Small Polaron Formation Research Articles

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.

Polaron Stabilization by Cooperative Lattice Distortion and Cation Rotations in Hybrid Perovskite Materials.

Solution-processed organometallic perovskites have rapidly developed into a top candidate for the active layer of photovoltaic devices. Despite the remarkable progress associated with perovskite materials, many questions about the fundamental photophysical processes taking place in these devices, remain open. High on the list of unexplained phenomena are very modest mobilities despite low charge carrier effective masses. Moreover, experiments elucidate unique degradation of photocurrent affecting stable operation of perovskite solar cells. These puzzles suggest that, while ionic hybrid perovskite devices may have efficiencies on par with conventional Si and GaAs devices, they exhibit more complicated charge transport phenomena. Here we report the results from an in-depth computational study of small polaron formation, electronic structure, charge density, and reorganization energies using both periodic boundary conditions and isolated structures. Using the hybrid density functional theory, we found that volumetric strain in a CsPbI3 cluster creates a polaron with binding energy of around 300 and 900 meV for holes and electrons, respectively. In the MAPbI3 (MA = CH3NH3) cluster, both volumetric strain and MA reorientation effects lead to larger binding energies at around 600 and 1300 meV for holes and electrons, respectively. Such large reorganization energies suggest appearance of small polarons in organometallic perovskite materials. The fact that both volumetric lattice strain and MA molecular rotational degrees of freedom can cooperate to create and stabilize polarons indicates that in order to mitigate this problem, formamidinium (FA = HC(NH2)2) and cesium (Cs) based crystals and alloys, are potentially better materials for solar cell and other optoelectronic applications.

Donor defects and small polarons on the TiO2(110) surface

The role of defects in the chemical activity of the rutile TiO2(110) surface remains a rich topic of research, despite the rutile (110) being one of the most studied surfaces of transition-metal oxides. Here, we present results from hybrid functional calculations that reconcile apparently disparate views on the impact of donor defects, such as oxygen vacancies and hydrogen impurities, on the electronic structure of the (110) rutile surface. We find that the bridging oxygen vacancy and adsorbed or substitutional hydrogen are actually shallow donors, which do not induce gap states. The excess electrons from these donor centers tend to localize in the form of small polarons, which are the factual cause of the deep states ∼1 eV below the conduction band, often observed in photoelectron spectroscopy measurements. Our results offer a new framework for understanding the surface electronic structure of TiO2 and related oxides.

Mobile Polaronic States in α-MoO3: An ab Initio Investigation of the Role of Oxygen Vacancies and Alkali Ions.

Some oxides have the ability to trap excess electrons in the form of small polarons. Here, using first-principles techniques, we investigate the interaction of excess electrons with α-MoO3. Polarons are found to be about 0.6 eV more stable than delocalized electrons. They can propagate with a high degree of anisotropicity along different crystallographic directions with the lowest barrier found to be about 0.08 eV. In addition to the band gap photoexcited charge carriers that can populate such polaron states, we investigate the role of oxygen vacancies as an intrinsic source of electrons. We also investigate intercalated alkali ions that can form complexes with the created polarons in the lattice. The alkali-polaron complex (AxMoO6, A = alkali ion) binding energies are relatively low, making it easy for the complex to dissociate. This, coupled with the low polaron migration energies, can generate a non-negligible contribution to electronic conductivity even in the absence of illumination, which is experimentally verified. Combined, this light-induced intercalation of alkali ion in MoO3 and its subsequent deintercalation (complex dissociation) processes lead to a novel self-photocharghing phenomenon.

Charge transport perpendicular to the high mobility plane in organic crystals: Bandlike temperature dependence maintained despite hundredfold anisotropy

