Epitaxial Ferroelectric Films Research Articles

Polarization states of polydomain epitaxialPb(Zr1−xTix)O3thin films and their dielectric properties

Ferroelectric and dielectric properties of polydomain (twinned) single-crystal Pb(Zr1-xTix)O3 thin films are described with the aid of a nonlinear thermodynamic theory, which has been developed recently for epitaxial ferroelectric films with dense laminar domain structures. For Pb(Zr1-xTix)O3 (PZT) films with compositions x = 0.9, 0.8, 0.7, 0.6, 0.5, and 0.4, the "misfit strain-temperature" phase diagrams are calculated and compared with each other. It is found that the equilibrium diagrams of PZT films with x > 0.7 are similar to the diagram of PbTiO3 films. They consist of only four different stability ranges, which correspond to the paraelectric phase, single-domain tetragonal ferroelectric phase, and two pseudo-tetragonal domain patterns. In contrast, at x = 0.4, 0.5, and 0.6, the equilibrium diagram displays a rich variety of stable polarization states, involving at least one monoclinic polydomain state. Using the developed phase diagrams, the mean out-of-plane polarization of a poled PZT film is calculated as a function of the misfit strain and composition. Theoretical results are compared with the measured remanent polarizations of PZT films grown on SrTiO3. Dependence of the out-of-plane dielectric response of PZT films on the misfit strain in the heterostructure is also reported.

Stress induced monoclinic phase in epitaxial BaTiO3 on MgO

We present a detailed strain analysis of epitaxial ferroelectric films taking into account multiple sources of strain, including the lattice mismatch between the film and the substrate, thermal strains due to differences in the thermal expansion coefficients of the film and the substrate, and relaxation by the formation of interfacial dislocations. The lattice parameters of the film are calculated using a thermodynamic formalism coupled with the strain analysis. The theoretical model shows that epitaxial (001) BaTiO3 films on (001) MgO are expected to display successive phase transformations with decreasing temperatures that are different than the bulk. This is verified experimentally for 50nm thick (001) BaTiO3 films grown on (001) MgO substrates at 720°C using pulsed laser deposition. A synchrotron x-ray diffraction study displays two slope changes in the temperature dependence of the out-of-plane lattice constant. This indicates that two phase transformations exist in the film as a function of temperature with transition temperatures and lattice constants that are consistent with the theoretically predicted phases. Theoretical results show that the first transformation at around 270°C corresponds to a paraelectric-ferroelectric transition. The ferroelectric phase has an orthogonal symmetry (Amm2) with in-plane polarization components. The transformation at around −20°C is an Amm2↔Pm transition between two ferroelectric phases. The ferroelectric Pm phase is monoclinic compared to the rhombohedral R3m phase in bulk.

In-Plane and Out-of-Plane Ferroelectric Instabilities in EpitaxialSrTiO3Films

The in-plane and out-of-plane ferroelectric instabilities in compressed (100)-epitaxial SrTiO3 films were examined by infrared reflection spectroscopy. The strongly stiffened in-plane soft mode frequency softened very slowly on cooling. On the other hand, the silent mode appeared at around 150 K, indicating an out-of-plane ferroelectric transition. This behavior points to a split of in-plane and out-of-plane ferroelectric instability temperatures due to the lowered symmetry of the SrTiO3 lattice caused by mechanical misfit strain. Infrared spectroscopy provides a possibility to detect such an effect in the strained epitaxial ferroelectric films.

Thermodynamic and electrostatic analysis of threading dislocations in epitaxial ferroelectric films

The role of threading dislocations on the electrical properties of epitaxial ferroelectric films is analyzed using a thermodynamic formalism and basic electrostatics. The modeling is carried out for a 300nm thick (001) PbZr0.2Ti0.8O3 on (001) SrTiO3 which displays a large population of threading dislocations as determined by transmission electron microscopy. Results show that although the phase transformation characteristics of ferroelectric films containing threading dislocations are altered such that the transformation is “smeared” over a temperature interval due to local strain variations, these defects do not have as profound an effect on the electrical properties as the misfit dislocations.

