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Understanding Non-Radiative Recombination through Defect-Induced Conical Intersections Yinan Shu, B. Scott Fales, Wei-Tao Peng, and Benjamin G. Levine J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b01707 • Publication Date (Web): 11 Aug 2017 Downloaded from http://pubs.acs.org on August 13, 2017

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The Journal of Physical Chemistry Letters

Understanding Non-Radiative Recombination through Defect-Induced Conical Intersections Yinan Shu1, B. Scott Fales2,3, Wei-Tao Peng4, Benjamin G. Levine4* 1 Department of Chemistry, University of Minnesota, Minneapolis, MN 55455 2 Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305 3 SLAC National Accelerator Laboratory, Menlo Park, California 94025 4 Department of Chemistry, Michigan State University, East Lansing, MI 48824 * to whom correspondence should be addressed: [email protected] Abstract Defects are known to introduce pathways for the non-radiative recombination of electronic excitations in semiconductors, but implicating a specific defect as a non-radiative center remains challenging for both experiment and theory. In this perspective we present recent progress towards this goal involving the identification and characterization of defect-induced conical intersections (DICIs), points of degeneracy between the ground and first excited electronic states of semiconductor materials that arise from the deformation of specific defects. Analysis of DICIs does not require the assumption of weak correlation between electron and hole nor of stationary nuclei. It is demonstrated that in some cases an energetically accessible DICI is present even when no mid-gap state is predicted by single-particle theories (e.g. density functional theory). We review recent theoretical and computational developments that enable the location of DICIs in semiconductor nanomaterials and present insights into the photoluminescence of silicon nanocrystals gleaned from DICIs.

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Biography Yinan Shu earned his Ph.D. degree in Chemistry from Michigan State University in 2016 working under Prof. Benjamin G. Levine. He received B.S. degrees in Chemistry and Biological Science from Wuhan University (China) in 2011. He is currently a postdoctoral researcher under Prof. Donald G. Truhlar at University of Minnesota. His current research interests include developing and applying density-functional-theory-based electronic structure theory and molecular dynamics methods to understand photochemical processes. He is also interested in applying machine learning techniques to chemical problems. B. Scott Fales received his Ph.D. from Michigan State University in 2017 where he focused on graphical processing unit acceleration of multireference electronic structure methods. He is currently a postdoctoral scholar at the PULSE Institute at Stanford University where he is developing correlated approaches to solving problems in photochemistry and dynamics. Wei-Tao Peng is currently a Ph.D. candidate in the Department of Chemistry at Michigan State University. He received his undergraduate degree from Soochow University (Taiwan) in 2005 and M.S. degree from National Taiwan Normal University in 2007. After that, he worked as a research assistant at Academia Sinica and National Taiwan University before joining Michigan State University. His research interests are in the field of quantum dynamics. Benjamin G. Levine received his B.S. in Chemical Engineering at University of Illinois at Urbana-Champaign in 2001. He earned his Ph.D. in Chemistry from the same institution in 2007, working in the group of Prof. Todd J. Martínez modeling nonadiabatic molecular dynamics. After graduation, Ben did postdoctoral work with Prof. Michael L. Klein at University of Pennsylvania (2007-2009) and Temple University (2009-2011)—modeling biological and soft matter systems—before joining the faculty at Michigan State University (MSU) in 2011. He was promoted to the rank of Associate Professor in 2017. At MSU, Ben’s group develops and applies theoretical and computational methods for modeling non-radiative dynamics in several challenging areas: materials, atmospheric chemistry, and molecules in strong laser fields.



