QD Semiconductor

Published: September 21, 2011

r 2011 American Chemical Society 22089 dx.doi.org/10.1021/jp2058673 | J. Phys. Chem. C 2011, 115, 22089–22109

FEATURE ARTICLE

pubs.acs.org/JPCC

Hot Exciton Relaxation Dynamics in Semiconductor Quantum Dots:Radiationless Transitions on the NanoscalePatanjali 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 structurewhich is both novel and potentially useful for a variety of applications. Upon optical excitation of the dot, the initial excitonic state may beelectronically hot. The relaxation dynamics of this hot exciton is the primary event which controls key processes such as optical gain, hotcarrier extraction, and multiple exciton generation. Here, we describe femtosecond state-resolved pump/probe experiments on colloidalCdSe quantumdots that provide the first quantitativemeasure of excitonic state-to-state transition rates. Themeasurements andmodelinghere reveal that there are multiple paths by which hot electrons and hot holes relax. The immediate result is that there is no phononbottleneck for electrons or holes for excitons in quantum dots. This absence of phonon-based relaxation is confirmed by independentmeasurements 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 designingmaterials with relaxation properties targeted for specific applications.We conclude withconnection to hot exciton surface trapping. The process of surface trapping is the key step in creation of the photoproduct which canobscuremeasurements of optical gain,multiexciton recombination,multiple exciton generation, and single dot blinking.We show that hotexciton 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 beenunder intense investigation for an understanding of the influenceof quantum confinement effects upon the system’s response, aswell as for devices which aim to exploit these effects.1�15 Thechemically synthesized colloidal form of the quantum dot (QD)is also referred to as a semiconductor nanocrystal (NC). Regard-less of terminology, the simplest picture of the QD is that of aparticle in a sphere.16,17 This simple picture immediately ratio-nalizes the well-known size-dependent absorption and emissionspectral energies.18 This picture also suggests that the energylevel spacing in these QDs might be unique, size dependent, andultimately controllable. This situation of a controllable energyspectrum suggests that the time scales and pathways by whichexcited carriers relax might also be unique in these quantum dots.Hence, the question of hot carrier cooling has been extensivelyinvestigated 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

interest (Figure 1). One of the earliest motivations for develop-ment of quantum dots was for optical gain media. By virtue of thenarrow levels and large energy level spacing, it was anticipatedthat QDs would be ideal materials for the development ofefficient optical gain.13,19�21 In any gain system, the manifoldof levels should enable creation of either a three- or a four-levelsystem. In addition to the lasing transition, there should be rapidpopulation and/or depopulation of some of the levels to enablerealization of lasing. Hence the carrier cooling process is im-mediately connected to the development of interband opticalgain media mediated by fast exciton cooling (Figure 1a). Incontrast, slow exciton cooling should be useful for longerwavelength 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, 2011Revised: September 20, 2011

22090 dx.doi.org/10.1021/jp2058673 |J. Phys. Chem. C 2011, 115, 22089–22109

The Journal of Physical Chemistry C FEATURE ARTICLE

be extracted from the delocalized core states into an adjacentmedium. This charge extraction can take place from the lowestenergy level, or it can take place from higher levels, referred to ashot electron extraction.25 Hence the rate of charge transfer fromthe dot to the adjacent medium must compete with intrabandcooling (Figure 1b). It is worth noting that this charge migrationprocess can also be a simpler charge trapping process. In the caseof charge trapping, the carrier (electron or hole) gets trapped atlower energy states that might be surface, interface, or localizeddefect 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 MEGarose because of the possibility of using a larger fraction of thehigh-energy solar radiation to create additional carriers withoutcreation of waste heat. The idea is that a high-energy singleexciton state (X) is coupled to a manifold of multiexciton (MX)states. If the MEG rate is faster than the cooling rate, excitonfission into MX should dominate and thereby enable creation oflarger photocurrents in QD-based solar cell applications. Whilethere 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 isclear (Figure 1c). One aims to design materials for efficient MEGmuch like the ongoing effort to design materials for optical gainbased upon the underlying physics of relaxation andmultiexcitoninteraction. The very same basic processes govern the develop-ment of the MEG process and its optimization via materialsdesign.1.2. Overview of Electronic Structure of Semiconductor

