Hot Exciton Relaxation Dynamics in Semiconductor Quantum Dots

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Hot Exciton Relaxation Dynamics in Semiconductor Quantum Dots: Radiationless Transitions on the Nanoscale Patanjali Kambhampati* Department of Chemistry, McGill University, Montreal, QC, H3A 2K6, Canada ABSTRACT:

The ability to confine electrons and holes in semiconductor quantum dots (QDs) in the form of excitons creates an electronic structure which is both novel and potentially useful for a variety of applications. Upon optical excitation of the dot, the initial excitonic state may be electronically hot. The relaxation dynamics of this hot exciton is the primary event which controls key processes such as optical gain, hot carrier extraction, and multiple exciton generation. Here, we describe femtosecond state-resolved pump/probe experiments on colloidal CdSe quantum dots that provide the first quantitative measure of excitonic state-to-state transition rates. The measurements and modeling here reveal that there are multiple paths by which hot electrons and hot holes relax. The immediate result is that there is no phonon bottleneck for electrons or holes for excitons in quantum dots. This absence of phonon-based relaxation is confirmed by independent measurements of weak exciton
phonon coupling between the various excitonic states of the dot and the optical and acoustic phonons. We show that the divergence of prior results can be reconciled by adopting this multichannel picture of hot exciton relaxation dynamics. This picture establishes a framework for designing materials with relaxation properties targeted for specific applications. We conclude with connection to hot exciton surface trapping. The process of surface trapping is the key step in creation of the photoproduct which can obscure measurements of optical gain, multiexciton recombination, multiple exciton generation, and single dot blinking. We show that hot exciton surface trapping can effectively compete with hot exciton relaxation, thereby obfuscating these processes.

1. INTRODUCTION AND MOTIVATION 1.1. Motivation. The semiconductor quantum dot has been under intense investigation for an understanding of the influence of quantum confinement effects upon the system’s response, as well as for devices which aim to exploit these effects.1
15 The chemically synthesized colloidal form of the quantum dot (QD) is also referred to as a semiconductor nanocrystal (NC). Regardless of terminology, the simplest picture of the QD is that of a particle in a sphere.16,17 This simple picture immediately rationalizes the well-known size-dependent absorption and emission spectral energies.18 This picture also suggests that the energy level spacing in these QDs might be unique, size dependent, and ultimately controllable. This situation of a controllable energy spectrum suggests that the time scales and pathways by which excited carriers relax might also be unique in these quantum dots. Hence, the question of hot carrier cooling has been extensively investigated since the earliest work in quantum dots. The motivation for investigating hot carrier relaxation (i.e., cooling) can be connected to several situations of contemporary r 2011 American Chemical Society

interest (Figure 1). One of the earliest motivations for development of quantum dots was for optical gain media. By virtue of the narrow levels and large energy level spacing, it was anticipated that QDs would be ideal materials for the development of efficient optical gain.13,19
21 In any gain system, the manifold of levels should enable creation of either a three- or a four-level system. In addition to the lasing transition, there should be rapid population and/or depopulation of some of the levels to enable realization of lasing. Hence the carrier cooling process is immediately connected to the development of interband optical gain media mediated by fast exciton cooling (Figure 1a). In contrast, slow exciton cooling should be useful for longer wavelength intraband (intraexcitonic) lasers.22 QDs have also seen considerable interest in photovoltaic (PV) applications.4,9
12,23,24 In a PV environment, the charges are to Received: June 22, 2011 Revised: September 20, 2011 Published: September 21, 2011 22089

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Figure 2. Illustration of how a quantum dot interpolates between the bulk and molecular limits. In the case of molecules, there is a small number of electronic states which are dressed by phonon progressions and singlet/triplet exchange. In the case of bulk semiconductors, a continuum of electronic states is formed, along with a bandgap that corresponds to the HOMO
LUMO transition in molecules. In the case of semiconductor quantum dots, there is a quantized manifold of electron/hole states that arises from quantum confinement effects. Each level that is shown is further dressed by phonon progressions and exchange splittings which are not shown.

Figure 1. Illustration of hot carrier cooling in semiconductor quantum dots. The cooling process in green competes with other processes. (a) Illustration of the role of carrier cooling on the development of quantum dot lasers. The initially pumped state is hot (P-type exciton). This hot exciton cools to a lower state, SA, the lowest absorbing state(s). The absorbing state is energetically separated from the emitting state(s), SE, by the exciton Stokes shift, δX. Fast cooling enables realization of a threelevel interband lasing system, whereas slow cooling enables intraband lasing. (b) The exciton can also experience charge migration to surfaces, interfaces, and defects. This depopulation of delocalized core states can create photoproducts which can obscure measurement. This depopulation is also important for charge extraction in photovoltaic environments. Notably, the depopulation via charge trapping can compete with hot exciton cooling, thereby creating hot carrier charge extraction and trapping. (c) The cooling process connects with multiple exciton generation (MEG) in that the MEG fission rate must be faster than the hot exciton cooling rate.

be extracted from the delocalized core states into an adjacent medium. This charge extraction can take place from the lowest energy level, or it can take place from higher levels, referred to as hot electron extraction.25 Hence the rate of charge transfer from the dot to the adjacent medium must compete with intraband cooling (Figure 1b). It is worth noting that this charge migration process can also be a simpler charge trapping process. In the case of charge trapping, the carrier (electron or hole) gets trapped at lower energy states that might be surface, interface, or localized defect states. Finally, the exciton cooling process connects to an area of considerable recent interest, multiple exciton generation (MEG) or carrier multiplication (CM).4,12,26
41 The interest in MEG arose because of the possibility of using a larger fraction of the high-energy solar radiation to create additional carriers without creation of waste heat. The idea is that a high-energy single exciton state (X) is coupled to a manifold of multiexciton (MX) states. If the MEG rate is faster than the cooling rate, exciton fission into MX should dominate and thereby enable creation of larger photocurrents in QD-based solar cell applications. While there is some controversy as to the magnitude and the origin of

the effect,28,29,31
33,36,41,42 the connection to exciton cooling is clear (Figure 1c). One aims to design materials for efficient MEG much like the ongoing effort to design materials for optical gain based upon the underlying physics of relaxation and multiexciton interaction. The very same basic processes govern the development of the MEG process and its optimization via materials design. 1.2. Overview of Electronic Structure of Semiconductor Quantum Dots. While the electronic structure of quantum dots is not the topic of this Review, a brief review is helpful toward understanding the dynamical processes that are the focus of this review. The role of quantum confinement effects upon the electronic structure and linear spectroscopy of quantum dots has been extensively discussed elsewhere3,6,14,15,43
47 and will only be briefly reviewed here. The physical confinement of electrons and holes in the QD results in quantization of the available states. Due to the charge carriers being confined to these small volumes, the Coulombic binding of these charges gets large, and the formation of a strongly bound exciton results. Hence an investigation of the structure and dynamics of excitons in quantum dots—their excitonics—is the ultimate path toward rational implementation of these materials into device applications. The quantum dot interpolates between the molecular and the bulk semiconductor limits both in terms of physical size and more importantly in terms of electronic structure (Figure 2). In the case of molecules, the system obviously shows quantization by virtue of the small number of electrons. The electronic states such as singlets (S0, S1) and triplets (T1) are often well resolved. These states are further dressed by vibrational progressions arising from Franck
Condon factors thereby giving further breadth to the linewidths of electronic transitions. In the bulk limit, the large number of electrons results in a convergence toward a continuum of the density of electronic states. In the case of semiconductors, there is a bandgap separating the unoccupied conduction band (CB) from the occupied valence band (VB). This bandgap is the bulk analogue of the HOMO
LUMO transitions in molecules. By virtue of being intermediary in size, the quantum dot retains aspects of both molecular electronic structure and bulk semiconductor electronic structure. Like the molecule, the QD shows some discrete transitions and exchange splittings. Like the bulk semiconductor, the QD supports a continuum of electronic states at higher energy and can support multiple excitations per particle. The quantization of the CB and VB bulk states yields a manifold of quantized electron and hole states (Figure 2). Each of these states can experience molecular 22090

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Figure 3. Overview of the electronic structure and the linear spectroscopy of semiconductor quantum dots. Data are from colloidal CdSe quantum dots, used to illustrate the ideas. (a) The electronic structure of the dot can be understood in terms of the exciton picture, in which each exciton is comprised of a specific electron/hole state. The density of excitonic states converges toward a continuum at higher energy. (b) The electronic structure can also be understood in terms of the electron/hole picture. The electron states arise from quantum confinement of the bulk conduction band (CB) states, whereas the hole states arise from quantum confinement of the bulk valence band (VB) states. Transitions into specific electron/hole (excitonic) states are shown with arrows corresponding to their color in the case of CdSe. (c) The linear absorption spectrum shows peaks which can be assigned to specific excitonic transitions. Nonlinear femtosecond spectroscopic experiments can be performed by pumping into each initial excitonic state to monitor carrier dynamics with excitonic state selectivity. (d) The energy levels spread as a function of dot size. The energy of the excited exciton above the lowest exciton (X1) is plotted as a function of the energy of X1. Data are adapted from ref 41.

