On the kinetics and thermodynamics of excitons at the surface of semiconductor nanocrystals: Are there surface excitons?

Accepted Manuscript chemphys Perspective On the kinetics and thermodynamics of excitons at the surface of semiconductor nanocrystals: Are there surface excitons? Patanjali Kambhampati PII: DOI: Reference:

S0301-0104(14)00308-5 http://dx.doi.org/10.1016/j.chemphys.2014.11.008 CHEMPH 9205

To appear in:

Chemical Physics

Please cite this article as: P. Kambhampati, On the kinetics and thermodynamics of excitons at the surface of semiconductor nanocrystals: Are there surface excitons?, Chemical Physics (2014), doi: http://dx.doi.org/10.1016/ j.chemphys.2014.11.008

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On the kinetics and thermodynamics of excitons at the surface of semiconductor nanocrystals: Are there surface excitons? Patanjali Kambhampati* Department of Chemistry, McGill University, Montreal, QC, H3A 0B8, Canada

The surface of semiconductor nanocrystals is one of their defining features by virtue of their nanometer size. Yet the surface is presently among the most poorly understood aspects of nanocrystal science. This Perspective provides an overview of spectroscopic work that has revealed the first insights into the nature of the surface, focusing upon CdSe nanocrystals. We focus on two aspects of surface processes in nanocrystals: the kinetics of surface trapping and the thermodynamics of core / surface equilibria. We describe femtosecond pump/probe spectroscopic experiments which reveal the signatures of carrier trapping at the surface. We also describe temperature dependent steady-state photoluminescence experiments which reveal new aspects of the surface. This work suggest that the surface emission is largely driven by homogeneous broadening via phonon progressions. The implications are that the surface electronic state bears similarity to the quantized excitonic core of the nanocrystal.

*Author to whom correspondence should be addresses: [email protected].

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1. Introduction In the decades since their discovery, semiconductor nanocrystals have been under intense investigation as a materials platform upon which to explore quantum confinement effects1-7, as well as path for development of materials based solutions to applications ranging from photovoltaics 8-12, displays and lighting 13-16, lasers 17,18, detectors 19,20, optical switching 21, and biological imaging 22. These nanocrystals (NC) are formed via solution phase growth23, and can result in the now well-known quantum confined excitons in colloidal quantum dots (QD). These colloidal quantum dots are somewhat distinct from their self-organized QD counterparts that are epitaxially grown via gas phase methods24. The key distinction lies at the surface of the dot itself. Self-organized QD which are grown by molecular beam epitaxy, consist of the dot physically embedded in a host semiconductor with lattice matching24. While there is an interface, there is no surface of which to speak. In contrast, the colloidal quantum dot is defined by their very surface itself. The physical surface of a spherical nanocrystal yields a colloidal quantum dot. Moreover, the nanocrystal form of the QD can be grown in a variety of geometries spanning spheres23, rods25-27, tetrapods28,29, radially graded alloys30-34, etc. Hence the surface of semiconductor nanocrystals is an essential part of their nature. Whereas semiconductor nanocrystals are defined by their surface, very little is known about this defining characteristic. The initial understanding of the surface of the nanocrystal was largely based upon steady state photoluminescence (PL) measurements. The PL from semiconductor nanocrystals arises from a thermalized distribution of excitons confined by the core of the nanocrystal35-37. The nature of the excitonic PL from the core is now reasonably well understood2, although new insights are still emerging via single dot spectroscopy38-40. Chemical

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modification of the surface of the NC has revealed that the broad, red emission seen in early NC arose from the surface of the nanocrystal. It was considered that the surface presented localized lattice defects 41. These defects created both unwanted trap PL as well as provided a constraint to producing bright and photostable PL from the excitonic core of the NC. Hence the primary goal of surface studies of nanocrystals has been to eliminate the unwanted trap PL42-44. In contrast to this historic view of the surface as a problem to be mitigated, our recent work has suggested that the surface is fundamental part of the nanocrystal system45-48. Moreover we propose that the surface may actually be profitably exploited for applications ranging from lighting, to sensing, to optoelectronic devices. In order to achieve these goals, one key element is missing: a microscopic understanding of the nature of the surface of semiconductor nanocrystals and the manner in which the core excitonic states couple to the surface. Here, we review our recent work on the kinetics and thermodynamics of surface trapping in CdSe semiconductor nanocrystals which has produced the first such picture of the factors which govern surface trapping the core excitonic states.

2. Background A. Simple observations of the surface of semiconductor nanocrystals The physical and electronic structure of the core of nanocrystals in terms of excitons has been well described elsewhere2,4,5,49,50, and will only be briefly described here so as to set the stage to understand their surface electronic structure. Fig. 1 shows a transmission electron microscope (TEM) image of CdSe NC, along with schematic energy level diagrams in two representations. TEM work has revealed that NC are not necessarily spherical. Moreover, with inclusion of atomistic detail, the NC have surfaces with specific periodicities and terminations that are

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distinct from their bulk phase. With the large surface/volume ratio of NC, it is essential to understanding the electronic structure of these surfaces. In contrast to the surface electronic structure of NC, the quantized core electronic states are now well understood at various levels of theory2,4,5,49-51. The reader is referred to the many excellent reviews which cover this topic in detail. The main result is that a Fourier superposition of bulk Bloch states results in the well-known quantized states of the electron and the hole. Fig. 1 shows this manifold in the electron/hole representation as well as the exciton representation. These excitonic states can readily be observed in the linear absorption spectra, Fig. 2a. Shown is a representative absorption spectrum of CdSe NC. Also shown are laser spectra tuned into resonance with specific excitonic states so as to perform state-resolved femtosecond pump/probe spectroscopy5,6,52. This approach enables specificity in the initial excitonic state thereby enabling direct measurement of the influence of the initial state, as well as direct observation of hot exciton (or hot carrier) processes. Steady-state photoluminescence (PL) spectroscopy enables simple characterization of their radiative and non-radiative processes. Fig. 1b shows a PL spectrum of CdSe NC with strong PL from the band edge exciton at 2.5 eV and some trap PL spanning 1.6 – 2.3 eV. This trap PL has been known to exist for decades and has been assigned to defect emission from various sources. The defects are considered to arise at the surface of the NC based upon chemical passivation experiments. This hypothesis was further supported by the early work which demonstrated that growth of inorganic shells (e.g. ZnS) would increase the PL quantum yield, and strongly attenuate the trap PL at 300K. Hence the idea of shell growth has been to remove the unwanted defects, a process that was validated by the disappearance of the broadened and redshifted trap PL.

