Electrostatic Boundary Conditions and (Electro)chemical Interface Stability

Interface stability is a key factor for stable operation of electronic and electrochemical devices. This contribution introduces an approach for the operando analysis of interfaces using photoelectron spectroscopy employing a solid oxide electrochemical cell. The combined chemical and electronic information provided by the experiment reveals that not only chemical but also electrostatic boundary conditions are essential for interface stability. The approach is demonstrated using (anti-)ferroelectric (Pb,La)(Zr,Sn,Ti)O3 dielectrics

Global Positive Periodic Solutions of Generalized n

We consider the following generalized n-species Lotka-Volterra type and Gilpin-Ayala type competition systems with multiple delays and impulses: xi′(t)=xi(t)[ai(t)-bi(t)xi(t)-∑j=1n‍cij(t)xjαij(t-ρij(t))-∑j=1n‍dij(t)xjβij(t-τij(t))-∑j=1n‍eij(t)∫-ηij0‍kij(s)xjγij(t+s)ds-∑j=1n‍fij(t)∫-θij0‍Kij(ξ)xiδij(t+ξ)xjσij(t+ξ)dξ],a.e, t>0, t≠tk; xi(tk+)-xi(tk-)=hikxi(tk), i=1,2,…,n, k∈Z+. By applying the Krasnoselskii fixed-point theorem in a cone of Banach space, we derive some verifiable necessary and sufficient conditions for the existence of positive periodic solutions of the previously mentioned. As applications, some special cases of the previous system are examined and some earlier results are extended and improved

The Fermi energy in acceptor doped SrTiO3 and BaTiO3

In order to evaluate the presence of space charge layers and the magnitude of band bending at electrode interfaces of mixed ionic-electronic conductors we have evaluated the Fermi energies in the bulk and at interfaces of acceptor-doped SrTiO3, BaTiO3 and (Ba,Sr)TiO3. While the interface Fermi energy can be directly obtained using photoelectron spectroscopy (XPS) if conducting electrode materials are deposited, the determination of the bulk Fermi energy is more challenging due to the high resistivity of the samples. One approach is to use XPS on thin films deposited on conducting samples. In general, we observed a good agreement between upper and lower limits of Fermi energies at thin films surfaces and at interfaces. Surprisingly, the Fermi energy is hardly observed below EF-EVB≈2eV (see Fig. 1), although defect chemistry calculations predict values as low as EF-EVB≈2eV for acceptor doped samples, such as Fe-doped SrTiO3 or Mn-doped BaTiO3.c,d Even at anode interfaces of ionically polarized Fe-doped SrTiO3 single crystals,e at which the oxygen vacancy concentration should be very low, we have not observed lower Fermi energies. Please click Additional Files below to see the full abstract

The Fermi energy as common parameter to describe charge compensation mechanisms: A path to Fermi level engineering of oxide electroceramics

Chemical substitution, which can be iso- or heterovalent, is the primary strategy to tailor material properties. There are various ways how a material can react to substitution. Isovalent substitution changes the density of states while heterovalent substitution, i.e. doping, can induce electronic compensation, ionic compensation, valence changes of cations or anions, or result in the segregation or neutralization of the dopant. While all these can, in principle, occur simultaneously, it is often desirable to select a certain mechanism in order to determine material properties. Being able to predict and control the individual compensation mechanism should therefore be a key target of materials science. This contribution outlines the perspective that this could be achieved by taking the Fermi energy as a common descriptor for the different compensation mechanisms. This generalization becomes possible since the formation enthalpies of the defects involved in the various compensation mechanisms do all depend on the Fermi energy. In order to control material properties, it is then necessary to adjust the formation enthalpies and charge transition levels of the involved defects. Understanding how these depend on material composition will open up a new path for the design of materials by Fermi level engineering