like exchange interactions and vibrational (phonon) progressions which further add line width. Unlike molecules, each of these states can easily be multiply populated based upon the degeneracy of the state. The subtle but important point in quantum dots is the physical point at which these quantum confinement effects arise, how to rigorously describe them, and how these effects confer function for the dot. While the electronic structure of the QD will not be discussed in detail here, it is important to note the richness of the electronic structure and the hierarchies in theory needed to provide a minimal explanation of key phenomena.6 The main levels of theory are: particle-in-a-sphere (PIS),16,17 multiband effective mass approximation approach (EMA),44
46,48,49 and atomistic approaches such as the empirical pseudopotential method (EPM)47,50
58 and ab initio.59
65 The PIS approach does not explain many of the simplest aspects of the dot, such as the fluorescence Stokes shift or the nature of the excitonic transitions in the absorption spectrum. Hence, the minimal level of theory required to design and interpret these experiments is the EMA approach. EMA has been applied to these colloidal CdSe quantum dots by Efros, Bawendi, and Norris.44
46,48,49 Those studies have yielded tremendous insight into the electronic structure and linear optical properties of these materials. These EMA results have furthermore informed the design and much of the interpretation of our experiments6,42,66
79 summarized here. We note, however, that the atomistic (whether EPM or ab initio) approaches often yield qualitatively different results (e.g., ordering of states, bright/dark states, piezoelectricity, exciton cooling). Hence the level of theory used to understand the observables is quite important as will be discussed below. In most cases, we will follow the EMA treatment for its simple notation which facilitates connection to theory. As warranted by

the experiments, we will also connect to the higher levels of theory. The electronic structure of quantum dots is represented in Figure 3. The electronic structure can be described in terms of a series of excitonic states (Figure 3a). This excitonic level diagram can be recast as an electron/hole level diagram which gives further insight (Figure 3b). The electron/hole picture suggests that the excess electronic energy can be taken up by either the electron or the hole. These excitonic states are connected to the linear spectroscopy of quantum dots such as absorption, photoluminescence (PL), and photoconductance spectra. Figure 3c shows the linear absorption spectrum of the colloidal CdSe QD in toluene dispersion. This spectrum shows the well-known peaks in a QD absorption spectrum and relates them to the excitonic and electron/hole picture. The peaks in the linear spectra of CdSe have been assigned within the EMA picture in pioneering work by Norris, Bawendi, and Efros.44,45,48 Figure 3d shows how the energy of higher excitons above the band edge exciton (X1 or 1Se
1S3/2 in the EMA picture) spreads as the dot becomes smaller (larger X1 energy gap). The spreading of the energy levels as well as the electron/hole decomposition will be of considerable importance when discussing the dynamical problem of hot exciton relaxation. 1.3. Hot Exciton Relaxation in Quantum Dots. Unsurprisingly, the concept of hot exciton relaxation in quantum dots connects to research on relaxation processes in both bulk solids and molecules. In the case of bulk solids, an excited electron or hole will relax toward its lowest energy state (band edge) via emission of phonons.3,5 Hence the process of cooling is driven by the strength of electron
phonon coupling alone. While electron
phonon coupling might be weak in solids due to extended wave 22091

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Figure 4. Influence of particle size on the electronic structure of semiconductor quantum dots. As the particle becomes small, the intraband CB
VB energy gap increases as does the intraband level spacings. Since the energy gaps increase with decreasing particle size, a strong size dependence on the carrier relaxation dynamics was anticipated.

Figure 6. Early work employed phonon emission (a) and electron/hole Auger relaxation to explain the influence of quantum confinement effects upon hot electron cooling. The phonon-based approach was adapted from bulk theories of hot carrier thermalization. This phonon-based approach was chronologically first and predicted a dramatic slowing of electron cooling for smaller particles (c). This prediction was called the “phonon bottleneck”. Later, theory proposed the existence of an Auger scattering type of relaxation channel in which the electrons transfer energy to the hole. The computed transition rates and their functional form show marked differences (d). The transition rates such as kphonon and kAuger correspond to specific pathways as discussed in the text.

Figure 5. Schematic illustration of the chronology of multiexciton generation, relaxation, and recombination. At t = 10 fs, an initial Poisson distribution of excitons is created by the pump pulse. This schematic illustrates the case of a homogeneous population of N = 3. At t = 500 fs, the initially hot multiexciton distribution thermalizes (relaxation). At t = 3 ps, the thermalized distribution of triexcitons undergoes multiexciton recombination (MER), thereby generating a hot biexciton distribution. At t = 3.5 ps this biexciton distribution thermalizes. At t = 30 ps the thermalized biexcitons undergo MER, thereby generating a hot single exciton. At t = 30.5 ps the single exciton thermalizes.

functions, the rate is fast due to the continuous density of electronic states. Since the density of states is continuous, only one quanta of phonons needs to be emitted to dissipate the excess energy of the electronically hot carriers. This topic of hot carrier relaxation (also called cooling and thermalization) has been well investigated in bulk solids. In the case of molecules, this relaxation process has been equally well investigated under the guise of radiationless transitions.80
86 There is now a wellestablished body of experimental and theoretical literature that provides a detailed map of the manner in which an excited molecule dissipates its excess electronic energy. Since the quantum dot retains aspects of the electronic structure of molecules and solids, the question of what governs the time scales and pathways of hot carrier relaxation is not obvious. In the case of strongly confined semiconductor quantum dots, the electronic level spacings can be 100
300 meV, much larger than the phonon energies. Hence, it was anticipated from bulk theories of carrier cooling that the relaxation of hot carriers should be much slower in

quantum dots.3,5,87
90 This situation gave rise to a search for this “phonon bottleneck”, based upon early theory. As the dot gets smaller, the spreading of the energy levels (Figure 4) was expected to further reveal the influence of the phonon bottleneck and will certainly increase the presence of uniquely quantum dot type relaxation pathways that govern the specific dynamical processes. The generic dynamical processes are outlined in Figure 5. Initially, a short laser pulse will produce a nonequilibrium distribution of hot excitons. This distribution will first thermalize and then undergo nonradiative multiexciton (MX) recombination (MER). The MER process reduces the MX multiplicity and creates a lower MX that is electronically hot. This process will continue until complete thermalization is reached. Each of these processes of relaxation and recombination is to be evaluated to determine both rates and, importantly, the pathways which determine the rates. Independent of the historical artifact of the phonon bottleneck, the goal of precision measurement of hot carrier relaxation and a rigorous understanding of the pathway(s) has been under intense investigation for nearly two decades. This Review describes some of the main concepts and results which treat this key problem in the basic science of semiconductor quantum dots.

2. EVALUATING EXCITON RELAXATION IN QUANTUM DOTS Much experimental and theoretical work has been conducted on evaluating the relaxation dynamics of hot excitons in semiconductor quantum dots (Figure 6). Due to the larger electronic level spacings from quantum confinement, early theory predicted 22092

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The Journal of Physical Chemistry C that electron relaxation should be slower for quantum confined structures.3,5,87
90 This phonon “bottleneck” was expected, as multiphonon emission via the Fr€ohlich interaction would be required to climb down the manifold of electronic states. The electronic energy gaps are ∼150
350 meV, in comparison to the longitudinal optical (LO) phonon energy of ∼30 meV. In contrast to these predictions, experimental measurements showed fast subpicosecond to picosecond electron relaxation dynamics in colloidal semiconductor quantum dots.3,14,91
98 More recent theory proposed the presence of a confinement enhanced Auger relaxation pathway in which the electron unidirectionally transfers energy to the hole.55,99,100 This process can be fast in quantum dots due to a larger wave function overlap and reduction in momentum conservation requirements due to spatial localization. Experiments have qualitatively shown that smaller particles have faster electronic relaxation rates, consistent with the presence of an ultrafast Auger channel for electrons.3,91
94 Theory has predicted that the electron relaxation times are ∼0.1
2 ps, with a size dependence in which the rate could be flat or decreasing with particle radius. An alternative situation was probed in which the hole was spatially decoupled from the electron.22,101,102 The femtosecond Auger channel requires the presence of the hole to accept the excess energy from the electron. In the event that the hole is decoupled from the electron, the Auger channel becomes deactivated for the electron. Thus a spatially decoupled hole would allow for observation of the electron dynamics in isolation from the hole. Decoupling of the hole was achieved by using hole traps at the surface of the colloidal quantum dot or by nongeminate carrier capture in epitaxially grown quantum dots.103 In the case of the epitaxially grown quantum dots, ligands are absent, and a phonon bottleneck was observed. In a sequential pumping scheme, experiments by Guyot-Sionnest et al. and Klimov et al. on colloidal quantum dots showed that the electron dynamics proceeds on the 3
30 ps time scale in the absence of the femtosecond Auger channel.22,101,102 The experiments by Guyot-Sionnest et al. furthermore showed that under these circumstances the surface ligands had a pronounced effect on the time scale of electron relaxation from 1P to 1S.101 These experiments showed that in the absence of the Auger channel the electron relaxes on a picosecond time scale. These experiments furthermore showed that the pathway for electron relaxation has a dominant contribution from a surface ligand based channel, provided the Auger channel is removed. While the electron has a femtosecond Auger channel in CdSe quantum dots, the holes do not. The electron level spacings are ∼3 greater than the hole level spacings for CdSe quantum dots. As such, it was expected that the holes should have a phonon bottleneck at the final stages of relaxation near the band edge. Experiments by Klimov et al93 and subsequently by Hendry et al.104 probed relaxation dynamics of the hole. Klimov and coworkers used a combination of transient absorption (TA) and transient photoluminescence (PL) to monitor hole relaxation. These experiments suggest that the hole relaxation slows down closer to the valence band edge due to the sparser density of states at the band edge. These experiments furthermore suggest that there was a phonon bottleneck near the band edge for the holes. However, these experiments were not able to monitor state-to-state dynamics and furthermore cannot measure the relevant dynamics with the 10 fs precision required for quantitative determination of the state-to-state transition rate for holes. A key difficulty in spectroscopic experiments on quantum dots is that both initial and final excitonic states need to be

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spectroscopically prescribed. For example, with fixed excitation wavelengths (e.g., 400 nm excitation) larger particles will necessarily measure electron and hole relaxation dynamics. In all but the smallest particles, the hole will get up-pumped by the electron and then relax through the valence band. Regardless of the instrumental time resolution, photoluminescence measurements cannot measure the hole dynamics of interest with quantitative precision. Specificity in the final hole state was achieved by Hendry et al.104 using time-resolved terahertz spectroscopy. These experiments monitored the arrival time of the hole to the band edge from an arbitrary initial state. The initial state depended upon the size of the quantum dot. These experiments suggested that the arrival time of the hole was ∼350 fs, provided the electron was initially in its lowest-energy 1S state. The key point is that no prior experiment has been able to monitor the hole dynamics with specificity in the initial and the final excitonic states, along with the time resolution needed to quantitatively measure the relevant processes. While hot exciton relaxation dynamics in semiconductor quantum dots has been extensively studied, a clear picture of the relevant processes had remained elusive. The key difficulty is due to the sizedependent excitonic spectrum.6,44,66,68,69 This size dependence means that the same initial excitonic states are not necessarily populated for each size of quantum dot. Furthermore, since these are multilevel systems, the relaxation dynamics will not necessarily be characterized by simple functions which represent transition rates. Most experiments which use the pump/probe (transient absorption) approach use excitation at 400 nm (3.1 eV). Under these excitation conditions, the electron will not necessarily be initially prepared in its 1P state. Instead the electron will be in some higher-lying state.58 Thus, the electron relaxation will follow sequential kinetics. An additional difficulty is that the density of states shows that the initial electronic state could be a mixture of 1S, 1P, or 2S.44,58 In the case of excitation directly into a 1S electron state (X1), there will be an instantaneous development of population into 1S. If the excitation were directly into 1P (X4), then there would be exponential development of population, and if the excitation were into a state higher in energy than 1P (denoted 2S for simplicity), a nonexponential buildup would take place. Thus, the measured electron relaxation will follow a sum of three signals consisting of a step function, single exponential, and nonexponential, convolved with the instrument response function (IRF).6,66,68,69  ΔODðtÞ ¼ A1S þ A1P e
k1 t þ A2S   1 þ