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The broadening and redshifting characteristic of trap PL was historically rationalized by a broad distribution of trap states, Fig. 1c. Since hot exciton relaxation5,6,53,54 on the 0.1 – 1 ps timescale is much faster than exciton radiative recombination on the 1 – 10 ns timescale in CdSe NC, PL takes place from fully relaxed or cold exciton states. Within the multiband effective mass approach (EMA) 4,55, the lowest coarse excitonic state, X1 is denoted as 1Se-1S3/2. This coarse exciton state is further split into fine structure states which will not be further discussed here. The narrow linewidth (~ 50 – 100 meV) of the core excitonic PL arises from fine structure effects, weak exciton-phonon coupling, dephasing, and inhomogeneous broadening from the size dispersion (5%). As the trap PL is often redshifted by 0.3 – 0.5 eV from the band edge PL, and is also ~0.5 eV in width, the simple picture of defects in solids suggest that the observed broadening and redshifting arises from a distribution of trap states. The larger the linewidth the larger the distribution. And the larger the redshifting, the deeper the traps are within the bandgap. These traps could be either electron or hole traps based upon the NC/ligand system. But in the case of CdSe NC with the standard amine or phosphine oxide ligands, it is expected to primarily be hole traps due to Se atoms being ill-passivated42-44. Based upon this simple picture, the NC community has worked to produce well passivated NC surfaces that are defect free as evidenced by the absence of trap PL42-44.

B. Influence of surface passivation on the excitonic processes While well passivated NC no longer show trap PL at 300K, it is not obvious that the surface has no importance upon the spectroscopy and excitonic processes in NC. One can merely conclude that simple PL spectroscopy at room temperature does not reveal further insight into the nature of the surface. In contrast, recent femtosecond spectroscopy measurements have shown a direct

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impact of the surface – even for well passivated NC with no trap PL at room temperature. Several examples from our work18,56-61 are briefly reviewed here so as to identify the impact of the surface on exciton dynamics. The two primary dynamical processes in nanocrystals are exciton relaxation (cooling), and exciton recombination5,6. Both represent central issues in NC science and have been discussed extensively in the literature5,6, including our work utilizing excitonic state-resolved pump/probe spectroscopy5,6,52-54,57. The relaxation processes typically take place on the 0.1 – 1 ps timescale, whereas the recombination processes take place on the 10 ps – 10 ns timescale. In each process, the historical issues had been the measurement of the rate of each process, as well as the pathways by which these dynamical processes may be controlled6,53,54. Hot exciton relaxation corresponds to the primary event upon absorption of a photon5,6,5254

. Since bulk carrier relaxation takes place via phonon emission, it was assumed that phonon

emission would also be the pathway for carrier relaxation in nanocrystals. Hence as the quantum size effects gave rise to increased energy level spacings, it was assumed that there would be a bottleneck to exciton cooling via this phonon pathway. Since this bottleneck was not observed in the early experiments, additional pathways were invoked. The primary pathway for hot electron relaxation was proposed to be an Auger based electron to hole energy transfer process62. This idea was confirmed by experiments1,53,63,64. In contrast, the hole was anticipated to show a phonon bottleneck due to the Auger relaxation process being unidirectional. Our work on hole dynamics54 in CdSe NC revealed the absence of a phonon bottleneck for holes as well as electrons53. These experiments suggested that the surface plays an important role in hot exciton processes.

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Fig. 3 shows the state-to-state transition rate for hot holes relaxing as a function of particle size for CdSe NC passivated with organic ligands. There is a clear absence of the anticipated phonon bottleneck, as the state-to-stae transition rate is size independent. We were able to rationalize all hot electron and hot hole relaxation processes in terms of a multi-channel picture of hot exciton dynamics. Rather than assume a single path for some dynamical process, we considered that there should be multiple paths for electrons and holes to relax53,54. In the case of both electrons and holes, they will have wavefunctions which have significant overlap with the organic ligands which passivated the surface of the NC. We assumed a coupling between the NC excitonic states and the vibrational modes of the organic ligands. Based upon the data, we found that a non-adiabatic model via electron-ligand non-Born-Oppenheimer interactions could successfully reproduce the experimental data. The idea is that electronic transitions can dissipate their energy via non-adiabatic coupling to the ligands as an additional degree of freedom for the NC system. These simple calculations are now finding further support via the high level atomistic quantum dynamics calculations by Prezdho65-68. Upon relaxation to the band edge states, the cooled or thermalized excitons will recombine via radiative or non-radiative means. Under low excitation conditions, the radiative recombination on the 1-10 ns timescale competes with non-radiative recombination. This nonradiative path is dependent upon surface passivation as demonstrated by the near unity quantum yield for inorganically passivated NC at low temperatures. Under high excitation conditions, the NC can absorb multiple photons thereby producing multiple excitons per NC. The reader is referred to our prior work57,58,61,69 and a recent review7 for more discussion of multiexcitons (MX) in NC.

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Multiexcitons in NC are interesting for a few recent applications7. MX are key for optical gain and stimulated emission from NC. While there are some systems that exhibit optical gain at the single exciton level, most NC require at least a biexciton (XX) to enable gain. In photovoltaic applications, one aims to generate and harvest the MX prior to recombination. The MX can be produced via fission of a single high energy exciton – a process referred to as multiple exciton generation (MEG) or carrier multiplication (CM). In lighting and display applications, the carrier concentrations can be sufficiently large so as to produce multiexcitons, whose nonradiative processes need be understood so as to optimize the devices for high brightness. Finally, we have shown a wholly new application of MX in NC: optical gain switching as a path for ultrafast all-optical logic. While MX have importance to a variety of applications, the key factor remains their non-radiative decay and how it may be controlled via materials design. Multiexcitons in nanocrystals are believed to recombine via an Auger mechanism2,7,70. This mechanism has been supported by many experiments. Quantum confinement enhances the Auger recombination rates so as to produce recombination times on the 10-100 ps timescale, with higher MX states and smaller NC producing faster Auger based recombination. The experimental data arrives from pump/probe measurements in which the recovery of the band edge bleach is monitored. The initial work by Klimov suggested that this procedure can observe the recombination of biexcitons to tetraexcitons by a subtractive procedure2,70,71. Faster components of the pump/probe signal corresponding to recombination of higher MX. A similar approach was used by the MEG / CM community to quantify the yield of this process. Our work has showed that there are artifactual signals in such experiments that arise from surface trapping57.

