On the application of Marcus-Hush theory to small polaron chemical dynamics in oxides: its relationship to the Holstein model and the importance of lattice-orbital symmetries.

The chemical dynamics of small polaron hopping within oxides is often interpreted through two-site variations on Marcus-Hush theory, while from a physics perspective small polaron hopping is more often approached from Holstein's solid-state formalism. Here we seek to provide a chemically oriented viewpoint, focusing on small polaron hopping in oxides, concerning these two phenomenological frameworks by employing both tight-binding modelling and first-principles calculations. First, within a semiclassical approach the Marcus-Hush relations are overviewed as a two-site reduction of Holstein's model. Within the single-band regime, similarities and differences between Holstein derived small polaron hopping and the Marcus-Hush model are also discussed. In this context the emergence of adiabaticity (or, conversely, diabaticity) is also explored within each framework both analytically and by directly evolving the system wavefunction. Then, through first-principles calculations of select oxides we explore how coupled lattice and orbital symmetries can impact on hopping properties - in a manner that is quite distinct typical chemical applications of Marcus-Hush theory. These results are then related back to the Holstein model to explore the relative applicability of the two frameworks towards interpreting small polaron hopping properties, where it is emphasized that the Holstein model offers an increasingly more appealing physicochemical interpretation of hopping processes as band and/or coupling interactions increase. Overall, this work aims to strengthen the physically oriented exploration of small polarons and their physicochemical properties in the growing oxide chemistry community.

First-principles redox energy estimates under the condition of satisfying the general form of Koopmans' theorem: An atomistic study of aqueous iron.

In this work, we explore the relative accuracy to which a hybrid functional, in the context of density functional theory, may predict redox properties under the constraint of satisfying the general form of Koopmans' theorem. Taking aqueous iron as our model system within the framework of first-principles molecular dynamics, direct comparison between computed single-particle energies and experimental ionization data is assessed by both (1) tuning the degree of hybrid exchange, to satisfy the general form of Koopmans' theorem, and (2) ensuring the application of finite-size corrections. These finite-size corrections are benchmarked through classical molecular dynamics calculations, extended to large atomic ensembles, for which good convergence is obtained in the large supercell limit. Our first-principles findings indicate that while precise quantitative agreement with experimental ionization data cannot always be attained for solvated systems, when satisfying the general form of Koopmans' theorem via hybrid functionals, theoretically robust estimates of single-particle redox energies are most often arrived at by employing a total energy difference approach. That is, when seeking to employ a value of exact exchange that does not satisfy the general form of Koopmans' theorem, but some other physical metric, the single-particle energy estimate that would most closely align with the general form of Koopmans' theorem is obtained from a total energy difference approach. In this respect, these findings provide important guidance for the more general comparison of redox energies computed via hybrid functionals with experimental data.

Evolution of Surface Oxidation on Ta3N5 as Probed by a Photoelectrochemical Method.

In this work, we present an in situ method to probe the evolution of photoelectrochemically driven surface oxidation on photoanodes during active operation in aqueous solutions. A standard solution of K4Fe(CN)6-KPi was utilized to benchmark the photocurrent and assess progressive surface oxidation on Ta3N5 in various oxidizing solutions. In this manner, a proportional increase in the surface oxygen concentration was detected with respect to oxidation time and further correlated with a continuous decline in the photocurrent. To discern how surface oxidation alters the photocurrent, we experimentally and theoretically explored its impact on the surface carrier recombination and the interfacial hole transfer rates. Our results indicate that the sluggish photocurrent demonstrated by oxidized Ta3N5 arises because of changes in both rates. In particular, the results suggest that the N-O replacement present on the Ta3N5 surface primarily increases the carrier recombination rate near the surface and to a lesser degree reduces the interfacial hole transfer rate. More generally, this methodology is expected to further our understanding of surface oxidation atop other nonoxide semiconductor photoelectrodes and its impact on their operation.

Charge Transport Phenomena in Heterojunction Photocatalysts: The WO3/TiO2 System as an Archetypical Model.