Quantum Dots.While the electronic structure of quantum dotsis not the topic of this Review, a brief review is helpful towardunderstanding the dynamical processes that are the focus of thisreview. The role of quantum confinement effects upon theelectronic structure and linear spectroscopy of quantum dotshas been extensively discussed elsewhere3,6,14,15,43�47 and willonly be briefly reviewed here. The physical confinement ofelectrons and holes in the QD results in quantization of theavailable states. Due to the charge carriers being confined to thesesmall volumes, the Coulombic binding of these charges getslarge, and the formation of a strongly bound exciton results.Hence an investigation of the structure and dynamics of excitonsin quantum dots—their excitonics—is the ultimate path towardrational 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 andmore importantly in terms of electronic structure (Figure 2). Inthe case of molecules, the system obviously shows quantizationby virtue of the small number of electrons. The electronic statessuch as singlets (S0, S1) and triplets (T1) are often well resolved.These states are further dressed by vibrational progressionsarising from Franck�Condon factors thereby giving furtherbreadth to the linewidths of electronic transitions. In the bulklimit, the large number of electrons results in a convergencetoward a continuum of the density of electronic states. In the caseof semiconductors, there is a bandgap separating the unoccupiedconduction band (CB) from the occupied valence band (VB).This bandgap is the bulk analogue of the HOMO�LUMOtransitions in molecules. By virtue of being intermediary in size,the quantum dot retains aspects of both molecular electronicstructure and bulk semiconductor electronic structure. Like themolecule, the QD shows some discrete transitions and exchangesplittings. Like the bulk semiconductor, the QD supports acontinuum of electronic states at higher energy and can supportmultiple excitations per particle. The quantization of the CB andVB bulk states yields a manifold of quantized electron and holestates (Figure 2). Each of these states can experience molecular

Figure 1. Illustration of hot carrier cooling in semiconductor quantumdots. The cooling process in green competes with other processes. (a)Illustration of the role of carrier cooling on the development of quantumdot lasers. The initially pumped state is hot (P-type exciton). This hotexciton cools to a lower state, SA, the lowest absorbing state(s). Theabsorbing state is energetically separated from the emitting state(s), SE,by the exciton Stokes shift, δX. Fast cooling enables realization of a three-level interband lasing system, whereas slow cooling enables intrabandlasing. (b) The exciton can also experience charge migration to surfaces,interfaces, and defects. This depopulation of delocalized core states cancreate photoproducts which can obscure measurement. This depopula-tion is also important for charge extraction in photovoltaic environ-ments. Notably, the depopulation via charge trapping can compete withhot exciton cooling, thereby creating hot carrier charge extraction andtrapping. (c) The cooling process connects with multiple excitongeneration (MEG) in that the MEG fission rate must be faster thanthe hot exciton cooling rate.

Figure 2. Illustration of how a quantum dot interpolates between thebulk and molecular limits. In the case of molecules, there is a smallnumber of electronic states which are dressed by phonon progressionsand singlet/triplet exchange. In the case of bulk semiconductors, acontinuum of electronic states is formed, along with a bandgap thatcorresponds to the HOMO�LUMO transition in molecules. In the caseof semiconductor quantum dots, there is a quantized manifold ofelectron/hole states that arises from quantum confinement effects. Eachlevel that is shown is further dressed by phonon progressions andexchange splittings which are not shown.



like exchange interactions and vibrational (phonon) progres-sions which further add line width. Unlike molecules, each ofthese states can easily be multiply populated based upon thedegeneracy of the state. The subtle but important point inquantum dots is the physical point at which these quantumconfinement effects arise, how to rigorously describe them, andhow 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 electronicstructure and the hierarchies in theory needed to provide a minimalexplanation of key phenomena.6 The main levels of theory are:particle-in-a-sphere (PIS),16,17 multiband effective mass approxima-tion approach (EMA),44�46,48,49 and atomistic approaches such asthe empirical pseudopotential method (EPM)47,50�58 and abinitio.59�65 The PIS approach does not explainmany of the simplestaspects of the dot, such as the fluorescence Stokes shift or the natureof the excitonic transitions in the absorption spectrum. Hence, theminimal level of theory required to design and interpret theseexperiments is the EMA approach. EMA has been applied tothese colloidal CdSe quantum dots by Efros, Bawendi, andNorris.44�46,48,49 Those studies have yielded tremendous insightinto the electronic structure and linear optical properties of thesematerials. These EMA results have furthermore informed the designand much of the interpretation of our experiments6,42,66�79 sum-marized here. We note, however, that the atomistic (whether EPMor ab initio) approaches often yield qualitatively different results(e.g., ordering of states, bright/dark states, piezoelectricity, ex-citon cooling). Hence the level of theory used to understand theobservables 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 oftheory. The electronic structure of quantum dots is representedin Figure 3. The electronic structure can be described in terms ofa series of excitonic states (Figure 3a). This excitonic leveldiagram can be recast as an electron/hole level diagram whichgives further insight (Figure 3b). The electron/hole picturesuggests that the excess electronic energy can be taken up byeither the electron or the hole.These excitonic states are connected to the linear spectrosco-

