to show functionality, we have to apply electrodes which inherently modify all relevant electromechanical boundary conditions: strain is applied to the system, the depolarization field that promotes the formation of ferroelectric domains is partially screened in the electrodes and we have to consider a system of electrode–ferroelectric–electrode. In all cases where we cannot be certain about the quality of our fabrication it is required to also consider two interfaces between electrode and ferroelectric. These interfaces have turned out to be responsible for many effects in ferroelectric devices (imprint, parasitic capacitances, dielectric losses, etc.). What should a comprehensive theory of nanoscale ferroelectricity take into account? Clearly, there will be a structural change as the surface gains volume fraction. But what else may be important? Some recent experiments point into two more directions that have not been considered so far. For one, the chemical composition of a three-component system like all perovskites (ABO3 ) is a lot more difficult to control than in most one-component nanomagnets. Growth itself already is an issue [9] but the exact chemical composition is almost unknown and difficult to access as the volumes of ferroelectric nanostructures are small and often averaging is not feasible. The second issue directly originates from the analogy to the superparamagnetic limit: The soft-mode phonon (TO) (in analogy to the Larmorfrequency) tries to perform just the movement that is required to switch the structure. With an increasing number of ferroelectric unit cells it becomes exponentially unlikely that for a given temperature the structure will ever spontaneously switch. As we talk of maybe a thousand unit cells left (4 nm)3 this exponential term may no longer be lasting for ages but come to the timescale of our experiment since the soft-mode phonon will try at about 1012 s−1 to flip the polarization state. For ferromagnets this effect is known and clearly puts the thermodynamic limit to the miniaturization of magnetic memories.
Most considerations on the ferroelectric limit have been devoted to free particles so they should rather be referred to as the pyroelectric limit as they are investigating a necessary condition. The size driven transition has been monitored by various methods such as XRD, Raman-scattering, EPR and dielectric impedance spectroscopy. As the last method seems to be the most convenient one, it becomes increasingly popular but must be handled with caution. The subsequent considerations are also true for the other methods but inherently relevant for impedance spectroscopy. If grains are fabricated as individual particles with diameters of a few nanometers they have a strong electric field outside that sometimes feeds back into these grains and makes it energetically favorable to form domains. If these domains are 90◦ or 180◦ , depends on the choice of material, especially its tetragonality. Whenever these grains are pressed into a pellet or into a ceramic they are no longer individual but interact with all other dipoles in the vicinity. Size effects on those samples are therefore related to clusters of nanoparticles rather than the particles themselves. dc loss curves that may almost look like ferroelectric hysteresis loops (except for that they do not saturate) are easily mistaken as a proof of ferroelectricity. In order to investigate truly ferroelectric nanoparticles, we now only consider samples that are deposited onto a bottom electrode and that can somehow be contacted from top. Common metallic bottom electrodes such as platinum pay the ease of handling with the lack of epitaxy [10]. Epitaxial oxidic bottom electrodes like SrRuO3 and SrTiO3 :Nb give better crystallographic orientations and better control of the mechanical boundary conditions [11] but, e.g. have less screening of the depolarization field. A manifold of deposition techniques has been employed and goes beyond the scope of this paper but generally the two major semiconductor trends of top-down and bottom-up fabrication are also found in the field of ferroelectrics. Top-down fabricated structures often suffer from post-deposition treatment (e.g. ion emplantation from RIE). On the other side, bottom-up fabricated samples are practically disordered and show a wide distribution of size and shape. Recently a combination of top-down and bottom-up was successfully employed: TiO2 -seeds were predefined by e-beam lithography [12,13]. As TiO2 is a constituent of the perovkite lattice (alternating layers of TiO2 and e.g. PbO or BaO) they act as nucleation sites with a preference of almost two orders of magnitude for TiO2 as compared to platinum. The size distribution that is predefined by the growth conditions can be modified by chemical mechanical polishing [14]. A key experiment originated from Chu et al. [15] who used lead zirconate titanate (Pb(Zrx Ti1−x )O3 or PZT) on (0 0 1) SrTiO3 :Nb as a model system for the investigation of interfacial strain.