1 ðk1 e
k2 t
k2 e
k1 t Þ k2
k1

 X IRF ð1Þ

Here, k2  k2Sf1P and k1  k1Pf1S. Each k represents the total rate for a state-to-state transition which is comprised of several pathways which contain the desired dynamical information. Larger particles would follow even more complex kinetics with more highly excited initial states. Regardless of pulse duration, it would be impossible to precisely extract a transition rate, k1Pf1S, from a smoothly varying experimental transient. In contrast, an exciton selective approach can yield state-to-state exciton dynamics with specificity to either electron dynamics or hole dynamics ΔΔODðtÞ ¼ e
kt X IRF 22093

ð2Þ

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Figure 7. Representative femtosecond pump/probe transient absorption (TA) spectra of colloidal CdSe quantum dots in dispersion. The pump pulse is resonant with X4, and the continuum probe monitors the interband transitions in the visible. The TA spectrum (a) and contour plot (b) show both bleaching and absorptive signals. These signals evolve on a distribution of time scales and furthermore depend strongly upon the initial excitonic state into which one pumps.

Here, the k represents a specific state-to-state transition rate, whether for electrons or holes. By using various permutations of pump and probe wavelengths selected to be resonant with specific initial and final states, an exciton selective approach yields electron and hole relaxation dynamics with state-to-state specificity and a temporal precision of 10 fs, recovering the pulsewidth-limited precision that one expects for simple two-level systems.6,66,68,69 This temporal precision is essential to quantitatively establish the relative contributions of multiple relaxation pathways, each of which may have a distinct size dependence.

3. SPECTROSCOPIC PROBING OF HOT EXCITON RELAXATION WITH EXCITONIC STATE SPECIFICITY 3.1. Overview of the Spectroscopic Signals. While the electronic structure of excitons (X) in quantum dots can be understood by linear spectroscopy (e.g., absorption), the dynamics as well as the electronic structure of multiexcitons (MX) require the use of ultrafast nonlinear spectroscopy as a probe. Femtosecond pump/probe or transient absorption (TA) spectroscopy enables such a probe of hot exciton relaxation dynamics. The interpretation of these optical nonlinearities has been discussed at length in excellent reviews by Klimov.3,43 There are, however, some important subtleties that arise when employing our state-resolved approach to probing exciton dynamics.6,42,66
79 This approach enables closer inspection of the factors which govern the optical nonlinearities in QD and ultimately enables further probing of these dynamical processes. The majority of pump/probe TA experiments in CdSe and CdS quantum dots employs 400 nm (3.1 eV) excitation due to its convenience—it is the second harmonic of the 800 nm output from the commonly used Ti:sapphire laser system. Similarly, the experiment on PbSe and PbS quantum dots typically uses the fundamental 800 nm output for the same reasons.105,106 In this spectroscopic situation, the initially pumped exciton is not well specified. As a result, it is difficult to establish a rigorous picture of the source of the signals—the first step in the path toward precision measurement of the processes of interest. In our experiments, we use optical parametric amplifiers (OPA) to directly excite into specific initial excitonic states. The details of the experiment have been described elsewhere6,42,66
79 and will only be briefly reviewed here. The key step is to excite directly into the initial excitonic state of interest. Without this selective pumping,

no amount of time resolution would enable clean extraction of the state-to-state transition rates of interest, but more broadly, the absence of this selectivity in excitation places a barrier on our understanding of the spectroscopic signals and how they connect to the processes of interest. For these reasons, we typically use four OPA pump spectra for each size of dot, in addition to generic 400 nm excitation (Figure 3c). The OPA pulses are typically 30
40 fs in duration with a transform limited bandwidth of 50
60 meV, approximately the bandwidth of the band edge exciton. The probe light is derived from a single filament white light continuum generated in a sapphire crystal. The continuum is dispersion compensated as are the OPA pulses. The TA spectra are acquired in a chirp-free manner by scanning the monochromator and the delay stage to null out any residual dispersion in the continuum.107 In this manner, the timing uncertainties are (10 fs. Finally, we perform pump/probe experiments with two OPA spectra simultaneously. We do so by alternately chopping two OPAs at 333 Hz such to create a pulse sequence of pump1, pump2, no pump. This is done to better compare the signals under different pumping conditions. In our experiments, two experiments with two different pump wavelengths are done simultaneously with the same spectrometer conditions and the same quantum dot sample conditions—a point of considerable interest in light of recent studies on the importance of charging type photoproducts28,29,32,42,108 which may contaminate the experiment. Figure 7 shows a representative TA spectrum of the CdSe QD in toluene dispersion at 300 K. The pump pulse is resonant with X5 which is a nominally 1P type exciton.44,58,77 The TA transient spectrum in Figure 7 reveals both absorptive and bleaching signals that build up and decay on multiple time scales. The origin of the optical nonlinearities is outlined in Figure 8. Figure 8a shows TA spectra which are slices in time of the TA transient spectrum. These TA spectra were obtained at t = 50 fs, at the earliest stages of relaxation. At this stage, the system is essentially in the initially pumped state. The spectra were taken under conditions of X1 and X4 pumping, 1Se
1S3/2 and 1Pe
1P3/2 in EMA. These TA spectra reveal the presence of photoinduced bleaching and absorptions which strongly depend upon the initial excitonic state. These spectral features have been referred to as A1, B1, B2, A2, etc. by Klimov based upon whether they were absorptive or bleaching signals.3,43 This notation is widely used in the literature, although these features (e.g., A1) are 22094

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Figure 8. Decomposing the TA signals into the contributions from ground state bleaching (GSB), stimulated emission (SE), and excited state absorption (ESA). (a) A TA spectrum of CdSe quantum dots at t = 50 s, with a pump resonant with X1 and X4. X1 is the 1S type band edge exciton, and X4 is a 1P type hot exciton. The features are noted as A/B based upon whether that spectral region produces an induced absorption or a bleach. The TA spectra at 50 fs, prior to cooling, reveal clear differences based upon the pump-induced populations. The TA spectra are shown to be distinct from the Stark spectrum, which is approximately the second derivative of the absorption spectrum. (b) The bleaching signals arise from GSB and SE. (c) The absorptive signals arise from ESA due to biexciton formation. (d) Two pumps are shown in the electron/ hole picture such that they are resonant with X1 and X2. (e) When the probe is tuned to the B1 feature, the ΔOD transients are identical. This observation confirms that the B1 feature probes the electron state and is insensitive to holes, with their larger degeneracy.

not necessarily absorptive over all time or over all pump wavelengths.6,42,66,68,69,74,78,79 Hence a rigorous picture of the connection between the electronic structure of the dot and the source of these signals is necessary. The signals in these pump/probe experiments generically arise from three terms: ground state bleaching (GSB), stimulated emission (SE), and excited state absorption (ESA).109 These processes can be described at the photon (intensity) level or at the field (amplitude) level, should a more detailed picture be warranted. As the pump pulse brings population to the excited state, the GSB and SE terms will appear in the TA spectra (Figure 8b). GSB arises from removal of population from the occupied ground state. This process is also referred to as state filling or Pauli blocking. The excited state population can also experience stimulated emission by the probe (Figure 8b). Both GSB and SE terms will create bleaching signals in the TA spectrum. The ESA term is illustrated in Figure 8c at the field/amplitude level. Excited state absorption results from absorption from an excited state into a more highly excited state. In the case of molecules, ESA may arise from S1 f S2 types of transitions. In the case of semiconductors, the ESA arises from intraband absorption. Since the

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electronic structure of these semiconductor quantum dots is quantized, the equivalent of intraband absorption is intraexcitonic absorption. These transitions are typically in the mid-infrared (1000
5000 nm) and hence are far outside the visible probe window. In addition to creating a more highly excited single excitation (e.g., X1 f X4), the quantum dot can support multiple excitations per dot. This multiple excitation is minimally the biexciton (XX) but is generally a multiexciton (MX) state. MX processes are very important to the processes of multiexciton recombination (MER), multiple exciton generation (MEG), optical gain, and correlated photon emission. At the field level, the first two field
matter interactions arise from the pump pulse, thereby producing an excited state population. The third interaction is with the probe field which monitors absorption from X into XX. Provided 6 2EX, there will be a photoinduced absorption (PA). The PA is EXX ¼ due to the fact that exciton
exciton interactions stabilize the biexciton and lower its energy. Hence, absorption into the biexciton is typically red-shifted with respect to absorption into the single exciton. The discussion of ESA and biexciton formation warrants further mention due to inconsistent usage in the literature. In the early literature, the induced absorptions were described in terms of a Stark shifting picture.3 In the Stark approach, a trapped carrier creates a Stark field similar to a laboratory frame external Stark field.3,110,111 The Stark spectrum approximately follows the second derivative of the absorption spectrum. Since the early TA spectra without excitonic state selectivity resembled the second derivative of the absorption spectrum,3,92 the Stark approach appeared reasonable. In recent years, it has emerged that the biexciton picture (more generally MX) enables more insight.6,66,74,78 The experimental TA spectra are clearly quite different from the Stark-like derivative spectrum (Figure 8a). In short, the biexciton is the simplest way to describe the relevant signals, a topic that we have been investigating6,66,74,78 in parallel with these relaxation dynamics experiments. Having established the general features of the source of optical nonlinearities in quantum dots, we relate these signals to specific processes such as probing nonequilibrium electron/hole populations. This disentangling of the signals was discussed at length in our initial work66 and will only be briefly reviewed here. The B1 spectral feature was argued by Klimov to monitor only the population of the 1S electron due to the small degeneracy of the electron manifold and the large degeneracy of the hole manifold at these energies.3,92 We confirm this prediction in Figure 8d and e.66 OPA pulses are tuned into X1 and X2 initial excitonic states, while the probe is tuned to the B1 spectral feature. X1 and X2 share a common 1S state for the electron and differ only by the state of the hole, 1S vs 2S. The B1 bleaching signal is identical under both pumping conditions, verifying that the B1 feature monitors the electron population but is insensitive to the hole population. This method of analysis will be expanded below to further connect to specific hot electron and hot hole relaxation processes. 3.2. Unraveling Electron and Hole Processes from the Signals. The objective of this work is a precision measurement of carrier relaxation (i.e., cooling) processes in quantum dots. Since the term “cooling” itself is imprecise, it is preferable to consider measurement of an excitonic state-to-state transition rate.6,66,68,69 To measure such a transition rate, there must be specificity in the initial excitonic state prepared by the pump pulse as well as specificity in whether the electron or the hole is monitored by the probe pulse. Figure 9 outlines the approach which was discussed in detail in our prior works.6,66,68,69 22095