py of quantum dots such as absorption, photoluminescence(PL), and photoconductance spectra. Figure 3c shows the linearabsorption spectrum of the colloidal CdSe QD in toluenedispersion. This spectrum shows the well-known peaks in aQD absorption spectrum and relates them to the excitonic andelectron/hole picture. The peaks in the linear spectra of CdSehave been assigned within the EMA picture in pioneering workby Norris, Bawendi, and Efros.44,45,48 Figure 3d shows how theenergy of higher excitons above the band edge exciton (X1 or1Se�1S3/2 in the EMA picture) spreads as the dot becomessmaller (larger X1 energy gap). The spreading of the energy levelsas well as the electron/hole decomposition will be of consider-able importance when discussing the dynamical problem of hotexciton relaxation.1.3. Hot Exciton Relaxation in Quantum Dots. Unsurpris-

ingly, the concept of hot exciton relaxation in quantum dotsconnects to research on relaxation processes in both bulk solidsand molecules. In the case of bulk solids, an excited electron orhole will relax toward its lowest energy state (band edge) viaemission of phonons.3,5 Hence the process of cooling is driven bythe strength of electron�phonon coupling alone. While electron�phonon coupling might be weak in solids due to extended wave

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 ofa specific electron/hole state. The density of excitonic states converges toward a continuum at higher energy. (b) The electronic structure can also beunderstood in terms of the electron/hole picture. The electron states arise from quantum confinement of the bulk conduction band (CB) states, whereasthe hole states arise from quantum confinement of the bulk valence band (VB) states. Transitions into specific electron/hole (excitonic) states are shownwith arrows corresponding to their color in the case of CdSe. (c) The linear absorption spectrum shows peaks which can be assigned to specific excitonictransitions. Nonlinear femtosecond spectroscopic experiments can be performed by pumping into each initial excitonic state tomonitor carrier dynamicswith 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) isplotted as a function of the energy of X1. Data are adapted from ref 41.



functions, the rate is fast due to the continuous density ofelectronic states. Since the density of states is continuous, onlyone quanta of phonons needs to be emitted to dissipate theexcess energy of the electronically hot carriers. This topic of hotcarrier relaxation (also called cooling and thermalization) hasbeen well investigated in bulk solids. In the case of molecules, thisrelaxation process has been equally well investigated under theguise of radiationless transitions.80�86 There is now a well-established body of experimental and theoretical literature thatprovides a detailedmap of the manner in which an excited moleculedissipates its excess electronic energy.Since the quantum dot retains aspects of the electronic structure

ofmolecules and solids, the question of what governs the time scalesand pathways of hot carrier relaxation is not obvious. In the case ofstrongly confined semiconductor quantum dots, the electronic levelspacings can be 100�300 meV, much larger than the phononenergies. Hence, it was anticipated from bulk theories of carriercooling 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 thephonon bottleneck and will certainly increase the presence ofuniquely quantum dot type relaxation pathways that govern thespecific dynamical processes. The generic dynamical processesare outlined in Figure 5. Initially, a short laser pulse will produce anonequilibrium distribution of hot excitons. This distributionwill first thermalize and then undergo nonradiative multiexciton(MX) recombination (MER). TheMER process reduces theMXmultiplicity and creates a lower MX that is electronically hot.This process will continue until complete thermalization isreached. Each of these processes of relaxation and recombinationis to be evaluated to determine both rates and, importantly, thepathways which determine the rates. Independent of the histor-ical artifact of the phonon bottleneck, the goal of precisionmeasurement of hot carrier relaxation and a rigorous under-standing of the pathway(s) has been under intense investigationfor nearly two decades. This Review describes some of the mainconcepts and results which treat this key problem in the basicscience of semiconductor quantum dots.