4
A. R¨udiger, R. Waser / Journal of Alloys and Compounds 449 (2008) 2–6
field was shown by removal and subsequent re-adsorption of such a layer). Typically water and CO2 are the main adsorbates. On BaTiO3 surfaces CO2 is partially transformed into BaCO3 . A partial healing of these effects is possible but complex and usually requires a post-treatment control. Fig. 2. Cross-section transmission electron micrographs of small PZT islands grown on (0 0 1) STO:Nb substrate. Arrows point to misfit dislocations.
As the polarization is almost proportional to the tetragonality the use of a compressive substrate will (under the preservation of the unit cell volume) improve the ferroelectric performance. However, as Chu et al. confirm by high resolution transmission electron microscopy (HRTEM), the energy required to strain the material is partially released by the formation of edge dislocations (see Fig. 2). In the restricted geometry of a laterally confined ferroelectric nanoparticle there is a trade-off between improvement of the polarization by compressive strain and the demerit of an edge dislocation. These dislocations have an inhomogeneous strain field the symmetry of which locally suppresses ferroelectricity. Chu et al. observed large particles without ferroelectric response but with misfit dislocations while smaller particles free of dislocations were still active. As a consequence the interface as the main electromechanical boundary condition will have to be considered in all future model systems for the ferroelectric limit.
4. Time The smallest possible ferroelectric (let us ignore the electrode issues for a second) will probably look like ammonia where the protons define a reference plane and the nitrogen (with increased electron density) occupies either of the positions above or below that plane and gives rise to the dipole moment. However, as is known from the Maser, the above description is only appropri-
3. Composition Depending on the choice of the perovskite, the ferroelectric properties are very sensitive to the chemical composition. Piezoelectric force microscopy is a versatile tool to scan large areas for possible ferroelectric activity but some structures of lead oxide also exhibit piezoactivity. Therefore a nanoscopic control of the composition is mandatory but not trivial. Spaldin raised the question of what defines a material on the nanoscale [16] in a comment to Fong’s publication on ultrathin ferroelectric films [17]. The central unit cell should at least see one identical nearest neighbor in all directions to make sure that the chemical bonds are well-defined in all directions. This creates a volume of 27 unit cells, but still does not leave enough room for a domain wall. Since all switching that had been observed so far is based on the propagation of domain walls and clearly not on the Landau-switching of all dipoles simultaneously, it is an open question if such a structure will ever switch. Switching by domain wall movement reduces the required fields by several orders of magnitude to enable the polarization reversal at all. In that respect it is a matter of definition if surface reconstruction is considered a chemical or structural variation. Fong et al. observed a reconstruction in the uppermost atomic layers that cannot be thermodynamically bypassed. Less fundamental but omnipresent in samples that are exposed to air are adsorbate layers that modify the surface. The main impact becomes evident in scanning microscopy experiments where these adsorbates act as voltage dividers and drastically reduce the applied voltage to the sample [18] (a reduction of one order of magnitude for the actual
Fig. 3. Converse piezoelectric effect in ferroelectric perovskite islands investigated by PFM. (a) An electric field aligned parallel to the spontaneous polarization leads to a lifting of the cantilever due to d33 (out-of-plane signal). Superimposed, d31 causes a lateral contraction (b) antiparallel alignment of electric field and spontaneous polarization leads to a vertical contraction and a horizontal expansion of the ferroelectric. (c and d) If the electric field is orthogonal to the polarization a shear movement due to d15 occurs. This movement causes a torsional deformation of the cantilever causing the laser spot to move horizontally on the photodiode (in-plane signal). (e) An island polarized in the x–z plane will contribute to the in- as well as to the out-of-plane signal.