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Pull Quotes As such, identification and characterization of these defect-induced conical intersections (DICIs) allows one to connect material structure to the propensity for non-radiative decay. However, the wisdom of assuming weak electron-hole correlation may be questionable when the electron and/or hole become localized to a defect, as occurs during SRH recombination; localization leads to stronger correlation, requiring a true many-body description of the electronic structure. Even in the absence of a mid-gap state, a nanoparticle can have an energetically accessible DICI, and therefore an efficient pathway for non-radiative recombination. In such cases—where a straightforward deformation of a defect leads to a biradicaloid structure—chemical intuition developed in physical organic chemistry can be used to predict structure-function relationships in semiconductor nanomaterials. Pull quotes are also in bold in the body of the manuscript


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The ability of a semiconductor to maintain long-lived electronic excitations plays a crucial role in its function in optoelectronic devices such as photovoltaic cells and light emitting diodes. Non-radiative recombination is a fundamental physical process that consumes such excitations before their energy can be harnessed to do useful work, converting electronic energy into useless heat. Shockley-Read-Hall (SRH) recombination,1,2 whereby an electronic excitation localizes to a defect and subsequently relaxes to the ground state, is known to be one of the most important processes limiting device efficiency.

Recombination at defects is particularly

important in indirect gap materials such as silicon, where radiative recombination is slow, and in nanomaterials, where the high surface-to-volume ratio leads to a very high effective concentration of defects.

Though the general idea that defects promote non-radiative

recombination has been established for over half a century, diagnosis of specific defects as nonradiative centers remains a challenge.3-7



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Figure 1. Illustrations of the mid-gap state picture of recombination (left) and the DICI picture (right). Key differences include the consideration of correlated many-electron states and nuclear motion in the DICI picture.

In two important ways, an electronic excitation localized to a defect closely resembles an electronic excitation in a molecule: a) it fills the volume of a small number of atoms, and b) its energy falls in the range between the near infrared (NIR) and the near ultraviolet (UV). Over the past several decades a predictive theory of non-radiative decay in molecules has evolved. One of the central tenets of this theory is that conical intersections, points of degeneracy between potential energy surfaces, facilitate non-radiative transitions between electronic states.8-13 By identifying conical intersection points and characterizing the surrounding PES, one can predict the propensity for a particular non-radiative process to occur and gain insight into its mechanism, in the same way that identifying and characterizing a transition state allows ground state reaction rates and mechanisms to be elucidated. It has recently been demonstrated that electronic excitations in semiconductor nanocrystals may also undergo non-radiative recombination via conical intersections.14 These intersections involve electronic excitations that are localized to specific defects and are accessed upon similarly localized distortions of the nuclear geometry. As such, identification and characterization of these defect-induced conical intersections (DICIs) allows one to connect material structure to the propensity for non-radiative decay. In this perspective, we discuss these first efforts to model DICIs. First, the picture of recombination that arises from DICIs will be contrasted with the widely adopted mid-gap state picture of recombination. Then we will present recent developments in electronic structure theory that enable the identification and


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characterization of DICIs. Finally, we will discuss what modeling DICIs has taught us about the photoluminescence of silicon nanocrystals and how the intuition developed in this work can be generalized to other materials. Mid-gap states and DICIs. The photophysics of materials is often viewed in terms of singleparticle states. In this picture, the key descriptor of the electronic structure of a material is the electronic band structure,15 i.e. the energies of single-electron states (orbitals) as a function of the wave vector (k, momentum) of the electron (Figure 1, left). In this picture, semiconductors are recognized by their band gaps. Electronic excitation involves the creation of a particle and hole in the conduction and valence bands, respectively. Defects introduce additional one particle states into the band structure. When these states fall within the band gap, they provide a ladderrung allowing electrons and holes to more easily shuttle between the conduction and valence bands, thus facilitating recombination. This mid-gap state picture of recombination is often extended to nanomaterials, where the finite extend of the material results in the replacement of continuous bands by a finite number of single-particle orbitals. This mid-gap state picture is widely used and often effective, but it is limited by the assumptions that underlie it. Inherent in the band description of electronic structure is the assumption that electrons and holes are weakly correlated. This is an excellent assumption in the limit of a pristine semiconductor. For example, in bulk silicon the exciton binding energy is only 14.7 meV, and the electron-hole correlation is therefore comparably small.