2. EVALUATING EXCITON RELAXATION IN QUANTUMDOTS

Much experimental and theoretical work has been conductedon evaluating the relaxation dynamics of hot excitons in semi-conductor quantum dots (Figure 6). Due to the larger electroniclevel spacings from quantum confinement, early theory predicted

Figure 4. Influence of particle size on the electronic structure ofsemiconductor quantum dots. As the particle becomes small, theintraband CB�VB energy gap increases as does the intraband levelspacings. Since the energy gaps increase with decreasing particle size,a strong size dependence on the carrier relaxation dynamics wasanticipated.

Figure 5. Schematic illustration of the chronology of multiexcitongeneration, relaxation, and recombination. At t = 10 fs, an initial Poissondistribution of excitons is created by the pump pulse. This schematicillustrates 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 multiexcitonrecombination (MER), thereby generating a hot biexciton distribution.At t = 3.5 ps this biexciton distribution thermalizes. At t = 30 ps thethermalized biexcitons undergo MER, thereby generating a hot singleexciton. At t = 30.5 ps the single exciton thermalizes.

Figure 6. Early work employed phonon emission (a) and electron/holeAuger relaxation to explain the influence of quantum confinement effectsupon hot electron cooling. The phonon-based approach was adaptedfrom bulk theories of hot carrier thermalization. This phonon-basedapproach was chronologically first and predicted a dramatic slowing ofelectron cooling for smaller particles (c). This prediction was called the“phonon bottleneck”. Later, theory proposed the existence of an Augerscattering type of relaxation channel in which the electrons transferenergy to the hole. The computed transition rates and their functionalform show marked differences (d). The transition rates such as kphononand kAuger correspond to specific pathways as discussed in the text.



that electron relaxation should be slower for quantum confinedstructures.3,5,87�90 This phonon “bottleneck” was expected, asmultiphonon emission via the Fr€ohlich interaction would berequired to climb down the manifold of electronic states. Theelectronic energy gaps are∼150�350meV, in comparison to thelongitudinal optical (LO) phonon energy of ∼30 meV.

In contrast to these predictions, experimental measurementsshowed fast subpicosecond to picosecond electron relaxationdynamics in colloidal semiconductor quantum dots.3,14,91�98 Morerecent theory proposed the presence of a confinement enhancedAuger relaxation pathway in which the electron unidirectionallytransfers energy to the hole.55,99,100 This process can be fast inquantumdots due to a larger wave function overlap and reduction inmomentum conservation requirements due to spatial localization.Experiments have qualitatively shown that smaller particles havefaster electronic relaxation rates, consistent with the presence of anultrafast Auger channel for electrons.3,91�94 Theory has predictedthat the electron relaxation times are ∼0.1�2 ps, with a sizedependence in which the rate could be flat or decreasing withparticle radius.

An alternative situation was probed in which the hole wasspatially decoupled from the electron.22,101,102 The femtosecondAuger channel requires the presence of the hole to accept the excessenergy from the electron. In the event that the hole is decoupledfrom the electron, the Auger channel becomes deactivated for theelectron. Thus a spatially decoupled hole would allow for observa-tion of the electron dynamics in isolation from the hole.

Decoupling of the hole was achieved by using hole traps at thesurface of the colloidal quantum dot or by nongeminate carriercapture in epitaxially grown quantum dots.103 In the case of theepitaxially grown quantum dots, ligands are absent, and a phononbottleneck was observed. In a sequential pumping scheme, experi-ments by Guyot-Sionnest et al. and Klimov et al. on colloidalquantum dots showed that the electron dynamics proceeds on the3�30 ps time scale in the absence of the femtosecond Augerchannel.22,101,102 The experiments by Guyot-Sionnest et al. further-more showed that under these circumstances the surface ligands hada pronounced effect on the time scale of electron relaxation from 1Pto 1S.101These experiments showed that in the absence of theAugerchannel the electron relaxes on a picosecond time scale. Theseexperiments furthermore showed that the pathway for electronrelaxation has a dominant contribution from a surface ligand basedchannel, provided the Auger channel is removed.

