Hole Surface Trapping in CdSe Nanocrystals: Dynamics, Rate

Letter pubs.acs.org/NanoLett

Hole Surface Trapping in CdSe Nanocrystals: Dynamics, Rate Fluctuations, and Implications for Blinking Francisco M. Gómez-Campos†,‡,§ and Marco Califano*,¶,§ †

Departamento de Electrónica y Tecnología de Computadores, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain CITIC-UGR, C/Periodista Rafael Gómez Montero, n 2, Granada, Spain ¶ Institute of Microwaves and Photonics, School of Electronic and Electrical Engineering, University of Leeds, Leeds LS2 9JT, United Kingdom ‡

S Supporting Information *

ABSTRACT: Carrier trapping is one of the main sources of performance degradation in nanocrystal-based devices. Yet the dynamics of this process is still unclear. We present a comprehensive investigation into the efficiency of hole transfer to a variety of trap sites located on the surface of the core or the shell or at the core/shell interface in CdSe nanocrystals with both organic and inorganic passivation, using the atomistic semiempirical pseudopotential approach. We separate the contribution of coupling strength and energetics in different systems and trap configurations, obtaining useful general guidelines for trapping rate engineering. We find that trapping can be extremely efficient in core-only systems, with trapping times orders of magnitude faster than radiative recombination. The presence of an inorganic shell can instead bring the trapping rates well below the typical radiative recombination rates observed in these systems. KEYWORDS: Trapping, CdSe nanocrystals, Auger processes, surface states, pseudopotential method NCs into thin films for device incorporation, as suggested by the large reduction of quantum yields (QYs) in these systems.9,10 Aging and phototreatment can also result in a loss of surface ligands and an increase of trapping sites,11−15 as can dilution and purification processes.7 Moreover, extrinsic trap states of various depths can be introduced by specific capping groups, depending on their electronegativity.16 The situation is complicated even further by the heterogeneity of the ligand/nanoparticle distributions within a sample and in samples synthesized in different conditions.17 Inorganic passivation, on the other hand, is believed to remove most trap states far from the optically active region of the NC core, increasing PL quantum yields and decreasing emission intermittency (blinking)18 sometimes, however, at the expense of introducing defects (and therefore trap sites, albeit of a different origin) at the interface19 if core and shell materials

T

he photophysics of semiconductor nanocrystal (NC) quantum dots is critically affected by surface interactions. In particular, charge carrier trapping at the surface (and interface, in the case of core/shell structures) represents a dominant effect in the decay dynamics of exciton and multiexciton states,1 reducing photoluminescence (PL) quantum yields, limiting the lifetime and bandwidth of optical gain, leading to large nonradiative losses in light-emitting diodes, hindering efficient charge transfer/transport for photovoltaic applications,2 limiting the switching speed and response time of NC field effect transistors,3 and generally negatively affecting the performance of NC-based optoelectronic devices. Yet very little is known about the specific mechanisms that govern this phenomenon. Owing to the partial passivation achieved by most ligands,4−8 unsaturated bonds are present on the NC surface. This gives rise to a distribution of intrinsic trap sites that can potentially trap electrons and/or holes at the surface. A further degradation of the passivating ligand coating, with consequent creation of more surface trap sites, may also be caused when casting the © XXXX American Chemical Society

Received: April 30, 2012 Revised: July 29, 2012

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dx.doi.org/10.1021/nl3016279 | Nano Lett. XXXX, XXX, XXX−XXX