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In order to carefully assess the role of the surface on multiexciton recombination, we performed experiments with different surface conditions, Fig. 4. The pump/probe transients of well passivated CdSe/ZnS NC reveal some notable reality checks. Since the band edge exciton in CdSe is only doubly degenerate, the signal should only monitor the recombination of biexcitons and single excitons. At high fluence, the signals should saturate in a simple manner reflecting this degeneracy. The data in Fig. 4a perfectly reproduces these intuitive expectations. In a well passivated NC, the standard pump/probe measurements can only resolve recombination of MX up to the maximum degeneracy of the probed state (in this case the band edge exciton). In contrast, the data on CdSe NC passivated with organic ligands shows a very different behavior, Fig. 4b&c. The data on fresh CdSe shows faster decay and a larger amplitude of the fast component than CdSe/ZnS. This difference is further amplified in the case of CdSe that had been phototreated. The phototreatment was simply to illuminate the unflowed NC sample for an hour. The differences between the data arises from surface charge trapping accumulated during the course of the experiment. For example, while the NC samples are ideally recirculated via a reservoir, in some cases recirculation is not possible or was not always done. Hence there is a clear possibility of a photoproduct being produced by constant illumination. This photoproduct may be some form a charged or surface trapped NC. The result of this photoproduct accumulation is the presence of faster components in the recovery of the band edge bleach signal that is typically used to monitor populations. Hence one could infer a faster component a high fluence monitors higher multiexcitons. However, doing so clearly provides false measures of higher multiexcitons. The highest MX multiplicity is determined by the degeneracy of the states probed. The discrepancies arose from failure to recognize the importance of surface charge trapping.

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This very same surface trapped state that arises from photoproducts in many experiments also has relevance to the multiexciton recombination (MER / CM) experiments72-85. The connection is that the MEG analysis is often done in a very similar manner to the evaluation of multiexciton recombination, described above. In the case of the MEG / CM experiments, the same pump/probe experiment is performed, with the data normalized to the long time tail in the transients, under some low fluence condition. Any faster response in the bleach recovery is then inferred as evidence of new carriers being generated. As shown above, the situation is not so simple. One can easily generate large amplitude signals that mimic the presence of higher multiexcitons but are merely due to the signal from a surface trapped state. Since many experiments are conducted upon NC with organic ligands, one should aim for a simple measure of surface quality that might suggest the presence of such artifactual signals in the pump/probe experiments on multiexciton recombination or generation. Experiments are commonly conducted upon NC passivated by some organic ligands, whether, CdSe, CdS, PbSe, PbS, etc. For any NC it is simple to measure a 300K PL spectrum to nominally quantify its surface quality. One aims for a reasonable PL quantum yield (10%) and no deep trap (surface) PL at room temperature. These two conditions are met by the vast majority of NC used for any time resolved experiment. The simple use of room temperature PL spectroscopy is not sufficient to provide insights into the surface quality or the nature of the surface electronic state. Hence one aims for more sophisticated measures of surface trapping processes and the manner in which the surface trapped states may be spectroscopically probed.

C. The influence of surface trapping upon key processes: optical gain, piezoelectricity, single NC blinking, and lighting.

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The surface of the NC is clearly an essential part of the physical nanocrystal. While the surface electronic state does not yet have the same level of understanding as core states, its importance upon the spectroscopy and its evaluation is clear. Beyond understanding the nature of the surface electronic structure of semiconductor nanocrystals, this surface trapping process has clear practical implications as well. The surface has been implicated as a key issue in a variety of situations, from optical gain to single particle blinking, briefly reviewed here. One of the initial motivations for semiconductor nanocrystals was for the development of novel lasers. By virtue of their quantum confined electronic structure, NC should have been an ideal optical gain material. In practice, experimental realization of optical gain in NC was not straightforward. Smaller NC often did not support optical gain via stimulated emission. The gain thresholds were strongly size dependent and surface ligand dependent for reasons that were not clear at the time86,87. Moreover the gain lifetimes were short, and inferred to be limited by Auger based multiexciton recombination. Our recent work18,60 demonstrated that all of these results could be understood based upon an excitonic state-resolved optical pumping scheme. Essentially all the early gain phenomenology arose from parasitic loss signals due to surface charge trapping. These points are illustrated with representative gain data in Figs. 5 and 6. Fig. 5 shows the stimulated emission spectra for CdSe and CdSe/ZnS NC. The CdSe NC have a gain lifetime of 4 ps whereas the same size CdSe/ZnS has a lifetime of 100 ps. One might simply assign the gain lifetimes as limited by Auger based multiexciton recombination. The difference in the lifetime based upon surface passivations shows that this simple picture is not complete. The gain lifetime in the CdSe/ZnS NC match the multiexciton recombination times, demonstrating that recombination limits gain lifetimes in the limit of ideally passivated NC. The shorter gain lifetime of CdSe NC is