Recent studies have demonstrated the high efficiency through which nanostructured core-shell WO3/TiO2 (WT) heterojunctions can photocatalytically degrade model organic pollutants (stearic acid, QE ≈ 18% @ λ = 365 nm), and as such, has varied potential environmental and antimicrobial applications. The key motivation herein is to connect theoretical calculations of charge transport phenomena, with experimental measures of charge carrier behavior using transient absorption spectroscopy (TAS), to develop a fundamental understanding of how such WT heterojunctions achieve high photocatalytic efficiency (in comparison to standalone WO3 and TiO2 photocatalysts). This work reveals an order of magnitude enhancement in electron and hole recombination lifetimes, respectively located in the TiO2 and WO3 sides, when an optimally designed WT heterojunction photocatalyst operates under UV excitation. This observation is further supported by our computationally captured details of conduction band and valence band processes, identified as (i) dominant electron transfer from WO3 to TiO2 via the diffusion of excess electrons; and (ii) dominant hole transfer from TiO2 to WO3 via thermionic emission over the valence band edge. Simultaneously, our combined theoretical and experimental study offers a time-resolved understanding of what occurs on the micro- to milliseconds (µs-ms) time scale in this archetypical photocatalytic heterojunction. At the microsecond time scale, a portion of the accumulated holes in WO3 contribute to the depopulation of W5+ polaronic states, whereas the remaining accumulated holes in WO3 are separated from adjacent electrons in TiO2 up to 3 ms after photoexcitation. The presence of these exceptionally long-lived photogenerated carriers, dynamically separated by the WT heterojunction, is the origin of the superior photocatalytic efficiency displayed by this system (in the degradation of stearic acid). Consequently, our combined computational and experimental approach delivers a robust understanding of the direction of charge separation along with critical time-resolved insights into the evolution of charge transport phenomena in this model heterojunction photocatalyst.

Interpreting interfacial semiconductor-liquid capacitive characteristics impacted by surface states: a theoretical and experimental study of CuGaS2.

Semiconductor-liquid interfaces are essential to the operation of many energy devices. Crucially, the operational characteristics of such devices are dependent upon both the flat band potential and doping concentration present in their solid-state semiconducting region. Traditionally, capacitive "linear" Mott-Schottky plots have often been utilized to extract these two parameters. However, significant concentrations of surface states within semiconductor-liquid junctions can give rise to strong non-linearities that prevent an effective linearity-based analysis. In this work, we detail a theoretical approach for estimating both the doping concentration and flat band potential from the capacitive characteristics of semiconductor-liquid junctions heavily impacted upon by surface states. Our theoretical approach is applied to CuGaS2 immersed in an aqueous electrolyte, for which excellent convergent values of the doping concentration and flat band potential are obtained across a wide range of impedance measurement frequencies. The results suggest a marked improvement over a linearity-based approach that could assist the analysis of many types of semiconductor-liquid junctions subject to high concentrations of surface states.

Ergodic and Nonergodic Dynamics of Oxygen Vacancy Migration at the Nanoscale in Inorganic Perovskites.

Perovskites are widely utilized either as a primary component or as a substrate in which the dynamics of charged oxygen vacancy defects play an important role. Current knowledge regarding the dynamics of vacancy mobility in perovskites is solely based upon volume- and/or time-averaged measurements. This impedes our understanding of the basic physical principles governing defect migration in inorganic materials. Here, we measure the ergodic and nonergodic dynamics of vacancy migration at the relevant spatial and temporal scales using time-resolved atomic force microscopy techniques. Our findings demonstrate that the time constant associated with oxygen vacancy migration is a local property and can change drastically on short length and time scales, such that nonergodic states lead to a dramatic increase in the migration barrier. This correlated spatial and temporal variation in oxygen vacancy dynamics can extend hundreds of nanometers across the surface in inorganic perovskites.

Fully Quantized Electron Transfer Observed in a Single Redox Molecule at a Metal Interface.