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are not lattice matched.20 Indeed, both interface- and surfacetrap dynamic signatures were recently identified in timeresolved PL measurements on CdSe/CdS/ZnS core/multipleshell NCs.21 Surface hole trapping was also observed in CdSe/ ZnS spherical dots,22 and CdSe/CdS/ZnS elongated structures,23 and signatures of surface-state emission were found in CdSe/ZnSe core/shell NCs.24 Despite it representing a central node in exciton relaxation dynamics, a comprehensive theoretical picture of the detailed mechanism of carrier transfer to a trapping site is, however, still elusive. In particular no explicit calculation of trapping rates using realistic trap state wave functions and reliable coupling matrix elements to core states exists. Many models have been proposed to qualitatively explain the trapping dynamics, but most of them are fundamentally variations of the Augerrecombination-mediated hypothesis,25 originally suggested to explain blinking,26−28 in which the presence of two (or more) electron−hole pairs in the NC enables efficient nonradiative energy transfer (Auger recombination, AR) between a recombining pair and one of the remaining carriers, which is ejected from the NC core and can end up either in a surface trap or in the surrounding matrix (the resulting “ionized″ state is dark as any subsequent photogeneration of an electron-hole pair is followed by a similarly efficient AR process, which is orders of magnitude faster than radiative recombination). A fundamental limitation of this model is that in order for AR to occur, at least two excitons need to be present in the NC. The interpretation of trapping events occurring at very low excitation densities, where the probability to create two excitons in one pulse is negligibly low, represents therefore a problem when the excitation rate is slower than the photoproduct radiative lifetime. Jones et al.21 explained the trap state dynamics they observed in time-resolved PL measurements in CdSe/CdS/ZnS samples, using classical Marcus electron transfer theory. 29 The parameters they obtained required a minimum of two trap distributions, K1 and K2, to reproduce the decay functions at 12 temperatures with remarkable accuracy. On the basis of their different reorganization energies, they were identified as surface trap sites on the ZnS shell and interfacial traps close to the CdSe core, respectively. From the fitting process, it was estimated that 13.1 trap states of K1 type and 1.2 of K2 type were present on average on a single NC. In that model, a single parameter set (reorganization energy λK and electronic coupling integral VK) was assumed for each radial “trap shell”, implying that all interactions with traps at a particular surface/interface were identical. This assumption, although not unreasonable, is questionable, as trap states in different locations on the surface may have different overlaps with the band edge wave functions, although nominally at the same distance from the dot center. Kern et al.30 studied the electron trapping kinetics in CdSe NCs without inorganic shells, using multiple population-period transient spectroscopy (MUPPETS).31 As in the case of Jones21 they also found highly disperse trapping rates, where the ensemble kinetics fit a slow power law t−α, with α = 0.16 over more than three decades in time, with each nanoparticle exhibiting, however, an exponential decay. They explained these highly heterogeneous rates by assuming a uniform distribution of 3−5 defect sites on each NC within the electric field created by the NC dipole moment. Knowles et al.32 applied a combination of transient absorption and time-resolved photoluminescence spectros-

copies to compile a charge-carrier resolved map of the radiative and nonradiative decay pathways from the band edge exciton, in CdSe NCs with their native ligands. They found evidence for multiple excitonic states where the hole is not in the valence band but in a trapped state and nevertheless still maintains a large coupling with the delocalized electron. By fitting their results to a sum of exponentials, they identified six decay components, spanning five decades in time from hundreds of femtoseconds to tens of nanoseconds and assigned them to the decay of three different subpopulations of NCs, differentiated by the distributions of available traps, each with distinct trapping constants. Different trapping pathways have been recently identified by Kambhampati’s group, depending on whether the initial state is a hot or cold exciton.1,11−13 Interestingly, in the case of a cold (i.e., band edge) exciton, surface trapping was observed to occur only for the hole but not for the electron. Since this is the most relevant excitonic configuration, as it can be obtained either by direct excitation, or as the final stage of relaxation, following a high energy excitation, in this Letter we will focus on the trapping of the band edge exciton at the NC surface/ interface in different structures (core-only and core/shell NCs) and for different shell materials (CdS and ZnS). Using LDAquality wave functions within the atomistic semiempirical pseudopotential approach, we investigate the efficiency of hole transfer to a variety of trap sites, characterized by different depths and degrees of wave function localization and overlap with core states, via the Auger-mediated trapping (AMT) mechanism schematically represented in Figure 1. This process

Figure 1. (a) Schematics of the Auger-mediated trapping mechanism considered in this work: the energy of the hole transition hs → ti from the band edge hs to the trap site ti is transferred nonradiatively to the core band edge s-like electron, which is excited into one of the core p states (all single-particle states in both conduction and valence bands used in the calculations are included in the schematics). (b) The different NC structures and traps configurations investigated: surface traps on (i) core-only and (ii−iv) core/shell NCs with different core sizes and shell materials; interface traps on (v−vi) core/shell NCs with different core sizes, shell materials, and shell thicknesses.

is the inverse of the Auger-mediated p-to-s electron relaxation, responsible for the absence of an observable phonon bottleneck in semiconductor NCs.1,14,33−36 It was originally proposed by Frantsuzov and Marcus37 in the first model that explained quantum dot blinking without assuming the existence of longlived electron traps. In that seminal paper,37 however, the trapping rates were not calculated explicitly but cast in exponential form B