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completely consistent with the 10 ps timescale of surface (hole) trapping in these NC. Hence optical gain lifetimes are limited by the faster of two processes: multiexciton recombination vs. surface charge trapping. The trapping of charges on the surface creates fast recombination multiexciton processes which limits the optical gain lifetimes7,58,60. One might assume that some initial electronically hot exciton will first thermalize and then trap at the surface. Our state-resolved approach has also shown the important hot-exciton surface trapping effects18,60. Fig. 6 shows the gain threshold and the gain cross section as a function of initial excitonic state for CdSe and CdSe/ZnS NC. The threshold increases as a function of electronic energy, an effect which is somewhat attenuated with better surface passivation by a ZnS shell. As before the shell attenuates surface trapping of relaxed excitons. But the clear energy dependence of the threshold indicates that these surface trapping effects arise prior to exciton relaxation. Hence the presence of hot exciton surface trapping can be a serious problem when pumping nanocrystals at some fixed wavelength, e.g. the 400 nm output from the commonly used Ti:sapphire systems. The significance of the above phenomena is that surface effects masked the true performance of NC for one application – optical gain and lasing. Very recently, NC based lasing has been demonstrated in the visible. While the result itself is impressive, there is not yet a clear understanding of how to design a nanocrystal for optical gain. Yet there is considerable evidence that surface effects play a key role in controlling the use of nanocrystals for lasing applications. The surface has been implicated other phenomena illustrating the ubiquitous nature of the surface. When a charge gets trapped at the surface, there is a large change in the charge distribution. This surface based change in polarization can manifest itself in phonon effects as well. We have explored these effects in both piezoelectricity59 and white light generation47. In

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these situations, the trapping of charges at the surface is a process to be exploited rather than one to be inhibited. These points will be discussed in further detail here. Perhaps one of the most well-known areas in which the surface of the nanocrystal has been implicated is in single NC blinking. The topic of NC blinking has been discussed in detail elsewhere88-96. The main point of relevance is the idea of photocharging97-101 or as we refer to it, surface trapping6,7,57. The common usage presently is that there is some process by which a charge is displaced from the core of the NC. The location of the charge is likely at the surface or interface, consistent with the fact that the blinking phenomenology is dependent upon the surface of the NC. Recently, NC have been developed that do not blink94. In all cases, the non-blinking NC have some way in which the surface physical/chemical structure is controlled. What is not clear is the nature of the electronic structure at the surface/interface that ultimately dictates blinking phenomena.

2. Observation of the kinetics of surface trapping processes via femtosecond spectroscopy Optical excitation of a nanocrystal will produce an electron/hole pair. These confined carriers correspond to the core excitonic states of the nanocrystal. The initial optically excited population of carriers may undergo trapping at the surface of the nanocrystal. Hence this kinetic process may be monitored via femtosecond pump/probe or transient absorption (TA) spectroscopy. In pump/probe measurements, the pump pulse produces the initial exciton in the core. And the probe pulse monitors the signals as the charges undergo the process of surface trapping. Fig. 7 illustrates the salient kinetics, as well as how these kinetics would be reflected a generic pump/probe experiment.

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A minimal kinetic model representing the nanocrystal includes three states. The core of the NC has two excitonic states and one surface state in this minimal model. Optical excitation can be directly into the lower excitonic state (e.g. the 1S type band edge exciton), or into the higher excitonic state corresponding to a hot exciton. Direct production of a cold exciton can only lead to surface trapping (in the absence of other detrapping mechanisms). This process can be monitored via some pump/probe signal as shown in Fig. 7. There are in fact many pump/probe signals in NC that have been well discussed in detail elsewhere. The key point is that these signals can be decomposed into monitoring either electron or hole dynamics. For the simplicity of discussion, however, the signals will be treated as generic. We have detailed the analysis of the pump/probe signals elsewhere5,6. Upon a pump pulse initially populating the cold exciton, the ensuing signals will monitor the kinetics of trapping to the surface. The pump pulse may also have excess energy and produce a hot exciton. This point is of particular practical importance as many experiments use 400 nm pump pulses which invariably produce hot excitons. Moreover the amount of excess energy is now size dependent thereby further obfuscating any investigation in which hot carrier effects are important. In the simplest case of kinetics involving a hot exciton, the kinetics are sequential: fast cooling followed by slower trapping. This limit is achieved when the rates of cooling are much faster than the rates of trapping. In this limit, the signal will show a simple bi-exponential form. We have measured the exciton cooling rates and surface trapping rates for CdSe NC. While cooling ( 0.1 – 1 ps) is certainly faster than trapping (1 – 100 ps), the timescales are similar enough that hot carrier trapping can become important5,6. In a case where cooling is a few times faster than trapping, one encounters the third situation illustrated in Fig. 7. We assume some signal for the three excitons: hot, cold, trapped. Now including competition kinetics, the

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signal does not directly monitor either rate. The key point is to know the relevant signals, from which this simple kinetic model produces rates. The simple kinetic model was used to illustrate the relevant processes and how competition kinetics between hot exciton cooling and trapping becomes a key issue. The next issue is to relate these kinetics to the real pump/probe signals. Fig. 8 schematically illustrates a pump/probe transient absorption (TA) spectrum of some generic NC. Again, the details of the spectroscopy have been discussed in detail elsewhere5,6. In this schematic, we consider the NC the following pump/probe scenarios57. The pump pulse populates the band edge exciton which will produce bleaching signals. The probe may also measure induced absorptions which arise from two distinct effects: absorption into a biexciton, or re-excitation into the electronic continuum. In the case of absorption into the biexciton, there will be a small induced absorption due to the biexciton binding causing a redshifting of the levels. This effect has been discussed in detail by us, and has revealed both the electronic structure of biexcitons as well as their dynamics5,7,52,56-58,61,69. It is less commonly considered that the pump produced band edge exciton can be excited into the continuum. Since the linear absorption spectra of NC show strong absorptions at high energy, these transitions are clearly one photon allowed. Any NC has large density of states (DOS) at twice the energy of the band edge exciton. Under the assumption that transitions are allowed from the band edge into the higher energy continuum states, these transitions will be reflected in the TA spectra. Since the probe monitors absorption into the excited state, absorption into the continuum will yield a broad, featureless induced absorption. In the presence of both types of transitions, the TA spectra will show both narrowband and broadband induced absorptions.

