Review

Ferroelectricity at the Nanoscale: Local Polarization in Oxide Thin Films and Heterostructures

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Science  23 Jan 2004:
Vol. 303, Issue 5657, pp. 488-491
DOI: 10.1126/science.1092508

Abstract

Ferroelectric oxide materials have offered a tantalizing potential for applications since the discovery of ferroelectric perovskites more than 50 years ago. Their switchable electric polarization is ideal for use in devices for memory storage and integrated microelectronics, but progress has long been hampered by difficulties in materials processing. Recent breakthroughs in the synthesis of complex oxides have brought the field to an entirely new level, in which complex artificial oxide structures can be realized with an atomic-level precision comparable to that well known for semiconductor heterostructures. Not only can the necessary high-quality ferroelectric films now be grown for new device capabilities, but ferroelectrics can be combined with other functional oxides, such as high-temperature superconductors and magnetic oxides, to create multifunctional materials and devices. Moreover, the shrinking of the relevant lengths to the nanoscale produces new physical phenomena. Real-space characterization and manipulation of the structure and properties at atomic scales involves new kinds of local probes and a key role for first-principles theory.

The movement and storage of electrical charges and the manipulation of the electric fields they produce are the basis of the operation of computer processors and memories. The modern electronics industry demands an ever greater decrease in switching time and length scales, approaching the level of individual electrons and atoms. Although continued improvements in conventional semiconductor designs can to some extent address these needs, there is increasing motivation to consider alternative paradigms. In ferroelectric oxides (13), electric polarization, bound charges, and large electric fields are produced by displacements of individual atoms, and devices based on ferroelectric materials therefore can be made in principle to operate on atomic scales.

It is helpful to look at the crystal structure of the prototypical perovskite ferroelectric, BaTiO3 (Fig. 1A). In the room-temperature ferroelectric tetragonal structure (Fig. 1, B and C), the Ti and Ba sublattices are shifted relative to the negatively charged oxygens, producing a polarization (net dipole moment per unit volume) of 26 μC/cm2 (1). This shift breaks the cubic symmetry, resulting in six symmetry-equivalent variants with polarizations along the x, y, and z axes. The polarization of a single variant, regarded within macroscopic electrostatics, produces a bound surface charge on the order of 1.5 × 1014 electrons/cm2 and an internal electric field that, if unscreened, approaches 300 MV/cm. Domain walls separate variants with polarization in different directions (1, 4). An applied electric field can be used to switch between the symmetry-related variants, and the direction of the polarization is stable when the field is removed. For bulk ferroelectrics, the coercive field (the electric field required to switch the polarization) is generally relatively modest, on the order of 10 to 100 kV/cm, much smaller than that estimated for uniform switching through the high-symmetry structure from first-principles calculations. This small value reflects the fact that switching generally occurs through nucleation and growth of domains (5), which are processes with lower energy barriers.

Fig. 1.

Crystal structure of the perovskite ferroelectric BaTiO3. (A) High temperature, paraelectric, cubic phase. (B and C) Room temperature, ferroelectric, tetragonal phases, showing up and down polarization variants. The atomic displacements are scaled to be clearly visible.

Although the textbook description of ferroelectricity is expressed in a macroscopic framework, there are excellent reasons to think that the length scales can in principle be reduced to a few nanometers. Even in bulk, the domain walls separating different variants are of thickness 0.5 to 1.0 nm (1 to 2 lattice constants) (4), far thinner than domain walls in most ferromagnets. First-principles calculations have shown that the high-symmetry cubic phase is unstable to the displacement of even a small cluster of atoms, producing local polarization (6). The contribution of the long-range electrostatic interactions to the stability of local polarization can be manipulated by imposing appropriate electrical boundary conditions (7). However, to achieve this length-scale reduction and to characterize and understand the scaling of the physics of ferroelectricity, it is essential to have tools for synthesis, characterization, and theoretical analysis at the nanoscale.

We review the recent experimental and theoretical breakthroughs in our atomic-scale understanding of the properties of ferroelectrics and discuss the implications for new applications. We describe the developments in synthesis, progress in first-principles theoretical approaches to ferroelectrics and what the results suggest about the behavior of ferroelectrics at the nanoscale and, finally, the application of advanced nanoscale characterization techniques. All three ingredients play critical roles in the development of new types of devices and in the purposeful design and synthesis of new artificially structured ferroelectric materials.

