Small Polaron Formation Research Articles

Formation of Small Polaron and Polaronic Charge Transfer within BiVO4 Photocatalyst

Harnessing the power of solar energy plays an essential role in developing renewable energy technologies to supplement or perhaps replace fossil fuel utilization. The green energy technology has the potential to address the challenges of growing energy demand and climate changes around the world. Production of H2 from water splitting via photo-electrochemical process is one of the potential green technologies. BiVO4 is one of the best photoanode material for water oxidation as well as photo-catalyst for H2 evolution via water splitting. Despite being an efficient photo absorber material, it has poor charge transport properties. It is anticipated that some of the conduction electrons get bind to specific lattice sites and form polarons, and hence, the charge transfer within this material happens via the polaron hopping from one lattice site to another. In this present study, we have studied the polaron formation at cationic lattice sites and calculated the site to site polaron hopping barrier along a specific hopping pathway in the framework of density functional theory (DFT) with the Hubbard parameter U for self-energy correction of localized d electrons. Finally, the polaron transfer rate, mobility, and diffusion coefficient will also be presented. The work of MNH is supported by NSF grant #1609811. We also acknowledge the computational time from Texas Advanced Computing Center (TACC).

Quantum dynamics of the small-polaron formation in a superconducting analog simulator

We propose a scheme for investigating the nonequilibrium aspects of small-polaron physics using an array of superconducting qubits and microwave resonators. This system, which can be realized with transmon or gatemon qubits, serves as an analog simulator for a lattice model describing a nonlocal coupling of a quantum particle (excitation) to dispersionless phonons. We study its dynamics following an excitation-phonon (qubit-resonator) interaction quench using a numerically exact approach based on a Chebyshev-moment expansion of the time-evolution operator of the system. We thereby glean heretofore unavailable insights into the process of the small-polaron formation resulting from strongly momentum-dependent excitation-phonon interactions, most prominently about its inherent dynamical timescale. To further characterize this complex process, we evaluate the excitation-phonon entanglement entropy and show that initially prepared bare-excitation Bloch states here dynamically evolve into small-polaron states that are close to being maximally entangled. Finally, by computing the dynamical variances of the phonon position and momentum quadratures, we demonstrate a pronounced non-Gaussian character of the latter states, with a strong antisqueezing in both quadratures.

The role of electron–vibron interaction and local pairing in conductivity and superconductivity of alkali-doped fullerides

We investigate the competition between the electron–vibron interaction (interaction with the Jahn–Teller phonons) and the Coulomb repulsion in a system with the local pairing of electrons on the 3-fold degenerate lowest unoccupied molecular orbital (LUMO). The el.–vib. interaction and the local pairing radically change conductivity and magnetic properties of alkali-doped fullerides AnC60, which would have to be antiferromagnetic Mott insulators: we have shown that materials with n=1,5 and A=K,Rb are conductors but not superconductors; n=3 and A=K,Rb are conductors and superconductors at low temperatures, but with A=Cs they are Mott–Jahn–Teller insulators at normal pressure; n=2,4 are nonmagnetic Mott insulators. Thus superconductivity, conductivity and insulation of these materials have common nature. Using this approach we obtain the phase diagram of A3C60 analytically, which is the result of interplay between the local pairing, the el.–vib. interaction, Coulomb correlations, and formation of small radius polarons.

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.

Chemical, Structural, and Electronic Characterization of the (010) Surface of Single Crystalline Bismuth Vanadate

We have structurally, chemically and electronically characterized the most stable (010) surface of a Mo-doped BiVO4 single crystal. Low energy electron diffraction (LEED) reveals that the surface is not significantly reconstructed from a bulk termination of the crystal. Synchrotron based X-ray spectroscopies indicate no surface enhancement of any of the crystal constituents and that the Mo dopant occupies tetrahedral sites by substituting for V at the surface. Using resonant photoemission to study the valence band structure as the V L3 edge is scanned we observe an intraband gap state associated with reduced vanadium formed by the Mo doping. This state is likely associated with small polaron formation. This feature is enhanced at a photon energy that is not resonant with any of the main features in the absorption spectrum of the pristine BiVO4. This indicates that the additional electron from Mo doping likely induces further distortion of the VO4 tetrahedral units and generates a new conduction band state...

Ultrafast Electron Trapping and Defect-Mediated Recombination in NiO Probed by Femtosecond Extreme Ultraviolet Reflection-Absorption Spectroscopy.