Elastic coupling between 90° twin walls and interfacial dislocations in epitaxial ferroelectric perovskites: A quantitative high-resolution transmission electron microscopy study

A quantitative high-resolution transmission electron microscopy study has been performed on tetragonal, single-crystalline $\mathrm{Pb}({\mathrm{Zr}}_{0.4}{\mathrm{Ti}}_{0.6}){\mathrm{O}}_{3}$ islands grown on Nb-doped $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}(001)$ substrates, revealing the strain fields of a 90\ifmmode^\circ\else\textdegree\fi{} ferroelastic twin wall and the nearby interfacial dislocation. The twin wall, showing a width of $\ensuremath{\sim}1.5\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and compressive strain features, is elastically coupled to the tensile-type strain of an edge dislocation having an out-of-plane Burgers vector, indicating an intimate interaction of the strain fields of both crystallographic defects. The long-range strain field of the dislocation core imposes a potential barrier on the twin wall, limiting its translational mobility under an applied electric field. The substrate clamping in the epitaxial island further acts as a restoring force on the electric-field-induced wall movement. The ensemble of these electromechanical boundary conditions thus indicates that the ferroelastic twin wall in the island should be immobile upon external electric fields. A further discussion also suggests that this complex interplay of the substrate clamping and the interfacial dislocation should account for the reported low twin-wall mobility in continuous, epitaxial ferroelectric perovskite films under an electric field.

Intrinsic effective piezoelectric coefficients of an epitaxial ferroelectric film

Due to substrate clamping, the effective piezoelectric coefficients of an epitaxial ferroelectric film are usually different from those of bulk materials. The modifications of intrinsic piezoelectric responses by film–substrate in-plane stresses are quantitatively illustrated for a ferroelectric film with arbitrary orientation and structure. Consequently, the intrinsic effective piezoelectric coefficients of an epitaxial ferroelectric film are generally formulated.

Comparison of electrical properties of (100)∕(001)-oriented epitaxial Pb(Zr0.35,Ti0.65)O3 thin films with the same (001) domain fraction grown on (100)Si and (100)SrTiO3 substrates

Epitaxial tetragonal Pb(Zr0.35Ti0.65)O3 (PZT) films with a (100)∕(001) orientation and one and three in-plane variants were grown, respectively, on (100)cSrRuO3∕∕(100)SrTiO3 and (100)cSrRuO3∕∕(111)Pt∕∕(100)yttria stabilized zirconia (YSZ)∕∕(100)Si substrates by pulsed-metalorganic chemical vapor deposition, and their domain structure and electrical properties were investigated systematically. PZT films with the same volume fraction of c domains were grown on SrTiO3 and Si substrates by controlling the deposition temperature and film thickness. The relative dielectric constants at 1kHz were 370 and 450, respectively, for the films on the SrTiO3 and on the Si, even though both films had the same volume fractions, whereas the dielectric losses were almost the same. The remanent polarization and coercive field at the maximum applied electric field of 350kV∕cm were almost the same for both films, 30μC∕cm2 and 135kV∕cm, respectively. These results suggest that the key factor determining the ferroelectric property in epitaxial ferroelectric film is the relative volume fraction of c domains.

Physics of thin-film ferroelectric oxides

This review covers the important advances in recent years in the physics of thin film ferroelectric oxides, the strongest emphasis being on those aspects particular to ferroelectrics in thin film form. We introduce the current state of development in the application of ferroelectric thin films for electronic devices and discuss the physics relevant for the performance and failure of these devices. Following this we cover the enormous progress that has been made in the first principles computational approach to understanding ferroelectrics. We then discuss in detail the important role that strain plays in determining the properties of epitaxial thin ferroelectric films. Finally, we look at the emerging possibilities for nanoscale ferroelectrics, with particular emphasis on ferroelectrics in non conventional nanoscale geometries.

Effective Direct Piezoelectric Constants in Epitaxial Ferroelectric Films as MEMS Sensors

AbstractFollowing our previous work on the converse piezoelectric constant- in epitaxial ferroelectric films for MEMS actuator applications, the orientation dependence of the direct piezoelectric constants , and are generally formulated, which can help to predict and optimize the performance of piezoelectric MEMS sensor devices based on ferroelectric thin films. Numerical results are obtained and discussed for Pb(ZrxTi1-x)O3 thin films grow on Si substrates with various compositions and structures.

Figure of Merit and Limiting Characteristics of Tunable Ferroelectric Microwave Devices

Microwave application of ferroelectrics is very promising for electrically tunable microwave devices based on the electric field dependence of the dielectric permittivity. Tunable filters and controllable phase shifters are successfully designed as integrated circuits based on multilayer structures containing thin epitaxial ferroelectric (FE) film. As a rule lumped ferroelectric capacitors are used as the tunable components. Quality of the capacitor can be evaluated using Commutation Quality Factor (CQF). There is a unique connection between the Figure of Merit of a tunable microwave device and the CQF of the FE capacitors used. The Figure of Merit gives the upper limit of the quality of a tunable device based on the FE components.