Materials Synthesis

Breakthroughs in materials processing are the driving technology behind the ideas described here. It has now become possible to make heterostructures in which single-crystalline perovskite-oxide films of thicknesses down to 1 to 2 lattice constants can be epitaxially matched at atomically sharp interfaces that are flat over hundreds of square microns (8). Typically, these films are prepared with advanced thin-film vapor deposition techniques, including molecular beam epitaxy, sputtering, pulsed laser ablation, and metal organic chemical vapor deposition. Special surface treatments allow for the preparation of substrate surfaces with specific surface terminations (9, 10). Several studies have shown that the resulting oxide films are indeed of very high crystalline quality (8, 11). Appropriate choice of the substrate material permits one to control the lattice mismatch between a ferroelectric film and its substrate, allowing for the growth of coherent films, typically up to a critical thickness of tens of nanometers.

Superlattices containing oxide ferroelectrics can be obtained through a natural extension of these techniques, by alternating thin-film layers of different constituents. In the example of a BaTiO3/SrTiO3 superlattice (Fig. 2) (12), the crystalline quality and sharpness of the interfaces are similar to those of AlAs/GaAs semiconductor heterostructures (13). Several groups have succeeded in growing and theoretically analyzing two-constituent ferroelectric superlattices with a common cation, for example, BaTiO3/SrTiO3 (1416), BaTiO3/PbTiO3 (17), and KNbO3/KTaO3 (18, 19), with properties tunable by varying the superlattice period and the ratio of the constituents. There is also interest in the dielectric properties of superlattices in which the cation arrangement itself breaks up-down inversion symmetry, such as CaTiO3/SrTiO3/BaTiO3 and “tricolor” superlattices (2022).

Fig. 2.

High-resolution transmission electron microscopy images of (A) BaTiO3/SrTiO3 and (B) AlAs/GaAs superlattices grown by molecular beam epitaxy. [(A) is reprinted from (12) with permission from Elsevier, (B) is reprinted from (13) with permission from Wiley.]

Now that the capability to produce high-quality ultrathin ferroelectric films and superlattices is available, novel applications can be realized by incorporating such films into heterostructures with other materials. In particular, the largest class of ferroelectric oxides, the perovskites [including Pb(Zr,Ti)O3 (PZT) and BaTiO3] are structurally related to many other technologically interesting materials, including high-Tc superconductors, ferromagnets, and insulators with large dielectric constants. Heterostructures that combine ferroelectrics with other functional materials can be expected to exhibit physical properties that are unusual, if not unprecedented, in naturally occurring compounds (22, 23). One can design superlattice materials that couple the distinct properties of the two (or more) constituents, resulting in new multifunctional behavior, one example being “multiferroic” superlattices of ferromagnetic insulators and ferroelectrics.

In another illustration of a novel heterostructural effect, the incorporation of a polarized ferroelectric into a two-component thin-film heterostructure geometry can produce high electric fields in the second component (a superconductor, ferromagnet, correlated metal, or a second ferroelectric) (24). Ferroelectric field effects leading to changes of resistance and to switching between superconducting and insulating behavior in very thin high-temperature superconducting films have been demonstrated (25), as well as modulation of the magnetotransport properties of colossal magnetoresistance compounds (26). With this approach, superconducting and magnetic switches can be fabricated, and it should be possible to produce ultradense field-effect transistors with negligible depletion widths (a few lattice constants) (27).

For the incorporation of single-crystal ferroelectrics into integrated electronics devices, the epitaxial combination of ferroelectric materials with single-crystal semiconductors, such as Si and GaAs, is critical. A methodology has been developed to deposit epitaxial complex oxides, such as SrTiO3, on Si with an alkaline earth oxide buffer layer. The buffer both inhibits the formation of an amorphous, interfacial SiO2 layer at the oxide/Si interface (28) and allows the epitaxial growth of a wide range of oxides that cannot be grown directly on Si. These materials may be particularly useful for high dielectric constant applications. Ferroelectric PZT has been deposited epitaxially with a variety of techniques on SrTiO3/Si structures (2931); BaTiO3 has been grown on Ge; and epitaxial SrTiO3 has been grown on GaAs. The combination of ferroelectrics with GaAs will permit the integration of piezoelectric devices, such as surface acoustic wave devices, with the high-performance optoelectronic capabilities of GaAs.

