Stability of a ferroelectric phase with electrical domains in multilayers

Multilayer BaTiO3-SrTiO3 and PbTiO3-SrTiO3 structures with different electrical domain states are studied using a Landau-Ginzburg-Devonshire free energy. Polarizations in the layers are computed for multi-domain and single-domain states where the paraelectric-to-ferroelectric volumetric layer ratio is varied. It is shown that the ferroelectric layers with electrical domains are thermodynamically more stable than the single-domain ferroelectric state. High domain wall energies result in the stabilization of the paraelectric state in the ferroelectric layers for large depolarizing fields. It is concluded that the stability of single-domain state ferroelectric layers correspond to a very small paraelectric-to-ferroelectric ratio after which multi-domain ferroelectric state is favored

Phase transitions in ferroelectric-paraelectric superlattices

Within the phenomenological Landau–Ginzburg–Devonshire theory, we discuss the paraelectric-ferrolectric transition in superstructures consisting of ferroelectric and paraelectric layers of equal thickness. The polar axis of the ferroelectric is perpendicular to the layer plane as expected in fully strained BaTiO3/SrTiO3 superstructures on SrTiO3 substrates with pseudomorphic electrodes. We concentrate on the electrostatic effects and do not take into account the boundary conditions other than the electrostatic ones. We find that when the ferroelectric phase transition in the superstructures is into a multidomain state, both its temperature and its character, i. e., the profile of the polarization appearing at the phase transition is strongly influenced by the nature of the near-electrode region. This is also the case for the layer thickness separating the single-and multidomain regimes of the transition. Such a finding makes us question the idea that these superstructures can be thought of as infinite systems, i.e., periodic superstructures similar to a crystal. The irrelevance of this idea in certain conditions is demonstrated by comparing the phase transitions in two different superstructures consisting of ferroelectric and paraelectric layers of the same thickness. In one of them, the ferroelectric layer is in immediate contact with an ideal metallic electrode, whereas at the other boundary, it is the paraelectric layer that is in contact with the electrode. In another superstructure, one paraelectric layer is split in two equal parts which are placed as the first and last layer between the electrodes and the ferroelectric layers which are closest to the electrodes. We show (with some formal reservations) that the phase transition temperature in the first superstructure can be over 100 °C more than in the second one if the material parameters of BaTiO3/SrTiO3 are used for the estimations. Moreover, the profile of the polarization arising at the phase transition is inhomogeneous along the superstructure and has the maximum amplitude in the ferroelectric layer contacting the electrode. We argue that this situation is general and results in smearing of the phase transition anomalies for the layer thicknesses corresponding to multidomain transitions. The work is mainly analyical but numerical methods have been used to support some statements that have been put forward as hypotheses

Very large dielectric response from ferroelectric nanocapacitor films due to collective surface and strain relaxation effects

Dependence of the dielectric response of ferroelectrics on defect types, particularly those with long range strain fields in confined geometries have been often mentioned, especially in interpreting experimental results in films. However, detailed discussions on the mechanisms with which defects alter properties, particularly in the presence of interfaces imposing certain boundary conditions, are seldom made. Here, we studied the thickness dependence of transition temperatures and dielectric response of Metal/BaTiO3/Metal ferroelectric nanocapacitor structures grown on SrTiO3 using a phenomenological approach accounting for the equations of electrostatics and semiconductors. Relaxation of the misfit strain via misfit dislocations amplify the surface effects in films below a critical thickness and favor electrical domains leading to very large dielectric responses in this regime. Thin film structures with relaxed misfit strain in this work are fully-depleted in the presence of moderate densities of impurities (~1025 m-3). This is due to the reduction of polarization amplitude parallel to the film normal and its mplications for near-micron thick films are discussed. Consequently, the misfit dislocation sites have nearly no free carrier localization, making the role of these sites on leakage currents highly questionable. Dielectric response of intrinsic thicker films (>40 nm) are mostly under the influence of strain relaxation only with minimal interface impact in the limit of ideal electrodes. Our results point out that control of the dislocation density can lead to non-conventional functionalities in ferroelectric thin film capacitors via electromechanical coupling of properties to structure and domain stabilization