Charge carrier mobility in van der Waals bonded organic crystals is strongly dependent on the transfer integral between neighboring molecules, and therefore the anisotropy of charge transport is determined by the molecular arrangement within the crystal lattice. Here we report on temperature dependent transport measurements along all three principal crystal directions of the same rubrene single crystals of high purity. Hole mobilities are obtained from the carrier transit time measured with high-frequency admittance spectroscopy perpendicular to the molecular layers $({\ensuremath{\mu}}_{c})$ and from the transfer characteristics of two field-effect transistor (FET) structures oriented perpendicularly to each other in the layers $({\ensuremath{\mu}}_{a}$ and ${\ensuremath{\mu}}_{b})$. While the measurements of the field-effect channels confirm the previously reported high mobility and anisotropy within the $ab$ plane, we find the mobility perpendicular to the molecular layers in the same crystals to be lower by about two orders of magnitude $({\ensuremath{\mu}}_{c}\ensuremath{\sim}0.2\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}/\mathrm{Vs}$ at $300\phantom{\rule{0.16em}{0ex}}\mathrm{K})$. Although the bandwidth is vanishingly small along the $c$ direction and the transport cannot be coherent, we find ${\ensuremath{\mu}}_{c}$ to increase upon cooling. We show that the delocalization within the high mobility $ab$ plane prevents the formation of small polarons and leads to the observed ``bandlike'' temperature dependence also in the direction perpendicular to the molecular layers, despite the incoherent transport mechanism.

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.

Cation Distribution in Ni-Mn-O Spinel System for the Application of IR Sensors

For NiMn2O4 systems, the mixed valence of manganese on B-sites arises from the displacement of bivalent cations, such as Ni2+, from A-sites to B-sites which results in a corresponding proportion of Mn3+ cations on B-sites disproportionate to Mn2+ and Mn4+, and the Mn2+ cations move to the A-sites to compensate Ni2+ vacancies. With the assistance of random crystal field fluctuations and the mixed valence of manganese eventually leads to the formation of localized small polarons which accomplish a thermally activated hopping conduction between Mn3+ and Mn4+ cations on octahedral sites. In this study, we have investigated the structural and electrical properties of NixMn3-xO4 system. And, we have comprehensively measured the electrical transport mechanism, the temperature coefficient of resistance and infrared detection performance for the application of infrared radiation detectors.

Small polarons and point defects in barium cerate

Barium cerate (${\mathrm{BaCeO}}_{3}$) is a well-known ionic conductor of both hydrogen and oxygen. In applications, it is frequently doped (for instance with Y) to increase stability and promote diffusion. However, the effects of doping and native defects are not fully understood. Computational studies have been stymied by the nature of the conduction band, which is made up of cerium $4f$ states. These states present a challenge to ab initio techniques based on density functional theory within the standard approximations for exchange and correlation. Using a hybrid functional, we investigate the effects of hydrogen impurities and native defects on the electrical and optical properties of ${\mathrm{BaCeO}}_{3}$. We discuss the tendency of excess electrons or holes to localize in the form of small polarons. We also explore the interactions of polarons with hydrogen impurities and oxygen vacancies, and their impact on luminescence properties.

Optical nonlinearities of small polarons in lithium niobate

An overview of optical nonlinearities of small bound polarons is given, which can occur in the congruently melting composition of LiNbO3. Such polarons decisively influence the linear and nonlinear optical performance of this material that is important for the field of optics and photonics. On the basis of an elementary phenomenological approach, the localization of carriers in a periodic lattice with intrinsic defects is introduced. It is applied to describe the binding energies of four electron and hole small polarons in LiNbO3: small free NbNb4+ polarons, small bound NbLi4+ polarons, small bound NbLi4+:NbNb4+ bipolarons, and small bound O− hole polarons. For the understanding of their linear interaction with light, an optically induced transfer between nearest-neighboring polaronic sites is assumed. It reveals spectrally well separated optical absorption features in the visible and near-infrared spectral range, their small polaron peak energies and lineshapes. Nonlinear interaction of light is assigned to the optical formation of short-lived small polarons as a result of carrier excitation by means of band-to-band transitions. It is accompanied by the appearance of a transient absorption being spectrally constituted by the individual fingerprints of the small polarons involved. The relaxation dynamics of the transients is thermally activated and characterized phenomenologically by a stretched exponential behavior, according to incoherent 3D small polaron hopping between regular and defect sites of the crystal lattice. It is shown that the analysis of the dynamics is a useful tool for revealing the recombination processes between small polarons of different charge. Nonlinear interaction of small polarons with light furthermore results in changes of the index of refraction. Besides its causal relation to the transients via Kramers-Kronig relation, pronounced index changes may occur due to optically generated electric fields modulating the index of refraction via the linear electro-optic effect, also. Based on a microscopic picture and by considering the local structural environment of bound polarons, the appearance of photovoltaic currents is explained straightforwardly as a result of the optically induced carrier transfer. Both transient absorption and index changes are spatially confined to the intensity profile of the interacting light allowing for the recording of efficient mixed absorption and phase volume holograms. By means of holographic spectroscopy, these small-polaron based optical nonlinearities are verified either without or with the action of the linear electro-optic effect; their prominent features are highlighted by appropriate experimental studies wherin the ultrafast response on the picosecond time scale is the most recognized one. Based on these findings, the consequences for applications of LiNbO3 in the field of nonlinear optics and photonics are presented. Besides visionary examples like real-time, 3D holographic displays, the impact of optical nonlinearities of small polarons for present applications are discussed with frequency conversion and respective limiting effects, such as green-induced infrared absorption and optical damage, as important example.