Long-range electron transfer is a ubiquitous process that plays an important role in electrochemistry, biochemistry, organic electronics, and single molecule electronics. Fundamentally, quantum mechanical processes, at their core, manifest through both electron tunneling and the associated transition between quantized nuclear vibronic states (intramolecular vibrational relaxation) mediated by electron-nuclear coupling. Here, we report on measurements of long-range electron transfer at the interface between a single ferrocene molecule and a gold substrate separated by a hexadecanethiol quantum tunneling barrier. These redox measurements exhibit quantized nuclear transitions mediated by electron-nuclear coupling at 4.7 K in vacuum. By detecting the electric force associated with redox events by atomic force microscopy (AFM), with increasing AFM oscillation amplitude, the intensity of the observed  cantilever resonance frequency shift peak increases and then exhibits a series of discrete steps that are indicative of quantized nuclear transitions. The observed peak shapes agree well with a single-electron tunneling model with quantized nuclear state transitions associated with the conversion of the molecule between oxidized and reduced electronic states. This technique opens the door to simultaneously investigating quantized electron and nuclear dynamics in a diverse range of systems.

Relating Franck-Condon blockade to redox chemistry in the single-particle picture.

In this work, we explore Franck-Condon blockade in the "redox limit," where nuclear relaxation processes occur much faster than the rate of electron transfer. To this end, the quantized rate expressions for electron transfer are recast in terms of a quantized redox density of states (DOS) within a single phonon mode model. In the high temperature regime, this single-particle picture formulation of electron transfer is shown to agree well with the semi-classical rate and DOS expressions developed by Gerischer and Hopfield. Upon incorporation into a two electrode formulation, utilizing the master equation approach, the low temperature quantized conductance features of Franck-Condon blockade are reproduced. Moreover, at sufficiently large reorganization energies, it is argued that Franck-Condon blockade should also be observable in room temperature systems. In general, this work aims to further bridge descriptions of electron transfer and transport in the single-particle picture.

Electrical Stressing Induced Monolayer Vacancy Island Growth on TiSe2.

To ensure practical applications of atomically thin transition metal dichalcogenides, it is essential to characterize their structural stability under external stimuli such as electric fields and currents. Using vacancy monolayer islands on TiSe2 surfaces as a model system, we have observed nonlinear area evolution and growth from triangular to hexagonal driven by scanning tunneling microscopy (STM) subjected electrical stressing. The observed growth dynamics represent a 2D departure from the linear area growth law expected for bulk vacancy clustering. Our simulations of monolayer island evolution using phase-field modeling and first-principles calculations are in good agreement with our experimental observations, and point toward preferential edge atom dissociation under STM scanning driving the observed nonlinear area growth. We further quantified a parabolic growth rate dependence with respect to the tunneling current magnitude. The results could be potentially important for device reliability in systems containing ultrathin transition metal dichalcogenides and related 2D materials subject to electrical stressing.

Measuring Spatially Resolved Collective Ionic Transport on Lithium Battery Cathodes Using Atomic Force Microscopy.

One of the main challenges in improving fast charging lithium-ion batteries is the development of suitable active materials for cathodes and anodes. Many materials suffer from unacceptable structural changes under high currents and/or low intrinsic conductivities. Experimental measurements are required to optimize these properties, but few techniques are able to spatially resolve ionic transport properties at small length scales. Here we demonstrate an atomic force microscope (AFM)-based technique to measure local ionic transport on LiFePO4 to correlate with the structural and compositional analysis of the same region. By comparing the measured values with density functional theory (DFT) calculations, we demonstrate that Coulomb interactions between ions give rise to a collective activation energy for ionic transport that is dominated by large phase boundary hopping barriers. We successfully measure both the collective activation energy and the smaller single-ion bulk hopping barrier and obtain excellent agreement with values obtained from our DFT calculations.

Electron transfer from the perspective of electron transmission: Biased non-adiabatic intermolecular reactions in the single-particle picture.

In this work, we revisit Hopfield's formulation of non-adiabatic electron transfer between uncorrelated redox species within the single-particle picture description of electron transmission commonly applied in solid-state systems. The formulation is applied to a model system, similar to that often found in solid-state electron tunneling studies, consisting of redox species separated by an insulating tunneling barrier. Redox tunneling across such an insulator is predicted to demonstrate a marked asymmetry, ranging from one to three orders of magnitude between forward and reverse bias electron transfer rates, when reactants possess dissimilar reorganization energies. This significant asymmetry is shown to arise from trapezoidal reshaping of the integrated Gamow tunneling barrier and corresponding transmission probability under an applied bias. In general, this work aims to further bridge concepts between the electron transfer and transport communities.