While the electron has a femtosecond Auger channel in CdSequantum 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 phononbottleneck at the final stages of relaxation near the band edge.Experiments by Klimov et al93 and subsequently by Hendryet al.104 probed relaxation dynamics of the hole. Klimov and co-workers used a combination of transient absorption (TA) andtransient photoluminescence (PL) to monitor hole relaxation.These experiments suggest that the hole relaxation slows downcloser to the valence band edge due to the sparser density ofstates at the band edge. These experiments furthermore suggestthat there was a phonon bottleneck near the band edge for theholes. However, these experiments were not able to monitorstate-to-state dynamics and furthermore cannot measure therelevant dynamics with the 10 fs precision required for quanti-tative determination of the state-to-state transition rate for holes.

A key difficulty in spectroscopic experiments on quantumdots is that both initial and final excitonic states need to be

spectroscopically prescribed. For example, with fixed excitationwavelengths (e.g., 400 nm excitation) larger particles will neces-sarily measure electron and hole relaxation dynamics. In all butthe smallest particles, the hole will get up-pumped by the electronand then relax through the valence band. Regardless of theinstrumental time resolution, photoluminescence measurementscannot measure the hole dynamics of interest with quantitativeprecision. Specificity in the final hole state was achieved byHendry et al.104 using time-resolved terahertz spectroscopy.These experiments monitored the arrival time of the hole tothe band edge from an arbitrary initial state. The initial statedepended upon the size of the quantum dot. These experimentssuggested that the arrival time of the hole was∼350 fs, providedthe electron was initially in its lowest-energy 1S state. The keypoint is that no prior experiment has been able to monitor thehole dynamics with specificity in the initial and the final excitonicstates, along with the time resolution needed to quantitativelymeasure the relevant processes.

While hot exciton relaxation dynamics in semiconductor quantumdots has been extensively studied, a clear picture of the relevantprocesses had remained elusive. The key difficulty is due to the size-dependent excitonic spectrum.6,44,66,68,69 This size dependencemeans that the same initial excitonic states are not necessarilypopulated for each size of quantum dot. Furthermore, since thesearemultilevel systems, the relaxation dynamics will not necessarily becharacterized by simple functions which represent transition rates.

Most experiments which use the pump/probe (transientabsorption) approach use excitation at 400 nm (3.1 eV). Underthese excitation conditions, the electron will not necessarily beinitially prepared in its 1P state. Instead the electron will be insome higher-lying state.58 Thus, the electron relaxation willfollow sequential kinetics. An additional difficulty is that thedensity of states shows that the initial electronic state could be amixture of 1S, 1P, or 2S.44,58 In the case of excitation directly intoa 1S electron state (X1), there will be an instantaneous develop-ment of population into 1S. If the excitation were directly into 1P(X4), then there would be exponential development of popula-tion, and if the excitation were into a state higher in energy than1P (denoted 2S for simplicity), a nonexponential buildup wouldtake place. Thus, the measured electron relaxation will follow asum of three signals consisting of a step function, singleexponential, and nonexponential, convolved with the instrumentresponse function (IRF).6,66,68,69

ΔODðtÞ ¼ A1S þ A1Pe�k1t þ A2S

�

� 1 þ 1k2 � k1

ðk1e�k2t � k2e�k1tÞ

� ��X IRF

ð1ÞHere, k2 � k2Sf1P and k1 � k1Pf1S. Each k represents the totalrate for a state-to-state transition which is comprised of severalpathways which contain the desired dynamical information.Larger particles would follow even more complex kinetics withmore highly excited initial states. Regardless of pulse duration, itwould be impossible to precisely extract a transition rate, k1Pf1S,from a smoothly varying experimental transient. In contrast, anexciton selective approach can yield state-to-state exciton dynamicswith specificity to either electron dynamics or hole dynamics

ΔΔODðtÞ ¼ e�kt X IRF ð2Þ



Here, the k represents a specific state-to-state transition rate,whether for electrons or holes. By using various permutationsof pump and probe wavelengths selected to be resonant withspecific initial and final states, an exciton selective approach yieldselectron and hole relaxation dynamics with state-to-state speci-ficity and a temporal precision of 10 fs, recovering the pulse-width-limited precision that one expects for simple two-levelsystems.6,66,68,69 This temporal precision is essential to quantita-tively establish the relative contributions of multiple relaxationpathways, each of which may have a distinct size dependence.