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Figure 9. Judicious combinations of pump/probe wavelengths can be prescribed to reveal specific cooling processes with excitonic state-to-state specificity. (a) A linear absorption spectrum of CdSe quantum dots. The main features are noted in the exciton and the electron/hole picture. The electron/hole notation of the states is within the multiband effective mass approach. With four pump spectra (X1, X2, X3, X4) and four probe features (A1, B1, B2, A2), only select combinations are useful. (b) The B1 probe is shown with the X1 and X4 pump. (c) The A1 probe is shown with the X1 and X2 pump. (d) Since the B1 feature only probes the electron state, the difference between the transients in (b) monitors the time-dependent hot electron survival probability for 1P f 1S. (e) Since X1 and X2 both have an electron in the 1S state, the only dynamics comes from the relaxing hole in X2. Hence, the differences in the transients in (c) reflect the hole cooling process of 2S3/2 f 1S3/2.

Figure 8a shows a linear absorption spectrum as well as four OPA pump spectra used to perform these state-resolved measurements. With four bands into which one can directly pump (X1, X2, X4, X5) and four key features in the TA spectra (A1, B1, B2, A2), there are 16 combinations of pump/probe transients that might be used for probing hot carrier processes in QDs.66 We contrast this suite of observables with the commonly used approach of arbitrary pumping at 400 nm combined with only a B1 probe. The 400 nm pump/B1 probe enables a qualitative estimate of electron cooling; however, it does not enable a quantitative measure of a well-specified transition rate for electrons, and it does not enable disentangling of electron and hole relaxation processes. We have previously discussed this matrix of pump/probe combinations and identified that only a small set of these combinations are useful for extracting specific carrier dynamics (electron vs hole) with the desired state-to-state specificity.66 Those results will only be briefly discussed here. As initially proposed by Klimov and subsequently confirmed by us, the B1 feature in the TA spectrum is only sensitive to the electron population. Hence pumping directly into X1 (1Se
1S3/2 in EMA) will instantaneously produce a B1 bleach without any ensuing dynamics.6,66,68,69 The experimental data in Figure 9b confirm this expectation. Pumping directly into X4 (1Pe
1P3/2) should produce a bleach that builds up exponentially due to the 1Pf1S electron relaxation process. The difference between the X4 and X1 pumped

transients (ΔΔOD(t)) will then directly monitor the hot electron relaxation process (P1Se(t)) with state specificity (Figure 9d).6,66,68,69 A similar approach was used to directly monitor hole dynamics.6,66,68,69 Recognizing that X1 and X2 (1Se
2S3/2) share a common 1S state for the electron, the only difference is the state of the hole. Since the electron does not undergo any dynamics on this time scale when in its 1S state (surface trapping is much slower74), the only dynamics in the signals will be hot hole relaxation from 2S f 1S. Precisely because both excitons share a common electron state, both pumping conditions produce identical B1 signals (Figure 8d and e). However, other signals in the TA spectra remain useful. In particular, the A1 signal reflects the magnitude of the biexciton-based level shift (ΔXX) (Figure 8).6,66,74,78 The A1 transients under these two pumping conditions are shown in Figure 9c. It is worth noting that the A1 signal for the X1 pump is actually not absorptive as the label suggests. Instead, it is an attenuated bleach due to a small ΔXX. The induced absorption develops as ΔXX becomes larger, as we have previously shown. In this case, the difference between the A1 transients directly monitors the hot hole population relaxation from 2S f 1S (Figure 9e). The spectroscopic methods summarized here reveal that there is a rich spectroscopy to these QDs. The many signals available in a TA spectrum along with the capacity for direct excitonic pumping enable a tremendous increase in the precision with 22096

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Figure 10. State-resolved femtosecond pump/probe measurements reveal the lifetimes of the first excited state of the electron (1P) and hole (2S3/2) states with excitonic state-to-state selectivity. (a) The hot electron lifetime as a function of particle size reveals that smaller particles have shorter lifetimes. The spectroscopic method produces experimental uncertainties that are sufficiently small to enable quantitative measurement of the functional form of hot electron cooling for the first time. (b) The first excited state of the hole shows a lifetime which is completely size independent. The energy dissipation rate for electrons (c) and holes (d) shows a complete absence of a relaxation (phonon) bottleneck for either.

which one can monitor hot electron dynamics and a new window into monitoring hot hole dynamics. The results of this approach are summarized below. 3.3. Breaking the Phonon Bottleneck for Electrons and Holes in Quantum Dots. Due to the importance of hot exciton relaxation in a wide variety of applications, it is essential to have a detailed map of the time scales and pathways of relaxation. Prior work on high-quality colloidal CdSe quantum dots by Klimov has confirmed the Auger relaxation path for electrons.3,91,92 By spatially decoupling the electron and the hole, Guyot
Sionnest22,94,101 and Klimov102 have both shown that the surface ligands can play a strong role in electron relaxation. Finally, terahertz experiments by Bonn have provided the first direct measure of the electron to hole Auger scattering process in QDs.104 What is missing in all cases is a measure of electron and hole transition rates (rather than cooling) with excitonic state specificity. Such a level of precision is required to cleanly measure the processes of interest and to furthermore offer an experimental benchmark for comparison to theory. For example, theories by Efros99 and Zunger55 both suggest rapid Auger-based electron relaxation, but the absolute values and the functional forms of each calculation are quite different (Figure 6d). The earlier electron cooling experiments cannot provide such a test due to the large uncertainties ((100 fs for processes that are 100
200 fs in duration).3,91,92 By measuring state-to-state transition rates for electron relaxation rather than a qualitative estimate of cooling, we recover the pulsewidth-limited timing precision of a simple two-level system (Figure 9d and e). The size-dependent transition rates for electrons and holes are shown in Figure 10. These data confirm the early work by Klimov3,91,92 that electron relaxation (in the presence of a hole) is very fast and gets faster for smaller dots (Figure 10a). This result is consistent with the Auger scattering picture of hot electron relaxation in the QD. The main new result is that we obtain such a measure with specificity and precision ((10 fs) to enable a rigorous measure of

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the absolute value as well as the functional form of this hot electron transition rate.6,66,68,69 We find that the electron transition rate follows a R
1(0.1 functional form, which can be compared against benchmark calculations, e.g., the recent ab initio work by Prezhdo.59
64 The more interesting result is that the lifetime of the hot hole (2S) is completely size independent (Figure 10b).68,69 This result is completely at odds with the prevailing picture of hot exciton relaxation. In the recent view, electrons will relax via an Auger channel (holes present), thereby breaking the phonon bottleneck for electrons. In contrast, the holes should still be governed by a phonon bottleneck since the Auger channel is unidirectional for CdSe. The directionality arises from the relative sparseness of the CB vs VB manifolds. We contrast these results to earlier work by Klimov93 and Bonn104 which measure hole cooling. In those works, the hole cooling was estimated for dynamics throughout the entire VB manifold. In both cases, a well-specified transition rate between fixed initial/final states was not measured as we show here. These results are not inconsistent with the prior work. Rather, they afford a more precise measure of the dynamics of interest. To evaluate how carrier cooling is controlled by QD size and to evaluate the presence or absence of a phonon bottleneck, one can plot the energy dissipation rate vs the energy gap of these specific state-to-state transition processes. Figure 10c and d shows that both electrons and hole have energy relaxation rates that increase with smaller dots and furthermore increase with energy gap. Hence, there is a breaking of the phonon bottleneck for both electrons and holes for excitons in these colloidal quantum dots. This result suggests that the phonon-based relaxation pathway and the very search for the “phonon bottleneck” was simply an early theory that needs to be extended to create a more complete picture of hot exciton relaxation pathways in quantum dots.

4. WHAT IS THE MECHANISM OF HOT EXCITON RELAXATION IN QUANTUM DOTS? 4.1. Overview of Relaxation Pathways in Nanocrystal Quantum Dots. The topic of hot carrier relaxation in quantum

dots has seen divergent experimental and theoretical literature. The question is what is the mechanism of hot exciton relaxation? In a more chemical picture, one might ask what is the coordinate for this process. The early theory proposed phonon emission as the channel, and later theory proposed an electron/hole Auger scattering process for electron relaxation. Subsequent theories that have been inspired by experiment now include coupling to ligands via differing schemes such as Forster energy transfer (FRET)101 or electron vibration energy transfer (EVET),112 as well as nonadiabatic coupling between ligands and excitonic states via the breakdown of the Born
Oppenheimer approximation.68,69 Figure 11 schematically illustrates these possible transition pathways. The aim of experiments has been to verify the proposed channels and establish the pathway for hot exciton relaxation. Due to the divergence in the experimental literature, the controversies have largely remained. The value of these precision measurements66,68,69 is to provide precisely the feedback to enable the original question to be answered. Given the presence of multiple possible pathways for relaxation as well as the presence of both electrons and hole to relax, disentangling of the relative contributions to the total measured relaxation process is essential. While it is qualitatively 22097

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Figure 11. Relating the experimental observations to theory, (a) a phonon emission based channel was initially proposed for hot carrier relaxation in quantum dots. (b) An electron/hole Auger scattering based theory was subsequently proposed for governing hot electron relaxation in quantum dots. This process was expected to be dominant due to confinement-induced electron/hole overlap, combined with relaxing momentum conservation due to the finite size of the particles. More recent proposals involve coupling to surface ligands in either a FRET/ EVET scheme (c) or a nonadiabatic scheme (d).