A. R¨udiger, R. Waser / Journal of Alloys and Compounds 449 (2008) 2–6
ate if we look sufficiently fast. On a timescale of seconds the nitrogen will have swapped places billions of times and nobody would ever consider this a reasonable choice for a memory. In other words: the two thermodynamically equivalent states are only metastable. A more concise discussion of ferroelectricity on the nanostructure should therefore postulate a stable polarization that can be reversed by an external field. How crucial this point is requires the knowledge of the double well potential for a given sample size. The bulk values of several hundred meV will provide a stable polarization already above a threshold of a few unit cells but for the aforementioned structural implications, the double well is likely to decrease with sample size and therefore feeds back into the temporal stability. 5. Piezoelectric force microscopy The most powerful tool to investigate individual ferroelectric nanoparticles is piezoelectric force microscopy (PFM) where a conducting tip of an AFM is brought into contact with a ferroelectric sample. The displacement of the cantilever (lateral and vertical) due to the piezoelectric shape variation is monitored as a deflection of a laser beam on a quadrupole photo-diode (see Fig. 3). For geometrical reasons the lateral sensitivity is higher than the vertical one (depending on the cantilever but typically of the order of 10). However, the lateral signal also contains information on the shape of the islands and the topography feeds back into the signal. We have demonstrated on individual nanoislands that we can see a lateral deflection of the cantilever even for cases where the symmetry of the sample does not permit any such movement by the direction of the polarization and have given a
5
discussion on symmetry breaking in the sample-tip system as the origin of these lateral signals. Our finite element analysis indicates that any sample inhomogeneity, e.g. due to strain variations give rise to lateral signals that are not necessarily associated to ferroelectric domains. These additional sources have to be kept in mind when interpreting PFM scans (see Fig. 4). In many other cases, PFM is used to monitor the domain configuration of an islands. As we detect amplitude and phase of a ferroelectric nanostructure, domains will show up as 180◦ phase shifts or as a variation of lateral and vertical signal (90◦ domains). In contrast to topography scans where the resolution is limited by the tip curvature, these scans – even with a small indentation – provide almost point contacts and domains widths as small as 4 nm have been observed. The proof of ferroelectricity then additionally requires the reversal of the piezoelectric tensor which is usually achieved by an external voltage above the scanning voltage that reverses the polarization. Subsequent scanning in the PFM mode confirms the reversibility of a ferroelectric domain. 6. Conclusions The progress in the nanofabrication of ferroelectrics has produced samples below 50 nm that still exhibit ferroelectricity down to a height of a few unit cells. From a fundamental point of view the question to what limit the miniaturization can be driven requires a detailed understanding and knowledge of the underlying electromechanical processes. We are only on the verge of new insights with spatially resolved techniques that allow us to monitor ferroelectricity in individual structures. As we deepen our understanding of these structures, the morphology, composition and timescale become increasingly relevant down to an atomic level. An appropriate choice of substrate, electrode and fabrication process, will soon make functional ferroelectrics clearly below 10 nm lateral extension accessible and widen the range of applications. References
Fig. 4. Lateral piezoelectric scan of PZT nanoislands grown on (0 0 1) SrTiO3 :Nb (500 nm)2 . The polarization is pointing out of the plane, therefore, from symmetry considerations there should be no lateral signal at all. All signals displayed originate from various sample inhomogeneities.
[1] J.F. Scott, Ferroelectric Memories, Springer Book, 2000. [2] A. R¨udiger, T. Schneller, A. Roelofs, S. Tiedke, T. Schmitz, R. Waser, Appl. Phys. A 80 (2005) 1247. [3] W.L. Zhong, B.D. Qu, P.L. Zhang, Y.G. Wang, Phys. Rev. B 50 (1994) 12375. [4] W.L. Zhong, Y.G. Wang, P.L. Zhang, B.D. Qu, Phys. Rev. B 50 (1994) 698. [5] C.L. Wang, S.R.P. Smith, J. Phys.: Condens. Matter 7 (1995) 7163. [6] Y.G. Wang, W.L. Zhong, Phys. Rev. B 51 (1995) 17235. [7] M. Dawber, K.M. Rabe, J.F. Scott, Rev. Mod. Phys. 77 (2005) 1083. [8] E.D. Mishina, T.V. Misuryaev, N.E. Sherstyuk, V.V. Lemanov, A.I. Morozov, A.S. Sigov, Th. Rasing, Phys. Rev. Lett. 85 (2000) 3664. [9] M. Dawber, I. Szafraniak, M. Alexe, J.F. Scott, J. Phys.: Condens. Matter 15 (2003) L667. [10] R. Waser, T. Schneller, S. Hoffmann-Eifert, P. Ehrhart, Integr. Ferroelectr. 36 (2001) 3. [11] I. Szafraniak, C. Harnagea, R. Scholz, S. Bhattacharyya, D. Hesse, M. Alexe, Appl. Phys. Lett. 83 (2003) 2211. [12] S. B¨uhlmann, P. Muralt, S. von Allmen, Appl. Phys. Lett. 84 (2004) 2614. [13] S. Clemens, T. Schneller, A.V.D. Hart, F. Peter, R. Waser, Adv. Mater. 17 (2005) 1357.
