Small Electron Polarons Research Articles

Transport properties of electron small polarons in a V2O5 cathode of Li-ion batteries: a computational study.

Employing the first-principles plane-wave approach, we explored the behavior of electron transport in the V2O5 cathode. Polaron migrations along different crystallographic directions in the presence and absence of Li+ ions were systematically examined using linear interpolation (LE) and nudged elastic band (NEB) methods. We find that the NEB calculations, based on structural optimizations of TS structures, generally exhibit lower hopping barriers than those obtained from the LE calculations. Both methods consistently predict that the [010] hopping, in the presence and absence of a nearby Li+ ion, is kinetically least favorable since the migration involves displacements of rigid 3-coordinated O atoms. Computations based on the LE method reveal anisotropic polaron mobilities where the estimated hopping frequencies within the layer are approximately one order of magnitude higher than the normal. The prediction based on the LE calculations is consistent with the experimental results. Lithiation dramatically affects the behavior of polaron movement. It significantly increases the reaction energies and hopping barriers due to the strong polaron-ion interaction. In addition, it is predicted that polaron hopping in the V2O5 cathode is non-adiabatic where lithiation has negligible effects on the adiabaticity.

Geometry Distortion and Small Polaron Binding Energy Changes with Ionic Substitution in Halide Perovskites.

Halide perovskites have demonstrated remarkable performance in optoelectronic applications. Despite extraordinary progress, questions remain about device stability. We report an in-depth computational study of small polaron formation, electronic structure, charge density, and reorganization energies of several experimentally relevant halide perovskites using isolated clusters. Local lattice symmetry, electronic structure, and electron-phonon coupling are interrelated in polaron formation in these materials. To illustrate this, first-principles calculations are performed on (MA/Cs/FA)Pb(I/Br)3 and MASnI3. Across the materials studied, electron small polaron formation is manifested by Jahn-Teller-like distortions in the central octahedron, with apical PbI bonds expanding significantly more than the equatorial bonds. In contrast, hole polarons cause the central octahedron to uniformly contract. This difference in manifestation of electron and hole polaron formation can be a tool to determine what is taking place in individual systems to systematically control performance. Other trends as the anion and cations are changed are established for optimization in specific optoelectronic applications.

A polaron approach to photorefractivity in Fe : LiNbO3

The thermally activated, incoherent hopping of small electron polarons generated by continuous illumination in iron-doped lithium niobate is simulated by a Marcus-Holstein model for which all the input parameters are known from literature. The results of the calculations are compared with a comprehensive set of data obtained from photorefractive, photogalvanic and photoconductive measurements under green light excitation on samples with different doping levels and stoichiometries in the temperature range between and room temperature. We show that the temperature and composition dependence of the photorefractive observables can be interpreted by a change in the abundance of the different hop types that a polaron performs before being captured by a deep Fe trap. Moreover, by a comparison between experimental and numerical data we obtain new insights on the initial photo-excitation part of the photorefractive process. In particular all results are consistent if a single value of the photogalvanic length is assumed for all the samples and all the temperatures. The photo-generation efficiency ϕ under green light excitation (somewhere denoted as quantum efficiency) is also estimated. It appears to decrease from 10%–15% at room temperature to about 5% at 150 K. This behavior is qualitatively interpreted in terms of a temperature-dependent re-trapping probability of the light-emitted particles from the initial Fe donor center.

Corresponding Orbitals Derived from Periodic Bloch States for Electron Transfer Calculations of Transition Metal Oxides.