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Fig. 9 shows experimental TA spectra in CdTe NC. While the majority of our studies have been on CdSe NC, these effects are strongest in CdTe56. Shown are CdTE NC with different quality of surface passivation. The spectra on the left correspond to fresh CdTe with reasonable photoluminescence (PL) quantum yield (1 – 10% typically at 300 K). The spectra on the right are aged CdTe with no measurable PL. The only difference in the linear spectra is the PL quantum yield. In contrast, the TA spectra show marked differences. Both TA spectra show the narrowband bleaching signals. And both show the induced absorptions that indicate a biexciton based origin to those signals. In contrast, only the aged CdTe with the degraded surface show the broadband induced absorptions discussed above. The main point of the TA signal analysis is that a detailed inspection of the various pump/probe signals can be used to monitor either electron or hole dynamics. One specific kinetic process is the trapping of charges (electrons or holes) to the surface trap states. Hence the kinetics of surface trapping may be probed, provided a proper understanding of the relevant signals as we outline here. These points have been discussed in detail in our prior works. With this understanding, the trapping of energetically hot carriers may also be monitored, as we have shown previously in various systems. In addition to the incoherent TA signals of electronic processes, these experiments also have coherent signals that may be exploited to probe surface trapping processes. For suitably short pump pulses, direct optical excitation will yield coherent phonons. The oscillation amplitude of these coherent phonons can be related to their coupling strength in a straightforward manner using the displaced harmonic oscillator model. Our work on CdSe NC has shown that both optical and acoustic phonon are coupled to the confined core excitons in nanocrystals5,6,59,102,103. The main point is that the phonon couplings must be for the core states

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and not for the surface trapped state. Most likely the majority of resonance Raman experiments on NC measure the coupling to a surface trapped state due to the build up of trapped charges during the course of the experiment. The same is true for single dot PL measurements. In contrast, time domain measurements are performed prior to trapping and hence only measure the coupling of the phonons to the optically coupled core states into which one directly excites5,6,59,102,103. Pump/probe measurements of coherent optical and acoustic phonons in CdSe NC are shown in Fig. 10. Excitation can be into the cold, band edge exciton, or into the higher excitons which can support large exciton densities. Pumping into the band edge exciton at single exciton densities produces weak modulations in the pump/probe signal. From these oscillation amplitudes one extracts the coupling via the femtosecond pump pulse102,103. However, the NC can be pumped into higher states with greater degeneracy. In particular, the electronic continuum that is accessible with 400 nm pumping can support dozens of excitons per NC thereby creating an excitonic plasma. This hot carrier distribution can rapidly thermalize thereby creating a vibrational impulse from cooling itself. Alternatively, the hot carriers can undergo direct surface trapping. In this situation, the trapping itself corresponds to the impulse which drives coherent phonons. In the case of CdSe NC, we have shown that hot carrier trapping can proceed on the 1 ps timescale, which is shorter than the 2 ps period of the acoustic phonon. Hence the piezoelectric field formed by a surface trapped charge impulsively launches coherent acoustic phonons59. In short, coherent phonons are an additional marker by which to monitor surface trapping processes. One of the main points from these pump/probe measurements of exciton-phonon coupling is that the excitonic core states are all weakly coupled to the phonon modes. Fig. 11

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shows the couplings for CdSe NC as a function of excitonic state. The coupling of the excitonic states is small, which becomes important when discussing the origin of the PL linewidth. The more recent single dot PL measurements reveal very weak phonon progressions104 in contrast to the earlier single dot work105. The most recent PL measurements are completely consistent with our femtosecond time domain measurements. This consistency suggests that the surface trapping effects have been ameliorated in these newer NC. In contrast, to the surface trap is very strong. The coupling to the surface trap state is obtained from resonance Raman measurements which measure the time integral of the polarization. Time integrated, these experiments largely measure the coupling of a surface trapped exciton rather than a core exciton. These couplings will be used below to analyze the steady state PL spectra from the core and surface states.

3. Observation of the thermodynamics of surface trapping via steady-state photoluminescence spectroscopy Femtosecond pump/probe measurements have revealed the kinetics of carrier trapping at the surface of semiconductor nanocrystals5-7,56-59,61. Yet a simple inspection of the energy levels suggests a basic problem. Since the surface trap state is lower in energy than the band edge exciton, one might expect all carriers to relax to the trap states18. In this case there would be no PL at all, in contrast to observation. This inconsistency suggests that the relation between the surface and the core is not so simple. In lieu of these more sophisticated pump/probe measurements, and still newer coherent two dimensional electronic (2DE) spectroscopy measurements106-111, one aims for a simple measure of the nature of the surface. Steady state PL spectroscopy is the simplest such tool, and has been extensively used to monitor surface quality and to suggest at the nature of the surface

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trap state(s). When using PL to monitor the surface of the NC, the simplest measure is the PL quantum yield (QY) from the band edge exciton. The QY for CdSe is typically 1 – 10% at 300K and can be >50% for well-passivated core/shell NC at 300K. Hence the QY at 300K is often used a simple measure of the quality of surface passivation. Higher QY implies “better” surface passivation. By engineering the surface to maximize QY, the NC community has aimed to understand the nature of surface traps and how they dictate PL from NC. A key aspect of spectroscopic and even transport studies on the surface of nanocrystals is that they do not focus on a surface specific observable. Instead most surface studies focus upon controlling some core excitonic process, with some surface effect. The simplest and most common measure of surface effects is QY for core PL as noted above. One can also measure PL lifetimes112,113 and their temperature dependence in order to infer the effects of the surface on PL from the core. More recent work from Alivisatos and Sargent has investigated transport and other signatures of surface effects. In each case what is missing is a direct spectroscopic signature of the surface. In addition to the PL from the core, NC also show broadened and redshifted PL that is associated with surface traps45-48. This trap PL, Fig. 1, is usually seen as a signature of a poorly passivated NC. This trap PL was more routinely observed in early syntheses, supporting this premise. While CdSe NC typically show no trap PL at 300K in current syntheses, CdS NC still show strong surface PL suggesting a surface that is more enriched in traps or defects. In our prior femtosecond experiments on the kinetics of surface trapping, we considered the surface trap state to be the lowest energy state18,61. We rationalized the presence of core PL by assuming a thermal equilibrium between the band edge exciton and the surface. Hence any carrier trapped at the surface will have an opportunity to equilibrate and emit from the core. In

