Mobile Surface Traps in CdSe Nanocrystals with Carboxylic Acid

ARTICLE pubs.acs.org/JPCC

Mobile Surface Traps in CdSe Nanocrystals with Carboxylic Acid Ligands Oleksandr Voznyy* Institute for Microstructural Sciences, National Research Council of Canada, Ottawa K1A 0R6, Canada

bS Supporting Information ABSTRACT: We have performed ab initio calculations of electronic properties of the realistic Cd-rich CdSe nanocrystals with covalently bound carboxylic acid (X-type) ligands. Configurations both with and without surface traps can be prepared depending on the amount and geometry of the adsorbed ligands. We find that Cd and Se dangling bonds do not necessarily create surface traps, whereas traps originating from ligands can form near the top of the valence band. Some of the ligands are found to be mobile on the surface and this mobility is accompanied by a spectral diffusion of the associated trap energy levels. This provides the first atomistic example of the processes required to explain the emission wavelength and lifetime variations, and blinking of the nanocrystals.

’ INTRODUCTION Since the discovery of colloidal semiconductor nanocrystals (NCs) they have found tremendous amount of applications in bioimaging,1 lasing,2 diodes,3 single-photon sources,4 photovoltaics,5 etc. owing to a wide range of techniques6 available to tune their optical and electronic properties. Many of those applications rely on emission properties of NCs (quantum yield, emission wavelength broadening and diffusion, Stokes shift, blinking) which are strongly affected by different types of defects, supposedly residing at the surface.7 Surface traps may also affect the multiexciton generation yields8 and charge carriers extraction, relevant, e.g., for photovoltaics. Understanding better the source of the trap states can help to develop the synthesis procedures to reduce or ultimately eliminate the traps. In contrast to absorption properties, which are determined mainly by the bulk crystalline structure and the macroscopic properties of the NCs (size, shape),9,10 surface and thus emission properties require a more detailed knowledge on atomic scale. The exact atomistic nature of surface defects remains unknown11
13 and the interpretation of experimental data is thus often based on available theoretical models. Several semiempirical studies of ligated surfaces are available14
18 but this methodology does not reliably capture surface reconstructions and charge redistributions. Few ab initio studies of the NC surfaces available to date addressed only the bare surfaces19
25 or weakly bound (L-type) ligands.26
30 However, more and more experimental data suggest that the main type of ligands present on the surface are the covalently bound (X-type) ligands, e.g., deprotonated carboxylic or phosphonic acids.31
33 Theoretical studies of such ligands on CdSe and PbSe only start to emerge.30,33
35 In this work we investigate from first principles the atomistic nature of the surface states in NCs. To do this, we choose CdSe NCs without structural defects, small enough to be treated within Published 2011 by the American Chemical Society

the density functional theory (DFT) but large enough to distinguish delocalized (core) and localized (trap) states, with carboxylic acid ligands bound covalently. We find that even such an idealized and small model is rich enough to create structures with or without surface trap states, depending on the amount of ligands. Contrary to expectations, apparently more passivated structures (with more ligands and less dangling bonds) exhibit more surface traps. Our most important finding is the presence of mobile surface ligands whose energy levels fluctuate respectively, a feature required by several phenomenological models of blinking.36
38 We will discuss whether the observed diffusion on its own is capable of explaining the fluorescence intermittency, and whether it is capable of producing switchable longlived trap states.

’ COMPUTATIONAL METHODS Calculations were performed within DFT using the SIESTA code.39 Generalized gradient approximation in a Perdew
Burke
Ernzerhoff formulation, Troullier-Martins norm-conserving pseudopotentials with nonlinear core corrections, semicore d-states included in valence shell for Cd, optimized double-ζ plus polarization basis sets, and 300 Ry mesh cutoff for charge density were used throughout. Geometries were optimized until forces on atoms below 40 meV/Å were achieved. Full simulation input files are provided in the Supporting Information. The convergence of the simulation parameters and the general validity of our approach were tested by reproducing previous DFT results for bare19 and ligated28 CdSe nanoclusters. Received: June 20, 2011 Revised: July 11, 2011 Published: July 14, 2011 15927

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Figure 2. Optimized geometries of acetate on CdSe NC surface: (a and b) on (001) Cd-rich surface facet of the NC and (c and d) on (111) Cd-rich facet. The atoms legend is the same as in Figure 1.