Scanning nonlinear absorption in lithium niobate over the time regime of small polaron formation

Nonlinear absorption is studied in presence of small polaron formation in lithium niobate using the z-scan technique and ultrashort laser pulses with pulse durations of 70 – 1,000 fs. A model for the analysis of the transmission loss as a function of pulse duration is introduced that considers (i) the individual contributions of two-photon and small polaron absorption, (ii) the small polaron formation time and (iii) an offset time between the optical excitation of free carriers by two-photon absorption and the appearance of small polarons. It is shown that the model allows for the analysis of the experimentally determined z-scan data with high precision over the entire range of pulse durations using a two-photon absorption coefficient of β = (5.6 ± 0.8) mm/GW. A significant contribution by small polaron absorption to the nonlinear absorption is uncovered for pulse durations exceeding the characteristic small polaron formation time of ≈ 100fs. It can be concluded that the small polaron formation time is as short as (70 – 110) fs and the appearance of small polaron formation is delayed with respect to two-photon absorption by an offset of about 80 fs.

Structural and dielectric properties of doped ferrite nanomaterials suitable for microwave and biomedical applications

The sol–gel auto-combustion method was adopted to synthesize nanomaterials of single-phase X-type hexagonal ferrites with the composition of Sr2−xGdxNi2Fe28−yCdyO46 (x=0.00, 0.02, 0.04, 0.06, 0.08, 0.10 and y=0, 0.1, 0.2, 0.3, 0.4, 0.5). The structural properties were carried out by XRD analysis and the lattice parameters show variation with the doping of Gd–Cd. The average particle size measured by TEM was in the range of 8–10nm which is beneficial in obtaining suitable signal-to-noise ratio in recording media and biomedical applications. The room temperature resistivity enhanced with the increase of the dopant concentration. The increase in resistivity indicates that the synthesized materials can be considered good for the formation of the multilayer chip inductors (MLCIs) as well as for the reduction of eddy current losses. The dielectric constant decreased with the increase in the frequency which is the general reported trend of the hexagonal ferrites and can be explained on the basis of Koop׳s theory and Maxwell–Wagner polarization-model. The abnormal dielectric behavior indicates the formation of small polarons in the material. The maximum value of tangent loss at low frequencies reflects the application of these materials in medium frequency devices (MF).

Period-doubling reconstructions of semiconductor partial dislocations

Atomic-scale understanding and control of dislocation cores is of great technological importance, because they act as recombination centers for charge carriers in optoelectronic devices. Using hybrid density-functional calculations, we present period-doubling reconstructions of a 90° partial dislocation in GaAs, for which the periodicity of like-atom dimers along the dislocation line varies from one to two, to four dimers. The electronic properties of a dislocation change drastically with each period doubling. The dimers in the single-period dislocation are able to interact, to form a dispersive one-dimensional band with deep-gap states. However, the inter-dimer interaction for the double-period dislocation becomes significantly reduced; hence, it is free of mid-gap states. The Ga core undergoes a further period-doubling transition to a quadruple-period reconstruction induced by the formation of small hole polarons. The competition between these dislocation phases suggests a new passivation strategy via population manipulation of the detrimental single-period phase. Theoretical simulations suggest a pathway toward reducing the population of efficiency-draining defects in gallium arsenide (GaAs) solar cells. Modern, multilayered light-harvesting devices can have lattice mismatches at interfaces where the crystals meet, and this can create dislocations - two-dimensional ribbons of atoms that disrupt the bulk crystal structure. Joongoo Kang from DGIST in Daegu, Korea, and collaborators at the USA's National Renewable Energy Laboratory have used sophisticated density-functional calculations to analyse GaAs dislocations that had different patterns of partnered atomic dimers. Repetitive ‘single-period’ dimers had deep gap states that degrade the optoelectronic performance. But less dense ‘double-period’ and newly discovered ‘quadruple-period’ structures can compete with the single-period phase and limit its influence — a passivation strategy that may be realized through shallow p-type doping of GaAs, suggest the researchers. Using hybrid density-functional calculations, we present period-doubling reconstructions of a 90° partial dislocation in GaAs, for which the periodicity of like-atom dimers along the dislocation line varies from one to two, to four dimers. The electronic properties of a dislocation change drastically with each period doubling, suggesting a new passivation strategy by biasing the competition between these phases through the tuning of the carrier density in the dislocation.