Understanding the chemical nature of defect sites as well as the mechanism of defect-mediated recombination is critical for the rational design of energy conversion materials with improved efficiency. Using femtosecond extreme ultraviolet (XUV) spectroscopy in conjunction with X-ray photoelectron spectroscopy (XPS), we present results on the ultrafast electron dynamics in NiO prepared with varying concentrations of defect states. We find that oxygen vacancy defects do not serve as the primary recombination center, but rather the recombination rate scales linearly with the density of Ni metal defects. This suggests that grain boundaries between Ni metal and NiO are responsible for fast carrier recombination in partially reduced NiO. Our kinetic model shows that the photoexcited electrons self-trap via small polaron formation on the subpicosecond time scale. Additionally, we estimate an absolute measurement of small polaron formation rates, direct versus defect-mediated recombination rates, and the small polaron diffusion coefficient in NiO. This study provides important parameters for engineering NiO based materials for solar energy harvesting applications.

Formation and dynamics of small polarons on the rutile TiO2 (110) surface

Charge trapping and formation of polarons is a pervasive phenomenon in transition metal oxide compounds, in particular at the surface, affecting fundamental physical properties and functionalities of the hosting materials. Here we investigate via first-principle techniques the formation and dynamics of small polarons on the reduced surface of titanium dioxide, an archetypal system for polarons, for a wide range of oxygen vacancy concentrations. We report how the essential features of polarons can be adequately accounted in terms of few quantities: the local structural and chemical environment, the attractive interaction between negatively charged polarons and positively charged oxygen vacancies, and the spin-dependent polaron-polaron Coulomb repulsion. We combined molecular dynamics simulations on realistic samples derived from experimental observations with simplified static models, aiming to disentangle the various variables at play. We find that depending on the specific trapping site, different types of polarons can be formed, with distinct orbital symmetries and different degree of localization and structural distortion. The energetically most stable polaron site is the subsurface Ti atom below the undercoordinated surface Ti atom, owing to a small energy cost to distort the lattice and a suitable electrostatic potential. Polaron-polaron repulsion and polaron-vacancy attraction determine the spatial distribution of polarons as well as the energy of the polaronic in-gap state. In the range of experimentally reachable oxygen vacancy concentrations the calculated data are in excellent agreement with observations, thus validating the overall interpretation.

Photoexcited Small Polaron Formation in Goethite (α-FeOOH) Nanorods Probed by Transient Extreme Ultraviolet Spectroscopy.

Small polaron formation limits the mobility and lifetimes of photoexcited carriers in metal oxides. As the ligand field strength increases, the carrier mobility decreases, but the effect on the photoexcited small polaron formation is still unknown. Extreme ultraviolet transient absorption spectroscopy is employed to measure small polaron formation rates and probabilities in goethite (α-FeOOH) crystalline nanorods at pump photon energies from 2.2 to 3.1 eV. The measured polaron formation time increases with excitation photon energy from 70 ± 10 fs at 2.2 eV to 350 ± 30 fs at 2.6 eV, whereas the polaron formation probability (85 ± 10%) remains constant. By comparison to hematite (α-Fe2O3), an oxide analogue, the role of ligand composition and metal center density in small polaron formation time is discussed. This work suggests that incorporating small changes in ligands and crystal structure could enable the control of photoexcited small polaron formation in metal oxides.

The Benefit and Challenges of Zero-Dimensional Perovskites.

To break free of the limitations imposed by three-dimensional (3D) perovskites, such as their lackluster stability, researchers have opened new frontiers into lower-dimensional perovskite derivatives. Thanks to advances in solvent-based synthesis methods, zero-dimensional (0D) inorganic perovskites, mainly Cs4PbBr6, have recently reemerged in various forms (from single crystals to nanocrystals) as materials with properties that bridge organic molecules and inorganic semiconductors. These properties include intrinsic Pb2+ ion emission, large exciton binding energy, and small polaron formation upon photoexcitation, in addition to anomalous green photoluminescence with improved stability and high quantum yield. Moreover, the demonstration of Cs4PbBr6-based light-emitting diode (LED) devices highlights the accelerating efforts toward their applications and motivates further investigations of these emerging materials. This Perspective summarizes the progress in the field of Cs4PbBr6 perovskites, focusing on their molecular-electronic properties and hotly debated green photoluminescence. We conclude by presenting the implications of the unique findings and suggesting opportunities for the future development and applications of these 0D perovskites.