An approach for modeling electron transfer in solids and at surfaces of iron-(oxyhydr)oxides and other redox active solids has been developed for electronic structure methods (i.e., plane-wave density functional theory) capable of performing calculations with periodic cells and large system sizes efficiently while at the same time being accurate enough to be used in the estimation of the electron-transfer coupling matrix element, V AB, and the electron transfer transmission factor, κel. This method is an extension of the valence bond theory electron transfer method for molecules and clusters implemented by Dupuis and others and used extensively by Rosso and co-workers in which scaled corresponding orbitals derived from the Bloch states are used to calculate the off-diagonal matrix elements H AB and S AB. A key development of the present work is the formulation of algorithms to improve the accuracy of the integration of the exact exchange integral in periodic boundary conditions. This method is demonstrated on model systems for electron small polaron transfer in iron-(oxyhydr)oxides, including bare Fe2+-Fe3+ ions, and in [Fe3+(OH2)2 (OH-)2)] nn+ chains representing the common edge-sharing Fe octahedral motif in these materials.

The elusive role of NbLi bound polaron energy in hopping charge transport in Fe: LiNbO3

Charge transport due to small polarons hopping among defective (bound polarons) and regular (free polarons) sites is shown to depend in a non-trivial way on the value of the stabilization energy provided by the lattice distortion surrounding the charge carriers. This energy, normally not directly accessible for bound polarons using spectroscopic techniques, is determined here by a combination of experimental and numerical methods for the important case of small electron polarons bound to defects in the prototype ferroelectric oxide lithium niobate. Our findings provide an estimation of the polaron stabilization energy and demonstrate that in lithium niobate both free and bound polarons contribute to charge transport at room temperature, explaining the fast decay of the light-induced bound polaron population observed by transient absorption spectroscopy.

Photoinduced small polarons bound to hydrogen defects in rutile TiO2

Photoinduced absorption in rutile ${\mathrm{TiO}}_{2}$ has been studied by means of Fourier transform infrared spectroscopy. It is shown that near-band-gap illumination results in a charge-state transition of a hydrogen defect with an O--H stretch mode at 3500 ${\mathrm{cm}}^{\ensuremath{-}1}$, as evidenced by the appearance of an anticorrelated vibrational mode with a blueshift of $\ensuremath{\sim}1.3\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. The charge-state transition is accompanied by a broad near-infrared absorption band with maximum intensity at $\ensuremath{\sim}7000\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. Our data on both the photoinduced vibrational mode and the near-infrared absorption can be conclusively explained in the framework of a model of small electron polarons bound to a Ti atom adjacent to the O--H group of the hydrogen defect.

Effect of intrinsic point defects on ferroelectric polarization behavior of SrTiO3

The effect of a variety of intrinsic defects and defect clusters in bulk and thin films of SrTiO$_3$ on ferroelectric polarization and switching mechanism is investigated by means of density-functional-theory (DFT) based calculations and the Berry phase approach. Our results show that both the titanium Ti$_\mathrm{Sr}^{\bullet \bullet}$ and strontium Sr$_\mathrm{Ti}^{"}$ antisite defects induce ferroelectric polarization in SrTiO$_3$, with the Ti$_\mathrm{Sr}^{\bullet \bullet}$ defect causing a more pronounced spontaneous polarization and higher activation barriers of polarization reversal than Sr$_\mathrm{Ti}^{"}$. The presence of oxygen vacancies bound to the antisite defects can either enhance or diminish polarization depending on the configuration of the defect pair, but it always leads to larger activation barriers of polarization switching as compared to the antisite defects with no oxygen vacancies. We also show that the magnitude of spontaneous polarization in SrTiO$_3$ can be tuned by controlling the degree of Sr/Ti nonstroichiometry. Other intrinsic point defects such as Frenkel defect pairs and electron small polarons also contribute to the emergence of ferroelectric polarization in SrTiO$_{3}$.

Effect of polaronic charge transfer on band alignment at the Cu/TiO2 interface

We present a first principles investigation into the electronic properties of an extended interface between rutile ${\mathrm{TiO}}_{2}$ and Cu. We show that owing to the highly polarizable nature of ${\mathrm{TiO}}_{2}$, the interface is unstable to the spontaneous formation of small electron polarons at the interface. The resulting dipole leads to an increase in the conduction band offset by 0.4 eV and the presence of a band of occupied states related to Ti $d$ states 1.4 eV below the Fermi energy. This effect should be expected more generally at interfaces between highly polarizable oxides and metals but is missed by standard first principles approaches. Given the ubiquitous nature of such interfaces, this previously overlooked effect may have important implications for diverse applications across science and technology.