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200 μeV37 based on an estimated value of about 3 × 1011 s−1 for the rate of the non-Auger, phonon-assisted 1p-to-1s electron relaxation.34 This choice, although having some influence on the value of the trapping rate at resonance (i.e., for Ef = Ei), determines primarily the rate of change of the lifetime as a function of energy for Ef ≠ Ei: the smaller the value of Γ, the larger the variation of the trapping rates with E. Given that most of the trapping transitions considered here do not occur at resonance, increasing Γ would generally decrease the trapping times, increasing the trapping efficiency (further details and a comparison of the rates calculated using different values of Γ can be found in the Supporting Information). For T ≠ 0 a Boltzmann average over the initial states was computed (the effect of temperature on the calculated trapping rates is discussed in more detail in the Supporting Information). The single-particle energies and wave functions were calculated using the plane-wave semiempirical pseudopotential method described in ref 40, including spin−orbit coupling, and excitonic effects were accounted for via a configuration interaction scheme.41 (More detailed information on the theoretical method can be found in the Supporting Information). Core-Only Nanocrystals: Very Strongly Confined Systems (R = 14 Å). The results of our investigation show that, as in the case of the electron,30 the hole trapping times are highly dispersed and range from hundreds of femtoseconds to tens of nanoseconds, even in the case of a single trap. This can be clearly seen in Figure 2a, where we show the calculated AMT rates for selected surface states, positioned at different locations on the surface of a NC core with R = 14.6 Å. In the main panel, we account for possible variations ΔE in the trap depth around its calculated position (ΔE = 0), due to both internal and external causes, such as the presence of an intrinsic dipole moment in the NC,30 or the interaction with the dielectric environment (where more or less electronegative capping molecules and different types of solvents may be present).42 The effect of energy diffusion of the sp splitting in the CB, for a fixed trap depth, is displayed in the inset of Figure 2a, for the case of two different traps (ΔE = 0 corresponds to no diffusion). Trapping times as fast as hundreds of femtoseconds are observed, with variations of about 2 orders of magnitude for energy diffusions as small as 1 meV. Although the magnitude of these oscillations is consistent with that obtained by Frantsuzov and Marcus37 with their phenomenological model, the maximum rates obtained here are 2 orders of magnitude larger. Similarly to what was found by Jones et al.,21 we identify two trap distributions, according to their trapping efficiency. However, unlike in ref 21 in our case they are not located at different distances from the NC center (one on the outermost ZnS shell and the other at the CdSe core/shell interface) but are all situated on the core surface. Interestingly, their trapping efficiency is associated to the type of Se dangling bonds (single or double) they were created from: type I traps (obtained by unpassivating single dangling bonds) exhibit trapping times of nanoseconds or above, whereas type II traps (where one of a pair of dangling bonds was unpassivated, see Supporting Information for details) are generally more efficient with typical trapping times of the order of 1 to 100 ps, in NCs with R = 14.6 Å. There are some exceptions, though. Figure 3 displays a position-resolved map of hole surface trapping rates for a NC with R = 14.6 Å, (the rates shown were obtained by removing a single passivant at a time). Se passivants are shown in color

⎛ (ε − ε )2 ⎞ i ⎟ k t(ε) = ∑ Ai exp⎜ − 2 Γ ⎝ ⎠ i

and, most importantly, the crucial parameter Ai, which gives the trapping amplitude, as well as the other quantities (the transition energies εi and the broadening Γ), were determined empirically. The whole kt(ε) curve, in fact, was obtained from assumptions based exclusively on empirical data and observations. And, despite its behavior being crucial for the applicability of the model, no explicit calculation of these rates has ever been performed. This is what we aim to do here. Other mechanisms could account for the observed efficient hole trapping at the surface: a simple diffusion model has been proposed,38,39 where the carrier average transit time from the center of a NC of radius R to its surface is given by τ = R2/π2D (where D is the diffusion coefficient). As in the case of Jones et al.,21 however, this model predicts identical trapping times for traps located at the same radial distance from the NC center and therefore for virtually all surface traps in the case of a spherical NC. Alternative trapping mechanisms could include coupling to phonons or energy transfer to high frequency molecular vibrational modes of the ligand shell, similar to the process proposed by Guyot-Sionnest et al.16 to explain the electron 1P-to-1S relaxation in the absence of a hole. Obtaining a reliable estimate of AMT rates and assessing the efficiency of this process, apart from furthering our understanding of carrier trapping kinetics in these systems, is of paramount importance for identifying which of these mechanisms is the main responsible for the degradation of the performances of many NC-based devices and devise strategies to suppress unwanted effects in future designs. In what follows we will address the following fundamental questions: How efficient is band edge hole Auger-mediated transfer to a surface/interface-localized site compared to radiative recombination? Are hole trapping rates as highly distributed as recent experimental observations seem to indicate? If so, what are the origins of this spread? Does the specific chemistry of the ligands and/or solvent need to be taken into account to explain the trapping process? What is the effect of the presence of inorganic shells of different semiconductor materials on the trapping efficiency? Can realistic AMT rates account for all the features requested to explain blinking? The AMT rates were calculated in Se-centered, nearly spherical, quasi-stoichiometric CdSe core-only NCs with wurtzite crystal structure and R = 14.6 and 19.2 Å, and CdSe/CdS and CdSe/ZnS core/shell NCs with Rcore = 10.2, 14.6, and 19.2 Å, and Rshell ≥ Rcore + 1 ML. Auger rates for the transition |1es,1hs⟩ → |1ep,1ht⟩ (see Figure 1) from the band edge exciton to a surface trapped exciton (es and hs are the conduction band minimum [CBM] and the valence band maximum [VBM], both with s-like symmetry, while ep and ht are the electron p-like states and the hole trap state) were calculated using Fermi’s Golden Rule applying a Lorentzian line broadening to the delta function, according to36 (kAMT)i =