Phase-Field-Crystal Model for Electromigration in Metal Interconnects.

We propose an atomistic model of electromigration (EM) in metals based on a recently developed phase-field-crystal (PFC) technique. By coupling the PFC model's atomic density field with an applied electric field through the EM effective charge parameter, EM is successfully captured on diffusive time scales. Our framework reproduces the well-established EM phenomena known as Black's equation and the Blech effect, and also naturally captures commonly observed phenomena such as void nucleation and migration in bulk crystals. A resistivity dipole field arising from electron scattering on void surfaces is shown to contribute significantly to void migration velocity. With an intrinsic time scale set by atomic diffusion rather than atomic oscillations or hopping events, as in conventional atomistic methods, our theoretical approach makes it possible to investigate EM-induced circuit failure at atomic spatial resolution and experimentally relevant time scales.

The role of relative rate constants in determining surface state phenomena at semiconductor-liquid interfaces.

In this work, we present a theoretical study of surface state occupation statistics at semiconductor-liquid interfaces, as it pertains to the evolution of H2 and O2 through water splitting. Our approach combines semiclassical charge transport and electrostatics at the semiconductor-liquid junction, with a master rate equation describing surface state mediated electron/hole transfer. As a model system we have studied the TiO2-water junction in the absence of illumination, where it is shown that surface states might not always equilibrate with the semiconductor. Non-trivial electrostatics, for example including a shifting of the Mott-Schottky plateau in capacitive measurements, are explored when deep-level surface states partially equilibrate with the liquid. We also endeavor to explain observations of non-linearity present in Mott-Schottky plots, as they pertain to surface state occupation statistics. In general, it is intended that the results of this work will serve to further the use and development of quantitative device modeling techniques in the description of H2 evolution at semiconductor-liquid junctions.

Interfacial Screening in Ultrafast Voltammetry: A Theoretical Study of Redox-Active Monolayers.

The impact of interfacial screening on electron transfer (ET) at ultrashort time scales is theoretically investigated on redox active monolayers by linear sweep voltammetry (LSV). The charging current associated with the nanosecond screening process is an important experimental determinant in finding both the reorganization energy (λ) and electronic coupling (|M|) through ultrafast methods. On the one hand, time dependent decay of the charging current mitigates its impact on the current contribution from faradaic processes, while on the other hand, allowing substantial decay translates into a reduced upper-bound of applicable scan rates, which are crucial for ultrafast characterization. Analysis of the decay in the charging current suggests that the desired screening may be achieved for relatively weakly coupled systems within the charging time constant. For weakly coupled systems, the scan rate corresponding to nanoscale charging time constants appears to be suitable for the ultrafast investigation of ET characteristics. Moreover, the level of screening achieved at nanosecond decay times is shown to change with the coverage of electrode surface by monolayers; which appears to be accompanied by sharp drops in the time constant during successive saturation of interfacial layers by supporting ions (SI). These observations are expected to help design electrochemical device systems with interfaces capable of high faradaic efficiency at ultrafast limits.

Emergence of Metallic Properties at LiFePO4 Surfaces and LiFePO4/Li2S Interfaces: An Ab Initio Study.

The atomic and electronic structures of the LiFePO4 (LFP) surface, both bare and reconstructed upon possible oxygenation, are theoretically studied by ab initio methods. On the basis of total energy calculations, the atomic structure of the oxygenated surface is proposed, and the effect of surface reconstruction on the electronic properties of the surface is clarified. While bare LFP(010) surface is insulating, adsorption of oxygen leads to the emergence of semimetallic behavior by inducing the conducting states in the band gap of the system. The physical origin of these conducting states is investigated. We further demonstrate that deposition of Li2S layers on top of oxygenated LFP(010) surface leads to the formation of additional conducting hole states in the first layer of Li2S surface because of the charge transfer from sulfur p-states to the gap states of LFP surface. This demonstrates that oxygenated LFP surface not only provides conducting layers itself, but also induces conducting channels in the top layer of Li2S. These results help to achieve further understanding of potential role of LFP particles in improving the performance of Li-S batteries through emergent interface conductivity.