obvious that the phonon-based channel cannot explain these results, an independent verification of the strength of exciton
phonon coupling would be an important point in assessing the contribution of phonons to the cooling process. 4.2. Phonon Contributions to Relaxation: Exciton
Phonon Coupling. 4.2.1. Overview. Much like hot carrier relaxation dynamics, the problem of exciton
phonon coupling in quantum dots has seen much divergence in the experimental and theoretical literature.72,73,113,114 The problem of exciton
phonon coupling is central to quantum dot science in that it is a key parameter in the factors that determine linewidths for optical nonlinearities, for its thermal and electrical resistance properties, and for its role in hot carrier relaxation—the topic of this review. One aims to obtain an independent measure of the strength of exciton
phonon coupling to reconcile the experimental observations of the relevance of phonon-based relaxation channels. The quantized manifold of excitonic states is coupled to two phonon degrees of freedom: high-frequency optical phonons (∼200 cm
1) and low-frequency confined acoustic phonons (∼20 cm
1) . The relevant optical phonon is the polar longitudinal optical mode (LO) which is coupled via the polar Fr€ohlich interaction. The relevant acoustic phonon is the confined radial breathing mode which is coupled via the deformation potential as well as via piezoelectric effects. The coupling between the electronic and vibrational (phonon) degrees of freedom can be represented in the standard displaced harmonic oscillator approach (Figure 12a). The potentials between the various states may involve nuclear displacements, Δ, in dimensionless normal coordinates. This displacement is related to the Huang
Rhys coupling constant, S, via S = Δ2/2. The coupling strength is pωphononS. The strength of exciton
phonon coupling has itself seen considerable controversy as illustrated by the wide variance in the computed115
121 and measured113,122
136 coupling strengths for both optical and acoustic modes. In colloidal CdSe quantum

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dots, nearly all early experiments have observed either the optical or the acoustic modes but not both.72,73,114 As a result there is tremendous divergence in the experimental literature. The theoretical work has seen similar divergence with up to 3 orders of magnitude difference in the computed coupling strengths.72,73,114 This divergence in the theoretical results indicates the difficulty in obtaining realistic wave functions for the QD as well as reveals that exciton phonon coupling is itself a tremendously sensitive probe of the excitonic state. We have measured the exciton
phonon coupling in colloidal CdSe quantum dots using this state-resolved femtosecond pump/probe approach.6,72,73 In a femtosecond pump/probe transient, oscillations are readily apparent (Figure 12b). Appropriate experimental considerations must be taken such that the pump pulses are vibrationally impulsive (∼50 fs), the probe pulse is tuned to the point of maximum slope in the absorption spectrum, and experiments are done with sufficient care as to resolve these weak oscillations. Subtraction of the slowly varying excitonic contribution more clearly reveals the oscillations due to wavepacket motion of coherent optical and acoustic phonons (Figure 12c). Fourier transform of these oscillations reveals the spectra of the phonon modes which are coupled to this excitonic transition (X1 pump in the case of Figure 12). Notably, this was the first observation of coupling to both phonon modes in these highquality colloidal CdSe quantum dots.6,72,73 As described below, these oscillatory signals can be used to extract the exciton
phonon coupling strength in a straightforward manner. Doing so enables simulation of the relevant frequency domain spectra such as PL and resonance Raman spectra (Figure 12e and f). The way in which these oscillations are related to the relevant coupling strength is illustrated in Figure 13. A vibrationally impulsive pump pulse creates a phonon wavepacket via coherent superposition of phonon eigenstates.109 Two field
matter interactions with the pump pulse can produce an excited state electronic population with a vibrational coherence (Figure 13a). This vibrational coherence will generate an excited state wavepacket and is referred to as displacive excitation of coherent phonons (DECP). Alternatively, the first interaction with the pump pulse can create an electronic coherence. This coherence then evolves, followed by stimulated emission back to the ground state to create a ground state electronic population and vibrational coherence from the second interaction. This pathway is referred to as resonance impulsive stimulated Raman scattering (RISRS). Both terms generally contribute to the wavepacket motion that results in the experimentally observed coherent oscillations in the pump/probe signals.109 When the system undergoes wavepacket dynamics, the coherent phonons modulate the dynamic absorption spectrum— the transient absorption spectrum of the pumped sample. As the wavepacket oscillates on the potential(s), the energy gap is modulated (Figure 13c). It is also possible for the wavepacket motion to modulate the oscillator strength via non-Condon effects (Figure 13d). Modulation in the energy gap can be viewed as frequency modulation (FM) of the transient spectrum which will result in a π/2 phase shift when probing at the peak or the rising edge of the spectrum. In contrast, modulation in the oscillator strength can be viewed as amplitude modulation (AM) of the transient spectrum which will not result in a phase shift. Hence, measurement of the phase shift at different probe wavelengths reveals the relative contributions of the AM and FM terms which can then be used to extract the coupling strengths. The experimental results are shown in Figure 13e and f. The data reveal a perfect π/2 phase shift indicating pure frequency 22098

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Figure 12. Evaluating the coupling of excitons to phonons. (a) The exciton
phonon coupling can be understood in terms of the displaced harmonic oscillator picture. The displacements yield the coupling strength. (b) Experimental observation of coherent phonons in CdSe dots enables measurement of the exciton
phonon coupling. The transient here is for the X1 pump and A1 probe. (c) Subtraction of the slow population decay reveals the residual oscillations which reveal wavepacket motion of the coherent optical and acoustic phonons. (d) FFT of the residuals recovers the spectra of the coupled modes as well as their relative coupling strength. The time domain data can be transformed to predict the single dot photoluminescence spectrum (e) and the resonance Raman spectrum (f). The experimental resonance Raman spectra are contaminated by photoinduced surface trapping/charging. Gray lines are experimental data, and red lines are fits/simulations.

modulation of the dynamic absorption spectrum. Since the oscillations are purely due to energy gap modulation, one obtains a simple result that the amplitude of the oscillation is directly proportional to the coupling strength via Aosc = (dOD/dω)Δω. Here, Aosc is experimental oscillation amplitude; dOD/dω is the derivative of the absorption spectrum; and Δω is the coupling strength in energy units. 4.2.2. State-Resolved Exciton
Phonon Coupling: Intrinsic vs Extrinsic Coupling. This method of obtaining exciton
phonon coupling strengths can be used to measure the coupling for any given excitonic state as well as to measure the size dependence of the coupling. This information will be used to reconcile the presence or absence of phonon-based relaxation pathways. The results of this approach are shown in Figure 14. Figure 14a and b shows the exciton
phonon coupling strength for CdSe quantum dots with R = 2.7 nm for specific excitonic states. The state labeled Xcontinuum corresponds to excitation into the continuum at 400 nm (3.1 eV), whereas Xsurface corresponds to an exciton with surface-trapped charges. The main trends are that as the exciton cools to lower energy the coupling strength increases and that the process of surface trapping tremendously increases the coupling strengths. As these are the first measurements of this coupling with excitonic state specificity, insight is immediately obtained into the nature of the excitonic states as well as the origin of the experimental divergence.6,72,73 Since the polar optical phonons are coupled via the polarization-based Fr€ohlich interaction, the data show that the excitonic

polarization increases for the lower states. The acoustic modes show a similar dependence, albeit less pronounced. Since the coupling is proportional to the polarization of the excitonic wave function, these results indicate that the lower excitonic states show a larger electron
hole polarization than the higher states. This state-dependent polarization might be exploited for applications based upon quantum dot polarization effects. These data enable reconciliation of many of the prior experimental divergences based upon knowledge of how strongly each excitonic state couples to each mode. For example, the commonly used 400 nm excitation will not generate either optical or acoustic phonons due to weak coupling, rather than due to time resolution. Typical 400 nm pulses are ∼100 fs in duration, which is vibrationally impulsive for the acoustic modes and close to impulsive for the optical modes. The near universal absence of either mode in 400 nm pumping experiments (including ours) is purely due to coupling effects—the excitonic continuum is much less polar than, e.g., the band edge exciton. This question of polarization of the excitonic wave functions was previously discussed by Guyot-Sionnest94,137
139 and suggests the atomistic origin50,140 of these effects. The extremely strong coupling of both modes to Xsurface is noteworthy due to its connection between time domain (pump/ probe, photon echoes) and time integrated frequency domain (photoluminescence, resonance Raman, hole burning) experiments. This result also bears connection to the recent multiple exciton generation controversy, discussed in Section 5. 22099

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The Journal of Physical Chemistry C It was initially proposed by Krauss and Wise113,123,124 and also Efros141 that the time integrated CW experiments probe the

Figure 13. Relating the observed coherent phonons to the underlying wavepacket dynamics and to the extraction of exciton
phonon coupling constants. The coherent phonons can be generated by excited state wavepackets (a) or ground state wavepackets (b). The excited state wavepacket was historically called Displacive Excitation of Coherent Phonons (DECP), and the ground state mechanism was called Resonant Impulsive Stimulated Raman scattering. Both generally contribute to the observed oscillations. (c) The wavepacket motion can modulate the energy gap which yields frequency modulation of the dynamic absorption spectrum with an associate π/2 phase shift going from the B1 to A1 probe. (d) The wavepacket motion can also modulate the transition moment with no associated phase shift. (e) Representative probe spectra, chosen to monitor the phase shift. (f) The data show a perfect π/2 phase shift which indicated pure frequency modulation and simple extraction of the exciton
phonon coupling constants.

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coupling of a dot with accumulated charges created during the course of the experiment. Hence CW experiments will measure the coupling of this photoproduct, whereas ultrafast time domain experiments can in principle measure the intrinsic coupling. Much like the seminal work by Krauss and Wise,113,123,124 our CW Raman results on colloidal CdSe quantum dots reveal extremely strong coupling to the optical phonons and weak coupling in the ultrafast time domain experiments.6,72,73 Essentially, the time domain experiments tend to measure the intrinsic coupling of the delocalized excitonic states of interest. In contrast, the frequency domain (continuous wave) experiments measure the average coupling which is dominated by surface states. Hence, the CW experiments do not measure the intrinsic exciton
phonon coupling, precisely as proposed by Krauss, Wise, and Efros. The subtlety in the time domain experiments is that they still can produce a photoproduct consisting of a surface-trapped exciton. Hence, if experiments are performed at high pump fluences or with insufficient sample flow rate, the oscillations and the extracted coupling can be much larger.79,129,132,142 The subtlety arises from the time scale of the surface trapping process, discussed in detail in Section 5. If the surface trapping rate is not vibrationally impulsive, there will be no effect on the measured oscillations. Since the surface trapping rates are vibrationally impulsive for the acoustic modes but not impulsive for the optical modes, only the acoustic modes grow in amplitude based upon the accumulation of a surface-trapped (i.e., excitonically polarized) photoproduct.42,79 Typical surface trapping time scales for these CdSe nanocrystals passivated with organic ligands (amines) are ca. 10 ps from the band edge exciton (X1)74 and can increase to 1 ps for X274 and rise to 0.1 ps for higher lying excitons.42,79 These rates are in principle tunable by chemical control of the surface ligands. These experiments on exciton
phonon coupling provide independent verification of weak coupling to both optical and acoustic phonons, confirming that phonons do not strongly control the time scales and pathways of hot exciton relaxation. These phonon results also provide a perspective on the nature of the multiple exciton generation controversy, discussed in Section 5.