Figure 1. Optimized structure of the [Cd56Se50(OAc)13]1- nanocrystal used in calculations. Green arrow marks the missing Cd atoms on the (001) facet; red arrow, an “extra” ligand.

Different synthesis procedures of CdSe nanocrystals have been reported, with trioctylphosphine (TOP), trioctylphosphine oxide (TOPO), amines, and carboxylic and phosphonic acid ligands available in solution. The resulting stoichiometry of ligands on surface, however, is usually not well quantified. For phosphine-based synthesis, species not even considered to exist in solution were found recently to be the main ligands on NC surfaces and were shown to come from impurities in solvents or in source materials.32,40 Modeling of such ligands is also complicated by their higher structural complexity and increased amount of possible binding geometries. We thus choose carboxylic acids (known to be the sole ligands in phosphine-free synthesis31,41
45) as prototypical ligands for current study. Zincblende structure is used throughout, since it is known to be preferred with carboxylic acid based synthesis,31,41,44,45 in contrast to wurtzite structure usually reported for synthesis with TOP/TOPO. We prepare our models by carving a sphere out of zincblende CdSe bulk and removing all singly bonded atoms. On the facets where the formation of two dangling bonds per atom is unavoidable we give preference to Cd-termination, leading to Cdenriched clusters, as suggested by experiments.11,31,32,43 Acetate (CH3COO
) is used as a representative model of the longer fatty acid ligands. The diameter of the NC is adjusted to obtain a structure that matches as close as possible the charge neutrality condition intended to reduce the amount of surface states:14,15 NCd  ð þ 2Þ þ NSe  ð-2Þ þ NAc  ð-1Þ ¼ 0

ð1Þ

This condition has its roots in the second Pauling rule and is also similar to the electron counting rule used to determine stable semiconductor surface reconstructions.46,47 Both approaches aim to ensure that the total amount of electrons in the system will match the amount of bonds (in the idealized bulk-like structure this means 4 bonds per Cd or Se and 1 bond per acetate); that is, in general, they are not related to the balance of electronic and ionic charges. In the absence of surface Se dimers, eq 1, counting all NC atoms, remains valid and provides identical results to the more general electron counting rule, which considers only the surface atoms. One can see from eq 1 that the amount of ligands should be equal twice the excess of Cd atoms. The structure of the cluster thus can be widely varied by adjusting either the amount of ligands, adding/removing Cd or Se atoms, or artificially charging the cluster as a whole.

Prepared in such a way [Cd56Se50(OAc)13]1- cluster is shown in Figure 1. Our model is Cd-rich and has a tetrahedral shape, similar to that of the thiolated ultrastable clusters48,49 and also typically observed for larger CdSe NCs with carboxylic ligands.31 It maintains the bulk-like local geometries for all atoms after optimization, representing well the bigger NCs with surface faceting. The three facets available are beneficial for modeling of ligand absorption all within one model. We believe that our structure is a better representative of the solution-prepared NCs than the highly reconstructed nonligated stoichiometric Cd33Se33 cluster often observed in laser ablation experiments50 and used in previous theoretical works.19,24,28,33 For clarity of the presentation we choose to describe the results for the cluster with ∼1.6 nm diameter and minimal amount of ligands. To comply with the electroneutrality condition (eq 1), the model in Figure 1 has several Cd atoms removed from the (001) facets (green arrow in Figure 1). One “extra” ligand is added (red arrow), compensated by a net charge
1 of the cluster as a whole. These artifacts do not affect the overall conclusions of the paper: a similar Cd68Se50(OAc)36 chargeneutral model with more Cd and ligands can be built (see Figure S1 in the Supporting Information) and was in fact the starting point in our simulations. Test calculations were also performed on smaller zincblende clusters, as well as a wurtzite NC of ∼3 nm diameter.