This weak

interaction between electron and hole is the result of spatial delocalization; the exciton Bohr radius in silicon is 4.3 nm. However, the wisdom of assuming weak electron-hole correlation may be questionable when the electron and/or hole become localized to a defect, as occurs



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during SRH recombination; localization leads to stronger correlation, requiring a true many-body description of the electronic structure.16 The notion that a single band structure describes the electronic structure of a material also assumes that the nuclei are roughly stationary. Similar to the assumption of weak correlation, this assumption is sound in the limit of a delocalized electronic excitation, where only a small fraction of an electron is perturbed in the vicinity of each nucleus. However, in the limit that the electron and/or hole are strongly localized to a defect, the accuracy of this assumption is questionable. In fact, it is well known that in molecules—whose sizes and excitation energies are comparable to defects—the nuclei often distort dramatically in the presence of an electron excitation. The existence of similar effects in excited defects in semiconductors has been known for some time.17 Neither of these assumptions is inherent to the potential energy surface (PES) picture that is widely employed in molecular photochemistry; nuclear motion and (depending on the choice of electronic structure method) strong correlation are included in the PES. As is well known, each many-electron state of the system has its own PES. An illustration of PESs of the three states hypothesized to be most relevant to the non-radiative recombination of a defective semiconductor nanoparticle is shown in the right panel of Figure 1. After excitation and rapid electronic cooling, the nanoparticle likely populates a quantum-confined exciton state, in which the electron and hole are delocalized over the entire nanoparticle. The PES of this state is nearly parallel to the ground state PES, because the excitation is delocalized and thus does not strongly influence any particular nuclei. However, a defect-localized excited state may be accessed by displacement along some nuclear coordinate (likely distorting the structure of the defect). Transitioning to the defect-localized state may involve a barrier crossing. The defect-localized


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excited state may then intersect the ground state at a DICI, resulting in a fast transition to the ground state. The nanoparticle is likely to undergo efficient non-radiative recombination via DICI if three conditions are met: 1) The DICI exists, 2) the DICI is energetically accessible—that is, it falls within the optical band gap—and 3) the DICI is dynamically accessible—there is not an insurmountable energetic barrier preventing it from being accessed.

Figure 2. a) The HOMO and LUMO of the Si269H188O nanocrystal as computed at the CAMB3LYP/LANL2DZ level of theory are delocalized, thus there is no mid-gap state. The surface epoxide defect is marked by a red arrow. b) The best estimate of the silicon epoxide DICI energy (≤1.8 eV) is well below the vertical excitation energy (4.3 eV) of this same nanocrystal, indicating the existence of an accessible pathway for non-radiative recombination, despite the absence of a mid-gap state.

We wish to emphasize that the mid-gap state and DICI pictures of recombination are consistent with one another, but not equivalent. As will be discussed below, it is well established that orbital near-degeneracy brings about conical intersections in molecules.18 It is therefore not 9 ACS Paragon Plus Environment


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surprising that a defect that introduces a mid-gap state would also introduce DICIs; distortion of the nuclei can tune the energy of the mid-gap state, bringing it into near-degeneracy with the valence band, the conduction band, or some other mid-gap state. However, not all conical intersections arise from mid-gap states. Consider the Si269H188O nanoparticle pictured in the left panel of Figure 2. This particle is a prolate spheroid (long axis 2.7 nm, short axis 2.0 nm) with a silicon epoxide (Si-Si-O ring) defect on its surface, marked by a red arrow. At its ground state minimum energy geometry, the highest occupied and lowest unoccupied

molecular

orbitals

(HOMO and

LUMO;

as

computed

at

the CAM-

B3LYP19/LANL2DZ20 level of theory) are delocalized over the entire particle with only a small fraction of the density localized on the defect, indicating that the defect does not introduce a midgap state. However, after the defect is deformed by stretching the Si-Si bond of the epoxide ring, a conical intersection is accessed. As indicated in the right panel of Figure 2, the energy of the DICI (≤1.8 eV, as estimated from ref.

