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At least 487 records · Page 27

Computational Fermi Level Engineering and Doping-Type Conversion of Ga2O3 Via Three-Step Processing

Ga2O3 is being actively explored for power electronics, deep-ultraviolet optoelectronics, and other applications due to its ultra-wide bandgap and low projected fabrication cost of large-size and high-quality crystals. N-type doping of Ga2O3 can be achieved and tuned, but p-type doping faces fundamental obstacles due to deep character of acceptor levels and polaron transport of resulting holes. However, successful engineering of Ga2O3 based devices requires critical control of doping density, Fermi level position, and free carrier concentration, providing opportunities for predictive process simulation. We use first-principles defect theory and defect equilibrium calculations to simulate a 3-step growth-annealing-quench protocol for hydrogen assisted Mg doping in Ga2O3, taking into account the hydrogen-oxygen-water gas phase equilibrium. We predict type conversion to a net p-type regime following O-rich annealing after growth under reducing conditions in the presence of H2. This process is similar to the Mg acceptor activation by H removal in GaN. We show that there is an optimal temperature that maximizes the net acceptor density during the equilibrium annealing step for a given Mg doping level. Quenching of non-equilibrium annealed samples then results in a Fermi level EF below mid-gap down to about EV +1.5 eV, creating a significant number of uncompensated neutral MgGa0 acceptors. The resulting free hole concentration in quenched samples is very low (109 – 1012 cm-3) due to deep energy level of these Mg acceptors, but this type converted Ga2O3 material can create a significant built-in field in a p-n junction with an adjoining n-type material. Additionally, the electron concentration is greatly suppressed in such acceptor-doped Ga2O3, which could enable the use as a current blocking layer to fabricate normally-off (enhancement-mode) vertical Ga2O3 based metal-oxide-semiconductor field effect transistors (MOSFETs), and as a guard ring for edge termination in MOSFETs and Schottky barrier diodes (SBDs) with increased breakdown voltage.

CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS,M↗

Significant Role of Oxygen Dopants in Photocatalytic PFCA Degradation over h-BN

The activation of the C(sp 3 )–F bond is extremely difficult due to its unreactive nature. The importance of this bond activation is recently highlighted because extensive distribution of perfluorocarboxylic acids (PFCAs) (C n F 2n+1 COOH) has emerged as a challenging environmental issue. Photocatalytic degradation of PFCAs over a few semiconducting light absorbers is known to remove these water and soil resilient contaminants but with limited efficiency. This work reports density functional theory calculations, through which we present a detailed mechanistic study of photocatalytic degradation of CF 3 COOH (the shortest member of the PFCA family) over hexagonal boron nitride (h-BN). Here, our results clearly demonstrate that the existence of point defects is necessary to activate the h-BN plane for photocatalytic dissociation of the C–F bond. Specifically, we show that vacancies create strong Lewis acid or base sites (B or N vacancy, respectively) that facilitate the activation of the C(sp 3 )–F bond considerably. Furthermore, this study presents vivid theoretical evidence for the significant role of oxygen dopants, which mitigate the strength of the active sites and promote PFCA degradation over h-BN. Our calculations suggest that while the very stable intermediates generated during the reaction, in the case of h-BN with B or N vacancies, practically poison the catalyst, oxygen dopants make the degradation much more plausible and controllable. This work thus provides both an explanation for recently observed photocatalytic activity of h-BN to decompose PFCAs and valuable insights for exploring defected two-dimensional materials for activating and removing the fluorine-containing contaminants from water and soil.

54 ENVIRONMENTAL SCIENCES↗

Oxygen and carbon in silicon

The properties of the early transistors were determined by the minority-carrier lifetime, as is the silicon photovoltaic solar cell. Most of the devices on the modern integrated circuits are majority carrier devices, in part to avoid this lifetime dependence. The micro-electronics industry typically starts with wafers with a minority-carrier lifetime of 1000 micro-seconds, but during device fabrication this lifetime is reduced to beflow 1 micro-second, in spite of extraordinary cleanliness and precautions. Process-induced defects (PID) include point defects, defect complexes, line defects, and bulk precipitates. One of the aspects that needs to be better understood is the nature of minority carrier recombination at line defects and at precipitates. Some of the PIDs are known to be related to the fast-diffusers of the iron-series transition elements. One of the common techniques of dealing with these elements is intrinsic gettering by the oxygen precipitates. But even in the gettered state, there may be a residual effect on the lifetime. Oxygen is an almost ubiquitous impurity in silicon and plays an important role in both integrated circuits and solar cells. The isolated oxygen interstitial is electrically inactive, but in its various aggregated forms it has a variety of electrical activities. The agglomeration and precipitation of oxygen, including impurity gettering and the complicating role of carbon, is discussed.