Theoretical Description

In parallel with advances in laboratory synthesis, the past decade has seen a revolution in the atomic-scale theoretical understanding of ferroelectricity, especially in perovskite oxides, through first-principles density-functional-theory (DFT) investigations. A key conceptual advance was establishing the correct definition of the electric polarization as a bulk property through the Berry phase formalism (32, 33). The accuracy of DFT for characterizing the ground-state structures of ferroelectrics was first determined for the prototypical cases of BaTiO3 and PbTiO3 (34) and later extended to many other ferroelectric perovskites (35). The calculation of phonon dispersion relations through density functional perturbation theory has greatly increased our understanding of the lattice instabilities of the perovskite structure in various representative compounds (36). As computational power and algorithmic efficiency have improved, it has become possible to study increasingly complex systems, such as surfaces (37), superlattices (15), and compounds with complex cation ordering or quasirandom ordering to simulate solid solutions (38, 39). Results include atomic arrangements and polarization-related quantities such as dielectric and piezoelectric coefficients as well as other quantities relevant to multifunctional ferroelectrics, such as magnetic ordering and transport properties. In this way, experiment and theory are beginning to achieve a common ground in addressing the key questions arising in the study of ferroelectricity at the nanoscale.

When Ferroelectrics Get Very Thin/Small: Theory and Experiment

The characteristic properties of bulk ferroelectrics are related to the polarization and can be expressed in the language of macroscopic electrostatics. The ground state of a macroscopic sample is not uniformly polarized but lowers its electrostatic energy through the formation of domains, in exact analogy to ferromagnets. Other bulk properties, such as pyroelectricity, piezoelectricity, and dielectric susceptibility, are defined as derivatives of the polarization with respect to temperature, stress, and applied electric field, respectively.

Although continuum theories are expected to be valid only on length scales much longer than a lattice constant, it has repeatedly been found that such theories, exemplified by Landau-Devonshire theory, are useful for films and heterostructures down to the nanoscale. This is partly because the width of relevant domain walls is about one lattice constant (4), and also reflects the strong dominance of electrostatics in the structural energetics. Within this framework, many of the characteristics of nanoscale ferroelectrics can be faithfully reproduced. One example is the coupling of strain and polarization in the ultrahigh uniform strain states that can be sustained with lattice mismatching in films and superlattice layers below the critical thickness (40, 41). Another is the clamping effect of the substrate on dielectric and piezoelectric response (42, 43). The large internal fields that can occur in equilibrium in such geometries are also describable in a quasi-continuum theory (44). Landau theories also can include a surface term, modeling the effect of the free surface on the state of the film (45).

We use a combination of first-principles atomistic and quasi-continuum considerations to address the question: What sets the limits on the minimum size of a stable domain? It was long thought that in perovskites, the symmetry breaking that leads to spontaneous polarization was a collective effect, with a substantial critical polarized volume being necessary to stabilize local polarization. However, first-principles linear-response studies of the structural energetics of the cubic perovskite structure suggest that this structure can be unstable against the polarization of even very small regions (1 to 5 unit cells) (6). The ultimate limit for the minimum thickness of a perpendicularly polarized ferroelectric film and for the lateral dimensions of a ferroelectric island or domain thus approaches a couple of lattice constants (46). At this limit, surface reconstructions need to be considered, because they may ultimately prevent the realization of ferroelectricity (47, 48). Regarding the critical lateral size, it is interesting to note that for atomic-scale ferroelectric domains and domain walls, unlike in magnetic applications, the electric field is generally screened by free external charges, preventing crosstalk. A lateral size of 1 nm (about 2 lattice constants) corresponds to an areal device density approaching 100 Tb/cm2, a million times as high as today's dynamic random access memory densities.