A first principles scanning tunneling potentiometry study of an opaque graphene grain boundary in the ballistic transport regime.

We report on a theoretical interpretation of scanning tunneling potentiometry (STP), formulated within the Keldysh non-equilibrium Green's function description of quantum transport. By treating the probe tip as an electron point source/sink, it is shown that this approach provides an intuitive bridge between existing theoretical interpretations of scanning tunneling microscopy and STP. We illustrate this through ballistic transport simulations of the potential drop across an opaque graphene grain boundary, where atomistic features are predicted that might be imaged through high resolution STP measurements. The relationship between the electrochemical potential profile measured and the electrostatic potential drop across such a nanoscale defect is also explored in this model system.

Chemically homogeneous and thermally reversible oxidation of epitaxial graphene.

With its exceptional charge mobility, graphene holds great promise for applications in next-generation electronics. In an effort to tailor its properties and interfacial characteristics, the chemical functionalization of graphene is being actively pursued. The oxidation of graphene via the Hummers method is most widely used in current studies, although the chemical inhomogeneity and irreversibility of the resulting graphene oxide compromises its use in high-performance devices. Here, we present an alternative approach for oxidizing epitaxial graphene using atomic oxygen in ultrahigh vacuum. Atomic-resolution characterization with scanning tunnelling microscopy is quantitatively compared to density functional theory, showing that ultrahigh-vacuum oxidization results in uniform epoxy functionalization. Furthermore, this oxidation is shown to be fully reversible at temperatures as low as 260 °C using scanning tunnelling microscopy and spectroscopic techniques. In this manner, ultrahigh-vacuum oxidation overcomes the limitations of Hummers-method graphene oxide, thus creating new opportunities for the study and application of chemically functionalized graphene.

Wafer-level photocatalytic water splitting on GaN nanowire arrays grown by molecular beam epitaxy.

We report on the achievement of wafer-level photocatalytic overall water splitting on GaN nanowires grown by molecular beam epitaxy with the incorporation of Rh/Cr(2)O(3) core-shell nanostructures acting as cocatalysts, through which H(2) evolution is promoted by the noble metal core (Rh) while the water forming back reaction over Rh is effectively prevented by the Cr(2)O(3) shell O(2) diffusion barrier. The decomposition of pure water into H(2) and O(2) by GaN nanowires is confirmed to be a highly stable photocatalytic process, with the turnover number per unit time well exceeding the value of any previously reported GaN powder samples.

Terminating surface electromigration at the source.

Based on an extensive search across the periodic table utilizing first-principles density functional theory, we discover phosphorus to be an optimal surface electromigration inhibitor on the technologically important Cu(111) surface--the dominant diffusion pathway in modern nanoelectronics interconnects. Unrecognized thus far, such an inhibitor is characterized by energetically favoring (and binding strongly at) the kink sites of step edges. These properties are determined to generally reside in elements that form strong covalent bonds with substrate metal atoms. This finding sheds new light on the possibility of halting surface electromigration via kink blocking impurities.

Formation of graphene p-n superlattices on Pb quantum wedged islands.

On the basis of first-principles calculations within density functional theory, we report on a novel scheme to create graphene p-n superlattices on Pb wedged islands with quantum stability. Pb(111) wedged islands grown on vicinal Si(111) extend over several Si steps, forming a wedged structure with atomically flat tops. The monolayer thickness variation due to the underlying substrate steps is a sizable fraction of the total thickness of the wedged islands and gives rise to a bilayer oscillation in the work function of Pb(111) due to quantum size effects. Here, we demonstrate that when a graphene sheet is placed on the surface of such a Pb wedged island, the spatial work function oscillation on the Pb wedged island surface caused by the underlying steps results in an oscillatory shift in the graphene Dirac point with respect to the Fermi level. Furthermore, by applying an external electric field of ∼0.5 V/Šin the surface normal direction, the Fermi level of the system can be globally tuned to an appropriate position such that the whole graphene layer becomes a graphene p-n superlattice of seamless junctions, with potentially exotic physical properties and intriguing applications in nanoelectronics.