Charges and Charged Defects in Pb-based Ferro- and Antiferroelectric Ceramics

Ferroelectric (FE) and antiferroelectric (AFE) ceramics are widely used in capacitors for various purposes because of their specific dielectric properties and outstanding insulating nature. Several types of charges and charged point defects are considered to exist in these materials, participating in the mechanisms of charge compensation from different perspectives, such as the compensation within the bulk material which determines the electrical conductivity, the compensation at the domain walls which rationalizes the domain structures, and the compensation at the electrode/dielectric interfaces which screens the depolarization fields and thereby stabilizes the switched FE states. Therefore, identifying these charge carriers and understanding their compensation behavior are fundamental to the design and optimization of these FE and AFE materials. In this work, three composition series based on the well-known Pb-based perovskite AFE system (Pb,La)(Zr,Sn,Ti)O_3 (PLZST) were studied by dc conductivity measurement and X-ray photoelectron spectroscopy (XPS). By combining these two characterization techniques, fundamental correlations in terms of the electronic structures could be explored between the charge compensations and the dielectric properties. These ceramic samples were prepared with traditional solid-state reaction method. Prior to the conductivity and XPS studies, several basic characterizations were performed first, including hysteresis loops, dielectric permittivities, crystalline structures by X-ray diffraction, and microstructures by scanning electron microscopy, in order to get the basic information of the sintered ceramics. High resistivity is a necessary condition for the FE and AFE materials, and it can be described principally by the charge compensation and transport within the bulk. In order to get an overview of the conduction behavior of these samples, dc conductivities were measured under different thermal and electrical conditions. Variations in the conductivity, which are very likely caused by the migration and redistribution of oxygen and/or lead vacancies, have been observed. The comparisons among different compositions reveal that donor- or “net-donor” doping can effectively reduce the conductivity of these Pb-based ceramics. The Arrhenius relations of the donor-doped samples are nearly parallel at 300°C—400°C, indicating very similar transport mechanisms. Besides, a higher conductivity has been noticed in a field-induced FE state compared to that in its AFE state before the AFE-to-FE phase transition. This implies an additional conducting contribution in a FE phase, probably related to the existence of charged domain walls. As it has been realized in the conductivity studies that the low conductivities of these Pb-based dielectrics cannot be well explained without taking the traps for electrons and holes into account, a novel in situ XPS method has been developed to explore such traps within the band gap of a dielectric. Making use of the migration of oxygen species, the sandwich capacitor structure can be operated as a solid electrochemical cell, where the dielectric acts as the electrolyte. Electrochemical reduction and oxidation, which can be characterized by XPS, are expected to take place at the cathodic and anodic interfaces, respectively. By this means, the reduction and oxidation potentials, which indicate the existence of trap levels, are used to identify the upper and lower limits of the Fermi energy of the dielectric, respectively. In this work, an electron trap Pb^{2+/0} has been detected in some of the studied materials, different from the electron trap Ti^{4+/3+} and the hole trap Pb^{2+/3+} that are widely accepted in the literature on Pb(Zr,Ti)O_3. Moreover, the observation of the reduced Pb exhibits a composition dependence, implying that the preferred site for such reduction might be related to the dopants or the states at the bottom of the conduction band. Regarding the charge compensation at the electrode/dielectric interfaces, selected FE and AFE compositions have been studied by another in situ XPS approach, where sufficiently high electric fields can be applied to the sandwich capacitor structure in order to change the polarization state within the bulk ceramic and XPS is measured meanwhile through a thin top electrode. According to the electrode screening theory, an extra electric potential drop occurs at the electrode interface when the bound charges and the free compensating charges are spatially separated by a screening length. This extra potential drop can be characterized by a binding energy shift of the dielectric elements in the XPS spectrum. By detecting such emission shifts, the magnitude of FE polarization, the extent of dipole alignment, and the depth of the charge compensation can be analyzed. In this part, electrode-material-dependent asymmetric screening behavior has been observed for the FE samples. Moreover, no binding energy shift has been seen at the electrode/AFE interface even when the applied field already exceeds the AFE-to-FE transition point. This implies a fundamental discrepancy between the electrode/FE and the electrode/AFE interfaces in terms of the depth where the bound charges of a FE state are compensated. Based on these observations, several screening models that involve charge injection through the electrode interfaces have been suggested, in which the previously mentioned trap levels of electrons and/or holes may play certain roles. The novelty of this work is reflected in both technology and research. New technical strategies of XPS have been developed for extracting useful information from insulating bulk materials, which is usually thought to be difficult because of the charging problem. More importantly, this work can highlight the roles of different charges existing in the dielectric materials and provide some fundamental understanding of the dielectric properties from the viewpoint of electronic structures

Large-time dynamics of discrete-time neural networks with McCulloch-Pitts nonlinearity

We consider a discrete-time network system of two neurons with McCulloch-Pitts nonlinearity. We show that if a parameter is sufficiently small, then network system has a stable periodic solution with minimal period 4k, and if the parameter is large enough, then the solutions of system converge to single equilibrium

Existence and Global Attractivity of Positive Periodic Solutions for The Neutral Multidelay Logarithmic Population Model with Impulse

Suffiicient and realistic conditions are established in this paper for the existence and global attractivity of a positive periodic solution to the neutral multidelay logarithmic population model with impulse by using the theory of abstract continuous theorem of k-set contractive operator and some inequality techniques. The results improve and generalize the known ones in Li 1999, Lu and Ge 2004, Y. Luo and Z. G. Luo 2010, and Wang et al. 2009. As an application, we also give an example to illustrate the feasibility of our main results