Γ ℏ

∑ n

i|ΔH |fn

2

(E fn − E i)2 + (Γ/2)2

(1)

In (eq 1) |i⟩ and |f n⟩ are the initial and final excitonic states, Ei and Efn are their energies, ΔH is the Coulomb interaction and ℏ/Γ is the lifetime of the final states. The value used here is Γ = C


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Figure 3. Position-resolved map of the AMT rates calculated for a NC with R = 14.6 Å, by removing a single passivant at a time. Only hole trap states are colored. Se and Cd atoms and Cd passivants are shown in gray. The cartoon depicts a schematics of the AMT transition.

elements (numerator of (eq 1)) as a function of the energy difference between the initial excitonic state and the lowermost final excitonic state. If this difference is negative, the energy is not conserved in the transition (as there is no overlap between the energy windows of initial and final states - see cartoon in Figure 2b); if it is positive, however, energy is only conserved if the difference does not exceed the width of the final states energy window ( 18 Å. However, building on the knowledge acquired studying smaller NCs, we were able to

Figure 2. AMT rates (a) and matrix elements (b) calculated for transitions to selected traps on the surface of a CdSe core with R = 14.6 Å. The rates are plotted as a function of the variation of the trap depth ΔE, around its calculated position ΔE = 0. The legend indicates the number of the trap and its type (I or II, see text) and position (t = top, c = corner, m = middle, b = bottom) on the surface. The latter is also illustrated in the spacefill representation of the NC (atomistically accurate) where the different traps are color coded to match the curve relative to their calculated AMT rates (the white and gray atoms represent Se and Cd passivants, respectively). The inset in panel (a) displays the effect on the AMT rates of energy diffusion of the s-p splitting in the conduction band for a fixed trap depth (ΔE = 0 in a). The matrix elements are displayed as a function of the energy difference between the initial excitonic state Ei(n) and the lowermost final excitonic state Ef(1). The different regimes corresponding to the positive and negative values of Ei(n) − Ef(1) are schematically depicted by the cartoons. The legend in (b) reports the trapping times for the different traps calculated for ΔE = 0 in (a).

whereas all other species present (Se and Cd atoms and Cd passivants) are shown in gray. Although it is apparent that type I traps have small trapping rates, not all type II traps are very efficient (removal of a yellow or green passivant in a double bond yields rather inefficient traps. More details on this can be found in the Supporting Information). These findings of distributed trapping rates for traps nominally located at equal distance from the NC center contrast with simple assumptions of distance-related trapping efficiencies and coupling strengths.21,37−39,43 As can be deduced from a careful inspection of both (eq 1) and Figure 2, two effects are at play in the determination of the magnitude of kt: the Auger coupling and the energy conservation in the AMT transition. These two contributions are decoupled in Figure 2b, where we show the AMT matrix D