Engineering Polarons at a Metal Oxide Surface.

Polarons in metal oxides are important in processes such as catalysis, high temperature superconductivity, and dielectric breakdown in nanoscale electronics. Here, we study the behavior of electron small polarons associated with oxygen vacancies at rutile TiO_{2}(110), using a combination of low temperature scanning tunneling microscopy (STM), density functional theory, and classical molecular dynamics calculations. We find that the electrons are symmetrically distributed around isolated vacancies at 78K, but as the temperature is reduced, their distributions become increasingly asymmetric, confirming their polaronic nature. By manipulating isolated vacancies with the STM tip, we show that particular configurations of polarons are preferred for given locations of the vacancies, which we ascribe to small residual electric fields in the surface. We also form a series of vacancy complexes and manipulate the Ti ions surrounding them, both of which change the associated electronic distributions. Thus, we demonstrate that the configurations of polarons can be engineered, paving the way for the construction of conductive pathways relevant to resistive switching devices.

Charge transport properties of bulkTa3N5from first principles

Tantalum nitride is considered a promising material for photoelectrochemical water splitting, however, its charge transport properties remain poorly understood. We investigated polaronic and band transport in ${\mathrm{Ta}}_{3}{\mathrm{N}}_{5}$ using first-principles calculations. We first studied the formation of small polarons using density-functional theory (DFT) including $\mathrm{DFT}+U$ and hybrid functionals. We found that electron small polarons may occur but hole polarons are not energetically favorable. The estimated polaronic mobility for electrons is at least three orders of magnitude smaller than that measured in ${\mathrm{Ta}}_{3}{\mathrm{N}}_{5}$ films, suggesting that the main transport mechanism for both electrons and holes is bandlike. Since band transport is strongly affected by the carrier effective masses, and ${\mathrm{Ta}}_{3}{\mathrm{N}}_{5}$ is known to have large electron and hole effective masses, we also investigated whether substitutional impurities or strain may help lower the effective masses. We found a significant reduction in both electron and hole effective masses (up to 17% for electrons and 39% for holes) under applied strain, which may lead to a substantial improvement (up to 30% for electrons and 15% for holes) in the carrier mobilities.

Electron small polarons and their transport in bismuth vanadate: a first principles study.

Relatively low electron mobility has been thought to be a key factor that limits the overall photocatalytic performance of BiVO4, but the behavior of electrons has not been fully elucidated. We examine electron localization and transport in BiVO4 using hybrid density functional theory calculations. An excess electron is found to remain largely localized on one V atom. The predicted hopping barrier for the small polaron is 0.35 eV (with inclusion of 15% Hartree-Fock exchange), and tends to increase almost linearly with lattice constant associated with pressure and/or temperature changes. We also examine the interaction between polarons, and discuss the possible concentration-dependence of electron mobility in BiVO4.

Computational Investigation of Electron Small Polarons in α-MoO3

The properties of electron small polarons in α-MoO3 are investigated computationally employing density-functional-theory with Hubbard-U corrections (DFT+U) and hybrid functionals (HSE06). These met...

Density functional theory based calculation of small-polaron mobility in hematite

The mobility of electron small polarons in hematite, $\ensuremath{\alpha}$-${\text{Fe}}_{2}$${\text{O}}_{3}$, is calculated by density functional theory within the generalized gradient approximation including Hubbard $U$ corrections. Our work goes beyond previous computational investigations of this system by computing both the prefactor and activation energies for adiabatic polaron transport. The results obtained using a Hubbard $U$ value of 4.3 eV yield a calculated value of the room-temperature basal plane mobility of 0.009 S*${\text{cm}}^{2}$/s, which compares to within an order of magnitude with experimental measurements. Further, the values of the electronic-coupling parameter in the Marcus theory for small-polaron transport are estimated from DFT$\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}U$ calculations of the defect energy levels in the stable and saddle-point configurations. Our results predict an adiabatic polaron transfer, in good agreement with previous wave function based calculations.