14

) is below the computed vertical excitation energy (4.3

eV at the CISNOr-CASCI/LANL2DZ level of theory). Even in the absence of a mid-gap state, a nanoparticle can have an energetically accessible DICI, and therefore an efficient pathway for non-radiative recombination. Identification and characterization of DICIs. To predict if a particular material will undergo non-radiative recombination via DICI, we require accurate and efficient electronic structure tools for computing the coupled PESs of nanoscale systems. The most widely used method for identifying conical intersections in molecules is the state-averaged complete active space selfconsistent field (SA-CASSCF) method.21 Because it treats all electronic states on equivalent theoretical footing, it can correctly describe the topology of conical intersections. Unfortunately, until recently, computational cost limited SA-CASSCF to systems of ~20 non-hydrogen atoms,


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whereas nanoparticles typically have greater than ~50 non-hydrogen atoms. In addition to its large computational cost, SA-CASSCF is not a size-intensive method;22 that is, errors in computed vertical excitation energies grow with an increase in the number of excitable subsystems. For example adding an excitable defect to the surface of a silicon nanoparticle will degrade the quality of the description of the quantum-confined excited state. This flaw may be surprising to seasoned electronic structure theorists, who know that full configuration expansions such as CASSCF are rigorously size extensive, consistent, and intensive in a particular orbital basis. The lack of size intensivity in SA-CASSCF arises not from the complete active space expansion, but instead from the state averaging procedure that determines the orbitals, which cannot be extended to larger systems composed of multiple excitable subsystems in a sizeintensive manner. A rigorous explanation is provided in ref. 22. In an effort to avoid these difficulties, it would be appealing to adopt inexpensive singlereference methods such a linear response time-dependent density functional theory (LRTDDFT).23,24

However, with standard functionals and approximations LR-TDDFT cannot

properly describe the topology of conical intersections involving the electronic ground state, and thus is inappropriate for studying non-radiative recombination.25 This issue (which arises for other single reference methods such as configuration interaction singles and equation-of-motion coupled cluster theories, as well), results from the absence of couplings between the reference state and the configurations comprising the response states. Multireference methods avoid this difficulty by inclusion of doubly-excited determinants and relaxation of the reference orbitals. With these issues in mind, we have developed the configuration interaction singles natural orbital (CISNO-) complete active space configuration interaction (CASCI) method.22 In contrast to CASSCF, CASCI methods separate the determination of the orbitals from the



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configuration interaction coefficients. Thus, they are variationally inferior to CASSCF, and are often thought of as inexpensive approximations to it.26-30 However, well thought out CASCI methods can actually provide qualitatively superior results to CASSCF in many cases. For example, CASCI methods can ease the selection of the active space or be more numerically stable than the self-consistent alternative.22,31,32 The CISNO-CASCI method has been designed to be size-intensive, therefore its application to large nanoscale systems is more justified than that of SA-CASSCF. For computing the vertical excitation energies of molecules, CISNOCASCI has comparable accuracy to SA-CASSCF relative to the highly accurate complete active space second order perturbation theory. We note that the floating occupation molecular orbital (FOMO-) CASCI method is also size intensive and is likely of value in the study of DICIs.29,33

Figure 3. Times to solution for GPU-accelerated CASCI calculations with active spaces ranging from (6,6) to (16,16) (abbreviated (M, N), where M and N are the numbers of active electrons and orbitals, respectively) for systems ranging in size from pyrazine to an Si72H64 nanoparticle. This nanoparticle is a prolate spheroid with long dimension 1.7 nm and short dimension 1.4 nm. All calculations used the 6-31G** basis. This figure is adapted from ref. 34.


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Though CASCI methods are typically less computationally costly than SA-CASSCF, the large size of nanoparticles requires further acceleration to enable routine identification of DICIs. To this end, graphics processing unit (GPU) accelerated implementations of CASCI and CASSCF have been developed,34,35 utilizing the fast two-electron integral, self-consistent field, and configuration interaction singles codes in the TeraChem software package.36-38 These GPUaccelerated algorithms allow the calculation of the CASCI wave function of a Si72H64 silicon nanoparticle with a 16-electron/16-orbital active space and an all-electron, polarized basis set in 39 minutes (see performance data in Figure 3). GPU-accelerated analytic gradient code for CISNO-CASCI, FOMO-CASCI, and SA-CASSCF has recently been developed,39,40 enabling geometry optimizations and ab initio molecular dynamics simulations of nanoscale systems in the vicinity of conical intersections. With these tools in hand it is now possible to identify and characterize the potential energy surfaces around DICIs in true nanoscale systems.