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that in larger NCs, type II traps can be so shallow (i.e., so energetically close to the band edge states) that they are likely to interact with the VBM, undergoing a sort of hybridization, which results in a deeper penetration of their wave function into the NC core (although the charge density in this region is about 2 orders of magnitude smaller than on the surface, where the passivant has been removed), yielding larger Auger couplings. This results in a higher trapping rate despite energy nonconservation in the transition. On the other hand, type I traps are more localized on the surface and, especially if located close to the Cd-terminated surface normal to the c axis, as it is the case for t168, experience smaller overlaps with the band edge hole states, resulting in much smaller AMT matrix elements. A similar behavior, in terms of energy distribution and wave function localization, was previously predicted to occur for anion-derived hole surface states (i.e., states created by unpassivating S dangling bonds), in similarly sized CdS NCs (with R = 4a, where a is the CdS bulk lattice constant), using an atomistic tight-binding method.45 We find, however, that deep penetration into the core is not sufficient for a trap wave function to guarantee large AMT coupling, as its overlap with the VBM wave function can still be small if the peaks of the respective charge densities occur at different locations. The different degree of wave function overlap is also reflected in different binding energies of the surface-trapped exciton: we calculate a value of 260 meV for the most inefficient trap (t168) compared with about 400 meV for the most efficient one (t71), assuming a dielectric constant εout = 2.234. Such highly distributed trapping times are in agreement with the results of a recent experimental study by Knowles et al.,32 where the presence of several populations of traps in solutionphase samples of CdSe NCs was suggested as the origin of the observed distribution (from 1 ps to 50 ns) of band edge exciton decay time constants. Our calculated trapping times are also consistent with the estimate of 10−20 ps1 as an upper limit for excited state (or hot exciton) surface trapping times. In fact, this process is expected to occur on a faster time scale compared to the band edge exciton trapping dynamics considered here, due to the larger overlap between the wave functions of highly excited carriers and those of the surface states. With a lower limit of about 1 ps for small NCs and of about 100 ps for larger ones, the trapping times calculated here confirm the validity of these predictions. Furthermore their weak temperature dependence found in our study (see Section 3 in the Supporting Information) seems to suggest that the dramatic increase in PL quantum yield observed at low temperature in these systems could be due to a “freezing” of the traps activation mechanism, rather than to a temperature dependence of the trapping mechanism itself. Core/Shell Structures: Surface Traps. Surface trapping rates are expected to be affected by the presence of inorganic passivation (i.e., in the case of core/shell NCs), principally owing to a reduction of the coupling with band edge states, caused by the larger separation between the relative wave functions. We investigated the effect of the presence of shells made of the most commonly used semiconducting materials, CdS and ZnS (ZnSe), which provide different degrees of confinement to the core states, on the calculated hole transfer time to a surface state. The results are presented in Figure 5 and Figure S8 (Supporting Information). In order to isolate the effect of reduced overlap between trap states and coredelocalized states from possible reductions in trapping rates due to different trapping efficiencies of the trap itself (which we

identify all the relevant regions of the NC surface and deduce from symmetry consideration a reliable description of the rates for the whole trap states distribution for a NC with R = 19.2 Å, based on a limited sampling. An example of the AMT rates of a subset of traps used in such a sampling is presented in Figure 4, where the results are plotted using the same criteria as in Figure 2.

Figure 4. AMT rates (a) and matrix elements (b) calculated for selected traps in different locations on the surface of a CdSe core NC with R = 19.2 Å. See Figure 2 for details on the representation.

In this case energy resonance between initial and final excitonic states is never achieved, regardless of the type of traps considered. Nevertheless there is a clear difference in efficiency between type I and type II traps, the former characterized by typical trapping times of the order of tens to hundreds of nanoseconds, whereas the latter exhibiting typical trapping times of the order of hundreds to thousands of picoseconds. The origin of this difference can be traced back to the different strength of AMT coupling with core states experienced by the two types of traps, which can vary by as much as 3 orders of magnitude between very efficient and very inefficient traps (see Figure 4b). In contrast, in the case of NCs with R = 14 Å, the AMT integrals of type I and type II traps differ by at most a factor of 10 (see Figure 2b). The different behavior in that case reflects the transition to extremely strong spatial confinement, occurring for R < 18 Å,44 where the overlap between surface states and core states does not show large position-dependent variations. In this regime, the amplitude of the core states on the surface is almost isotropically distributed and the extent of the wave function localization is similar for every trap, regardless of its position on the surface. In contrast, we find E