6
A. R¨udiger, R. Waser / Journal of Alloys and Compounds 449 (2008) 2–6
[14] S. Clemens, T. Schneller, R. Waser, A. R¨udiger, F. Peter, S. Kronholz, T. Schmitz, S. Tiedke, Appl. Phys. Lett. 87 (2005) 142904. [15] M. Chu, I. Szafraniak, R. Scholz, C. Harnagea, D. Hesse, M. Alexe, U. G¨osele, Nat. Mater. 3 (2004) 87. [16] N.A. Spaldin, Science 304 (2004) 1606.
[17] D.D. Fong, et al., Science 304 (2004) 1650. [18] F. Peter, K. Szot, R. Waser, B. Reichenberg, S. Tiedke, J. Szade, Appl. Phys. Lett. 85 (2004) 2896. [19] T. Schmitz, K. Prume, B. Reichenberg, S. Tiedke, A. Roelofs, R. Waser, J. Eur. Ceram. Soc. 24 (2004) 1145.
Size effects in nanoscale ferroelectrics A. R¨udiger ∗ , R. Waser Center of Nanoelectronic Systems for Information Technology, Institute of Solid State Research, Research Center Jue¨oich, 52425 Juelich, Germany Received 8 November 2005; received in revised form 23 December 2005; accepted 30 December 2005 Available online 21 December 2006
Abstract Ferroelectrics are among the most advanced candidates of fast non-volatile memory materials. How do the properties of the commonly used perovskites such as PbTiO3 , Pb(Zrx Ti1−x )O3 (PZT) and BaTiO3 change with size? Is there a fundamental limit showing up below which ferroelectricity irrevocably ceases? While the operating voltage as the predominant driving force for commercial applications shifted the thickness down to a few unit cells, ferroelectrics are now on the verge of true nanoscale integration of laterally confined structures. Top-down, bottom-up approaches and their combination provide samples far below 100 nm and indicate that the interaction of electrode and ferroelectric becomes increasingly relevant in terms of strain, screening of the depolarization field and fatigue resistance. As the qualitative understanding of nanoscale ferroelectricity advances the ferroelectric limit appears to be below 10 nm thus paving the road for further miniaturization. © 2007 Published by Elsevier B.V. Keywords: Ferroelectric; Piezoelectric; Atomic force microscopy; FeRAM
1. Introduction Ferroelectrics make use of two thermodynamically equivalent groundstates of the spontaneous polarization that can be reversed by and external electric field. This type of memory is therefore non-volatile. As the structures are shrinking in thickness, the operation voltage has dropped below one volt, and the switching speed is only limited by the RC time constants of the circuit [1]. So we practically have a fast and energy-efficient nonvolatile but charge-based memory. How small can this device become and still provide a detectable amount of charge? The commonly used perovskites are wide-bandgap semiconductors so dc-conductivity can be omitted for bulk samples where the detected switching current is solely displacive. The polarization as expressed by a bound surface charge density (C/m2 ) is thickness independent but rapidly shrinks with area (see Fig. 1). For typical materials we are left with only 6000 electrons for a capacitor of 100 nm × 100 nm. A device of 10 nm × 10 nm will therefore have to operate with 60 electrons. Irrespective of all challenges to operate at these current levels, a fundamental question arose from the analogy to ferromag-
∗
Corresponding author. Tel.: +49 2461 61 4732; fax: +49 2461 61 2550. E-mail address: [email protected] (A. R¨udiger).