Corbett, J. W.↗

Excited States of Crystalline Point Defects with Multireference Density Matrix Embedding Theory

Accurate and affordable methods to characterize the electronic structure of solids are important for targeted materials design. Embedding-based methods provide an appealing balance in the trade-off between cost and accuracy-particularly when studying localized phenomena. Here, we use the density matrix embedding theory (DMET) algorithm to study the electronic excitations in solid-state defects with a restricted open-shell Hartree-Fock (ROHF) bath and multireference impurity solvers, specifically, complete active space self-consistent field (CASSCF) and n-electron valence state second-order perturbation theory (NEVPT2). In this work, we apply the method to investigate the electronic excitations in an oxygen vacancy (OV) on a MgO(100) surface and find absolute deviations within 0.05 eV between DMET using the CASSCF/NEVPT2 solver, denoted as CAS-DMET/NEVPT2-DMET, and the nonembedded CASSCF/NEVPT2 approach. Next, we establish the practicality of DMET by extending it to larger supercells for the OV defect and a neutral silicon vacancy in diamond where the use of nonembedded CASSCF/NEVPT2 is extremely expensive.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Novel and effective surface passivation for high efficiency n- and p-type Silicon solar cell

The project objective was to develop a novel Si surface passivation method using chalcogens, sulfur (S) and/or selenium (Se), as passivating elements, to withstand industry-standard high temperature contacting and metallization schemes for p-type Si based passivated emitter and rear contact (p-PERC) solar cells. The back surface passivation of PERC cells has been improved drastically with the invention and successful application of an Al 2 O 3 passivation layer. However, the front n + diffused junction surface is still poorly passivated by the standard amorphous silicon nitride (SiNx) anti-reflection coating (ARC) layer. This project sought to address the passivation challenges of both front n+ emitter and undiffused p-Si back surface. Improved p-PERC solar cell performance with open circuit voltage (V OC ) > 680 mV and efficiency of 22% were targeted to validate superior defect passivation properties as compared to standard SiO 2 / Al 2 O 3 passivation. During this project, we systematically investigated process-structure-properties-performance relationships of this novel advanced defect passivation approach. The S/Se passivation was carried out by reacting industrial Czochralski (Cz) Si wafers in H 2 S and H 2 Se gases in a chemical vapor deposition (CVD) reactor at temperatures up to 700°C. After an exhaustive optimization of the process parameters (temperature, time, and gas concentration), we established an optimized process and demonstrated extremely low surface recombination velocities (SRVs) of 1.5 cm/s and 8 cm/s on n-type and p-type Si, respectively, by S-passivation. In-depth surface and interface characterization were performed using soft x-ray and photoelectron spectroscopies (XPS, UPS, XES), combined with capacitance-voltage-frequency (C-V-f) measurements, to decipher the surface chemical/electronic structure and interface defect state densities. These measurements provided critical understanding of the defect passivation mechanism and elucidated the presence of surface S-Si bonds, a reduction of surface dipoles, and low interface state densities (D it ) < 10 11 cm -2 ev -1 . We also found that the Se-passivation is inferior to the S-passivation (by at least one order of magnitude in SRV). Application of the optimized S-passivation to the n+ diffused emitter surface led to a low surface recombination current density, J0 ≈ 40 fA/cm 2 (~ 1/4 of the industry-standard SiNx-passivation), and high implied V OC (686 mV) in p-PERC solar cell structures. The S-passivation process also was found to improve the bulk quality of the p-type Si, better than the SiO 2 or Al 2 O 3 passivation processes. After successful demonstration of efficient passivation of Si surface defects by S, we extensively studied the air, thermal, and illumination stability of the passivation structure. S-passivation itself degrades in air due to competing reactions with moisture and oxygen to form oxides, which can be eliminated by a SiNx capping layer (also acting as a anti-reflective coating). After SiNx process optimization, we demonstrated illumination and thermally stable S-passivation with SRV < 5 cm/s and J 0 < 80 fA/cm 2 . These enhancements in Si passivation, incorporated into p-PERC cells, achieved an efficiency of 19.93% with V OC = 649 mV, using manufacturing metallization and contacting schemes. The low cell performance (cell V OC is much less than the implied V OC = 686 mV, anticipated from surface passivation) was identified due to degradation of S-passivation during the metal firing step (out-diffusion of S from the Si interface to the SiNx surface). The S-passivation of Si surfaces shows significant promise with excellent passivation quality, essential for high performance (high V OC , high efficiency) solar cells. Integration of this innovative defect passivation into devices, however, demands further development of the capping layer, low temperature (<700°C) metallization process, and/or engineering of advanced device structures. Surface passivation-dominated advanced Si solar cells, such as tunnel oxide passivated contacts and Si heterojunctions, are increasingly of interest due to their high-performance potential and will have a growing photovoltaic market share in the near future.