Intrinsic Photoexcited Charge Trapping from Small Polaron Formation in α-Fe2O3

Polaron formation and hopping is known to diminish carrier mobility in the ground state of metal oxide photocatalysts. Trap states, however, are usually cited as the cause of limited carrier mobility and short carrier lifetimes in the photoexcited state. We investigate how small polaron formation controls the ultrafast localization and trapping of photoexcited carriers in hematite (α-Fe2O3), potentially bridging these two pictures. Ultrafast transient extreme ultraviolet (XUV) spectroscopy of the Fe M2,3 edge measures a sub-5 fs shift in charge density from the oxygen to the iron atom following optical excitation. An energetic splitting of the Fe M2,3­ edge is then measured on a 100 fs timescale, with the kinetics of the splitting matching those typically associated with trap or mid-gap states in hematite. The splitting of the Fe M2,3 edge, however, is best reproduced by predictions for small polaron localization of the photoexcited carriers, and not the pre-edge absorption or bleach expected for mid-gap states. The polaron formation efficiency versus visible light excitation energy is measured to match the discrepancy between the photoconversion efficiency and visible light absorption of hematite. These results therefore suggest that small polaron formation is responsible for the intrinsic recombination and transport issues that currently limit hematite’s performance. In particular, the increased small polaron formation rate at near-band gap excitation may result in the decreased visible light photoconversion efficiency. Possible materials routes to overcoming small-polaron localization, as well as the role of small polarons in other metal oxide photocatalysts, will be discussed.

Molecular behavior of zero-dimensional perovskites.

Low-dimensional perovskites offer a rare opportunity to investigate lattice dynamics and charge carrier behavior in bulk quantum-confined solids, in addition to them being the leading materials in optoelectronic applications. In particular, zero-dimensional (0D) inorganic perovskites of the Cs4PbX6 (X = Cl, Br, or I) kind have crystal structures with isolated lead halide octahedra [PbX6]4- surrounded by Cs+ cations, allowing the 0D crystals to exhibit the intrinsic properties of an individual octahedron. Using both experimental and theoretical approaches, we studied the electronic and optical properties of the prototypical 0D perovskite Cs4PbBr6. Our results underline that this 0D perovskite behaves akin to a molecule, demonstrating low electrical conductivity and mobility as well as large polaron binding energy. Density functional theory calculations and transient absorption measurements of Cs4PbBr6 perovskite films reveal the polaron band absorption and strong polaron localization features of the material. A short polaron lifetime of ~2 ps is observed in femtosecond transient absorption experiments, which can be attributed to the fast lattice relaxation of the octahedra and the weak interactions among them.

Polaron-induced phonon localization and stiffening in rutile TiO2

Small polaron formation in transition metal oxides, like the prototypical material rutile TiO$_2$, remains a puzzle and a challenge to simple theoretical treatment. In our combined experimental and theoretical study, we examine this problem using Raman spectroscopy of photo-excited samples and real-time time-dependent density functional theory (RT-TDDFT), which employs Ehrenfest dynamics to couple the electronic and ionic subsystems. We observe experimentally the unexpected stiffening of the $A_{1g}$ phonon mode under UV illumination and provide a theoretical explanation for this effect. Our analysis also reveals a possible reason for the observed anomalous temperature-dependence of the Hall mobility. Small polaron formation in rutile TiO$_2$ is a strongly non-adiabatic process and is adequately described by Ehrenfest dynamics at time scales of polaron formation.

Time-resolved Element-selective Probing of Charge Carriers in Solar Materials.

We review our recent results on the implementation of picosecond (ps) X-ray absorption spectroscopy to probe the electronic and geometric structure of centres formed by photoexcitation of solar materials such as TiO2 polymorphs and inorganic Cs-based perovskites. The results show electron localization at Ti defects in TiO2 anatase and rutile and small hole polaron formation in the valence band of CsPbBr3, all within 80 ps. This method is promising for the study of the ultrafast time scales of such processes, especially with the advent of the Swiss X-ray Free Electron Laser (SwissFEL).