’ RESULTS Ligand Geometries and Energetics. Figure 2 presents the optimized geometries of the ligands. First we populate all available adsorption sites on a (001) facet, the remaining “extra” ligand is then placed elsewhere on the surface. Binding energies were computed for charge-neutral desorbed species, without corrections for solvent effects. Obtained values should not be used for direct comparison with experiment, nevertheless, they are reliable for relative comparison of different adsorption sites. Adsorption of the ligand on a (001) facet (Figure 2a,b) is the most stable since its departure would leave one (or both) Cd with two dangling bonds. Calculated binding energy of the deprotonated acetate (Eb > 4 eV) is much larger than the values reported previously for protonoated case (Eb < 1 eV),27,33 consistent with similar findings for CdSe33 and PbSe34 surfaces. Simulations starting from the ‘bridge’ (Figure 2a) or “chelate” geometries (similar to Figure 2d) both relaxed to a ‘tilted bridge’ geometry (which is ∼0.25 eV lower in energy), with one of the oxygens bonding to two Cd atoms (Figure 2b). This geometry is consistent with Cd NMR data for CdSeTe magic-size NCs43 and single-crystal XRD data for some Cd salts.51 Previous theoretical studies on smaller Cd33Se33 clusters could not resolve 15928

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The Journal of Physical Chemistry C the tilt and reported bridge structure as the most stable one.33 Due to small energy difference, at room temperature the ligand will be continuously switching between the bridge and left-tiltedand right-tilted-bridge configurations. Adsorption on a Se-rich (
111) facet is unfavorable since Se dangling bond is filled with electrons and repels the oxygen. The ligand tries to move to a nearby Cd atom on a (001) facet (as also reported previously27,28). If however this is not possible, e.g., when ligand is placed in the middle of Se (
111) facet, the ligand pulls out the Cd atom from the underlying layer, breaking its bond to the even deeper Se atom and leaving that Se with a dangling bond. Such a reconstruction stabilizes the ligand on the surface but remains ∼1 eV less favorable than adsorption on a Cd-rich (111) facet. On a Cd-rich (111) facet, the extra ligand adsorbs in either bridge (Figure 2c) or chelate (Figure 2d) geometry. The “titlted bridge” geometry is not favorable due to a larger distance between Cd atoms, a three-bonded geometry of Cd prohibiting its large inplane displacements, and the preference for a normal direction of the Cd dangling bond. Binding energies Eb ∼ 2
3 eV depend on the exact cluster geometry and the amount of ligands and are noticeably weaker than on (001) facet. We find that adsorption of the extra ligand on the already occupied Cd atoms of a (001) facet (sites a,b in Figure 1) is still possible and is in fact slightly more stable than on (111) facet (sites c,d). The energy difference between the most and the least stable geometries of the extra ligand (bridge on sites a-b vs chelate on site d, respectively) is ∼0.6 eV. Mobility of Ligands. Bridge geometry on (111) facet is only 0.2 eV more stable than the chelate. We did not perform the analysis of the vibrational modes in the chelate geometry to determine whether it is the saddle point of the transition between two bridge structures or it is a local energy minimum. In the latter case the actual barrier for diffusion may increase slightly, otherwise, diffusion should be possible already at temperatures as low as 50 K. Molecular dynamics simulations at 420 K (typical experimental temperature) indeed confirm that the ligand can easily switch between the bridge and chelate geometries and can “walk” from site to site (see Figure 2, panels c and d) on a subpicosecond time scale. Only the ligands adsorbed on (111) facets can diffuse. On the Cd56Se50(CH3COO)12 cluster, which is similar to experimental magic-size thiolated clusters,48,49 we do not have such ligands at all. However, on Cd68Se50(CH3COO)36 (see the Supporting Information), which likely represents better the real synthesis conditions with the excess of Cd and ligands in solution, there are many ligands capable to diffuse. We expect that even at the highest coverage, ligand diffusion would not be eliminated since steric repulsion between the ligands does not allow covering every surface atom.18 Mobility of the covalently bound (X-type) ligand on a surface is unexpected but not surprising; numerous examples of such behavior can be found, e.g., mobile adatoms, ligands, and ligand
adatom complexes on Au(111);52 diffusion of covalently bound species on surface is also considered crucial for the formation of organic self-assembled monolayers on semiconductor surfaces.53,54 Nevertheless, mobility was never fully appreciated for ligands on NCs, although NCs partially covered by ligands were studied theoretically previously.27,28 We speculate that the nature of the carboxylate ligand, utilizing two oxygen atoms to bind to the surface and thus being able to cover two surface atoms, helps it to reduce the diffusion barrier significantly, compared to singlebonded ligands studied previously.