0925-8388/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.jallcom.2005.12.133
netism. How small can such a structure be made and still be ferroelectric [2]? The situation is fundamentally different from superparamagnetism as the coupling force has a very long interaction length as compared to magnetism. The unit cell dipoles are electrostatically coupled and strain also propagates several unit cells across the material. This is why the phenomenological mean-field Landau–Ginzburg–Devonshire theory was successfully employed to describe many features of ferroelectricity and its phase transitions on a macroscopic scale. But as the structures shrink down to the length-scales of ferroelectric coupling we should wonder to what extent the assumptions of mean-field theories still hold true. And indeed, in order to account for some size-driven effect, the polynomial description of the free-energy had to be expanded by two more terms: a surface energy term and a polarization gradient term both of which contain parameters that are not experimentally accessible [3–6]. Ab initio calculations are on the way together with a comprehensive survey on thin films provided by Dawber et al. [7]. The surface plays a major role as its volume fraction increases with decreasing overall volume: the polarization gradient is a direct consequence of a modified surface. There is plenty of experimental evidence that the surface behaves different from the bulk [8]. Talking about the surface it has to become clear that ferroelectricity in contrast to mere pyroelectricity does not only involve a structural prerequisite (polar axis) but the need for reversibility which
A. R¨udiger, R. Waser / Journal of Alloys and Compounds 449 (2008) 2–6
3
All the aforementioned three contributions: structure, composition and time will also depend on the shape of our structures as a dipole–dipole interaction is highly anisotropic and as strain can be used to intensify the tetragonality and therefore the polarization. 2. Structure
Fig. 1. Single shot hysteresis loop with in situ compensation (no averaging) in a stand-alone 300 nm × 300 nm PZT capacitor [19].
goes far beyond the structure. So the mere existence of a noncentrosymmetric phase with a polar axis is necessary, but not sufficient to pinpoint ferroelectricity. A pyroelectric in that sense is a ferroelectric where the breakdown-voltage is smaller than the coercive field. Once we want to show functionality, we have to apply electrodes which inherently modify all relevant electromechanical boundary conditions: strain is applied to the system, the depolarization field that promotes the formation of ferroelectric domains is partially screened in the electrodes and we have to consider a system of electrode–ferroelectric–electrode. In all cases where we cannot be certain about the quality of our fabrication it is required to also consider two interfaces between electrode and ferroelectric. These interfaces have turned out to be responsible for many effects in ferroelectric devices (imprint, parasitic capacitances, dielectric losses, etc.). What should a comprehensive theory of nanoscale ferroelectricity take into account? Clearly, there will be a structural change as the surface gains volume fraction. But what else may be important? Some recent experiments point into two more directions that have not been considered so far. For one, the chemical composition of a three-component system like all perovskites (ABO3 ) is a lot more difficult to control than in most one-component nanomagnets. Growth itself already is an issue [9] but the exact chemical composition is almost unknown and difficult to access as the volumes of ferroelectric nanostructures are small and often averaging is not feasible. The second issue directly originates from the analogy to the superparamagnetic limit: The soft-mode phonon (TO) (in analogy to the Larmorfrequency) tries to perform just the movement that is required to switch the structure. With an increasing number of ferroelectric unit cells it becomes exponentially unlikely that for a given temperature the structure will ever spontaneously switch. As we talk of maybe a thousand unit cells left (4 nm)3 this exponential term may no longer be lasting for ages but come to the timescale of our experiment since the soft-mode phonon will try at about 1012 s−1 to flip the polarization state. For ferromagnets this effect is known and clearly puts the thermodynamic limit to the miniaturization of magnetic memories.