14 SOLAR ENERGY↗

Coherent Erbium Spin Defects in Colloidal Nanocrystal Hosts

We demonstrate nearly a microsecond of spin coherence in Er 3+ ions doped in cerium dioxide nanocrystal hosts, despite a large gyromagnetic ratio and nanometric proximity of the spin defect to the nanocrystal surface. The long spin coherence is enabled by reducing the dopant density below the instantaneous diffusion limit in a nuclear spin-free host material, reaching the limit of a single erbium spin defect per nanocrystal. We observe a large Orbach energy in a highly symmetric cubic site, further protecting the coherence in a qubit that would otherwise rapidly decohere. Spatially correlated electron spectroscopy measurements reveal the presence of Ce 3+ at the nanocrystal surface, which likely acts as extraneous paramagnetic spin noise. Even with these factors, defect-embedded nanocrystal hosts show tremendous promise for quantum sensing and quantum communication applications, with multiple avenues, including core-shell fabrication, redox tuning of oxygen vacancies, and organic surfactant modification, available to further enhance their spin coherence and functionality in the future.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

NASA research on refractory compounds.

The behavior and properties of the refractory carbides, nitrides, and borides are being investigated by NASA as part of its research aimed at developing superior heat resistant materials for aerospace applications. Fundamental studies on the electronic and defect structures of the carbides indicate that there is promise for improving the strength and ductility of these materials. Studies of the zirconium-carbon-oxygen system show that zirconium oxycarbides of different compositions and lattice parameters can be formed between 1500 and 1900 C and are stable below 1500 C. More applied studies show that hot working generally improves the microstructure and therefore the strength of TiC and NbC. Sintering studies on UN indicate that very high densities can be achieved. Hot pressing of cermets of HfN and HfC produces good mechanical properties for high temperature bearing applications.

Gangler, J. J.↗

JPL lithium doped solar cell development program

One of the most significant problems encountered in the use of silicon solar cells in space is the sensitivity of the device to electron and proton radiation exposure. The p-diffused-into-n-base solar cells were replaced with the more radiation tolerant n-diffused-into-p-base solar cells. Another advancement in achieving greater radiation tolerance was the discovery that the addition of lithium to n-base silicon resulted in what appeared to be annealing of radiation-induced defects. This phenomenon is being exploited to develop a high efficiency radiation resistant lithium-doped solar cell. Lithium-doped solar cells fabricated from oxygen-lean and oxygen-rich silicon were obtained with average initial efficiencies of 11.9% at air mass zero and 28 C, as compared to state-of-the-art n-p cells fabricated from 10 ohm cm silicon with average efficiencies of 11.3% under similar conditions. Lithium-doped cells demonstrated the ability to withstand three to five times the fluence of 1-MeV electrons before degrading to a power equivalent to state-of-the-art solar cells. The principal investigations are discussed with respect to fabrication of high efficiency radiation resistant lithium-doped cells, including starting material, p-n junction diffusion, lithium source introduction, and lithium diffusion.