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Figure 3. Projected density of states of (a) free CH3COOH molecule, (b) Cd56Se50(CH3COO)12 cluster, (c and d) [Cd56Se50(CH3COO)13]1cluster with an “extra” ligand in the bridge and chelate geometries, respectively. A 50 meV Gaussian broadening of the peaks is used. (e
g) charge densities of the HOMO for the cases of no extra ligand, bridge, and chelate ligand, respectively.

Electronic and Optical Properties. Electronic properties of the NCs are summarized in Figure 3. Valence band of the NC is formed predominantly from Se 4p states (yellow), whereas the conduction band consists of Cd 5s states (green), similarly to bulk CdSe either in zincblende or wurtzite structures. The corresponding localization of the holes on Se and electrons on Cd atoms is visible in the charge density plots of the HOMO (Figure 3e) and LUMO (Figure S2, Supporting Information), respectively. In the absence of “extra” ligands (a charge-neutral Cd56Se50(CH3COO)12 cluster (Figure 3b), the HOMO and LUMO are delocalized over the whole NC, both forming S-like envelopes (Figure 3e and Figure S2 in the Supporting Information). The three levels above the LUMO have P-like envelopes (Supporting Information, Figure S2). The HOMO
LUMO optical transition is allowed (bright). This cluster has no surface traps despite numerous surface atoms not covered by ligands (see Figure 1). Since the electroneutrality condition is satisfied, the resulting dangling bonds are either completely filled (Se) or completely empty (Cd) and do not get into the band gap. The absence of the trap states in the gap is a well-known fact for reconstructed flat surfaces.46,47 Similar observations were also made previously for the self-healed bare19,22 and ligated28 Cd33Se33 clusters and PbSe NCs,25 where surface traps were observed only on surface atoms with more than one dangling bond. Ligand-related levels in our NC remain deep in the valence and conduction bands (red and black bands in Figure 3b) and their significant broadening compared to a free ligand molecule (Figure 3a) indicates strong mixing with CdSe. Introduction of the “extra” ligand does not affect the delocalized electron and hole states, except for some distortion of their 15929