Low-temperature monoclinic phase in epitaxial (001) barium titanate on (001) cubic substrates

The possibility of the existence of a low temperature monoclinic phase in epitaxial (001) BaTiO3 films on a (001) compressive substrate is analyzed theoretically and compared to recent experimental data from literature. There is good agreement between the theoretical findings and the experimentally observed behavior. The formation of the monoclinic phase arises from the point group reduction due to the rotation of the polarization vector commensurate with the variations in the in-plane strain state

Phase transformation characteristics of barium strontium titanate films on anisotropic substrates with (001)//(001) epitaxy

The role of anisotropic misfit strains on the spontaneous polarization of (100) oriented Ba0.6Sr0.4TiO3 thin films on (100) orthorhombic substrates is theoretically analyzed. A modified thermodynamic model is utilized to evaluate the equilibrium polarization values as a function of the anisotropic misfit strains. Results show that ferroelectric phases that cannot be observed in single-crystal Ba0.6Sr0.4TiO3 can be stabilized due to the reduction in the symmetry induced by the anisotropic strain state

Contribution of space charges to the polarization of ferroelectric superlattices and its effect on dielectric properties

A theoretical model is developed for ferroelectric bilayers and multilayer heterostructures that employs a nonlinear Landau-Devonshire formalism coupled with a detailed analysis of the depolarizing fields arising from the polarization mismatch across interlayer interfaces and the electrical fields of localized space charges at such interfaces. We first present how space charges alter the free-energy curves of ferroelectrics and then proceed with a numerical analysis for heteroepitaxial (001) PbTiO3-SrTiO3 (PTO-STO) bilayers and (001) superlattice structures on (001) STO substrates. The switchable (ferroelectric) and nonswitchable (built-in) polarizations and the dielectric properties of PTO-STO bilayers and superlattices are calculated as a function of the planar space-charge density and the volume fraction of the PTO layer. Similar to the temperature dependence of a monolithic ferroelectric, there exists a critical volume fraction PTO below which the bilayer or the superlattice is in the paraelectric state. This critical volume fraction is strongly dependent on the density of trapped charges at the interlayer interfaces. For charge-free (001) PTO-STO heteroepitaxial bilayer and superlattices, the critical fraction is 0.40 for both constructs but increases to 0.6 and 0.72, for the bilayer and the superlattice, respectively, for a planar space-charge density of 0.05 C/m(2). Furthermore, our results show that close to the vicinity of ferroelectric-paraelectric phase transition, there is a recovery in ferroelectric polarization. The dielectric-response calculations verify that there is sharp ferroelectric phase transformation for charge-free bilayers and superlattices whereas it is progressively smeared out with an increase in the charge density. Furthermore, our analysis shows that the dielectric constant of these multilayers at a given volume fraction of PTO decreases significantly in the presence of space charges

Carrier accumulation near electrodes in ferroelectric films due to polarization boundary conditions

We study the effect of surface polarization on the distribution of free carriers in a wide bandgap semiconductor ferroelectric (FE) film using a thermodynamic approach. We show that free carriers, namely, holes and electrons from ionizable impurities or atomic vacancies can accumulate near the film-electrode interface, if FE polarization profile has a very steep change near the surface that is specified by the extrapolation length. Such an outcome is just the opposite of what happens in a Schottky junction in a partially or fully depleted film. This is also an entirely different effect than what has been often studied in similar structures, where the work function and screening length of the electrode metal determines the electronic character of the interface. Even for low-to-moderate densities of ionizable defects with states within the bandgap close to the band edges, high densities of carriers can localize close to the electrodes in a single domain state FE film when above a critical thickness. For very low densities of such ionizable defects, short extrapolation lengths cause electrical domain formation with minimal carrier accumulation because of the already weak depolarizing fields. This is also true for films below a critical thickness with low-to-moderate densities of ionizable impurities, i.e., electrical domains get stabilized regardless of defect density. The implications of our findings for polarization controlled Schottky to Ohmic-like transition of an interface and experimental results are discussed. It is also found that interfaces of an n-type FE heterostructure can behave like a p-type depending on the barrier heights and impurity density. We conclude that, for low-to-moderate ionizable impurity densities, it is the rate of change of polarization at the interface with position rather than solely its presence that leads to carrier accumulation and that both interfaces can become Ohmic-like with opposite signs of carriers