Figure 14. Excitonic state-resolved measurements of the strength of coupling to optical (a) and acoustic (b) phonons. In both cases, the coupling is weak for the delocalized excitonic states but becomes strong for an exciton comprised of a surface-trapped state. There is no strong size dependence to the X1
phonon coupling for either optical (c) or acoustic (d) phonons. 22100

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Figure 15. Total transition rate is considered to be a sum of all possible pathways. In the case of holes (a) there are two transition paths. In the case of electrons (b) there are three paths. There is no phonon bottleneck in energy dissipation for either holes (c) or electrons (d) due to the presence of additional transition paths to carrier cooling. The presence of multiple transition paths suggests that each transition path might have a unique size dependence and might further be controlled by materials design to control the relaxation rate.

4.3. Multipath Picture Which Unifies Hot Exciton Relaxation Dynamics. Following the early literature on hot electron

relaxation, the experimental and theoretical work at that time suggested the presence of an alternative relaxation channel for hot electrons—the electron/hole Auger relaxation channel.55,99,100 This most recent work, along with the simple energy mismatch arguments, clearly suggest that phonon-based pathways are not responsible for controlling the rate of hot electron relaxation in these strongly confined quantum dots. Our independent measurement of weak exciton
phonon coupling6,73,74,79 further corroborates this view that phonons are of minor importance in controlling hot exciton dynamics. In contrast, experiments by Guyot-Sionnest were the first to demonstrate the importance of surface ligands in controlling hot electron relaxation.94,101 In these experiments, the electron was spatially decoupled from the hole to better focus on the influence of the surface ligands. Hence, some confusion arose as to the pathway by which hot electrons relax. In addition to these experiments on hot electron relaxation, our experiments summarized here have shown that there is an absence of a phonon bottleneck for holes as well.68,69 These seemingly disparate observations can be unified provided one views the process of hot exciton relaxation as taking place via multiple competing pathways. The experiments on high-quality colloidal quantum dots will be primarily discussed due to poor materials quality in the earliest work, e.g., doped glasses. In the case of colloidal CdSe quantum dots, the majority of attention was placed upon measurement of hot electron relaxation rather than hot hole relaxation. The controversy in the literature largely arose due to different experiments measuring different processes. In the simplest experiment, a hot exciton is optically generated, followed by hot electron relaxation—among a manifold of other processes. In a related experiment, the hole may be spatially decoupled, enabling measurement of a relaxing hot electron—not the same as a hot exciton.22,94,101,102 The geometric and functional difference between the two situations is in the extent of electron/hole interaction. It is specifically this interaction which is responsible for the Auger relaxation process. Hence hot electron relaxation in the excitonic configuration is designed to measure the Auger

process, whereas hot electron relaxation with a spatially decoupled hole is designed to measure all non-Auger-based relaxation paths for the excited electron. This identification of differences in available relaxation pathways enables a simple reconciliation of an earlier controversy as well as suggesting a unified picture of the larger problem of hot exciton relaxation. We proposed that there are multiple competing pathways in hot exciton relaxation.6,68,69 In this picture, the question at hand is no longer one of establishing the mechanism of relaxation but to understand and ultimately control the relative contributions of the manifold of pathways. Hence there should be a phonon-based path for both electrons and holes. There should also be a surface ligand based path, and finally there should be an Auger-based path for the case of electrons. There will not be an Auger path for holes due to larger level spacings in the VB manifold. In our multichannel approach, the aim is to unravel the contributions for the total rate as illustrated by ke ðRÞ ¼ kphonon ðRÞ þ kligand ðRÞ þ kAuger ðRÞ

ð3Þ

and kh ðRÞ ¼ kphonon ðRÞ þ kligand ðRÞ

ð4Þ

The total rate corresponds to the experimentally measured rate which corresponds to an electron or hole which has some experimentally determined size dependence. This total rate is ideally an excitonic state-to-state transition rate as measured here. The value of a state-to-state transition rate is initially that it enables greater precision in the specific process measured. The precision as well as control in the specific process (i.e., manifold of available pathways) is what uniquely enables assessment of the relative contributions of each path, e.g., phonons vs Auger. These individual paths need not have the same size dependence. The results of this multichannel approach to hot exciton relaxation are summarized in Figure 15. The experimentally measured state-to-state transition rate for hole relaxation is nearly size independent and is well reproduced by a relaxation pathway that is largely dictated by ligands, with minor contributions from 22101

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The Journal of Physical Chemistry C phonons. In contrast, the electrons show a strong size dependence with a major contribution from the Auger pathway, a minor contribution from surface ligands, and negligible contribution from phonons. The details of establishing this multichannel picture have been discussed elsewhere6,66,68,69 and will only be discussed briefly here. We first analyzed hole transition rates due to the presence of only two possible relaxation paths: phonon and ligands. While there are a variety of sophisticated phonon-based theories of carrier relaxation, they all point to the relative unimportance of this path. Hence we use a simple functional form for phonon-based hot carrier relaxation from Nozik.69,143 This functional form reproduces the expected phonon bottleneck for electrons and hole (Figure 15). We then invoked the existence of a nonphonon-based relaxation path for holes—the surface ligands. We note that the term phonon is used only for the optical and acoustic normal modes of the nanocrystal, and ligands are used to denote the molecular vibrations of the adsorbed surfactants and proximal solvent molecules. However, these terms may be used somewhat interchangeably. The initial proposal of the influence of surface ligands was from Guyot-Sionnest.101 They proposed an energy transfer based scheme, wherein the electronic energy from the carriers is transferred to molecular vibrations of adsorbed molecules. A similar approach was invoked by Banin and Rabani.112 We have invoked the existence of a nonadiabatic pathway wherein the ligand vibrations induce electronic transitions via a breakdown of the Born
Oppenheimer approximation.68,69 Nonadiabatic processes are well-known in quantum molecular dynamics and frequently drive ultrafast electronic processes, e.g., the dynamics of the solvated electron.144
153 In this process, the coupling of the electronic and vibrational degrees of freedom enables energy exchange. Hence, vibrational motion can mediate electronic transitions as well as electronic transitions creating molecular vibrations as is the case here. We evaluated the nonadiabatic transition rate in a golden rule form, utilizing the Hellman
Feynman theorem to simplify the functional form.68,69,154 This analysis shows that the relevant matrix element is a quotient of the Hellman
Feynman force and the relevant energy gap. For transitions driven by surface ligands, the force is proportional to the fraction of the hot carrier that tunnels into the ligands and solvent matrix. Smaller dots will have a larger fraction which couples to the surface. These smaller dots will also have a larger energy gap. The energy gap in the case of holes corresponds to E(2S3/2)
E(1S3/2) or E(X2)
E(X1), directly obtained from the linear absorption spectra. The force and the energy gap have nearly the same functional form, resulting in a quotient (the transition rate) which is size independent. Our calculations, described in detail elsewhere, include the effect of tunneling.68,69 Due to the simplicity of our calculations, we can only estimate the functional form of this nonadiabatic transition rate. We are not able to compute the absolute value. Nonetheless, with one adjustable parameter (the prefactors which scale the computed functional form), we are able to reproduce these precision measurements (Figure 15a). In this approach, we computed the kphonon(R) as well as the functional form for kligand(R). We then adjusted the amplitude of kligand(R) so the total rate fits the experimental rate. Notably, recent ab initio work by Prezhdo has shown the importance of these nonadiabatic processes,59,61,63 thereby confirming our initial proposal of mechanism(s). This proposal may be further tested via chemical control of the surface ligands, distance dependence

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via tunneling barriers, and via comparison to atomistic quantum dynamics calculations. We then use this approach to unravel the pathway(s) by which hot electrons relax (Figure 15b). The same phonon-based rate is used for electrons, with the appropriate 1P
1S electron energy gap, E(X4)
E(X1). The ligand-based rate is computed in the same manner, replacing the hole energy gap with the electron energy gap and using the functional form of the fraction of the hot electron in contact with ligands. These pathways are much less significant for electrons than holes mainly due to the larger electron energy gap. The Auger path is then taken to be the difference between the experimentally determined transition rate and the sum of the phonon and ligand channels (Figure 15b). The immediate point is that these precision experiments can be explained by this multichannel picture of hot exciton relaxation pathways in semiconductor quantum dots. The broader point is that the relaxation pathways may be controlled by suitable materials design. The earliest such example was by Guyot-Sionnest, in which the surface ligands were chosen to match or mismatch the electron energy gaps.101 In the nonexcitonic case of hot electron relaxation, this ligand control enabled control of the hot electron relaxation time. We have simply attenuated the strength of the ligand channels by spatially decoupling the ligands. This decoupling is achieved by passivating the CdSe dots with a ZnS layer, onto which the ligands are now bound. Doing so results in hole relaxation rates that are measurably longer and electron relaxation rates that are completely unchanged.69 These results are entirely consistent with our multichannel picture for both holes and electrons. In the case of holes, attenuating the ligand channel increases the relative contribution from phonons and reduces the total rate, precisely as observed. In the case of electrons, decoupling of the ligands produces no measurable effect on the transition rate. This observation is reconciled by considering that all measurable contribution to the total electron transition rate arises from the electron/hole Auger channel. Hence, attenuating the ligand channel has no effect.69 We evaluate the robustness of this picture by further comparison to recent experiments by Guyot-Sionnest on recovery of the phonon bottleneck.22 The initial observation of the phonon bottleneck may have been by Norris in epitaxial quantum dots.103 In those dots, there are no ligands to provide an alternative relaxation channel. Those experiments isolated dots which contained only electrons from dots which contained electrons and hole (excitons) via geminate carrier capture. In this situation, a fraction of the dots would have no Auger channel and thereby revealed the phonon bottleneck. To further explore this situation, in the high-quality colloidal quantum dots widely studied, Guyot-Sionnest found that full isolation of the electron from the hole and surface ligands enabled realization of extremely slow electron cooling (nanosecond rather than picosecond or femtosecond) and finally revealed the existence of the phonon bottleneck in these colloidal quantum dots. While the phonon bottleneck remains more of a historical artifact today, the main point here is the ability to control relaxation processes—a point of considerable motivation as described in the Introduction. We summarize this unified picture of hot carrier relaxation in Figure 16. Upon the basis of these state-resolved measurements, one is now poised to speak of excitonic transition processes rather than the more qualitative approach of carrier cooling. This idea is illustrated in Figure 16a. The pump pulse creates some initial excitonic population, e.g., X4. The primary transition process for X4 is Auger-based relaxation for the 1P electron which then 22102