How do these expectations play out in experiment and first-principles theory? The history of the investigation of this question highlights the technical challenges of studying complex oxides. Since the 1950s, finite size effects in ferroelectrics have been the subject of numerous studies, pointing to a critical particle size or film thickness (typically 10 nm) below which ferroelectricity disappears (49). Recent developments, however, suggest that this is not an intrinsic behavior of ferroelectric materials, but a reflection of the mechanical and electrical boundary conditions resulting from the synthetic methods used. New techniques and new materials, as well as first-principles calculations, have completely changed the picture. With single-crystal thin films grown on metallic substrates, local probe studies examining the piezoelectric response of the film have led to the conclusion that perpendicularly polarized perovskite PZT films down to at least 4 nm in thickness remain ferroelectric (50). Work on copolymer ferroelectrics has also found evidence for ferroelectricity in nanometer-thick layers (51). Recent first-principles calculations assuming short circuit boundary conditions suggest a critical thickness of 2.4 nm (44). Physically, this critical thickness comes from the imperfect screening of the depolarization field (44, 52). These results, which draw conclusions very different from previous studies, indicate that the screening of the depolarization field is the key to decreasing the critical film thickness.

In the lateral dimensions, substantial progress has been made in the achievement of small ferroelectrics, with ferroelectric islands having been obtained by ion milling (53) and through self-assembled nanostructures (54), although with dimensions that are still relatively large compared with the theoretical values discussed above. Recently, a promising route involving the growth of BaTiO3 nanorods has been investigated, with diameters as small as 5 nm having been achieved (55). With respect to the minimum lateral sizes of domains, x-ray synchrotron studies have generated useful information. Studies on thin PbTiO3 films reveal a nanoscale inplane structural modulation, which has been attributed to the formation of stripe patterns of alternating polarization (parallel to the growth direction), with a periodicity as small as 3 nm (48).

Nanoscale Characterization and Manipulation

The development of real-space probes of atomic and electronic structure has revolutionized our understanding of local structure in a wide variety of scientifically and technologically important systems. For the high-quality ferroelectric heterostructures that are now obtainable, the development and application of these real-space probe techniques enables the manipulation and characterization of nanoscale polarization domains, which can be used both for applications and to understand the fundamental limits on density: stability, read/write mechanism, domain dynamics, and switching speed.

Figure 3, A and B, illustrates the use of an atomic force microscope (AFM) to study ferroelectrics (5661). In the conventional approach to measuring polarization, the ferroelectric material is sandwiched between two electrodes, forming a capacitor. Applying a voltage between the two electrodes leads to switching of the ferroelectric polarization, and a simple circuit (the Sawyer-Tower circuit) allows for the determination of the remnant polarization Pr and coercive field Ec. In Fig. 3B, the top electrode has been replaced by the metallic tip of an AFM. Application of a voltage between the tip and the bottom electrode generates an electric field under the tip and allows local polarization switching under the tip (the polarization is parallel or antiparallel to the growth direction). Moving the tip over the sample surface allows for patterning of the domain structure. The same tip can be used to image the domain structure with a variety of techniques, including electric force microscopy and piezoelectric microscopy (5661). In piezoelectric imaging, the sample is subjected to a small ac applied field (<Ec), and the local linear piezoelectric response is measured with lock-in detection. The sign of the piezoelectric deformation reveals the sign of the ferroelectric polarization.

Fig. 3.

Methods to switch the ferroelectric polarization. (A) In a traditional ferroelectric capacitor, a voltage is applied across the ferroelectric with metallic gate electrodes. (B) In the scanning-probe approach, the top electrode is replaced by a conducting, nanoscale scanning probe, to which a voltage is applied.

Figure 4A shows an AFM topographic image of a 35-nm-thick, single-crystalline PZT film, and Fig. 4B shows the piezoelectric response over the same area after the writing of an array of 100 ferroelectric domains at a density of ∼3 Gbit/cm2. The domain structure is stable at room temperature, with the piezoelectric response remaining constant for periods of months, the length of the measurements. Recently, control of domain size through proper choice of tip shape, writing voltage, and writing time has been achieved, and arrays with densities reaching 30 Gbit/cm2 have been realized (61). Ultra-small domains of characteristic diameter 20 nm, corresponding to 200 Gbit/cm2 densities, have been reported with scanning nonlinear dielectric microscopy (62). AFM piezoelectric studies have also led to an understanding of domain-wall motion at the nanoscale. The domain-wall velocity has been extracted from static measurements of the domain size versus writing time. The results indicate that the domain-wall velocity varies as exp(–Ec/E)μ, where Ec is a critical field, E is the applied electric field, and μ is a dynamical exponent (61). In two-dimensional films, this behavior has been identified as a disorder controlled creep process (61).