However CASCI methods lack

dynamic electron correlation, and thus are prone to quantitative errors.

To date we have

addressed this problem using a simple QM/QM approach, similar to ONIOM.41

Similar

QM/MM embedding approaches have been used to excellent effect in modeling the excited states of complex biomolecules.42 Here we opt for QM/QM embedding because, unlike in flexible biomolecules, the primary environmental influence in semiconductor nanomaterials is the dielectric response of the electrons. This response is not described by standard MM force fields. Using multistate complete active space second order perturbation theory43 (MS-CASPT2) to describe a molecule-sized region around the defect allows a quantitative description of the energetics of DICIs involving defect-localized excitations.

This type of approach is possible



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because the electronic excitations involved in DICIs are truly local to the defect region. This can be seen in Figure 4, which shows the energy of three specific defects on the surface of silicon clusters ranging from the molecular- to the nanoscale. As can be seen, only weak dependence of the energy on system size is observed, inconsistent with quantum confinement effects. The chemical character of these excitations also does not depend on cluster size.14 The locality of the electronic excitations involved in DICIs also enables the application of ab initio molecular dynamics techniques to small cluster models of defects to first identify pathways for nonradiative recombination.44-47

Figure 4. The energies of conical intersections (relative to the ground state minimum energy) of three different defects as a function of cluster size, ranging from a small molecular model (14-15 Si atoms) to a true nanoparticle (44-50 Si atoms). This figure is reproduced from ref. 14.

Yet more challenging is the following case: It is likely that the electron and hole do not localize simultaneously. In this case, a charge transfer excitation (where one carrier is localized to the defect and the other is not) is populated during the recombination process, and the energy 14 ACS Paragon Plus Environment

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of this charge transfer state may control recombination kinetics. The accurate calculation of the PES of this charge transfer state places great demands on the electronic structure method employed; an accurate treatment of dynamical electron correlation is required for the entire nanoscale system, but the chosen method must also provide a proper topological description of the intersection. Towards similar ends, various amalgams of CASSCF and density functional theory (DFT),48-53 semiempirical energy-scaling approaches,54,55 and variants of LR-TDDFT56,57 have been proposed. Though, to the best of our knowledge, these methods have not yet been employed in the study of non-radiative recombination in semiconductors, this would be an interesting direction for research.

Figure 5.

The names, structures, and best estimates of the energy of the lowest conical

intersections of seven possible structures on the silicon surface. Best estimates are all computed at the MS-CASPT2 level of theory or using a QM/QM scheme based on an MS-CASPT2 level description of the defect region. Gray atoms indicate linkage to the remainder of the material.



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One final issue bears mention before proceeding to specific applications of this methodology. The results of both CASSCF and CASCI depend strongly on the choice of a userdefined active space of orbitals to be correlated. In general, it is not possible to choose this active space a priori, as intuitive active spaces are known to yield unphysical results in many cases. Here we again exploit the locality of the electronic excitations associated with DICIs. Having identified the most important geometries on the PES of a molecule-sized cluster model of the defect of interest (i.e. Franck-Condon point, excited state minima, and conical intersections), we choose an active space that yields good agreement between our low-cost CASCI level of theory and more trustworthy levels (typically CASPT2 and/or MRCI). The first guess at the appropriate active space often yields poor energetics that must be corrected, thus the process of choosing an active space is necessarily iterative. One might expect that modeling nanomaterials will require larger active spaces than smaller molecules do, but this is not the case in our experience. The locality of defect-localized excitations has allowed us to use small active spaces in all cases to date. Influence of DICIs on silicon nanocrystal photoluminescence. Though bulk silicon has an indirect band gap and thus does not emit light efficiently, nanostructured silicon is highly emissive.58,59 As such, silicon nanocrystals (SiNCs) have garnered much attention as potential earth-abundant and non-toxic materials for application in displays, solid state lasers, and biological imaging. Of both fundamental and technological interest is the strong dependence of the photoluminescence (PL) spectrum of SiNCs on surface chemistry,59,60 not surprising given that the fraction of atoms on the nanocrystal surface is roughly one half as the nanoparticle diameter approaches 1.0 nm. Hydrogen- or hydrocarbon-capped SiNCs exhibit strong quantum confinement effects, allowing the emission energy to be tuned across the visible spectrum.61,62