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The Journal of Physical Chemistry C envelopes (Figure S3 in the Supporting Information). This extra ligand, however, creates a new subband in the gap near the top of the valence band. Such positioning is expected for oxygen, being strongly electronegative and thus a strong acceptor. Similar behavior is expected for sulfur in thiolate ligands. A more careful examination shows that a similar ligand-related component shifted to higher energies appears for every ligand-related energy level (red and black PDOS bands with arrows in Figure 3c,d). Investigation of the wave functions in the newly formed subband confirms their localization on the ligand (Figure 3f,g). These (trap) states show a noticeable delocalization over the nearby surface Se atoms (Figure 3f and a strong yellow PDOS component of trap states in Figure 3c), despite that ligand is adsorbed on Cd. Increasing the amount of “extra” ligands increases the height and width of the trap band and leads to its significant overlap and mixing with valence states. The optical transitions from this trap band into LUMO are allowed by symmetry, and the intensity of such transitions depends mainly on their delocalization (i.e., overlap with LUMO). For the nanocrystal size used in this work, the intensity of such trap-LUMO optical transitions is comparable to the intensity of HOMO
LUMO transitions, consistent with the experimental observation of white emission from ultrasmall nanocrystals.43,44,55,56 For larger nanocrystals we expect the reduction of the trap-LUMO overlap and, consequently, reduction of the trap emission intensity relative to excitonic emission. The ligand in a chelate geometry couples weaker to the NC, resulting in its energy level being shifted deeper into the gap (purely red peak in Figure 3d) and a stronger charge localization on the ligand (Figure 3g). As a result, the optical transition from ligand to LUMO becomes practically invisible in absorption spectrum even for such a small NC. A varying pattern of ligands on the surface and their coupling to the states inside the dot will affect the overall shape of the electron and hole envelopes (Figure S3, Supporting Information) and the degree of their overlap (transition dipole moment), affecting in such a way the radiative lifetime of the exciton. In the presence of the competing (nonradiative) relaxation pathway, this can explain the fluctuating emission intensity observed experimentally.57 Similarly, the rearrangement of ligands may affect the energetic positions of the electron and hole states, resulting in a diffusion of exciton emission wavelength.58

’ DISCUSSION Role of Electronic Balance. Our simulations show that trapless NC surfaces can be prepared with minimal (and even without) participation of ligands. To achieve this, it is required to find a NC geometry where each surface atom possesses only a single dangling bond and the overall electronic balance (amount of electrons vs amount of bonds) of the NC is fulfilled. This is not possible for any NC stoichiometry but only for some specific sizes and/or shapes. Stronger ligand binding to a balanced NC also suggests a close relation of such trap-less NCs to magic size (ultrastable) NCs.44,48,49 Their potentially lower ligand coverage, however, would impose lower colloidal stability. In experimental conditions, such geometries may not always be achieved kinetically. Deviations from ideal stoichimetries and thus from electronic balance are ineviteable. As a result, partially filled, and thus situated in the gap, dangling bonds can form. The surface of the NC will try to self-heal (readjust the amount of

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bonds)19,22,47 by creating dimers, changing hybridization of atoms from sp3 to sp2, etc. However, even if this readjustment is able to eliminate the partially filled dangling bonds, the resulting local strains will affect the bandstructure, pushing some of the states into the gap. Charged ligands can help in restoring the electronic balance of the NC and at the same time preserving more bulk-like environment for surface atoms. Naively, this should help eliminate the amount of surface traps. However, some ligand geometries (e.g., on (111) facet) remain weakly bound to the surface and form the trap states themselves. Based on binding energies calculated for our model NC, one might expect the ligated (001) facet to be the most stable, favoring the cube-shaped NCs. Nevertheless, NCs of tetrahedral shape (i.e., (111)-terminated) are typically observed experimentally.31,59 Previously, for identical adsorption geometries on flat surfaces, we observed a strong dependence of binding energy on the electronic balance.53 For NCs, the balance may change with the change of NC size or shape due to possibility of charge transfer between different facets (independent of the chemical potentials of Cd, Se or ligands). Two facets, apparently unfavorable in the infinite surface calculations, may become favorable when brought together in a NC. Similar findings were recently reported for PbSe NCs.34 This highlights the inappropriateness of the infinite surface models for prediction of NC shape based on Wulff’s rule.26,59 It should be noted that cubic or platelet-like NCs (with only (001) facets) have been reported by adjusting the kinetics of NC synthesis59,60 and they represent an interesting system as potentially trap-less NCs. Our preliminary analysis suggests, however, that a cubic shape does not provide enough adsorption sites for ligands to fulfill the electronic balance of the NC (since ligand in bridge geometry covers two Cd sites). We expect, thus, that in order to become more stable than tetrahedral shape, cubic NCs have to adsorb additional ligands in less favorable geometries, potentially creating surface traps. Consequences for Blinking. Dependence of the trap level energy on ligand geometry, combined with the surface diffusion of the ligand, results in a spectral diffusion of the trap levels. Such a feature is a central requirement in some phenomenological models of blinking.36
38,61 The spectral diffusion due to switching bridge-chelate configurations observed in this work is so fast (subpicosecond) that it hardly can induce the irregularities in tunneling from the core to the traps required for the power-law blinking statistics.36,37 The ligand diffusion on a larger scale, however, provides a mechanism of a random walker in a phase space of dark and bright configurations.36 A switchable long-lived trap state, required by the conceptually similar multiple recombination centers (MRC) model of blinking,61 can be prepared within our model. As we have discussed, adsorption of the ligand on the Se-rich (
111) facet can be stabilized by pulling out the Cd atom from the subsurface layer. Here we note that this process is accompanied by the formation of a deep and strongly localized trap level in the gap. A low frequency of activating such defects (long fluorescence ON times) is achieved by the requirement for the diffusing ligand to appear in a specific area of the NC surface (especially if this area is energetically unfavorable). A longer fluorescence OFF state can be achieved by consecutive activation of multiple similar defects, as suggested in the original model.61 We believe that adsorption of ligand on Se facet can be sufficiently long-lived for nonradiative recombination to happen and render the NC dark. We cannot however estimate at this moment whether our particular example of a diffusion-activated 15930

