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

Wiener algebra for the quaternions

We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener-L\'evy type theorem and a factorization theorem. We give applications to Toeplitz and Wiener-Hopf operators

Phase Coexistence Near a Morphotropic Phase Boundary in Sm-doped BiFeO3 Films

We have investigated heteroepitaxial films of Sm-doped BiFeO3 with a Sm-concentration near a morphotropic phase boundary. Our high-resolution synchrotron X-ray diffraction, carried out in a temperature range of 25C to 700C, reveals substantial phase coexistence as one changes temperature to crossover from a low-temperature PbZrO3-like phase to a high-temperature orthorhombic phase. We also examine changes due to strain for films greater or less than the critical thickness for misfit dislocation formation. Particularly, we note that thicker films exhibit a substantial volume collapse associated with the structural transition that is suppressed in strained thin films

Layer thickness and period as design parameters to tailor pyroelectric properties in ferroelectric superlattices

We theoretically examine the pyroelectric properties of ferroelectric-paraelectric superlattices as a function of layer thickness and configuration using non-linear thermodynamics coupled with electrostatic and electromechanical interactions between layers. We specifically study PbZr0.3Ti0.7O3/SrTiO3 superlattices. The pyroelectric properties of such constructs consisting of relatively thin repeating units are shown to exceed the pyroelectric response of monolithic PbZr0.3Ti0.7O3 films. This is related to periodic internal electric fields generated due to the polarization mismatch between layers that allows tailoring of the shift in the transition temperature. Our results indicate that higher and electric field sensitive pyroresponse can be achieved from layer-by-layer engineered ferroelectric heterostructures

Strong dependence of dielectric properties on electrical boundary conditions and interfaces in ferroelectric superlattices

A computational study based on Landau-Ginzburg-Devonshire theory is carried out to understand the role of interfaces on the dielectric response of ferroelectric superlattices. Using heteroepitaxial (001) PbZr0.3Ti0.7O3/(001)SrTiO3 heterostructures on (001)SrTiO3 as an example, we show that electrostatic boundary conditions have a pronounced effect on the dielectric response far below the ferroelectric phase transition temperature. For a fixed total multilayer thickness, the average dielectric response can be improved significantly for superlattices with a small layer periodicity. This is due to the large total internal electric fields at the interlayer interfaces which originate from the polarization mismatch between layers

Strain induced variations in band offsets and built-in electric fields in InGaN/GaN multiple quantum wells

The band structure, quantum confinement of charge carriers, and their localization affect the optoelectronic properties of compound semiconductor heterostructures and multiple quantum wells (MQWs). We present here the results of a systematic first-principles based density functional theory (DFT) investigation of the dependence of the valence band offsets and band bending in polar and non-polar strain-free and in-plane strained heteroepitaxial In x Ga1- xN(InGaN)/GaN multilayers on the In composition and misfit strain. The results indicate that for non-polar m-plane configurations with [12¯10]InGaN // [12¯10]GaN and [0001]InGaN // [0001]GaN epitaxial alignments, the valence band offset changes linearly from 0 to 0.57 eV as the In composition is varied from 0 (GaN) to 1 (InN). These offsets are relatively insensitive to the misfit strain between InGaN and GaN. On the other hand, for polar c-plane strain-free heterostructures with [101¯0]InGaN // [101¯0]GaN and [12¯10]InGaN // [12¯10]GaN epitaxial alignments, the valence band offset increases nonlinearly from 0 eV (GaN) to 0.90 eV (InN). This is significantly reduced beyond x ≥ 0.5 by the effect of the equi-biaxial misfit strain. Thus, our results affirm that a combination of mechanical boundary conditions, epitaxial orientation, and variation in In concentration can be used as design parameters to rapidly tailor the band offsets in InGaN/GaN MQWs. Typically, calculations of the built-in electric field in complex semiconductor structures often must rely upon sequential optimization via repeated ab initio simulations. Here, we develop a formalism that augments such first-principles computations by including an electrostatic analysis (ESA) using Maxwell and Poisson\u27s relations, thereby converting laborious DFT calculations into finite difference equations that can be rapidly solved. We use these tools to determine the bound sheet charges and built-in electric fields in polar epitaxial InGaN/GaN MQWs on c-plane GaN substrates for In compositions x = 0.125, 0.25,…, and 0.875. The results of the continuum level ESA are in excellent agreement with those from the atomistic level DFT computations, and are, therefore, extendable to such InGaN/GaN MQWs with an arbitrary In composition