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order to further explore this hypothesis and to reveal more insight from simple steady state PL measurements, we measured the emission from various NC as a function of temperature45,46. Fig. 12 shows the PL spectra for CdSe, CdSe/ZnS, and CdS NC. In the case of the canonical CdSe system there is minimal trap PL at 300K and a good quantum yield of ~ 10% thereby suggesting a well-passivated NC with an absence of surface traps from which radiative recombination can take place. In contrast, as the temperature is lowered, the trap PL becomes prominent. The same effect is observed in CdSe/ZnS albeit with a weaker amplitude. Whereas these temperature dependent intensities are much stronger in CdS. What is apparent is that the PL spectra at 300K cannot be used as a predictor of trap PL at low temperature. Instead, the PL spectra over a wide temperature range offer meaningful insights. The PL spectra are plotted as integrated areas in Fig. 11 and as a ratio of surface / core emission in Fig. 12. The integrated areas show a clear temperature dependence for both the core as well as the surface PL bands. The temperature dependence of each band is distinct. In particular, the core PL from CdS does not increase for the first 200K drop in temperature, completely at odds with simple expectations. Summing both bands gives the total light emitted as a function of temperature. Only the total emitted light monotonically increases in amplitude as the temperature is lowered. This observation suggests that the conserved quantity for radiative recombination is the total PL, and not the core PL as is commonly assumed. The significance is that the emitting state of the NC is not necessarily the band edge exciton that has been extensively discussed in the literature. Instead, the emissive system is the entire nanocrystal which is comprised of a core and a surface. Both phases can emit and must be considered as a part of a composite system that is in thermal equilibrium.

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Insight into the thermodynamics of the surface/core equilibrium can be obtained from the ratio of the surface / core PL, Fig. 12. The ratios show a rich temperature dependence that is consistent with some thermally activated process by which carriers are redistributed between the core and surface of the NC. There is also a critical temperature at which the trend reverses itself. This rich temperature dependence of the PL spectra provide insight into the thermodynamics of the surface trapping process and can be used in concert with the femtosecond data to produce a detailed picture of the manner in which the states of the core and surface are coupled. There are three different approaches towards describing the surface of in light of the PL spectra45,46. Fig. 13 illustrates the three models, discussed in detail in our prior works. The main observable of a surface band with a large spectral broadening and redshifting with respect to the excitonic core PL can be rationalized by an energetic distribution of defect states that lie within the bandgap. In this deep trap model, the energy differences are much larger than kT. As a result there would be no observed temperature dependence to the relative PL areas. In contrast, a classical ET model isomorphic to Marcus theory can qualitatively describe the temperature dependence to the PL ratio. The problem with a purely classical model is that it requires the energy separation between the core and surface bands to be ~ kT which is not experimentally observed. In contrast, a semiclassical ET model isomorphic to Marcus-Jortner theory can explain both the broadening/redshifting as well as the temperature dependence of the PL areas. We have applied a semiclassical Marcus-Jortner ET model to describe the PL spectra of various NC over a thermodynamically relevant temperature range45,46. The simulations of the surface/core PL areas are shown in Fig. 12. The main observations are 1) that only the total PL area monotonically increases with lower temperature, and 2) there is a critical temperature at

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which the surface/core PL ratio reaches its maximum. This model well describes the temperature dependence of the PL areas. It moreover describes the broadening and redshifting and how they are connected, Fig. 14. Details of the simulations can be found in our prior works. Fig. 14a shows the origin of line broadening in the PL from the excitonic core of the NC as well as from the surface state. In the case of the core PL, the PL spectrum has very little line broadening from phonon progressions. The phonon couplings for the excitonic states are obtained from the pump/probe measurements of coherent phonons. Upon including homogeneous thermal broadening as well as inhomogeneous broadening from size distributions, the core PL spectra remain narrow. The phonon couplings for the surface state are obtained from resonance Raman spectroscopy. The large coupling for the surface state yields the broadened and redshifted surface PL spectrum. In the case of the surface PL, we assume only one surface state and the same extent of inhomogeneous broadening as for the core. With the surface state redshifted from the band edge exciton by ~ kT, sufficient for thermal equilibration, the surface PL spectrum retains the broadening and redshifting characteristic of experiment. To further identify the role of optical phonons in determining the surface PL spectra, we correlate the redshift between the core and the surface (δEcore-surface ) to the bandwidth (∆Esurface ) of the surface PL, Fig. 14b. Experimental data are shown for various CdSe NC. In the semiclassical ET model, the strong coupling to optical phonons is the origin of both the broadening and redshifting of the surface PL. Hence there should be a correlation between the two as shown by the simulations. The simulations well match the data suggesting that phonon progressions are indeed a primary origin to the lineshape of the PL from the surface.

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In this discussion a key point that is worth noting is the assumption of a single surface state from which emission takes place. Our simulations employ a minimal model invoking one surface state which is electronically coupled to one core excitonic state. The well-known fine structure of the band edge exciton is not necessary to invoke at this level. The simulations are consistent with the existence of a single surface electronic state of the nanocrystal, albeit with the same extent of inhomogeneous broadening as in the core excitonic states. Further work is currently underway in our laboratory in order to explore these ideas.

4. Hot exciton surface trapping processes via steady-state spectroscopy – the quantum yield spectrum Our investigations into surface trapping phenomena began with direct time domain measurements6,52,57,61. The kinetics of surface trapping can readily be monitored via pump/probe spectroscopy as we have discussed in detail above. With excitonic state-resolved pump/probe spectroscopy, one can monitor hot exciton (hot carrier) surface trapping. These hot carrier processes are important in a variety of situations as noted earlier. On aims for a simple steadstate measurement of hot exciton trapping. We use the term hot exciton surface trapping in order to be most general. Hot carrier trapping implies either electron or hole trapping which requires some a priori knowledge of which carrier is being trapped. In the case of CdSe NC, there is considerable literature which suggests hole trapping. The atomistic and chemical details are in their earliest stages of investigation. We6,18,114 and others115,116 have discussed measurement of excitation energy dependence of PL from NC and their heterostructures. This excitation energy dependence (EED) creates a