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These surface structures also result in high PL yields,63 but unfortunately are not stable upon exposure to oxygen at ambient conditions. Upon oxidation, the PL yield decreases,63 and the emission energy becomes insensitive to the particle size.62,64 For light emission applications, tunable, efficient PL is highly desirable, therefore the effect of oxidation is an impediment to the development of silicon-based materials for this purpose. Using the above-described methodological developments, we have conducted a survey of possible surface structures, in each case identifying the lowest energy conical intersection accessible upon excitation. Our best estimates of the energies of these intersections relative to their respective ground state minimum energies are reported in Figure 5. These energies are a reasonable estimate to the optical band gap at which efficient non-radiative decay pathways become accessible. For example, the conical intersection associated with an epoxide defect is 1.8-1.9 eV above the ground state minimum energy structure. One would therefore expect that particles with their lowest quantum-confined states significantly above 1.8-1.9 eV to undergo fast non-radiative decay upon excitation. Those with quantum-confined states significantly below this energy would more likely decay radiatively, because the DICI is energetically inaccessible. In our survey, we identified four defects that may introduce efficient non-radiative decay pathways accessible at visible or NIR energies: dangling bonds (under-coordinated silicon radicals on the silicon surface), silicon epoxide rings,14,44,46 Si=O double bonds,14,45 and hypervalently bound silyl anions (SiH3-).65 Dangling bonds have long been known to provide efficient pathways for non-radiative recombination,7,66 consistent with this work. The other three DICIs found to be accessible at visible energies will be discussed in more detail below. Conical intersections were also observed in clusters containing two additional structures—hydrogen-



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capped silicon (Si-H) surfaces and surface silanol (Si-OH) groups47—but these intersections are accessible only at UV energies.

Thus, they are not expected to influence visible

photoluminescence, consistent with the fact that they are widely viewed as good passivating structures. Unambiguous experimental verification of passage through a conical intersection is a tremendous challenge even in the simplest gas phase systems.67 Similar verification in systems as complex and heterogeneous as semiconductor nanomaterials is arguably impossible. However, in the field of molecular photochemistry conical intersections have become a textbook concept because they enable researchers to explain and even predict experimental observables such as PL yields and photochemical branching ratios. Toward building a similar portfolio in the photophysics of nanomaterials, here we highlight two examples where experimental observations of SiNC PL were explained through identification and characterization of DICIs. As noted above, oxidation of SiNCs results in emission that appears to be insensitive to particle size. Whereas the PL of electrochemically etched silicon with a hydrogen-terminated surface can be tuned across the visible spectrum by decreasing the particle size, upon oxidation the observed PL of the higher energy samples (yellow, green, blue, etc.) become orange (PL maximum ~2.1 eV).62 This size-insensitive emission—known as the slow- or S-band emission of oxidized nanostructured silicon because of its microsecond lifetime—has at times been attributed to emissive defects.62,68-72 However, the most frequently implicated defect, the Si=O double bond, introduces accessible conical intersections and thus cannot be the source of the PL.45 (Si=O bonds are also known to be quite unstable due to poor p-orbital overlap, so the extent to which they exist on the surface of real oxidized SiNCs is unclear.) PL lifetime,73 single particle PL linewidth,74 and single particle PL polarization75 measurements suggest that S-band