Chemical State, Site, Solid Solubility, and Magnetism of Fe in the Ferropericlase (Mg1–x Fe x )O Produced by Ball Milling of MgO and Fe

Ferropericlase (Mg1–xFex)O solid solution was prepared by ball milling of the mixture of MgO with a rock-salt structure and metal Fe powders in atmosphere and at room temperature. Differing from (Mg1–xFex)O prepared at high temperature by using MgO and FeO as starting materials, the solution of Fe in MgO is not continuous but limited in the ball milling process, and the solubility limit is less than 30 at. pct. About 92 pct of the Fe ions occupy the site of tetrahedral oxygen coordination in trivalent Fe (Fe3+) with high spin, whereas about 8 pct of the Fe ions occupy the site of octahedral oxygen coordination in bivalent Fe (Fe2+) with high spin. The Fe3+ and Fe2+ ions do not show a ferromagnetic but show a paramagnetic state. The as-milled (Mg1–xFex)O is metastable and decomposes to ferropericlase (Mg1–yFey)O (where y < x) and MgFe2O4 with spinel structure as annealed above 773 K (500 °C), and the content of Fe in the (Mg1–yFey)O increases with increasing annealing temperature. A bulk (Mg1–xFex)O was fabricated by annealing the as-milled (Mg1–xFex)O powders at 973 K (700 °C). It shows n-type conductivity, which is attributed to an electronic small polaron with an activation energy of 0.135 eV.

Intrinsic small polarons in rutile TiO2

Electron paramagnetic resonance (EPR) is used to identify the intrinsic electron small polaron in TiO${}_{2}$ crystals having the rutile structure. These self-trapped electrons are produced at very low temperature with 442 nm laser light. The defects form when a Ti${}^{4+}$ ion at a regular lattice site traps an electron and converts to a Ti${}^{3+}$ (3${d}^{1}$) ion. They become thermally unstable above \ensuremath{\sim}15 K. An activation energy of 24 meV describes this ``release'' of the electrons (either by a hopping motion or directly to the conduction band). The $g$ matrix is obtained from the angular dependence of the EPR spectrum. Principal values are 1.9807, 1.9786, and 1.9563 and principal axes are along high-symmetry directions in the crystal. The unpaired electron occupies an $|{x}^{2}\ensuremath{-}{y}^{2}\ensuremath{\rangle}$ orbital where $x$ and $y$ are in the equatorial plane of the TiO${}_{6}$ unit and $y$ is the [001] direction. These intrinsic small polarons serve as a prototype for many of the defect-associated Ti${}^{3+}$ ions often observed in this material. They also can be used as a computational test case to evaluate the validity of different approximations presently being employed in density-functional-theory modeling of point defects in TiO${}_{2}$ and other transition-metal oxides.

Electron Small Polarons and Their Mobility in Iron (Oxyhydr)oxide Nanoparticles

Electron mobility within iron (oxyhydr)oxides enables charge transfer between widely separated surface sites. There is increasing evidence that this internal conduction influences the rates of interfacial reactions and the outcomes of redox-driven phase transformations of environmental interest. To determine the links between crystal structure and charge-transport efficiency, we used pump-probe spectroscopy to study the dynamics of electrons introduced into iron(III) (oxyhydr)oxide nanoparticles via ultrafast interfacial electron transfer. Using time-resolved x-ray spectroscopy and ab initio calculations, we observed the formation of reduced and structurally distorted metal sites consistent with small polarons. Comparisons between different phases (hematite, maghemite, and ferrihydrite) revealed that short-range structural topology, not long-range order, dominates the electron-hopping rate.