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quantum yield spectrum rather than a single quantum yield for an arbitrary illumination wavelength. As the PL QY is associated with a surface trapping process, the QY spectra might report on hot exciton effects in surface trapping. In general the quantum yield spectrum represents a photo-action spectrum. The prior works on QY spectra in NC have shown conflicting results with some reports of an EED to PL and others showing none. There are two key issues here. The first is the invariable sample dependence. If PL is surface specific, surface conditions will dictate the QY spectrum. The non-trivial point is that there should be a way to connect a time domain kinetic measurement (hot exciton trapping) to a steady state thermodynamic measurement (PL QY). We have recently performed a detailed analysis of obtaining PL QY spectra in NC and how these spectra may or may not reflect hot carrier trapping processes48. A few experimental considerations arise when obtaining a QY spectrum. The first consideration is the deviation from Beer-Lambert behavior at high photon energies115. The second consideration is measuring the spectrally corrected PL117. The third consideration is that PL should be measured from the surface as well as the core when evaluating PL QY45,46. This last point is due to the total PL which is the conserved quantity rather than the core PL alone. Fig. 16 shows experimental QY spectra of two forms. Fig. 16a shows the PL QY spectra for two CdSe NC. As noted before, the spectra have been appropriately corrected and correspond to the total PL from both bands. At low energy there are spectral oscillations that arise from the size selection that takes place during PLE; the PLE spectral lines are slightly narrower than the absorption spectral lines. The data is free of such line narrowing artifacts when exciting into the continuum. The CdSe NC we have most recently explored do not show any marked EED to the PL. But this result can be case specific. Fig. 16b shows the QY spectra for the surface/core PL

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ratios. Here too there are some spectral oscillations due to size selection. The spectrum for the ratio is also fairly flat upon exciting into the continuum. Fig. 16c shows the PL QY spectra at various temperatures. There is not temperature dependence in these samples. Fig. 17 connect the experimental QY spectra to the various kinetic and thermodynamic processes that are relevant here. Fig. 17a extends the semiclassical ET model of surface trapping to include higher excitonic states. In the case of cold exciton surface trapping, there is thermodynamic equilibrium between the band edge exciton of the core of the NC and the surface state in this minimal model. In the case of hot exciton trapping, there is a kinetic competition between hot exciton cooling (relaxation) and hot exciton trapping. Once a hot exciton gets trapped at the surface, there is the competition kinetics between back charge-transfer from the surface to the core, vs. radiative recombination. Herein lies the central point in whether the kinetics of hot exciton surface trapping can be monitored via stead-state PL measurements. The charge-transfer times between the core and the surface estimated to be ~ 10 – 100 ps for forward trapping and an appropriately slower rate for backwards trapping as dictated by the semiclassical rate equations. Hot exciton cooling times are 0.1 – 1 ps with higher relaxation rates at higher energy. And hot exciton surface trapping times are 1 – 10 ps, thereby enabling effective competition kinetics between cooling and trapping. With the radiative lifetimes of 1 – 10 ns, the PL and PLE measurements are thereby in thermodynamic equilibrium between the core and the surface. Hence under these typical conditions there should be no QY spectrum due to the faster rates of charge transfer relative to radiative recombination. Fig. 17b shows how a PL QY spectrum will arise from hot exciton surface trapping provided the relevant rates are well matched. When there is no hot exciton trapping the QY spectrum is unity (normalized). Hot carrier trapping is introduced by empirical surface trapping

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rates, k(E), estimated from state-resolved pump/probe measurements. As temperature is lowered, the cold exciton forward and backwards trapping rates slow and begin to approach the radiative rates. Hence lower temperature is lowered, the QY spectrum becomes more prominent. In addition to the empirical surface trapping rate, this extended ET model enable prediction of the QY spectrum based upon the relevant free energies, Fig. 17c. The results are shown in Fig. 17d. We note that this simple model merely serves to illustrate the relevant kinetic processes. More sophisticated computational studies are needed to further explore these ideas.

5. Summary and outlook The nature of the surface of semiconductor nanocrystals is both central to their character, yet has been elusive for decades. The surface has primarily been seen as a problem to be mitigated by improvements in synthesis and passivation of the core of the nanocrystal. This work suggests that the surface is a fundamental aspect of NC and instead should be described and understood on equal footing to the well-known quantized excitonic states of the core. Time domain experiments have shown the kinetics of surface trapping from both cold as well as hot excitons. These experiments illustrate the pathways by which an excited state can trap at the surface of the NC. Yet the nature of the surface itself remains opaque. Remarkably, we find that steady-state photoluminescence spectroscopy at variable temperatures has produced the greatest insights into understanding the electronic structure of the surface, and the manner in which these surface state(s) are coupled to the core states. Our minimal model suggests that the broadening and redshifting that is characteristic of surface trap PL is largely derived from homogenous broadening rather than the traditional picture of an energetic distribution of trap states. Much like the excitonic states of the core of nanocrystals, these experiments are beginning to suggest a new

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way to think about the surface. In short, are there surface excitons? Further work is underway to address these new questions.

Acknowledgements. The contributions of an excellent group of graduate students is gratefully acknowledged, Samuel Sewall, Ryan Cooney, Pooja Tyagi, Jonathan Saari, Jonathan Mooney, and Michael Krause. The financial support of NSERC, CFI are gratefully acknowledged.

Biography. Kambhampati received his B.A. in Chemistry from Carleton College (USA) in 1992, and his Ph.D. in Chemical Physics from the University of Texas at Austin (USA) in 1998 under the supervision of Professor Alan Campion. He did his postdoctoral work with Paul Barbara at Texas from 1999 – 2001, and helped start up a photonics company from 2001 – 2003. He has been at McGill University (Canada) since 2003, where he is presently an Associate Professor. His research spans nanoscience to laser science.

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Figures.

Fig. 1. Transmission electron microscope (TEM) image of CdSe nanocrystals. Real nanocrystals are not necessarily spherical, have atomistic detail, and have a surface which must be considered, a). The confinement of charge carriers yields quantized states in the electron/hole representation, b). The exciton representation is convenient for correspondence to spectroscopic transitions, c).

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Fig. 2. Linear absorption spectrum of CdSe nanocrystals. Noted are several excitonic transitions into which one can perform excitonic state-resolved pump/probe spectroscopy as a probe of exciton dynamics, a). Photoluminescence (PL) typically arises from the band edge exciton following hot exciton relaxation. In addition to the exciton PL from the quantize core states of the nanocrystal, there can be PL from surface trap states, b). The broad bandwidth and large redshift of the trap PL relative to the excitonic core PL is typically assigned to an energetically broad distribution of trap states from which PL takes place, c).