Berman, P. A.↗

High quality flame deposited diamond films for infrared optical windows

The IR absorption in polycrystalline diamond films deposited in oxygen-acetylene flames is characterized using FTIR. The one-phonon absorption coefficient in the region from 7 to 12 microns that is related to extrinsic defects in the diamond films shows a strong dependence on the flame conditions as well as the substrate temperature. A high degree of diamond crystalline perfection, as judged from the undetectable one-phonon absorption, is achieved under the optimized deposition conditions for our flame setup. This is further supported by the sharp Raman peak at 1332/cm as well as the high purity in crystal orientation according to the X-ray diffraction pattern measured for the high quality diamond films.

Tzeng, Y.↗

Role of Undercoordinated Sites for the Catalysis in Confined Spaces Formed by Two-Dimensional Material Overlayers

Adding a two-dimensional (2D) overlayer on a metal surface is a promising route for activating reactants confined in the interfacial space. However, an atomistic understanding of the role played by undercoordinated sites of the 2D overlayer in the activation of molecules in this nanoscaled confined space is yet to be developed. In this paper, we study CO dissociation as a prototypical reaction to investigate CO activation in the confined space enclosed by Rh(111) and a monolayer of hexagonal boron nitride (h-BN). The effect of the space size (i.e., the distance between h-BN and the metal surface), the type of undercoordinated sites, and the size of the defect are explicitly studied by density functional theory with dispersion correction. The following temperature-programmed X-ray photoelectron spectroscopy measurement suggests that a small portion of the CO dissociated during the desorption, leaving the residual atomic oxygen incorporated into the h-BN lattice, which validates the theoretical prediction. Finally, the combination of theory and experiment calls for further attention to be paid to the role of undercoordinated sites in the 2D overlayers in confined systems forming potential new catalytic environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Task Sharing of Proton Incorporation in Vertically Aligned Nanocomposite Triple Conductors: Growth, Structure, and Surface Exchange Kinetics

As protonic ceramic electrolysis cells emerge for efficient H 2 production, there is a need to develop air electrode materials enabling fast, durable steam splitting and proton incorporation. Single-phase triple conductors may fail to satisfy the myriad performance/stability requirements, and their critical charge-carriers (holes, oxygen vacancies, and protons) are in competition, limiting their concentrations. Instead, we propose task-sharing, vertically aligned nanocomposites (VANs), comprising a proton conductor (BaZr 0.9 Y 0.1 O 3-δ ) and a redox-active mixed ionic electronic conductor (Ce 0.9 Pr 0.1 O 2-δ ), that may enable rapid proton surface exchange at the solid–gas interface and transport along the solid–solid heterointerfaces. We grew VANs by pulsed laser deposition and investigated the interplay between their processing conditions, structure, and proton and oxygen surface exchange kinetics. We varied the substrate temperature, laser repetition rate, laser fluence, and processing oxygen pressure. The crystallinity and phases were characterized by grazing-incidence X-ray diffraction, and the strain and structural order as a function of depth were evaluated by angle-dependent synchrotron X-ray pair distribution function analysis. To evaluate the potential for interdiffusion, the formation energies of substitutional defects were simulated with density functional theory. Corresponding structural analysis and elemental mapping were performed by scanning/transmission electron microscopy, energy-dispersive X-ray spectroscopy, and electron energy-loss spectroscopy, indicating distinct nanoscale compositional regions with a hierarchical structure embedded in individual VANs columns and minimal interdiffusion across a bilayer film. Proton and oxygen surface exchange coefficients (k H , k O ) and polarization resistances were evaluated by electrical and optical relaxations and impedance spectroscopy of VAN-incorporated protonic ceramic electrochemical cells, respectively, at 400–500 °C, demonstrating values comparable to some of the best-known triple and mixed conductors.