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emission arises from a quantum-confined exciton, not a defect-localized one. Density functional theory studies have suggested that interface effects compete with or even dominate quantum confinement effects in determining the band gaps of oxidized SiNCs.76,77 The DICIs predicted in our survey provide an explanation for the size-insensitivity of the S-band emission consistent with the experimental data suggesting emission from a quantumconfined state. Note that electrochemically etched silicon is not composed of a monodisperse set of SiNCs, but instead a heterogeneous mixture of particle sizes. The PL spectrum therefore contains contributions from SiNCs with a range of different sizes. As predicted by a Marcuslike-theory of exciton localization based on our computed intersections, the barrier to localization and subsequent non-radiative decay via conical intersection is strongly sizedependent (Figure 6).14 For example, the silicon epoxide DICIs have energies of 1.8-1.9 eV. As noted above, these energies are insensitive to particle size. As illustrated in the upper panel of Figure 6, the barrier to localization decreases with decreasing particle size (increasing energy of the quantum-confined exciton relative to the defect localized state). As such, upon oxidation, the PL of a heterogeneous sample of SiNCs would be dominated by low energy (red-to-orange) emission from larger particles, whereas the higher-energy emission of smaller SiNCs would be extinguished by non-radiative recombination via DICI. A similar argument applies to dangling bond DICIs, which are at a comparable energy (2.1 eV). This explanation is also consistent with the facts that emission above 2.5 eV is not observed in single-particle experiments on oxidized SiNCs75 and the lifetimes of emission of oxidized SiNCs decreases rapidly above 2.1 eV.78



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Figure 6. Lower panel: Estimated activation barriers for exciton localization for three defects as a function of the excitation energy to the quantum-confined state.

Upper panel: Idealized

representation of the PESs of the ground (gray), quantum-confined (green), and defect-localized (red) states of SiNCs of different sizes. The barrier to localization (crossing between the red and green curves), and thus the rate of recombination, is predicted to be strongly size-dependent, though the energy of the defect-localized conical intersection (crossing between the red and gray curves) is assumed to be exactly independent of particle size. This figure is reproduced from ref. 14.

In a recent combined experimental/theoretical study of SiNCs synthesized in a nonthermal plasma reactor, identification of a DICI also provides important insight into the PL


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yield.65 A five-fold increase in yield was observed upon heating such SiNCs at 160°C for 1 hr, suggesting a change in structure that reduced the propensity for non-radiative recombination. Subsequent experimental characterization yielded several important pieces of information regarding the relationship between structure and function. 1) Vibrational spectroscopy showed a reduction in surface silyl (-SiH3) groups upon similar heating, suggesting that these silyl groups may introduce pathways for non-radiative recombination that are responsible for the observed decrease in PL yield. 2) Upon similarly gentle heating, effusion of SiHx from the material was observed, suggesting that the interaction binding these silyl groups to the surface is weak relative to a Si-Si covalent bond. 3) Electron paramagnetic resonance spectroscopy ruled out the involvement of radical defects such as dangling bonds. Based on these observations and the knowledge that plasma-synthesized SiNCs often carry a negative charge,79 we hypothesized that a hypervalently bound silyl anion (SiH3-) defect may be responsible for the quenching. Calculations demonstrated that 1) the binding energy of a hypervalently bound silyl anion is consistent with the observed effusion, and 2) such defects introduce very low-lying conical intersections capable of dramatically reducing the PL yield (see Figure 5). The recent suggestion that hypervalent interactions with solvent molecules may introduce conical intersections that limit PL yield presents interesting directions for future studies along these lines.80 Future experimental efforts could provide additional strong evidence for DICIs. Single particle PL measurements that probe the same SiNCs before and after oxidation could directly address the question of whether the size-insensitivity of the S-band arises from DICIs or from emissive defects.

Anti-Stokes Raman measurements could directly identify the vibrational

modes that are excited upon recombination. An important feature of conical intersections is that the majority of the vibrational energy is initially released into two specific modes (the branching



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modes) upon recombination, so such measurements can be easily compared directly to theory. Finally, synthesis of molecular models of the defects in question followed by characterization of the recombination process by ultrafast spectroscopy would allow direct comparison of experiment to nonadiabatic molecular dynamics simulations of the same system.

Such

experiments eliminate the structural uncertainty inherent to working with nanomaterials and the small size of molecular models facilitates faster, more accurate computations.