Electrical Properties of LiTaO3 Single Crystals at 290–450 K

The investigation of the temperature dependence of the dark electrical conductivity of as grown LiTaO3 single crystals and the crystals reduced in vacuum was carried out. The reducing of the LT in vacuum at 830 K causes a removal diffusion of hydrogen and a partial loss of oxygen. It leads to recharging of transition metal impurities to the lowest valence state and blocking of hopping electronic conductivity. After filling of electronic traps, the process of small polaron formation takes place.

Defect Physics, Delithiation Mechanism, and Electronic and Ionic Conduction in Layered Lithium Manganese Oxide Cathode Materials

Layered LiMnO$_2$ and Li$_2$MnO$_3$ are of great interest for lithium-ion battery cathodes because of their high theoretical capacities. The practical application of these materials is, however, limited due to poor electrochemical performance. We herein report a comprehensive first-principles study of defect physics in LiMnO$_2$ and Li$_2$MnO$_3$ using hybrid-density functional calculations. We find that manganese antisites have low formation energies in LiMnO$_2$ and may act as nucleation sites for the formation of impurity phases. The antisites can also occur with high concentrations in Li$_2$MnO$_3$; however, unlike in LiMnO$_2$, they can be eliminated by tuning the experimental conditions during preparation. Other intrinsic point defects may also occur and have an impact on the materials' properties and functioning. An analysis of the formation of lithium vacancies indicates that lithium extraction from LiMnO$_2$ is associated with oxidation at the manganese site, resulting in the formation of manganese small hole polarons; whereas in Li$_2$MnO$_3$ the intrinsic delithiation mechanism involves oxidation at the oxygen site, leading to the formation of bound oxygen hole polarons $\eta_{\rm O}^{+}$. The layered oxides are found to have no or negligible bandlike carriers and they cannot be doped n- or p-type. The electronic conduction proceeds through hopping of hole and/or electron polarons; the ionic conduction occurs through lithium monovacancy and/or divacancy migration mechanisms. Since $\eta_{\rm O}^{+}$ is not stable in the absence of negatively charged lithium vacancies in bulk Li$_2$MnO$_3$, the electronic conduction near the start of delithiation is likely to be poor. We suggest that the electronic conduction associated with $\eta_{\rm O}^{+}$ and, hence, the electrochemical performance of Li$_2$MnO$_3$ can be improved through nanostructuring and/or ion substitution.

Possible polaron formation of zigzag graphene nano-ribbon in the presence of Rashba spin–orbit coupling

In this article we study the role of Rashba spin–orbit coupling and electron–phonon interaction on the electronic structure of zigzag graphene nanoribbon with different width. The total Hamiltonian of nanoribbon is written in the tight binding form and the electron–electron interaction is modeled in the Hubbard term. We used a unitary transformation to reach an effective Hamiltonian for nano ribbon in the presence of electron–phonon interaction. Our results show that small Rashba spin orbit coupling annihilates the anti-ferromagnetic phase in the zigzag edges of ribbon and the electron–phonon interaction yields small polaron formation in graphene nano ribbon. Furthermore, Rashba type spin–orbit coupling increases (decreases) the polaron formation energy for up (down) spin state.

Interband and polaronic excitations inYTiO3from first principles

YTiO3, as a prototypical Mott insulator, has been the subject of numerous experimental investigations of its electronic structure. The onset of absorption in optical conductivity measurements has generally been interpreted to be due to interband transitions at the fundamental gap. Here we re-examine the electronic structure of YTiO3 using density functional theory with either a Hubbard correction (DFT+U) or a hybrid functional. Interband transitions turn out to be much higher in energy than the observed onset of optical absorption. However, in case of $p$-type doping, holes tend to become self-trapped in the form of small polarons, localized on individual Ti sites. Exciting electrons from the occupied lower Hubbard band to the small-polaron state then leads to broad infrared absorption, consistent with the onset in the experimental optical conductivity spectra.