Recent Developments in Thermodynamic Theory of Ferroelectric Thin Films

AbstractThe nonlinear thermodynamic theory of epitaxial ferroelectric films has predicted several important strain-induced phenomena, which have been already observed experimentally. This justifies further development of this theory aiming at the better understanding of the structure/property relationships in thin-film ferroelectrics. To that end, a number of new theoretical studies have been performed recently. First, the thermodynamic formalism has been extended to epitaxial films grown on dissimilar substrates inducing anisotropic strains and a shear deformation in the film plane. Second, the polarization states and dielectric properties were calculated for polydomain Pb(Zr1-xTix)O3 films deposited on cubic substrates. Third, the effect of depolarizing field on the physical properties of strained single-domain films sandwiched between continuous electrodes was described. The results of these studies will be discussed in this paper.

Effect of thermal strain on the ferroelectric phase transition in polycrystalline Ba0.5Sr0.5TiO3 thin films studied by Raman spectroscopy

We have applied Raman spectroscopy to study the influence of thermal strain on the vibrational properties of polycrystalline Ba0.5Sr0.5TiO3 films. The films were grown by rf magnetron sputtering on Pt∕SiO2 surface using different host substrates: strontium titanate, sapphire, silicon, and vycor glass. These substrates provide a systematic change in the thermal strain while maintaining the same film microstructure. From the temperature dependence of the ferroelectric A1 soft phonon intensity, the ferroelectric phase transition temperature, TC, was determined. We found that TC decreases with increasing tensile stress in the films. This dependence is different from the theoretical predictions for epitaxial ferroelectric films. The reduction of the ferroelectric transition temperature with increasing biaxial tensile strain is attributed to the suppression of in-plane polarization due to the small lateral grain size in the films.

Can interface dislocations degrade ferroelectric properties?

A thermodynamic analysis has been carried out to investigate the role of dislocations in ferroelectric materials. Due to the coupling of the stress field of the dislocation and the polarization, there is a drastic variation in the polarization near the dislocation. These polarization gradients result in strong depolarizing fields that suppress the polarization in a region that extends over several nanometrers. In epitaxial ferroelectric films, these polarization gradients should result in the formation of dead layers that severely degrade ferroelectric properties. The detrimental effect of such regions will be enhanced in ultrathin ferroelectric thin films, and hence play a critical extrinsic role in size effect studies of ferroelectrics.

Structural characteristics of ferroelectric phase transformations in single-domain epitaxial films

Structural characteristics of phase transformations in epitaxial ferroelectric films are analyzed via a Landau–Devonshire thermodynamic formalism. It is shown that the phase transformation temperature, the lattice parameters, and the order of the phase transformation are a strong function of the misfit strain and are considerably different compared to unconstrained, unstressed single crystals of the same composition. Depending on the internal stress state, it is possible that the structural aspects of the paraelectric–ferroelectric phase transformation may be completely obscured in the presence of epitaxial strains. The thickness dependence of epitaxial stresses due to relaxation by misfit dislocations during film deposition is incorporated into the model using an “effective” substrate lattice parameter. There is a good quantitative agreement between the theoretical analysis and experimental observations reported in the literature on the variations in the lattice parameters and the phase transformation temperature with film thickness in epitaxial BaTiO3 films.

Thickness effect of ferroelectric domain switching in epitaxial PbTiO3 thin films on Pt(001)/MgO(001)

Epitaxial PbTiO3 thin films of various thicknesses were prepared by pulsed laser deposition on Pt(001)/MgO(001) substrates. Their ferroelectric domain structures and switching behavior were then investigated mainly using scanning force microscopy as a function of film thickness. Direct evidence of a-domain switching was observed under an external electric field, while its contribution to the total piezoelectric response was found negligible. Thinner epitaxial PbTiO3 films with higher c-domain population and larger tetragonality resulted in enhanced d33 piezoelectric coefficients. The results suggest that the key factor determining the piezoelectric response in epitaxial ferroelectric films is not the a-to-c domain switching but apparently the population of c-domains and their tetragonality.

Structural visualization of polarization fatigue in epitaxial ferroelectric oxide devices.