Figure 7. Illustration of the biradicaloid nature of the 5O epoxide DICI. Breaking of the Si-Si bond of the epoxide ring leads to a structure in which the sp3Si1 and pSi2 orbitals are nearly degenerate, which in turn leads to a biradicaloid intersection between the states with (sp3Si1)2 and (sp3Si1)(pSi2) electronic configurations. Gray atoms indicate linkage to the remaining material.

Chemical intuition for DICIs. The study of organic photochemistry has benefited from the development of chemical intuition that allows the prediction of photochemical behavior without performing quantitative simulations. Biradicaloid photochemistry is an example of such an intuitive concept.18 Upon excitation, many closed-shell molecules evolve toward biradicaloid geometries—i.e. geometries where the HOMO and LUMO are nearly degenerate. In such a region of the PES, a conical intersection may result from the near degeneracy of the electronic configurations arising from different occupations of the nearly degenerate HOMO and LUMO by 22 ACS Paragon Plus Environment

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the two associated electrons. The non-radiative decay processes of important classes of organic molecules such as polyenes and protonated Schiff bases are known to proceed by this mechanism.10,18,81 Six of the seven conical intersections reported in Figure 5 arise at biradicaloid structures. (The sole exception is the radical dangling bond.) Take, for example, the 5O epoxide defect, illustrated in Figure 7. Upon excitation to the defect-localized excited state, this structure undergoes a photochemical ring opening reaction, with the Si-Si bond breaking.46

Upon

breaking, one of the formerly bound silicon atoms (Si1) remains in a pyramidal sp3 conformation while the other (Si2) takes on a planar sp2 conformation. At this geometry the nonbonded sp3 orbital on Si1 is slightly lower in energy than the unhybridized p orbital on Si2. The result of this orbital near-degeneracy is an intersection between the configuration in which the occupied sp3 orbital is doubly occupied, (sp3Si1)2, and that in which each orbital is singly occupied, (sp3Si1)(pSi2). Similar bond breaking processes occur in the other five biradicaloid intersections; intersections are brought about by Si-Si bond breaking near the H-termination and silanol sites,47 Si-O and/or Si-Si bond breaking in the 3O epoxide defect,46 breaking of the hypervalent Si-Si bond in the silyl anion defect,65 and pyramidalization (i.e. sp2 to sp3 hybridization) of the double bonded Si atom in the Si=O double bond defect.45 In such cases—where a straightforward deformation of a defect leads to a biradicaloid structure—chemical intuition developed in physical organic chemistry can be used to predict structure-function relationships in semiconductor nanomaterials. Future prospects. Thus, the application of novel theoretical methods and GPU-accelerated computing is enabling the identification of conical intersections in semiconductor nanoparticles. These intersections are often associated with the distortion of specific defects on the particle



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surface, and as such provide insight into the relationship between surface structure and the function of the material. This is achieved without assuming weak correlation between electron and hole or stationary nuclei. Predictions arising from this approach are consistent with and supported by experimental data related to the photoluminescence of SiNCs. Important directions for future work include developing efficient tools for modeling the complex charge and energy transfer processes that precede recombination by conical intersection, carrying out additional joint theoretical and experimental studies to directly test the predictions made by this theory, investigating the possibility that DICIs may also occur in bulk defects, where nuclear motion is more constrained, and extending the search for DICIs to materials beyond silicon. Materials of particular interest include II-VI materials, for which a bounty of high-quality ultrafast photophysical experiments already exist,82 and lead-halide perovskites,83-85 whose low propensities for non-radiative recombination make them promising candidates for photovoltaic applications. In addition, identification of conical intersections whose energy is modulated by the interaction of a surface defect with a particular molecule may enable rational design of materials for photoluminescence-based sensing.

Acknowledgements This work was supported by the National Science Foundation under grant CHE-1565634. This work used the Extreme Science and Engineering Discovery Environment (XSEDE) under allocation CHE-140101. XSEDE is supported by the National Science Foundation under grant ACI-1548562.

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