36 MATERIALS SCIENCE↗

Primary intrinsic defects and their charge transition levels in β–Ga 2 O 3

A steady-state photocapacitance (SSPC) setup directly connected to the beamline of a MeV ion implanter is utilized to study primary intrinsic defects in β – Ga 2 O 3 generated by He implantation at cryogenic temperatures (120 K). At low temperatures, the migration of defects is suppressed, and hence the generation of primary intrinsic defects is expected to prevail. SSPC measurements reveal defect-related optical transitions in halide vapor-phase epitaxy (HVPE) -grown β – Ga 2 O 3 thin films with onset energies at 1.3 ( T 1 ) , 1.7 ( T 2 ) , 1.9 ( T 3 ) , 2.6 ( T 4 ) , 3.7 ( T 5 ) , and 4.2 eV ( T 6 ) . T 2 , T 4 , T 5 , and T 6 were observed in as-received HVPE-grown β – Ga 2 O 3 thin films, whereby T 2 is only sporadically observed. The introduction rates for T 3 , T 4 , as well as T 6 indicate an origin related to primary intrinsic defects. Notably, T 1 and T 3 are only observed after He implantation at cryogenic temperatures. Hybrid-functional calculations were performed to estimate the optical absorption cross-section spectra for the gallium ( Ga i ) and oxygen ( O i ) interstitials as well as the corresponding vacancies ( V Ga and V O , respectively), and compared with the measured onsets for optical absorption found by SSPC measurements. Indeed, we propose T 3 to be associated with Ga i ( + / + 2 ) and/or V GaI ( - 3 / - 2 ) , while T 4 is suggested to be related to V O K ( 0 / + ) ( K = I , II , III ) and/or V GaII ( - 3 / - 2 ) . Additionally, several further charge-state transition levels associated with V GaI and V GaII may contribute to T 4 and T 6 . We further studied the kinetics of the defects created with He implantation by exposing the sample to room temperature. The kinetics observed for T 3 and T 4 further support the proposed assignments of the corresponding defect signatures.

36 MATERIALS SCIENCE↗

Point defect induced incommensurate dipole moments in the K Ca 2 Nb 3 O 10 Dion-Jacobson layered perovskite

Local structural distortions due to isolated atomic defects and defect complexes strongly affect the macroscopic properties of oxide ceramics. While the characterization of local defect structures is more common in simple AB O 3 perovskites, unambiguous determination of the same in layered perovskites is more difficult due to their complex crystal structures. In this study, we combined x-ray pair distribution function and density functional theory calculations to characterize the structure of cation-oxygen divacancy pairs in a Dion-Jacobson (D-J) layered perovskite. Our results indicate that local incommensurate dipole moments with polarization density in the range of ~ 0.1–17μC/cm 2 are created due to divacancy-induced structural distortions in the D-J phase K Ca 2 Nb 3 O 10 . This is comparable with defect dipole moments observed in well-known perovskite ferroelectrics. The current results imply that controlling the atomic defects can potentially lead to significant control of dielectric properties in D-J layered perovskites.

3-dimensional systems↗

Defect Generation and Evolution in Irradiated Epitaxial Films and Heterostructures of Fe 3 O 4 and Cr 2 O 3

Abstract The functionality of nuclear structural materials, sensors, and microelectronics in harsh environments such as radiation relies on understanding defect generation and evolution processes in oxide layers. The initial radiation response of epitaxial thin films of Fe 3 O 4 (111), Cr 2 O 3 (0001), and Fe 3 O 4 (111)/Cr 2 O 3 (0001) heterostructures deposited on Al 2 O 3 (0001) by oxygen‐assisted molecular beam epitaxy and irradiated with 200 keV He + is characterized. X‐ray diffraction and X‐ray absorption near edge spectroscopy showed that the Cr 2 O 3 layers underwent significant lattice expansion and disordering under irradiation, whereas the Fe 3 O 4 layers do not exhibit noticeable changes. In contrast, positron annihilation spectroscopy revealed an evolution of cation vacancy point defects in the Fe 3 O 4 layers into larger vacancy clusters with increasing irradiation, while the cation vacancies in Cr 2 O 3 remained primarily as single vacancies and small clusters. The results suggest that the Fe 3 O 4 lattice can utilize the free volume of the larger vacancy clusters to relax but the small vacancies in the Cr 2 O 3 lattice do not facilitate relaxation. Comparing defect concentrations in the single layer films versus the heterostructure suggests that point defects may cross the interface from Fe 3 O 4 into Cr 2 O 3 . Together, these results enhance the understanding of the initial defect evolution mechanisms in oxide layers in harsh irradiation environments.