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5. PHOTOINDUCED CHARGING AND SURFACE TRAPPING PROCESSES

Figure 16. Schematic of the transition processes and a unified picture of exciton relaxation processes. (a) This excitonic state-resolved approach to transition processes enables measurement of state-to-state dynamics going from Auger heating of the holes, to hole cooling, to hole trapping at the surface. (b) The transition process is unified by considering the presence of multiple pathways which are controllable. (c) The different pathways do not have the same dependence upon particle size.

creates an energetic (hot) hole. This hot hole then relaxes through the VB manifold to yield the band edge exciton, X1. This band edge exciton can either radiatively recombine (not shown) or undergo surface trapping for either holes (shown) or electrons (not shown). The time scales for each of these transition processes are shown in Figure 16a, based upon our measurements summarized here. In addition to identifying excitonic transition processes, we are now able to identify the path(s) by which each of these transition processes takes place (Figure 16b and c). Since the total transition rate is now viewed as the sum of all possible transition paths, the carrier-specific transition process can be decomposed into the respective contributions. Figure 16b shows the pathways by which the electron relaxes: primarily via Auger relaxation with minor contributions from ligand channels and negligible contribution from phonons. The hole relaxes primarily via ligands with minor contribution from phonons. The relative contributions from the two leading pathways are noted in Figure 16c. Beyond providing a detailed picture of energy relaxation in these quantum dots, this picture enables rational design of the dot and its environment to control energy relaxation for specific applications such as quantum dot lasers or photovoltaics.

5.1. Hot Exciton Surface Trapping. The hot carrier relaxation processes discussed above can be considered more broadly to include related processes such as charge trapping into surface states42,74,79 and also multicarrier/exciton recombination.3,4,42,155,156 The multiexciton recombination (MER) process is much slower than these relaxation processes and can involve similar pathways such as Auger recombination—related but not identical to the Auger relaxation process discussed here. The MER process is also related to the complementary process of multiple exciton generation (MEG). Neither MER nor MEG will be further discussed to focus on relaxation processes that take place at conditions which generate mean occupancies of fewer than one exciton per dot. In this situation, the final relaxation process involves trapping of carriers from the band edge exciton to available trap states. This process of depopulating delocalized core states into localized surface/interface/defect states we refer to as surface trapping.42,74,79 The very same process has seen recent interest in light of the MEG controversy. In that context, the surface trapping process is referred to as photocharging.29,32,108,157 We have referred to this surface-trapped state as a polarized state rather than a charged state based upon the TA signals.42,79 We use the term “surface trapping” in the absence of clear evidence of photoionization which produces a charged dot. Nonetheless, there are a variety of terms used to describe the same process. At present, the nature of surfacerelated photoproduct, whether trapped or ionized, remains unclear. These colloidal quantum dots have surface states which reside midgap between the CB and VB. These states can be either electron or hole traps. The nature of the surface states in these QDs is a topic unto itself and is beyond the scope of this Review. Without mention of the microscopic nature of the surface states in QDs, we will identify the importance of these surface states and how they connect to the topic of hot exciton relaxation. A detailed treatment of the nature of these surface states will be presented elsewhere. The lowest delocalized excitonic state of the quantum dot is the band edge exciton, X1, comprised of electrons and holes in 1S orbitals. For the ideal QD, X1 is the lowest energy state. In the case of real QD, surface states are present at lower energy. These states can be seen in the spontaneous PL spectra, typically at lower temperatures. The excitonic PL is of narrow bandwidth (100 meV) and slightly Stokes shifted with respect to X1 (50 meV). In contrast, the PL from the surface states is broadband (300 meV) and much further red-shifted, consistent with its designation as a midgap state. These state-resolved measurements of exciton relaxation enable observation of the time scales and pathways by which excitons undergo surface trapping.42,74,79 A working knowledge of the signal origins in the TA spectra enables identification of the presence of electron and/or hole traps in these QDs. For example, pumping directly into X1 implies that no exciton cooling can take place. The only processes are radiative recombination on the nanosecond time scale and surface trapping. Our measurements on CdSe QDs reveal that under those material conditions holes are trapped at the surface, whereas electrons are not.74 This point was established by noting that the B1 transients (sensitive to electron 1S population) show no change in the first 100 ps. Hence electrons remain in their delocalized 1S state for CdSe QDs that are well passivated. In contrast, the A1 signal (sensitive to exciton charge distribution) changes dramatically over this time scale. Since the 22103

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Figure 17. In addition to relaxation/cooling, the excitons can experience surface trapping. This trapping process can proceed via the band edge exciton (X1). However, there can also be direct hot exciton surface trapping. The condition for hot carrier trapping is a surface trapping rate which competes effectively with carrier cooling. The population of these surface states is effectively a photoproduct which can obscure clean measurement of nearly all processes in quantum dots.

electron remains in the initially pumped state, the changes in the A1 signal can only arise from hole dynamics, i.e., hole trapping at the surface of the QD. We use the case of CdSe merely to illustrate how the TA signals can be used to identify specific trapping processes. In principle, either carrier may be trapped. Furthermore, this carrierspecific trapping process may be chemically controlled via surface ligands.158
164 The simplest picture of surface trapping is that it is the final stage in relaxation following hot exciton cooling (Figure 16a). The complicating point is that surface trapping can compete with exciton cooling.42,74,79 Essentially a simple competition kinetics analysis shows the yield of surface trapping from excited states (Figure 17). The pump pulse creates an initial hot exciton. In addition to cooling within the excitonic manifold, each of these hot exciton states may directly trap to the surface, provided the surface trapping rate can compete effectively with the hot exciton cooling rate(s). Since exciton cooling is completed within 1
2 ps, the excited state (hot carrier) surface trapping time scale should be at least 10
20 ps to compete. This competition between cooling and trapping may be controlled by the degree of surface passivation (Figure 17). An understanding of the TA signals can be used to provide real-time observation of the photoinduced surface trapping/ charging process (Figure 18). The ability to probe these trapping/charging processes in real time is essential to establish the pathways by which these photoproducts are created and ultimately managed. The premise is illustrated by a simple threelevel system, not including the ground state. We omit consideration of the ground state since it is populated on the nanosecond or slower time scale, too slow to be relevant here. We consider a hot exciton, a cold exciton, and a surface-trapped exciton. Each is taken to have a unique value of the A1 signal due to biexciton interactions. The hot exciton produces a strongly bound biexciton (Xhot + Xcold) and therefore has a large, positive ΔOD signal in the A1 region. The cold exciton produces a strongly bound biexciton (Xcold + Xcold) and therefore has an attenuated bleach in the A1 region. Finally, the trapped exciton produces a moderately bound biexciton (Xsurface + Xcold) and thus has a small, positive ΔOD signal in the A1 region. The qualitative nature of these signals has been discussed in our prior work42,66,74,78,79 and will be quantitatively discussed below. Pumping directly into Xcold means

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only cold (relaxed) exciton surface trapping takes place on a slow time scale. Pumping into Xhot without hot exciton trapping yields a signal which is clearly distinct from the case of a hot exciton trapping channel that competes with hot exciton cooling. Without hot exciton trapping, the processes of cooling and trapping are sequential and result in a clear production of Xcold as illustrated by a negative ΔOD. In contrast, the presence of hot exciton trapping creates a small, positive ΔOD due to a mixture of Xcold and Xsurface produced during the course of cooling. This schematic qualitatively illustrates how the A1 signal reflects hot exciton trapping, upon comparing the transient with different initial excitonic states prepared by the pump pulse. The process of excited state surface trapping (or hot carrier photocharging) is quantitatively illustrated in Figure 19 based upon our state-resolved measurements of surface trapping processes.6,42,66,68,69,74
76,78,79 Figure 19a shows pump/probe transients in this key A1 spectral region upon pumping into four initial excitonic states, one cold exciton and three hot excitons of increasing excess electronic energy. The fact that the signals do not meet upon completion of cooling (t < 2 ps) quantifies the above schematic illustration of excited state surface trapping. Essentially, the signals only meet after surface trapping is complete since some fraction of the hot excitons directly populates the surface excitonic state. While surface trapping from X1 is on the 50 ps time scale, surface trapping directly from X2 can compete with hot exciton relaxation from X2 to X1. This process extends to higher energy, ultimately creating a quantum yield spectrum70,75,76 or photoaction spectrum for surface trapping/charging/polarizing (Figure 19b). The process of hot exciton surface trapping is quantitatively analyzed for the simplest case of trapping from X1 vs X2, in Figure 19c and d. The experimental data can only be reproduced by some fraction of the hot excitons undergoing prompt, excited state surface trapping. 5.2. Relating Hot Exciton Surface Trapping to Exciton
Phonon Coupling, Optical Gain, Multiexciton Recombination, Multiple Exciton Generation, and Single Dot Blinking. The idea of surface trapping connects with hot exciton relaxation in that trapping can be considered a relaxation process and that trapping can compete with the intraexcitonic relaxation42,74,79 that is the primary topic of this review. The issue of trapping/ charging/polarizing is particularly relevant in that this photoproduct can obscure measurements of interest. Historically, the first discussion of surface trapping creating artifactual signals was discussed by Wise113 and Efros141 as described in Section 4.2. Wise and Efros had independently proposed that a very long-lived photoproduct is created by illumination. This photoproduct was invoked to reconcile the enormous differences in time domain and time integrated measurements of exciton
phonon coupling. Our measurements72,73 summarized above verify the predictions of Wise and Efros. This photoproduct consisting of a surfacetrapped exciton in CW experiments also reconciles surprising observations by Bawendi using single dot PL measurements.134,165
167 The early PL measurements revealed very strong coupling to LO phonons, surprisingly with a coupling that fluctuated for an individual dot. The fact that an ideally intrinsic measurement (coupling strength) fluctuates in time for a single particle clearly indicates that the measurement is either contaminated or not an intrinsic coupling measurement. The most recent experiments by Chilla et al. have converged upon our time domain results with very small coupling to LO phonons.136 This convergence is presumably enabled by dot quality in the case of the time integrated experiments, e.g., Raman, PL, hole burning. Hence, frequency domain time integrated 22104