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surface anion species being Se only for the CdSe core-only structure of case (i), in all cases (i−iv) we consider the same two surface states (t71 and t168, the most and least efficient, respectively, among the traps considered for a NC with R = 19.2 Å) whose trapping rates in case (i) were displayed in Figure 4. This assumption is, however, not unrealistic since, as mentioned earlier, S-derived hole trap states were found45 to exhibit similar characteristics to the Se-derived surface states considered here. Our model accounts for the effects of different shell materials through (a) the different confinement that conduction and valence band states experience in each material but also (b) the different dielectric constants used in the calculation of both exciton energies and AMT matrix elements (further details on the model can be found in the Supporting Information). The cases (i−iv) represent configurations with increasing confinement for the core wave functions, which are progressively removed farther away from the surface (see Supporting Information Figure S5) and, correspondingly, with decreasing coupling (i.e., overlap) with the trap state. In (i) both conduction and valence band states are allowed to sample the NC surface; in (ii) only the electron wave function can extend to the surface, whereas the hole is confined to a region of radius Rhole = 14.6 Å; in (iii) both electron and hole are confined to the same region with R = 14.6 Å; finally in (iv) the motion of both electron and hole is restricted to a 10.2 Å radius sphere. The calculated AMT rates for trap 71 decrease accordingly, with a trapping time of 79 ps for the core only NC, increasing by almost 1 order of magnitude for each step of increasing core state confinement away from the surface, up to a value of 89 ns for the CdSe/ZnS structure with the smallest core. This increase reflects the expected decrease of AMT coupling, shown by the matrix elements in Figure 5b. As the ZnS thickness in this last case is only ∼2 monolayers (MLs), the presence of thicker shells >4 MLs is expected to lead to a suppression of AMT. This is confirmed by the observation of blinking suppression in “giant” CdSe/CdS core/shell NCs.47 The situation is however completely different and seemingly counterintuitive when considering the least efficient trap (t168), for which the trapping time exhibits a nonmonotonic behavior with an overall decrease from (i) to (iv), due to the dominant role played by energy conservation (the energy denominator in (eq 1)) in this case (see Figure S8 and relative discussion in the Supporting Information for further details). Core/Shell Structures: Interface Traps. In the presence of an inorganic shell, however, traps can also occur at the core/ shell interface as well as on the external surface, as suggested by Jones et al.21 We model an interfacial trap as an unsaturated Se dangling bond on the CdSe core surface, surrounded by an inorganic semiconductor. The effect of the shell material is captured here by setting an appropriate value for the dielectric constant of the NC matrix (we choose εout = 8.9 to simulate the presence of common shell materials such as ZnS and ZnSe) in the calculation of both the excitonic energies and the AMT matrix elements. The radius of the shell is therefore irrelevant (provided the trap is at the interface) and our results are valid for arbitrary shell thicknesses. In Figure 6 and Figure S9 (of the Supporting Information), we compare the calculated Augermediated transfer rates to a trap on the surface of a CdSe core with, respectively, R = 14.6 Å and R = 19.2 Å, before and after shell growth, in the case of a type I (t89 for R = 14.6 Å, and t168 for R = 19.2 Å) and a type II (t95 for R = 14.6 Å, and t71

Figure 5. AMT rates (a) and matrix elements (b) for transitions to trap t71 on the surface of: a CdSe core-only NC with R = 19.2 Å (red curves), a CdSe/CdS core/shell NC with Rcore = 10.2 Å, and Rshell = 19.2 Å (black curves), a CdSe/ZnS core/shell NC with Rcore = 14.6 Å, and Rshell = 19.2 Å (green curves), and a CdSe/ZnS core/shell NC with Rcore = 10.2 Å, and Rshell = 19.2 Å (blue curves). The cartoons in (b) indicate the energy conservation conditions for the different transitions whose matrix elements are displayed. The legend in (b) reports the trapping times for the different configurations calculated for ΔE = 0 in (a).

have shown to vary greatly depending on the trap), we use the same trap in all calculations and reduce the effective coupling with the core by reducing the core size. In other words, we fix the maximum radius of the NC to Rmax = 19.2 Å, (and with it the position of the trap on the surface) and consider the following systems: (i) a CdSe core with Rcore = Rmax; (ii) a CdSe/CdS core/shell NC with Rcore = 10.2 Å, and Rshell = Rmax; (iii) a CdSe/ZnS core/shell NC with Rcore = 14.6 Å, and Rshell = Rmax; (iv) a CdSe/ZnS core/shell NC with Rcore = 10.2 Å, and Rshell = Rmax. It is well-known that a CdS shell only confines the holes but not the electrons. Indeed ab initio calculations46 showed recently that, owing to the negligibly small conduction band offset between CdSe and CdS in a nanostructure, the wave function of the electron band edge in a CdSe/CdS NC with total radius Rtot is almost indistinguishable from that calculated for a CdSe core with R = Rtot. The hole wave function was instead found46 to be strongly suppressed at the surface and mostly (but not exclusively) localized in the core region. In the presence of a ZnS shell, complete confinement to the CdSe core is expected for both electrons and holes, as suggested by the absence of any appreciable red shift in the observed optical spectra, following shell growth. Despite the F


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Figure 6. Comparison of AMT rates (a,b) and matrix elements (c,d) for transitions to: (1) traps (t95, a.d; t89, b.c) located at the surface of a CdSe NC with R = 14.6 Å, before (red curves), and after (cyan curves) the growth of a ZnS (or ZnSe) shell of arbitrary thickness, that does not passivate the trap; (2) traps (t71 and t168) on the shell surface of a CdSe/ZnS core/shell NC with Rcore = 14.6 Å, Rshell = 19.2 Å, (orange [t71] and black [t168] curves). The cartoons in (c,d) indicate the energy conservation conditions for the different transitions whose matrix elements are displayed. The legend in (c,d) report the trapping times for the different configurations, calculated for ΔE = 0 in (a,b).