36 MATERIALS SCIENCE↗

Equilibrium distribution of point defects in Fe-Y-O as a typical representative of nanocluster-strengthened alloys

The statistical mechanic approach has been used to estimate the equilibrium defect distribution in a multiphase system by minimizing its free energy using microstructural characteristics and a finite set of defects obtained by first-principles calculations. Recently the approach was extended to take in consideration defects at the interface of the precipitate and matrix. Herein we apply the developed approach to the investigation of the stability of bcc Fe containing yttria, Y 2 O 3 , nanoclusters as a prototype of nanostructured ferritic alloys. It has been obtained that (100)Fe-O interface is unstable with respect to vacancies production. In a contrast to (100)Fe-O interface, the so called Klim interface is stable, i.e. local vacancy concentration at this interface at 600 K is below 10 -12 . It has been demonstrated that due to large defect formation energies the ODS particles are extremely stable and the main defect corresponds to Fe atoms substitute Y in Y 2 O 3 precipitate. Moreover, under thermodynamic equilibrium condition, the preexist vacancies in bulk Fe do not accumulate oxygen atom. The later observation not necessarily forbid the existence of a large amount of preexisting Fe vacancy - oxygen atom clusters at the initial stages of alloy formation far from equilibrium.

36 MATERIALS SCIENCE↗

Design Principles in Engineering of Multigrain Nanocatalysts via Multiscale Electronic Structure Characterization

Engineering grain boundary (GB) strain provides a promising pathway to tune the catalytic properties of nanocrystals. However, structural heterogeneity from random grain orientation and geometry has limited clear structure–property correlations. Here, we utilize a multigrain Co3O4/Mn3O4 core/shell nanocrystal platform as a model system to systematically investigate how geometric misfit strain at GBs serves as catalytically active sites for the oxygen reduction reaction. Through precise subnanometer-level control over grain morphology and by integrating multiscale electronic structure characterization, we identify the electronic structural signature of GB defects and establish a direct correlation between localized strain fields and modified electronic states. Strain modulation at GBs alters the eg orbital energy levels, with elongation along the z-axis combined with shear strain stabilizing the eg states, in contrast to the destabilization observed under pure shear strain. This stabilization mechanism enhances the electrocatalytic activity and selectivity of strained GBs compared with strain-relaxed grain surfaces. Furthermore, we reveal that GBs exhibit a radial strain gradient, producing a spatial energy shift that further modulates local electronic structures, as resolved through the classification of electron energy loss spectroscopy data. Together, these findings demonstrate that geometric misfit strain enables precise tuning of grain geometry and the resulting electronic structures, offering a robust strategy for engineering next-generation nanocatalysts.

Cho, Min Gee↗

Behavior of lithium in irradiated solar cells.

The current state of the art in radiation resistant lithium-doped silicon solar cells is reviewed. Fabrication techniques are reviewed. Characteristics of lithium-doped cells are discussed. Behavior of lithium-doped cells during 1 MeV electron irradiation are studied for various types of cells. Effects of variations in lithium and oxygen concentration are shown and discussed. Capacitance measurements at various voltages, frequencies and temperatures are used to detect charges in lithium donor concentration and the formation of defects during irradiation. Physical models to explain the observed effects are presented.

Carter, J. R., Jr.↗

Theoretical studies of important processes in planetary and comet atmospheres

This is the fifth semi-annual progress report describing research on dissociative recombination reactions in planetary and comet atmospheres. The Appendix has two papers that describe NASA supported research. Both papers have been recently accepted for publication. The first paper, 'The Generation of O(S-1) from the Dissociative Recombination of O2(+)', describes in detail the Multichannel Quantum Defect (MQDT) theory used for the calculation of dissociative recombination (DR) cross sections and rates. The application to the generation of the upper state of the atomic oxygen green line emission is of great importance to the modelling of planetary atmospheres. The second paper in the Appendix, 'Dissociative Recombination of the Ground State of N2(+)', applies the methods described in the first paper to N2(+). We find remarkable agreement with the prior microwave afterglow experiments for both the total recombination rate and for its electron temperature dependence. However, the results disagree with recent merged beams results which gave cross sections that are a factor of five below the microwave afterglow experiments and the current results. DR of N2(+) is an important mechanism for generating energetic N atoms which can escape the atmosphere of Mars. Currently we are also continuing additional work on the DR of O2(+) which is aimed at calculating both the total DR rate as a function of ion vibrational level and the rate for production of O(D-1).

Guberman, Steven L.↗