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Figure 18. Schematic illustration of real time observation of hot exciton surface trapping. The A1 spectral feature is monitored in the experimental transients. This feature reflects the excitonic charge distribution via the biexciton induced energy shift. In the illustrative example here, we consider a minimal system consisting of a hot exciton, a cold exciton, and a surface-trapped exciton. Each exciton has some value for the ΔOD signal in the A1 spectral region. Direct excitation into the cold exciton tracks exciton trapping to the surface (left). Excitation into the hot exciton, followed sequentially by cold exciton trapping, has the two signals (Xhot vs Xcold pumping) meeting after cooling is complete (center). Excitation into the hot exciton, with direct-to-surface hot exciton trapping, has the signals meeting only at late time (right).

Figure 19. Relatively slow process of surface trapping is made more rapid by direct-to-surface trapping excited excitonic states. This process is referred to as excited state surface trapping, hot carrier trapping, and recently hot electron photocharging. The process involves direct excited state to surface state transitions that compete with excitonic relaxation/cooling. (a) The A1 signal for various initial excitonic states reveals excited state trapping processes. (b) The pump/probe signals of excited state surface trapping are consistent with CW characterization of absorption (Abs) and photoluminescence excitation (PLE) spectra. The PLE spectra deviate from the Abs spectra at higher energy. The normalized quantum yield (QY) spectrum is PLE/A. This QY spectrum can be considered a photoaction spectrum for surface trapping. See text for details. (c) The process of excited state surface trapping is illustrated for the simplest case of trapping directly from X2. (d) Direct surface trapping from X2 is reflected in the slow component of the ΔΔOD transients.

measurements of exciton
phonon coupling should be interpreted with caution in much the same way that MEG experiments are now understood to have the possibility of contamination by artifacts. This photoproduct is a key in understanding the nature of optical gain in quantum dots. The early work by Klimov and Bawendi showed that the development of optical gain was dependent

upon the surface properties of the dot.19,168 Upon the basis of the passivation of the dot and the host matrix, the performance metrics for optical gain showed tremendous variance. These gain metrics include the threshold and the size dependence. Our work on stateresolved studies of optical gain75,76 and multiexcitons74,78 has revealed the underlying cause of this response, as well as measures 22105

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The Journal of Physical Chemistry C to optimize gain in quantum dots. The idea is quite simple: one must minimize excited state absorptions in the gain (stimulated emission) spectral region. The excited state (photoinduced) absorptions arise from multiexcitons which are typically lower in energy than their single exciton building blocks due to Coulomb interactions. Our work showed that the surface-trapped exciton results in large photoinduced absorptions (loss) due to strongly bound biexcitons that are comprised of a surface exciton and a core exciton.6,74
76,78 The connection between optical gain and the relaxation processes of cooling and trapping arises from the excitonic state dependence to these processes. The surface state photoproduct is produced at higher yield and with much faster rates for higher energy excitons.42,74
76,79 The problem is most severe excitation into the continuum at 400 nm.42,79 Hence, the process of direct excited state surface trapping can explain much of the observed optical gain phenomena. This photoproduct consisting of a surface-trapped exciton is finally central to the recombination processes which guide the analysis of multiple exciton generation (MEG),4,12,26
42 multiexciton recombination (MER),3,42,43,156,169 and single dot blinking.42,71,170
180 The presence or absence of photoproduct-related artifacts in MEG experiments has garnered much recent attention. We discuss MEG, MER, and blinking together as they are all related to the process of nonradiative recombination of multiexcitons. Hence, the photoproduct can strongly affect not just exciton
phonon coupling and multiexciton interaction strengths but the rates of multiexciton recombination. The MER rate is of direct importance to several applications in that it can govern the lifetime of optical gain in quantum dots as well as determine the time scale for charge extraction of multiexcitons in a solar cell. The MER rate is furthermore of indirect importance to the controversial MEG and blinking experiments. In the case of MEG, the standard methods of MER analysis are used to report on the MEG yield, a topic of recent importance in quantum dot photovoltaic research. In the case of single dot blinking, it was proposed that the same MER mechanism of Auger recombination was responsible for the blinking process.181 Recent experiments have challenged this Auger recombination picture due to inconsistencies of the MER rates of a biexciton as compared to the implicit nonradiative decay of the dark/off state of the dot.170,171,182 Recent single dot PL experiments have shown that a charge accumulation process is at play in blinking,176,177,180 much like the charge accumulation problem in exciton
phonon coupling.72,73 Our recent work has shown that this photoproduct creates MER rates that can be an order of magnitude faster than the MER rate of a biexciton.42 This fast decay is only present when a photoproduct is present. The photoproduct can be spectroscopically identified, for the first time, by virtue of the TA signals discussed here. Our experiments have shown that under these trapping/charging/ polarizing conditions the MER rates are fast and yield false positive MEG signals.42 For the case of blinking, our experiments show that the MER rate for this photoproduct is identical to the predictions from the recent single dot PL experiments,171 points that are discussed in detail elsewhere.42 In short, the creation of a photoproduct comprised of a surface-trapped exciton can compete with hot exciton relaxation and can dramatically influence the interpretation of a wide variety of processes central to quantum dot science.

6. SUMMARY This Review presents an overview of the processes which govern relaxation of hot excitons in semiconductor quantum

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dots. The process of relaxation or cooling has been extensively investigated since the first discovery of the quantum dot, nearly two decades ago. The topic is important in that it is one of the main dynamical processes that govern function of these materials and serve to illustrate the extent to which quantum confinement effects on the nanoscale are truly well understood. This process of exciton relaxation is also of great importance to nanoscale devices such as quantum dot lasers and quantum dot photovoltaics. Despite clear motivation and long-standing experimental and theoretical investigations, the topic of hot exciton relaxation has been challenging for the community. This Review identifies some of the sources of these difficulties and provides a reconciliation in light of a multichannel approach to exciton relaxation dynamics. We have found that the vague process of carrier cooling can be replaced with a more precise description in terms of excitonic state-to-state transitions. We summarize here our experiments which provided the first measure of hot exciton relaxation processes with excitonic state specificity. This precision in measurement enabled disentangling of all possible processes with electron and hole specificity, as well as unification of hot carrier processes in terms of a multichannel or multipath picture. These measurements of hot exciton relaxation processes are connected to measurements of exciton phonon coupling, which independently confirm the picture established from the relaxation dynamics experiments. Finally, the process of hot exciton relaxation is extended to include hot exciton surface trapping, a process that has seen much recent interest in light of photoproducts that arise in measurements of optical gain, exciton
phonon coupling, single dot blinking, and multiple exciton generation.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ BIOGRAPHY

Patanjali Kambhampati received a B.A. in Chemistry from Carleton College in 1992 and a Ph.D. in Chemistry from the University of Texas at Austin in 1998. His doctoral work focused on ultrahigh vacuum surface studies of adsorbate
substrate charge transfer excitations and surface-enhanced Raman scattering under the supervision of Alan Campion. From 1999 to 2001 he was a Postdoctoral Associate with Paul Barbara, also at the University of Texas at Austin. His postdoctoral work focused on femtosecond laser spectroscopy of condensed phase chemical dynamics of the solvated electron and intramolecular electron 22106

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The Journal of Physical Chemistry C transfer. From 2001 to 2003 he was involved in early phase work in a fiber optic startup based in Los Angeles. At McGill University, where his group focuses on ultrafast dynamics in quantum dots, he was an Assistant Professor from 2003 to 2009 and is presently an Associate Professor.

’ ACKNOWLEDGMENT I would like to thank the current and past members for their contributions to the work summarized here. In particular, I gratefully acknowledge the contributions from Ryan Cooney, Samuel Sewall, Kevin Anderson, and D. M. Sagar, who performed the first generation of experiments in my lab. I also thank Eva Dias, Pooja Tyagi, Jon Saari, and Jonathan Mooney who are currently performing the next generation of experiments to further explore the topics discussed here. Financial support from CFI, NSERC, FQRNT, and McGill University is acknowledged. ’ REFERENCES (1) Alivisatos, A. P. J. Phys. Chem. 1996, 100, 13226–13239. (2) Alivisatos, A. P. Science 1996, 271, 933–937. (3) Klimov, V. I. J. Phys. Chem. B 2000, 104, 6112–6123. (4) Klimov, V. I. J. Phys. Chem. B 2006, 110, 16827–16845. (5) Nozik, A. J. Annu. Rev. Phys. Chem. 2001, 52, 193–231. (6) Kambhampati, P. Acc. Chem. Res. 2011, 44, 1–13. (7) Nozik, A. J. Nano Lett. 2010, 10, 2735–2741. (8) Nozik, A. J.; Beard, M. C.; Luther, J. M.; Law, M.; Ellingson, R. J.; Johnson, J. C. Chem. Rev. 2010, 110, 6873–6890. (9) Kamat, P. V. J. Phys. Chem. C 2007, 111, 2834–2860. (10) Kamat, P. V. J. Phys. Chem. C 2008, 112, 18737–18753. (11) Nozik, A. J. Phys. E (Amsterdam, Neth.) 2002, 14, 115–120. (12) Nozik, A. J. Inorg. Chem. 2005, 44, 6893–6899. (13) Kambhampati, P.; Mi, Z.; Cooney Ryan, R. Colloidal and SelfAssembled Quantum Dots for Optical Gain. In Comprehensive Nanoscience and Technology; Andrews, D. L., Scholes Gregory, D., Wiederrecht, G. P., Eds.; Academic Press: Oxford, 2011; Vol. 1, pp 493
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