for R = 19.2 Å) trap. We find that the Auger-mediated transfer efficiency to a type I trap such as t168 and t89 can be unaffected by the growth of an inorganic shell of arbitrary thickness if the shell does not passivate the dangling bond associated to that specif ic trap. On the other hand, the trapping time to a type II trap can increase by almost 3 orders of magnitude in a NC with R = 19.2 Å and by over 6 orders of magnitude in the case of an extremely strongly confined system (R = 14.6 Å) under identical conditions, leading to trapping rates ktj ≲ krad in all cases (a detailed discussion can be found in the Supporting Information). This suggests that the increase in QY usually observed following shell growth, could, contrarily to common beliefs, not be related to an improved passivation (i.e., the removal of traps from the core surface), but simply to an increase in trapping times, as the recent observation of interface−trap dynamic signatures in time-resolved PL measurements on CdSe/CdS/ZnS core/multiple-shell NCs21 would seem to confirm. This hypothesis is also consistent with the results of time- and frequency-resolved spectroscopic measurements of hole trapping performed in ref 11. Determining the origin of the QY increase following shell growth is of paramount importance for device applications. The presence of interface trap states in inorganically capped NCs could in fact affect their electronic charge transport properties. Indeed hole trapping has been recently identified as the cause of hysteretic response and low switching speed in field effect transistors based on solution-processed arrays of inorganically capped CdSe NCs.3 If the shell does not remove the core surface states, then interface traps will coexist with traps that may occur on the

shell surface. These two kinds of traps can exhibit similar trapping efficiencies, still however with ktj ≲ krad. This is the case, for example, for t168 (on the shell surface) and t95 (at the core/shell interface), as shown by the black and cyan curves in Figure 6a, and for t71 (shell surface) and t89 (interface) in Figure 6b (orange and cyan curves). If the shell does passivate the trap state on the CdSe core surface, then any eventual trap can only exist on the shell surface. Increasingly thick shells will then remove it further away from the core, reducing its coupling with the band edge delocalized states, leading to a complete suppression of AMT for thick enough shells, as discussed above and observed experimentally. The situation is, however, complicated by the fact that, as shown in recent TEM images,48 core/shell structures are not always spherical and the shell thickness itself may vary from 1 to more than 4 MLs both within a single NC and across the ensemble. This anisotropic growth of the shell can also lead to different behaviors of the trapping efficiency as a function of the nominal shell thickness, depending on the position of the trap on the surface. Multiple Traps. In the case of multiple traps (both randomly and uniformly distributed on the surface), we found that, unless two traps originate from the same Se atom (i.e., both passivants are removed from a double dangling bond), there is no interaction between the localized wave functions or, in other words, the traps are independent. As a consequence, the total trapping rate of a distribution of traps on a single NC is the sum of the rates of the single traps. Therefore, if an efficient trap is present, the total trapping time is going to be fast. The probability of having fast trapping is G


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absorption due to hole traps.1 Our results are consistent with this view and compatible with a contribution from hole trapping to the exciton population decay observed by Kern et al.30 Unlike in their case, however, the heterogeneity at the origin of the high rate dispersion is due here to intrinsic rather than external causes. The different location of the traps on the surface is sufficient to explain their different energies and coupling strengths with core states without the need for any interaction with external fields. Implications for Blinking. Several authors have suggested the presence of trapped charges to explain emission intermittency;37,49−52 one of the most attractive models, proposed by Frantsuzov and Marcus37 (recently also found consistent with the results of state-of-the-art off-state fluorescence decay times measurements in single CdSe/ZnS NC53), indeed associates the switching to an off state with the activation of a number of hole traps. The highly distributed trapping efficiencies that we find here, exhibiting large variations of the trapping rates as a function of the trap energy for a single trap, are a fundamental requirement of this model.37,54 In this respect, our investigation provides the first quantitative theoretical support to this essential aspect of one of the most successful blinking models to date. Despite all this, however, the Auger-mediated (or any other) trapping process alone is insufficient to reproduce the features observed in fluorescence intensity time traces and the relative “on-time” and “off-time” probability densities; in order to explain blinking, a further mechanism is required that accounts for the variation in time of either the energy of the transition (energy diffusion)37,51,54 or the activation (and deactivation) of the trap state(s).52 Conclusions. In summary, atomistic modeling of Augermediated hole transfer to localized gap states in CdSe nanocrystals, evidenced a complex behavior for the trapping rates with large variations occurring in both energy and coupling strength among trap states located at nominally the same distance from the dot center. The effects of the presence of inorganic shells of different materials and thicknesses were also shown to depend strongly on the type of trap considered (efficient or inefficient) for trap states located both at the surface and at the core/shell interface. NC with different sizes were studied, representative of very strong and strong confinement regimes. While in the former regime the AMT coupling was found to be similar for type I and type II traps, in the latter a clear separation was found between efficient and inefficient traps. The consequence is that for extremely confined structures trapping rates are dominated by energy conservation, whereas for larger structures it is a combined effect of AMT coupling strength and energy resonance in the trapping transition that determines the efficiency of a trap. In the case of efficient traps, the growth of a shell leads to a decrease of the trapping rates, whereas for inefficient traps, for which the trapping time is already slower than radiative recombination, the presence of a shell may not produce observable effects. The results of this study showed that in order to suppress hole trapping to levels where it is no longer competitive with radiative recombination the most effective strategy seems to be to modify the energetic position of the traps (pushing them deeper into the gap), as a small variation of their energy has been found to greatly vary their trapping efficiency. This can be achieved either externally (by using external electric fields or by modifying the dielectric environment of the NC) or intrinsically, by, for example, varying the