Fig. 4.

AFM images of ferroelectrics. (A) Topographic image of a 35-nm-thick, single-crystalline, ferroelectric PZT film grown on Nb-doped SrTiO3. The vertical scale is the film thickness. (B) Over the same area, a piezoelectric image of an array of 100 ferroelectric domains written in a uniformly polarized background. The areal density is ∼3 Gbit/cm2. In the piezoelectric imaging technique, a small ac voltage is applied to the sample through the AFM tip, exciting a local mechanical deformation whose phase depends on the polarization direction, allowing one to probe the domain structure. The amplitude of the piezoelectric displacement is below 0.1 nm.

The primary obstacle to ultrahigh-density scanning-probe ferroelectric storage devices is not the writing or stability of the local polarization, but the reading speed of the polarization state. This is complementary to the situation for ferromagnetic storage devices; modern magnetic read heads operate at comparatively high data rates, whereas possible writing densities are limited by domain wall thickness and the superparamagnetic limit. For ferroelectrics, the AFM can nondestructively detect the polarization through the piezoelectric response, but the process is slow because of the small size of the piezoelectric displacement. One way to increase the data rate is to use arrays of AFM tips, as has been demonstrated for polymer-based thermomechanical memories (63).

Control of the ferroelectric domain structure with scanning probes can also lead to new multifunctional devices in which the ferroelectric order is coupled to optical and electronic transport channels. With periodic inversion of domains, as in light frequency doubling, but with wavelengths down to a few hundred nanometers, a new concept for a high-frequency surface acoustic wave filter has recently been proposed (64). The same scanning probe control of the polarization can be used to induce nanoscale ferroelectric field effects, allowing one to read the ferroelectric state nondestructively and to draw nanoscale electronic features and circuits without traditional lithographic processing (60).

New Directions

The convergence of advances in synthesis, characterization, and theory of complex oxides leads to two main areas of opportunity: atomic-scale control, permitting the scaling down of conventional ferroelectric devices, and a tremendous versatility in combining ferroelectrics both with oxides with different physical behavior and with semiconductors, resulting in the possibility of new materials and device designs.

Although the capability of making ultrathin, atomically smooth films and refinements in AFM techniques will allow the scaling down of ferroelectric memories and field-effect devices, conventional designs may no longer be optimal at the nanoscale; a sound fundamental understanding of what happens at these length scales is necessary and could lead to new concepts and designs with improved performance. The understanding of finite size effects is now being intensively pursued through a combination of experimental studies and first-principles calculations. The mechanisms and dynamics of switching at the nanoscale is another emerging area of investigation, with the atomic-scale structure of domain walls, their motion in applied electric fields, and the nucleation of new domains all becoming increasingly accessible to experimental and first-principles investigation.

The demonstration of synthesis of atomically perfect heterostructures of ferroelectric oxides with dielectrics, piezoelectrics, superconductors, and magnetic oxides, as well as with semiconductors, opens a broad set of new research directions. Theory will play an important role in identifying artificially structured materials of interest, including new ferroelectrics and piezoelectrics with enhanced polarization and electromechanical responses, as well as dielectric/optical responses. Ferroelectric-complex oxide and ferroelectric-semiconductor heterostructures also suggest new classes of field-effect devices. Combined with the possibility of using scanning probes to manipulate ferroelectric domain structure, this approach may allow us to control magnetism, superconductivity, dielectric and optical response, and metallic behavior with nanoscale resolution.

We are at the threshold of an exciting period in nanoscale ferroelectricity. Recent advances in techniques for studying complex oxides now allow a meaningful dialog between experimentalists and theorists. Fundamental scientific issues and design of new materials and devices will be carried out in parallel, facilitating future breakthroughs.

References and Notes

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