Charge Transfer and Anharmonicity in Sn2P2S6 Ferroelectrics

The first-principles calculations in LDA approach were performed for Sn2P2S6 ferroelectrics. The evolution of energy band structure and charge density distribution clearly illustrate the stereoactivity of the tin atoms lone pair electrons and their leading role in the phase transition nature which is described by three-well potential. Energy levels and charge density distribution were calculated for the tin vacancies acceptor states and for the sulfur vacancies donor states in relaxed structure of the paraelectric phase. Taking into account the named donors and acceptors, small electron polarons at Sn+ cations and small hole polarons at S− anions, the relationship of thermally induced lattice multistability with light induced optical bistability for Sn2P2S6 ferroelectrics-semiconductors was established.

Irradiation-Induced Electron Tunnelling and Small-Polaron Hopping in Single-Crystalline YIG

In electron (e - )-irradiated (>10 23 e - m -2 ) single crystalline yttrium-ion Garnet (YIG), after moderate annealing, low-temperature (T < 125 K) magnetic after-effect (MAE) spectra are observed which are of striking similarity to the well investigated spectra occurring in magnetite (Fe 3 O 4 ) below the Verwey transition (T V 125 K). Our analysis shows that this similarity is the result of corresponding relaxation mechanisms in both systems, i.e. electron tunnelling and small-polaron hopping. Deeper insights into these mechanisms are obtained from a thorough inspection of these spectra and their physical preconditions in the two, a-priori, completely different ferrimagnetic systems: (i) semiconductor, transformed into a quasi-insulating state due to long-range ionic ordering at low-temperatures (Fe 3 O 4 ) and (ii) insulator, brought into a state of low resistivity due to radiation-induced perturbations of the charge equilibrium (YIG).

Computer simulation of defects in KTaO3.

Using atomistic computer simulation methods we propose a general overview of the point defect structure of ${\mathrm{KTaO}}_{3}$. A set of short-range potential parameters was derived using an empirical fitting procedure. These parameters were then applied within the framework of the shell model. We employed a two-region strategy in combination with the Mott-Littleton technique for defect calculations. Intrinsic defects including Frenkel and Schottky-type disorder, polarons, and reduction/oxidation mechanisms are treated in the study as well as a great number of extrinsic defects. The way these ions are introduced into the crystal, their agglomeration into defect complexes and possible off-center displacements are investigated. It is found that in ${\mathrm{KTaO}}_{3}$, intrinsic disorder is of minor significance and small electron polarons possibly are stable. The calculations support the idea that reduction is significantly influenced by preexisting oxygen vacancies, which result from charge compensation of accidental acceptor impurities in the material. Extrinsic monovalent ions substitute on the potassium site for which no charge compensation is necessary. Ions of other valencies are incorporated on both cation lattice sites which then gives rise to a charge self-compensation, in some cases combined with the formation of oxygen vacancies.

Polarons in the three-band Peierls-Hubbard model: An exact diagonalization study.

We have studied the three-band Peierls-Hubbard model describing the Cu-O layers in high-${\mathit{T}}_{\mathit{c}}$ superconductors by using Lanczos diagonalization and assuming infinite mass for the ions. When the system is doped with one hole, and for \ensuremath{\lambda} (the electron-lattice coupling strength) greater than a critical value, we found that the oxygens around one Cu contract and the hole self-traps forming a lattice and electronic small polaron. The self-trapped hole forms a local singlet analogous to the Zhang-Rice singlet in the undeformed lattice. We also studied the single-particle spectral function and the optical conductivity. We have found that the spectral weight, in general, is similar to that found in previous studies where the coupling with the lattice was absent. There is an anomalous transfer of spectral weight but, contrary to those studies, the spectral weight goes to these localized polaronic states. However, this polaronic shift does not seem enough by itself to explain pinning of the chemical potential observed in real materials. The peaks in the optical conductivity are also shifted, according to the polaronic shift, in the single-particle spectral functions. We compare our results to those obtained in inhomogeneous Hartree-Fock calculations and we discuss their relation with experiments.