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Fig. 3. The surface plays in important role in hot exciton cooling, the primary step following exciton creation. Hot exciton cooling is typically associated with internal degrees of freedom, such as Auger and phonon channels. The surface ligands represent one of the important pathways of hot exciton cooling in organically passivated CdSe nanocrystals, a). The relaxation pathway enabled by coupling to the surface ligands breaks the phonon bottleneck for holes, b). The magnitude of the surface ligand based channel can be controlled by either ligand or separation from the excitonic core, c).

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Fig. 4. The surface has a profound effect on the usual band edge bleach recovery signals probe multiexciton recombination kinetics as well as multiexciton generation. In CdSe/ZnS nanocrystals, the pump/probe signals show no artifacts, a). In CdSe nanocrystals surface charging artifacts manifest themselves as additional fast bleaching signals, b). In CdSe nanocrystals that are not flowed, the artifactual signals become more significant, c). The differences in the signals arise from surface charge trapping which creates faster recombination rates.

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Fig. 5. The surface has a strong effect on optical gain dynamics in CdSe nanocrystals. The stimulated emission lifetime in CdSe nanocrystals is limited by surface trapping and not by multiexciton (Auger) recombination, a). The stimulated emission lifetime in CdSe/ZnS nanocrystals is increased to be consistent with Auger recombination times due to improved surface passivation, b).

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Fig. 6. Hot exciton or hot carrier surface trapping controls optical gain phenomena. The optical gain threshold is a function of the initial excitonic state (energy), a). The stimulated emission cross section is also a function of the initial excitonic state, b). In both cases, this excitonic state (energy) dependence is somewhat attenuated by passivation with a ZnS shell.

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Fig. 7. Schematic representation of measuring the kinetics of surface trapping, including hot exciton trapping. The measurement represents a state-resolved pump/probe measurement. Pumping into a cold exciton (Left) and monitoring some appropriate signal reflects the kinetics of trapping from the cold excitonic state to the surface of the nanocrystal. Pumping into a hot exciton without hot exciton trapping (Center). Pumping into a hot exciton with hot exciton trapping (Right).

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Fig. 8. Schematic illustration of surface trapping signals in a pump/probe transient absorption (TA) spectrum. In each of three cases, the pump pulse populates the band edge exciton. The probe pulse then measures absorption into some biexcitonic state, a), or into the excitonic continuum, b), or into both, c). Each case has a corresponding TA spectrum, d), e), f), respectively. The TA spectrum represents the signals from each contribution in probe absorption. The surface trapping signals are reflected by the broadband photoinduced absorptions schematically illustrated in blue.

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Fig. 9. Experimental state-resolved pump/probe spectra of CdTe nanocrystals. Fresh CdTe nanocrystals with good surface passivation (Left). Aged CdTe nanocrystals with poor surface passivation (Right). The aged CdTe TA spectra show the broadband photoinduced absorptions that reflect surface trapping.

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Fig. 10. Coherent phonon measurements of surface trapping processes. Representative linear absorption spectrum of a CdSe nanocrystal, showing the symmetries of two excitonic states, a). An energy level diagram of the states showing the degeneracies, b). A simple displaced harmonic oscillator model illustrates exciton-phonon coupling and how it may vary with state, c). Pump/probe measurements of coherent optical and acoustic phonons in CdSe nanocrystals upon pumping into the band edge exciton, d). Since the excitonic continuum has a large degeneracy, one can create high electronic temperatures, e). These excitonic plasmas can impulsively trap charges at the surface of the nanocrystal thereby creating large amplitude coherent acoustic phonons, f).

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Fig. 11. The Huang-Rhys parameter (S) is a measure of the strength of exciton-phonon coupling. In the case of the polar optical phonon, it is a measure of the polarization of the excitonic state. The excitonic state dependence comes from state-resolved pump/probe measurements of coherent phonons. The excitonic state (energy) dependence of the coupling for the longitudinal optical (LO) phonon in CdSe nanocrystals, a). The excitonic state (energy) dependence of the coupling for the acoustic phonon in CdSe nanocrystals, b). The size dependence of the optical phonon coupling for the band edge exciton, c). The size dependence of the acoustic phonon coupling for the band edge exciton, d).

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Fig. 12. Steady state PL measurements of the surface of semiconductor nanocrystals, with CdSe (right) and CdS (left) columns. PL spectra at various temperatures, a) and b). Integrated areas for the core, surface, and total PL, c) and d). The temperature dependence of the surface:core PL ratio, e) and f).

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Fig. 13. Three models for describing the broadening and redshifting of surface trap PL. Deep trap model, a). Schematic temperature dependence of PL from a deep trap model, b). Classical electron transfer (ET) model, c). Schematic temperature dependence of PL from a Slassical ET model, d). Semi-classical ET model, e). Schematic temperature dependence of PL from a semiclassical ET model, f).

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Fig. 14. Optical phonons in the semiclassical ET model explain the broadening and redshifting of the surface PL. Simulated PL spectra of representative nanocrystals, a). The spectra are shown both without and with line broadening due to temperature and size dispersity. The relation between broadening (∆Esurface ) and redshifting (δEcore-surface ) for various CdSe nanocrystals, b).

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Fig. 15. The temperature dependence of the relative PL using a classical and a semi-classical ET model for CdSe, a) and CdS, b) nanocrystals. The semiclassical model better reproduces the low temperature response.

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Fig. 16. Evaluation of quantum yield spectra or excitation energy dependence of PL processes. The quantum yield spectrum for the total PL in CdSe NC, a). The yield spectrum for the surface/core PL ratio for various conditions, b). The total PL quantum yield at different temperatures, c).

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Fig. 17. The energy dependence of PL processes can be explained by a semiclassical ET model, a). The energy dependence arises from hot carrier surface trapping in a phenomenological hot exciton model, b). The semiclassical ET model can be extended to include higher energy excitonic states to correspond to hot carrier trapping, c). Simulated energy dependence of total PL in the microscopic model, d).

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Graphical abstract

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• • • • •

Highlights: The surface of semiconductor nanocrystals is one of their defining features. The kinetics of surface trapping can be monitored by pump/probe spectroscopy. The thermodynamics of surface trapping is revealed by photoluminescence spectroscopy. We produce the first microscopic picture of how excitons are coupled to the surface. We discuss the possibility of surface excitons in nanocrystals.

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