thus given by the ratio between the number of type II passivants and the total number of Se dangling bonds on the surface, which can be calculated exactly for each NC size: it ranges from 0.44 to 0.55 for 14.6 ≤ R ≤ 28 Å, exhibiting a slight, nonmonotonic variation with size. However, this is a rather crude approximation since, as we have seen previously, not all type II traps are very efficient. Nanocrystal Ensembles. Another interesting issue to be discussed is the effect of the presence of single traps in an ensemble of NCs, as this is the typical configuration investigated in most experimental settings. We assume that all hole surface traps have the same probability of being activated (i.e., all Se dangling bonds have the same probability of remaining unsaturated by the capping group). Considering that trapping is a nonradiative decay process in competition with radiative recombination, we can calculate the hole band edge population decay and hence the band edge exciton population decay of the ensemble, as f (τ ) ∝

∑ P(k t )e(−k τ) tj

j

(2)

A reasonable assumption is to consider the probability of a given trapping rate, P(ktj), to be proportional to the number Ntj of equivalent trapping sites on the NC surface. In other words, to assume that the most likely trapping rate for a single NC is that associated with the largest number of traps with that specific rate. The band edge exciton population obtained is displayed in Figure 7: f(t) approximately follows a power law

Figure 7. Trapping probability as a function of time for a NC ensemble with R = 14.6 Å. The calculated curve (black line) fits a power law t−α with α = 0.07 (red line) for decay times between 0.2 and 500 ps.

for over three decades. We fitted this expression (eq 2) to t−α and obtained α = 0.07 for decay times from 0.2 ps up to 500 ps (above 1 ns f(t) is dominated by the less efficient trapping states, i.e., those arising from the removal of a type I passivant, and exhibits an exponential decay). Interestingly a similar behavior was observed by Kern et al.30 in the band edge exciton population of CdSe cores, which exhibited a power law decay t−0.16 from 0.5 ps to 1.8 ns, despite an exponential decay at the single NC level. As the experimental technique they adopted (MUPPETS)31 is an extension of transient absorption spectroscopy, they attributed the observed decay to electron trapping, as absorbance is commonly believed to be insensitive to hole dynamics in this setup. However, this assumption has been recently challenged by Kambhampati’s group, who suggested the presence of a secondary contribution to H


Nano Letters

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NC shape to induce/enhance an internal dipole. The growth of inorganic shells can also drastically decrease the AMT rates below radiative recombination rates by decreasing the coupling with core states (in case the inorganic passivation removes all traps on the core surface) or by increasing the dielectric screening in the interaction (if the trap remains at the core/ shell interface). Ensemble dynamics revealed a power-law-like behavior over several decades in time, despite single NC exhibiting exponential decay. The results presented here were shown to verify the validity of an essential requirement of one of the most successful blinking models to date.

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ASSOCIATED CONTENT

S Supporting Information *

Method, influence of the value of the Lorentzian broadening Γ on the calculated trapping efficiencies, temperature effects, origin of inefficient type II traps, energy nonconservation in transitions to type I traps, modeling of core/shell structures, effect of decreased electron−hole coupling in core/shell structures on type I traps, core/shell structures: interface traps - detailed rate analysis. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions §

Both authors contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.C. gratefully acknowledges financial support from the Royal Society under the URF scheme. F.M.G.C. was supported by research project TEC2010-16211, funded by the Spanish Ministerio de Ciencia e Innovación, and the Regional Government of Andaluciá (project P09-FQM-4571).

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REFERENCES

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Hole Surface Trapping in CdSe Nanocrystals: Dynamics, Rate

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