Most considerations on the ferroelectric limit have been devoted to free particles so they should rather be referred to as the pyroelectric limit as they are investigating a necessary condition. The size driven transition has been monitored by various methods such as XRD, Raman-scattering, EPR and dielectric impedance spectroscopy. As the last method seems to be the most convenient one, it becomes increasingly popular but must be handled with caution. The subsequent considerations are also true for the other methods but inherently relevant for impedance spectroscopy. If grains are fabricated as individual particles with diameters of a few nanometers they have a strong electric field outside that sometimes feeds back into these grains and makes it energetically favorable to form domains. If these domains are 90◦ or 180◦ , depends on the choice of material, especially its tetragonality. Whenever these grains are pressed into a pellet or into a ceramic they are no longer individual but interact with all other dipoles in the vicinity. Size effects on those samples are therefore related to clusters of nanoparticles rather than the particles themselves. dc loss curves that may almost look like ferroelectric hysteresis loops (except for that they do not saturate) are easily mistaken as a proof of ferroelectricity. In order to investigate truly ferroelectric nanoparticles, we now only consider samples that are deposited onto a bottom electrode and that can somehow be contacted from top. Common metallic bottom electrodes such as platinum pay the ease of handling with the lack of epitaxy [10]. Epitaxial oxidic bottom electrodes like SrRuO3 and SrTiO3 :Nb give better crystallographic orientations and better control of the mechanical boundary conditions [11] but, e.g. have less screening of the depolarization field. A manifold of deposition techniques has been employed and goes beyond the scope of this paper but generally the two major semiconductor trends of top-down and bottom-up fabrication are also found in the field of ferroelectrics. Top-down fabricated structures often suffer from post-deposition treatment (e.g. ion emplantation from RIE). On the other side, bottom-up fabricated samples are practically disordered and show a wide distribution of size and shape. Recently a combination of top-down and bottom-up was successfully employed: TiO2 -seeds were predefined by e-beam lithography [12,13]. As TiO2 is a constituent of the perovkite lattice (alternating layers of TiO2 and e.g. PbO or BaO) they act as nucleation sites with a preference of almost two orders of magnitude for TiO2 as compared to platinum. The size distribution that is predefined by the growth conditions can be modified by chemical mechanical polishing [14]. A key experiment originated from Chu et al. [15] who used lead zirconate titanate (Pb(Zrx Ti1−x )O3 or PZT) on (0 0 1) SrTiO3 :Nb as a model system for the investigation of interfacial strain.
4
A. R¨udiger, R. Waser / Journal of Alloys and Compounds 449 (2008) 2–6
field was shown by removal and subsequent re-adsorption of such a layer). Typically water and CO2 are the main adsorbates. On BaTiO3 surfaces CO2 is partially transformed into BaCO3 . A partial healing of these effects is possible but complex and usually requires a post-treatment control. Fig. 2. Cross-section transmission electron micrographs of small PZT islands grown on (0 0 1) STO:Nb substrate. Arrows point to misfit dislocations.
As the polarization is almost proportional to the tetragonality the use of a compressive substrate will (under the preservation of the unit cell volume) improve the ferroelectric performance. However, as Chu et al. confirm by high resolution transmission electron microscopy (HRTEM), the energy required to strain the material is partially released by the formation of edge dislocations (see Fig. 2). In the restricted geometry of a laterally confined ferroelectric nanoparticle there is a trade-off between improvement of the polarization by compressive strain and the demerit of an edge dislocation. These dislocations have an inhomogeneous strain field the symmetry of which locally suppresses ferroelectricity. Chu et al. observed large particles without ferroelectric response but with misfit dislocations while smaller particles free of dislocations were still active. As a consequence the interface as the main electromechanical boundary condition will have to be considered in all future model systems for the ferroelectric limit.