Thickness driven stabilization of saw-tooth-like domains upon phase transitions in ferroelectric thin films with depletion charges

Ionized impurities have nearly always been neglected in discussing the limit of functionality of ferroelectric thin films. One would certainly expect that the thickness limit for functionality would be altered in the presence of ionized impurities, but how this would occur remains unclear. In this article, we analyze the domain structures as well as the phase transition temperatures in films with depletion charges for various film thicknesses. Depletion charges induce a position-dependent built-in field that leads to an inhomogeneous distribution of ferroelectric polarization. Such an inhomogeneity in the polarization results in strong depolarizing fields in films. We show that formation of saw-tooth-type domains is a way to circumvent the depolarizing fields, even in films with ideal electrodes. There is a critical film thickness above which the saw-tooth domains develop. On the other hand, the phase transition of the ultrathin structures with electrodes having a finite screening length, namely real electrodes, is always into the multidomain state during cooling from the paraelectric state, regardless of the presence of depletion charges. An important finding we have is that the transition temperature in films with real electrodes does not depend nearly at all on the depletion charge density unless it is very high (>10(26) ionized impurities/m(3)). Relatively thick films (>8 nm in this work) with real electrodes that have very high depletion charge densities have transition temperatures very similar to those with the same charge density, but with ideal electrodes, making us conclude that thick films with high depletion charge densities will hardly feel the finite screening effects. The results are provided for (001) BaTiO3 films grown on (001) SrTiO3 substrates with pseudomorphic top and bottom metallic electrodes

A theoretical treatment of THz resonances in semiconductor GaAs p–n junctions

Semiconductor heterostructures are suitable for the design and fabrication of terahertz (THz) plasmonic devices, due to their matching carrier densities. The classical dispersion relations in the current literature are derived for metal plasmonic materials, such as gold and silver, for which a homogeneous dielectric function is valid. Penetration of the electric fields into semiconductors induces locally varying charge densities and a spatially varying dielectric function is expected. While such an occurrence renders tunable THz plasmonics a possibility, it is crucial to understand the conditions under which propagating resonant conditions for the carriers occur, upon incidence of an electromagnetic radiation. In this manuscript, we derive a dispersion relation for a p-n heterojunction and apply the methodology to a GaAs p-n junction, a material of interest for optoelectronic devices. Considering symmetrically doped p- and n-type regions with equal width, the effect of certain parameters (such as doping and voltage bias) on the dispersion curve of the p-n heterojunction were investigated. Keeping in sight the different effective masses and mobilities of the carriers, we were able to obtain the conditions that yield identical dielectric functions for the p- and n-regions. Our results indicated that the p-n GaAs system can sustain propagating resonances and can be used as a layered plasmonic waveguide. The conditions under which this is feasible fall in the frequency region between the transverse optical phonon resonance of GaAs and the traditional cut-off frequency of the diode waveguide. In addition, our results indicated when the excitation was slightly above the phonon resonance frequency, the plasmon propagation attained low-loss characteristics. We also showed that the existence or nonexistence of the depletion zone between the p- and n- interfaces allowed certain plasmon modes to propagate, while others decayed rapidly, pointing out the possibility for a design of selective filters