Anisotropic polaron localization and spontaneous symmetry breaking: Comparison of cation-site acceptors in GaN and ZnO

The behavior of cation substitutional hole doping in GaN and ZnO is investigated using hybrid density functional calculations. Our results reveal that Mg substitution for Ga $({\mathrm{Mg}}_{\mathrm{Ga}})$ in GaN can assume three different configurations. Two of the configurations are characterized by the formation of defect-bound small polaron (i.e., a large structural distortion accompanied by hole localization on one of the neighboring N atoms). The third one has a relatively small but significant distortion that is characterized by highly anisotropic polaron localization. In this third configuration, ${\mathrm{Mg}}_{\mathrm{Ga}}$ exhibits both effective-mass-like and noneffective-mass-like characters. In contrast, a similar defect in ZnO, ${\mathrm{Li}}_{\mathrm{Zn}}$, cannot sustain the anisotropic polaron in the hybrid functional calculation, but undergoes spontaneous breaking of a mirror symmetry through a mechanism driven by the hole localization. Finally, using ${\mathrm{Na}}_{\mathrm{Zn}}$ in ZnO as an example, we show that the deep acceptor levels of the small-polaron defects could be made shallower by applying compressive strain to the material.

Analog superconducting quantum simulator for Holstein polarons

We propose an analog quantum simulator for the Holstein molecular-crystal model based on a superconducting circuit QED system in the dispersive regime. By varying the driving field on the superconducting resonators, one can readily access both the adiabatic and anti-adiabatic regimes of this model. Strong e-ph coupling required for small-polaron formation can also be reached. We show that small-polaron state of arbitrary quasimomentum can be generated by applying a microwave pulse to the resonators. We also show that significant squeezing in the resonator modes can be achieved in the polaron-crossover regime through a measurement-based scheme.

The origin of p-type conductivity in ZnM2O4 (M = Co, Rh, Ir) spinels

ZnM2O4 (M = Co, Rh, Ir) spinels are considered as a class of potential p-type transparent conducting oxides (TCOs). We report the formation energy of acceptor-like defects using first principles calculations with an advanced hybrid exchange-correlation functional (HSE06) within density functional theory (DFT). Due to the discrepancies between the theoretically obtained band gaps with this hybrid functional and the - scattered - experimental results, we also perform GW calculations to support the validity of the description of these spinels with the HSE06 functional. The considered defects are the cation vacancy and antisite defects, which are supposed to be the leading source of disorder in the spinel structures. We also discuss the band alignments in these spinels. The calculated formation energies indicate that the antisite defects ZnM (Zn replacing M, M = Co, Rh, Ir) and VZn act as shallow acceptors in ZnCo2O4, ZnRh2O4 and ZnIr2O4, which explains the experimentally observed p-type conductivity in those systems. Moreover, our systematic study indicates that the ZnIr antisite defect has the lowest formation energy in the group and it corroborates the highest p-type conductivity reported for ZnIr2O4 among the group of ZnM2O4 spinels. To gain further insight into factors affecting the p-type conductivity, we have also investigated the formation of localized small polarons by calculating the self-trapping energy of the holes.

High-density Two-Dimensional Small Polaron Gas in a Delta-Doped Mott Insulator

Heterointerfaces in complex oxide systems open new arenas in which to test models of strongly correlated material, explore the role of dimensionality in metal-insulator-transitions (MITs) and small polaron formation. Close to the quantum critical point Mott MITs depend on band filling controlled by random disordered substitutional doping. Delta-doped Mott insulators are potentially free of random disorder and introduce a new arena in which to explore the effect of electron correlations and dimensionality. Epitaxial films of the prototypical Mott insulator GdTiO3 are delta-doped by substituting a single (GdO)+1 plane with a monolayer of charge neutral SrO to produce a two-dimensional system with high planar doping density. Unlike metallic SrTiO3 quantum wells in GdTiO3 the single SrO delta-doped layer exhibits thermally activated DC and optical conductivity that agree in a quantitative manner with predictions of small polaron transport but with an extremely high two-dimensional density of polarons, ~7 × 1014 cm−2.