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The Journal of Physical Chemistry C defect (or multiple such defects activated consecutively) can last for hundreds of seconds. The presence of the whole band of trap states overlapping with the valence band in our model implies the need to populate all of those states with holes before excitonic emission becomes possible. In the absence of a similar trap band near the conduction band this would lead to accumulation of multiple electrons in the core. Recent findings challenging the validity of the (single) charging model of blinking8,62 suggested that photoluminescence quenching due to Auger process could still be compatible with experimental observations if multiple charging was possible. Significant imbalance in the amount of electrons and holes in the core is clearly easily achievable when many traps are available. Even in the presence of the energetic gap between the valence band and traps, the transfer of the carriers from core to traps would still be possible due to rare significant spectral shifts of the trap levels accompanying ligand diffusion. Similarly, in the presence of the shell, excitation with energies beyond the barrier also allows for a significant part of photogenerated holes to be lost into traps.

’ CONCLUSIONS In conclusion, we have investigated with ab initio methods the surface states in realistic CdSe NCs with carboxylic acid ligands, highlighting the importance of the electronic balance for the electronic properties and growth of the NCs. Developed prototypical model of the NCs should come useful for future simulations. We show that it is possible to construct trap-less NCs even in the presence of surface atoms with dangling bonds (i.e., uncovered by ligands). On the contrary, excess ligands can produce surface traps even in the idealized NCs. The ligand-related trap states are found to reside near the top of the valence band. NCs are found to be highly dynamic even when external environment is not considered. Some of the ligands have a negligible energy barrier for diffusion over the surface. Spatial diffusion is accompanied by a spectral diffusion of the trap energy levels and a varying degree of charge localization. Ligand diffusion can explain the emission wavelength and lifetime variations, and offers a flexible tool to build atomistic examples of the processes required by phenomenological blinking models. ’ ASSOCIATED CONTENT

bS Supporting Information. Simulation input files, 3D structures of the NCs, and charge densities of states from conduction band. This material is available free of charge via the Internet at http://pubs.acs.org. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT We thank Eleonora Piven, Kui Yu, Pavel Frantsuzov, Svetlana Kilina, and Pawel Hawrylak for fruitful discussions and NRCNSERC-BDC project for funding.

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dx.doi.org/10.1021/jp205784g |J. Phys. Chem. C 2011, 115, 15927–15932