4. Time The smallest possible ferroelectric (let us ignore the electrode issues for a second) will probably look like ammonia where the protons define a reference plane and the nitrogen (with increased electron density) occupies either of the positions above or below that plane and gives rise to the dipole moment. However, as is known from the Maser, the above description is only appropri-
3. Composition Depending on the choice of the perovskite, the ferroelectric properties are very sensitive to the chemical composition. Piezoelectric force microscopy is a versatile tool to scan large areas for possible ferroelectric activity but some structures of lead oxide also exhibit piezoactivity. Therefore a nanoscopic control of the composition is mandatory but not trivial. Spaldin raised the question of what defines a material on the nanoscale [16] in a comment to Fong’s publication on ultrathin ferroelectric films [17]. The central unit cell should at least see one identical nearest neighbor in all directions to make sure that the chemical bonds are well-defined in all directions. This creates a volume of 27 unit cells, but still does not leave enough room for a domain wall. Since all switching that had been observed so far is based on the propagation of domain walls and clearly not on the Landau-switching of all dipoles simultaneously, it is an open question if such a structure will ever switch. Switching by domain wall movement reduces the required fields by several orders of magnitude to enable the polarization reversal at all. In that respect it is a matter of definition if surface reconstruction is considered a chemical or structural variation. Fong et al. observed a reconstruction in the uppermost atomic layers that cannot be thermodynamically bypassed. Less fundamental but omnipresent in samples that are exposed to air are adsorbate layers that modify the surface. The main impact becomes evident in scanning microscopy experiments where these adsorbates act as voltage dividers and drastically reduce the applied voltage to the sample [18] (a reduction of one order of magnitude for the actual
Fig. 3. Converse piezoelectric effect in ferroelectric perovskite islands investigated by PFM. (a) An electric field aligned parallel to the spontaneous polarization leads to a lifting of the cantilever due to d33 (out-of-plane signal). Superimposed, d31 causes a lateral contraction (b) antiparallel alignment of electric field and spontaneous polarization leads to a vertical contraction and a horizontal expansion of the ferroelectric. (c and d) If the electric field is orthogonal to the polarization a shear movement due to d15 occurs. This movement causes a torsional deformation of the cantilever causing the laser spot to move horizontally on the photodiode (in-plane signal). (e) An island polarized in the x–z plane will contribute to the in- as well as to the out-of-plane signal.
A. R¨udiger, R. Waser / Journal of Alloys and Compounds 449 (2008) 2–6
ate if we look sufficiently fast. On a timescale of seconds the nitrogen will have swapped places billions of times and nobody would ever consider this a reasonable choice for a memory. In other words: the two thermodynamically equivalent states are only metastable. A more concise discussion of ferroelectricity on the nanostructure should therefore postulate a stable polarization that can be reversed by an external field. How crucial this point is requires the knowledge of the double well potential for a given sample size. The bulk values of several hundred meV will provide a stable polarization already above a threshold of a few unit cells but for the aforementioned structural implications, the double well is likely to decrease with sample size and therefore feeds back into the temporal stability. 5. Piezoelectric force microscopy The most powerful tool to investigate individual ferroelectric nanoparticles is piezoelectric force microscopy (PFM) where a conducting tip of an AFM is brought into contact with a ferroelectric sample. The displacement of the cantilever (lateral and vertical) due to the piezoelectric shape variation is monitored as a deflection of a laser beam on a quadrupole photo-diode (see Fig. 3). For geometrical reasons the lateral sensitivity is higher than the vertical one (depending on the cantilever but typically of the order of 10). However, the lateral signal also contains information on the shape of the islands and the topography feeds back into the signal. We have demonstrated on individual nanoislands that we can see a lateral deflection of the cantilever even for cases where the symmetry of the sample does not permit any such movement by the direction of the polarization and have given a
5
discussion on symmetry breaking in the sample-tip system as the origin of these lateral signals. Our finite element analysis indicates that any sample inhomogeneity, e.g. due to strain variations give rise to lateral signals that are not necessarily associated to ferroelectric domains. These additional sources have to be kept in mind when interpreting PFM scans (see Fig. 4). In many other cases, PFM is used to monitor the domain configuration of an islands. As we detect amplitude and phase of a ferroelectric nanostructure, domains will show up as 180◦ phase shifts or as a variation of lateral and vertical signal (90◦ domains). In contrast to topography scans where the resolution is limited by the tip curvature, these scans – even with a small indentation – provide almost point contacts and domains widths as small as 4 nm have been observed. The proof of ferroelectricity then additionally requires the reversal of the piezoelectric tensor which is usually achieved by an external voltage above the scanning voltage that reverses the polarization. Subsequent scanning in the PFM mode confirms the reversibility of a ferroelectric domain. 6. Conclusions The progress in the nanofabrication of ferroelectrics has produced samples below 50 nm that still exhibit ferroelectricity down to a height of a few unit cells. From a fundamental point of view the question to what limit the miniaturization can be driven requires a detailed understanding and knowledge of the underlying electromechanical processes. We are only on the verge of new insights with spatially resolved techniques that allow us to monitor ferroelectricity in individual structures. As we deepen our understanding of these structures, the morphology, composition and timescale become increasingly relevant down to an atomic level. An appropriate choice of substrate, electrode and fabrication process, will soon make functional ferroelectrics clearly below 10 nm lateral extension accessible and widen the range of applications. References
Fig. 4. Lateral piezoelectric scan of PZT nanoislands grown on (0 0 1) SrTiO3 :Nb (500 nm)2 . The polarization is pointing out of the plane, therefore, from symmetry considerations there should be no lateral signal at all. All signals displayed originate from various sample inhomogeneities.