Hole polarons and p -type doping in boron nitride polymorphs

Boron nitride polymorphs hold great promise for integration into electronic and optoelectronic devices requiring ultrawide band gaps. We use first-principles calculations to examine the prospects for $p$-type doping of hexagonal ($h\ensuremath{-}\mathrm{BN}$), wurtzite ($wz\ensuremath{-}\mathrm{BN}$), and cubic ($c\ensuremath{-}\mathrm{BN}$) boron nitride. Group-IV elements (C, Si) substituting on the N site result in a deep acceptor, as the atomic levels of the impurity species lie above the BN valence-band maximum. On the other hand, group-II elements (Be, Mg) substituting on the B site do not give impurity states in the band gap; however, these dopants lead to the formation of small hole polarons. The tendency for polaron formation is far more pronounced in $h\ensuremath{-}\mathrm{BN}$ compared to $wz\ensuremath{-}\mathrm{BN}$ or $c\ensuremath{-}\mathrm{BN}$. Despite forming small hole polarons, Be acceptors enable $p$-type doping, with ionization energies of 0.31 eV for $wz\ensuremath{-}\mathrm{BN}$ and 0.24 eV for $c\ensuremath{-}\mathrm{BN}$; these values are comparable to the Mg ionization energy in GaN.

Small Polaron Formation Leads to Intrinsic Photoexcited Charge Trapping in α-Fe2O3

The diminished carrier mobility in the ground-state of metal oxide photocatalysts is known to depend on polaron formation and hopping. Photo-excited dynamics and short carrier lifetimes, however, are usually associated with trap states. In this presentation, we investigate the role that small polaron formation plays in the ultrafast localization and trapping of photoexcited carriers in hematite (α-Fe2O3), potentially bridging these two pictures. Ultrafast transient extreme ultraviolet (XUV) spectroscopy on the Fe M2,3 edge measures a sub-5 fs shift in charge density from the oxygen to the iron atom following optical excitation. Small polaron localization of the photoexcited electrons begins on a 100 fs time scale, as measured by a splitting of the Fe M2,3 edge. The subsequent kinetics reproduce the lifetimes typically associated with trap or mid-gap states in hematite. The splitting of the Fe M2,3 edge, however, only matches predictions of polaron localization, and not the pre-edge absorption or bleach expected for mid-gap trap states. The measured polaron formation efficiency also matches the discrepancy between the incident photoconversion efficiency and the visible light absorption of hematite with varying excitation wavelength. These results suggest that sub-100 fs small polaron formation is responsible for the intrinsic recombination and transport issues that limit hematite’s performance, even when techniques such as nanostructuring or trap-state passivation are employed. The role of small-polaron localization in metal oxide photocatalysts, as well as possible materials routes to overcome this effect, will be discussed.

Effect of defects on the small polaron formation and transport properties of hematite from first-principles calculations

Hematite (α-Fe2O3) is a promising candidate as a photoanode material for solar-to-fuel conversion due to its favorable band gap for visible light absorption, its stability in an aqueous environment and its relatively low cost in comparison to other prospective materials. However, the small polaron transport nature in α-Fe2O3 results in low carrier mobility and conductivity, significantly lowering its efficiency from the theoretical limit. Experimentally, it has been found that the incorporation of oxygen vacancies and other dopants, such as Sn, into the material appreciably enhances its photo-to-current efficiency. Yet no quantitative explanation has been provided to understand the role of oxygen vacancy or Sn-doping in hematite. We employed density functional theory to probe the small polaron formation in oxygen deficient hematite, N-doped as well as Sn-doped hematite. We computed the charged defect formation energies, the small polaron formation energy and hopping activation energies to understand the effect of defects on carrier concentration and mobility. This work provides us with a fundamental understanding regarding the role of defects on small polaron formation and transport properties in hematite, offering key insights into the design of new dopants to further improve the efficiency of transition metal oxides for solar-to-fuel conversion.

Application of the Lany–Zunger polaron correction for calculating surface charge trapping

Defect calculations, using density functional theory in a local or semi-local approximation, in transition metal oxides are severely handicapped by the electron self-interaction error. The underestimation of the band gap may cause incorrect occupation of defect states and wrong formation energies, and the underestimated localization of the states disfavors the formation of small polarons. These problems can be avoided by using higher level approximations (GW or a correctly chosen hybrid functional), but those methods are computationally too expensive to be used for calculating surface defects in a periodic slab model. Lany and Zunger have suggested a convenient (low-cost) solution for solving the band-gap and charge delocalization problem, by applying a correction scheme to the standard local or semi-local approximations. Most importantly, the linearity of the total energy as a function of the fractional occupation numbers, is restored, leading to the fulfillment of the generalized Koopmans’ theorem. The method works well in the bulk but, as we show here, it is not accurate on the surface due to the different screening environment. We also show that by making the atom- and angular-momentum dependent parameters of the Lany–Zunger polaron-correction also coordination dependent, it is possible to correctly describe charge trapping in small polaron states on the anatase (1 0 1) and rutile (1 1 0) surfaces at a low computational cost.