Ferroelectric oxides, such as Pb(Zr,Ti)O(3), are useful for electronic and photonic devices because of their ability to retain two stable polarization states, which can form the basis for memory and logic circuitry. Requirements for long-term operation of practical devices such as non-volatile RAM (random access memory) include consistent polarization switching over many (more than 10(12)) cycles of the applied electric field, which represents a major challenge. As switching is largely controlled by the motion and pinning of domain walls, it is necessary to develop suitable tools that can directly probe the ferroelectric domain structures in operating devices-thin-film structures with electrical contacts. A recently developed synchrotron X-ray microdiffraction technique complements existing microscopic probes, and allows us to visualize directly the evolution of polarization domains in ferroelectric devices, through metal or oxide electrodes, and with submicrometre spatial resolution. The images reveal two regimes of fatigue, depending on the magnitude of the electric field pulses driving the device: a low-field regime in which fatigue can be reversed with higher electric field pulses, and a regime at very high electric fields in which there is a non-reversible crystallographic relaxation of the epitaxial ferroelectric film.

Impact of stress and long‐range interaction on ultrathin ferroelectric films

AbstractBased on the Landau–Devonshire type theory, the polarization, critical thickness, pyroelectric coefficient and correlation length of epitaxial ultrathin ferroelectric BaTiO3 films with first‐order phase transition have been investigated using the finite difference method. The theory not only allows for the influence of the stress attributed to lattice constant misfit between the ferroelectric film and the thick substrate, but also takes into account the long‐range dipole–dipole interactions. It is shown that both the compressive stress and the long‐range interaction increase the polarization and the Curie temperature, which can be compared with the experimental results, whereas the tensile stress reduces the polarization. In addition, both the stress and long‐range interaction remarkably affect the pyroelectric coefficient and the correlation length.

Ultrathin epitaxial ferroelectric films grown on compressive substrates: Competition between the surface and strain effects

The mean-field Landau-type theory is used to analyze the polarization properties of epitaxial ferroelectric thin films grown on dissimilar cubic substrates, which induce biaxial compressive stress in the film plane. The intrinsic effect of the film surfaces on the spontaneous polarization is taken into account via the concept of the extrapolation length. The theory simultaneously allows for the influence of the misfit strain imposed on the film lattice by a thick substrate. Numerical calculations are performed for PbTiO3 and BaTiO3 films under an assumption of the polarization reduction in surface layers. The film mean polarization is calculated as a function of film thickness, temperature, and misfit strain. It is shown that the negative intrinsic size effect is reduced in epitaxial films due to the in-plane compression of the film lattice. At room temperature, strong reduction of the mean polarization may take place only in ultrathin films (thickness ∼1 nm). Theoretical predictions are compared with the available experimental data on polarization properties of BaTiO3 films grown on SrRuO3 coated SrTiO3.

Thermodynamic theory of epitaxial ferroelectric thin films with dense domain structures

A Landau-Ginsburg-Devonshire-type nonlinear phenomenological theory is presented, which enables the thermodynamic description of dense laminar polydomain states in epitaxial ferroelectric thin films. The theory explicitly takes into account the mechanical substrate effect on the polarizations and lattice strains in dissimilar elastic domains (twins). Numerical calculations are performed for PbTiO3 and BaTiO3 films grown on (001)-oriented cubic substrates. The "misfit strain-temperature" phase diagrams are developed for these films, showing stability ranges of various possible polydomain and single-domain states. Three types of polarization instabilities are revealed for polydomain epitaxial ferroelectric films, which may lead to the formation of new polydomain states forbidden in bulk crystals. The total dielectric and piezoelectric small-signal responses of polydomain films are calculated, resulting from both the volume and domain-wall contributions. For BaTiO3 films, strong dielectric anomalies are predicted at room temperature near special values of the misfit strain.

Influence of domain boundary width on the statics of 90° domains in epitaxial ferroelectric thin films

The influence of the domain boundary width on the statics of single 90° elastic domains (twins) in epitaxial ferroelectric tetragonal films grown on a cubic substrate is theoretically investigated. The inhomogeneous internal stresses arising in polydomain epitaxial systems are calculated by the effective dislocation method. The elastic energy stored in the heterostructure is determined. The equilibrium domain size is found and the stability diagram for single domains at different wall widths is constructed by minimizing the total internal energy of the system. It is demonstrated that, as the domain boundary width 2w increases, the stability region of 90° domains increases and qualitatively changes for ultrathin films when the parameter 2w exceeds the specific critical value 2wcr. The equilibrium width 2w* of domain walls in thin films is predicted to be larger compared to the width 2w0 of domain boundaries in a macroscopic crystal.