[1] J.F. Scott, Ferroelectric Memories, Springer Book, 2000. [2] A. R¨udiger, T. Schneller, A. Roelofs, S. Tiedke, T. Schmitz, R. Waser, Appl. Phys. A 80 (2005) 1247. [3] W.L. Zhong, B.D. Qu, P.L. Zhang, Y.G. Wang, Phys. Rev. B 50 (1994) 12375. [4] W.L. Zhong, Y.G. Wang, P.L. Zhang, B.D. Qu, Phys. Rev. B 50 (1994) 698. [5] C.L. Wang, S.R.P. Smith, J. Phys.: Condens. Matter 7 (1995) 7163. [6] Y.G. Wang, W.L. Zhong, Phys. Rev. B 51 (1995) 17235. [7] M. Dawber, K.M. Rabe, J.F. Scott, Rev. Mod. Phys. 77 (2005) 1083. [8] E.D. Mishina, T.V. Misuryaev, N.E. Sherstyuk, V.V. Lemanov, A.I. Morozov, A.S. Sigov, Th. Rasing, Phys. Rev. Lett. 85 (2000) 3664. [9] M. Dawber, I. Szafraniak, M. Alexe, J.F. Scott, J. Phys.: Condens. Matter 15 (2003) L667. [10] R. Waser, T. Schneller, S. Hoffmann-Eifert, P. Ehrhart, Integr. Ferroelectr. 36 (2001) 3. [11] I. Szafraniak, C. Harnagea, R. Scholz, S. Bhattacharyya, D. Hesse, M. Alexe, Appl. Phys. Lett. 83 (2003) 2211. [12] S. B¨uhlmann, P. Muralt, S. von Allmen, Appl. Phys. Lett. 84 (2004) 2614. [13] S. Clemens, T. Schneller, A.V.D. Hart, F. Peter, R. Waser, Adv. Mater. 17 (2005) 1357.
6
A. R¨udiger, R. Waser / Journal of Alloys and Compounds 449 (2008) 2–6
[14] S. Clemens, T. Schneller, R. Waser, A. R¨udiger, F. Peter, S. Kronholz, T. Schmitz, S. Tiedke, Appl. Phys. Lett. 87 (2005) 142904. [15] M. Chu, I. Szafraniak, R. Scholz, C. Harnagea, D. Hesse, M. Alexe, U. G¨osele, Nat. Mater. 3 (2004) 87. [16] N.A. Spaldin, Science 304 (2004) 1606.
[17] D.D. Fong, et al., Science 304 (2004) 1650. [18] F. Peter, K. Szot, R. Waser, B. Reichenberg, S. Tiedke, J. Szade, Appl. Phys. Lett. 85 (2004) 2896. [19] T. Schmitz, K. Prume, B. Reichenberg, S. Tiedke, A. Roelofs, R. Waser, J. Eur. Ceram. Soc. 24 (2004) 1145.