Excitation-wavelength-dependent small polaron trapping of photoexcited carriers in α-Fe2O3.

Small polaron formation is known to limit ground-state mobilities in metal oxide photocatalysts. However, the role of small polaron formation in the photoexcited state and how this affects the photoconversion efficiency has yet to be determined. Here, transient femtosecond extreme-ultraviolet measurements suggest that small polaron localization is responsible for the ultrafast trapping of photoexcited carriers in haematite (α-Fe2O3). Small polaron formation is evidenced by a sub-100 fs splitting of the Fe 3p core orbitals in the Fe M2,3 edge. The small polaron formation kinetics reproduces the triple-exponential relaxation frequently attributed to trap states. However, the measured spectral signature resembles only the spectral predictions of a small polaron and not the pre-edge features expected for mid-gap trap states. The small polaron formation probability, hopping radius and lifetime varies with excitation wavelength, decreasing with increasing energy in the t2g conduction band. The excitation-wavelength-dependent localization of carriers by small polaron formation is potentially a limiting factor in haematite's photoconversionefficiency.

Disentangling the role of small polarons and oxygen vacancies in CeO2

The outstanding performance of cerium oxide $(\mathrm{Ce}{\mathrm{O}}_{2})$ as ion conductor or catalyst strongly depends on the ease of $\mathrm{C}{\mathrm{e}}^{4+}\ensuremath{\leftrightarrow}\mathrm{C}{\mathrm{e}}^{3+}$ conversion and oxygen vacancy formation. An accurate description of $\mathrm{C}{\mathrm{e}}^{3+}$ and oxygen vacancy is therefore essential to further progress in this area. Using the HSE06 hybrid functional, we investigate the formation and migration of small polarons $(\mathrm{C}{\mathrm{e}}^{3+})$ and their interaction with oxygen vacancies in $\mathrm{Ce}{\mathrm{O}}_{2}$, considering the small polaron and vacancy as independent entities. Oxygen vacancies are double donors and can bind up to two small polarons, forming a positively charged or neutral complex. We compute the electron self-trapping energy (i.e., energy gain when forming a small polaron), the small-polaron migration barrier, vacancy formation and migration energies, and vacancy-polaron binding energies. We find that small polarons weakly bind to oxygen vacancies, yet this interaction significantly contributes to the activation energy for hopping electronic conductivity. The results are compared with previous calculations and discussed in the light of available experimental data.

Effect of off-center ion substitution in morphotropic lead zirconate titanate composition

A detailed study of the effect of off-center donor ion (Sc3+) substitution on structural, microstructural, optical, dielectric, electrical, and ferroelectric properties of morphotropic composition of lead zirconate titanate electroceramics with the stoichiometric formula Pb0.85Sc0.10Zr0.53Ti0.47O3 (PSZT) and synthesized using a high energy solid-state reaction technique was carried out. Powder x-ray diffractometry was used to identify the stabilized tetragonal phase (space group P4mm) with considerably reduced tetragonal strain, c/a= 1.005. An analysis of the thermal dependence of the Raman results indicated a smooth displacive (ferroelectric-paraelectric) phase transition as revealed by the observed disappearance of the soft modes A1 (1TO) and A1 (2TO) above 460 K. The dielectric response of Pt/PSZT/Pt metal-ferroelectric-metal capacitors was probed over a wide range of thermal excursions (85–600 K) and ac signal frequencies (102–106 Hz). Thermally activated dynamic and static conduction processes indicate hopping conduction mechanism (Eact ≤ 0.015 eV) and the formation of small polarons caused by the electron and/or hole-lattice (phonon) interaction (Eact ≥ 0.1 eV) at low (100–300 K) and high temperatures (300–600 K), respectively. The reduction in remnant polarization obtained is in good agreement with the largely reduced tetragonal strain observed in this sample, (Pr ∝c/a−1). DC conduction is dominated by Poole-Frenkel mechanism that assumes a Coulombic attraction between detrapped electrons and positively charged stationary defect species in the polycrystalline matrix.