3. SPECTROSCOPIC PROBING OF HOT EXCITON RE-LAXATION WITH EXCITONIC STATE SPECIFICITY

3.1. Overview of the Spectroscopic Signals. While theelectronic structure of excitons (X) in quantum dots can beunderstood by linear spectroscopy (e.g., absorption), the dy-namics 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) spec-troscopy enables such a probe of hot exciton relaxation dynamics.The interpretation of these optical nonlinearities has been dis-cussed at length in excellent reviews by Klimov.3,43 There are,however, some important subtleties that arise when employing ourstate-resolved approach to probing exciton dynamics.6,42,66�79

This approach enables closer inspection of the factors whichgovern the optical nonlinearities in QD and ultimately enablesfurther 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 itsconvenience—it is the second harmonic of the 800 nm outputfrom the commonly used Ti:sapphire laser system. Similarly, theexperiment on PbSe and PbS quantum dots typically uses thefundamental 800 nm output for the same reasons.105,106 In thisspectroscopic situation, the initially pumped exciton is not wellspecified. As a result, it is difficult to establish a rigorous picture ofthe source of the signals—the first step in the path towardprecision 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 ofthe experiment have been described elsewhere6,42,66�79 and willonly be briefly reviewed here. The key step is to excite directly intothe initial excitonic state of interest. Without this selective pumping,

no amount of time resolution would enable clean extraction of thestate-to-state transition rates of interest, but more broadly, theabsence of this selectivity in excitation places a barrier on ourunderstanding of the spectroscopic signals and how they connect tothe 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 durationwith a transform limited bandwidth of 50�60 meV, approxi-mately the bandwidth of the band edge exciton. The probe light isderived from a single filament white light continuum generated ina sapphire crystal. The continuum is dispersion compensated asare the OPA pulses. The TA spectra are acquired in a chirp-freemanner by scanning the monochromator and the delay stage tonull out any residual dispersion in the continuum.107 In thismanner, the timing uncertainties are(10 fs. Finally, we performpump/probe experiments with two OPA spectra simultaneously.We do so by alternately chopping two OPAs at 333 Hz such tocreate a pulse sequence of pump1, pump2, no pump. This is doneto better compare the signals under different pumping conditions.In our experiments, two experiments with two different pumpwavelengths are done simultaneously with the same spectrometerconditions and the same quantum dot sample conditions—a pointof considerable interest in light of recent studies on the importanceof charging type photoproducts28,29,32,42,108 whichmay contaminatethe experiment.Figure 7 shows a representative TA spectrum of the CdSe QD

in toluene dispersion at 300 K. The pump pulse is resonant withX5 which is a nominally 1P type exciton.44,58,77 The TA transientspectrum in Figure 7 reveals both absorptive and bleachingsignals that build up and decay on multiple time scales. Theorigin of the optical nonlinearities is outlined in Figure 8.Figure 8a shows TA spectra which are slices in time of the TAtransient spectrum. These TA spectra were obtained at t = 50 fs,at the earliest stages of relaxation. At this stage, the system isessentially in the initially pumped state. The spectra were takenunder conditions of X1 and X4 pumping, 1Se�1S3/2 and1Pe�1P3/2 in EMA. These TA spectra reveal the presence ofphotoinduced bleaching and absorptions which strongly dependupon the initial excitonic state. These spectral features have beenreferred to as A1, B1, B2, A2, etc. by Klimov based upon whetherthey were absorptive or bleaching signals.3,43 This notation iswidely used in the literature, although these features (e.g., A1) are

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



not necessarily absorptive over all time or over all pump wave-lengths.6,42,66,68,69,74,78,79 Hence a rigorous picture of the con-nection between the electronic structure of the dot and thesource of these signals is necessary.The signals in these pump/probe experiments generically arise

from three terms: ground state bleaching (GSB), stimulatedemission (SE), and excited state absorption (ESA).109 Theseprocesses can be described at the photon (intensity) level or atthe field (amplitude) level, should a more detailed picture bewarranted. As the pump pulse brings population to the excitedstate, the GSB and SE terms will appear in the TA spectra(Figure 8b). GSB arises from removal of population from theoccupied ground state. This process is also referred to as statefilling or Pauli blocking. The excited state population can alsoexperience stimulated emission by the probe (Figure 8b). BothGSBand 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 anexcited state into amore highly excited state. In the case ofmolecules,ESA may arise from S1 f S2 types of transitions. In the case ofsemiconductors, the ESA arises from intraband absorption. Since the

electronic structure of these semiconductor quantum dots is quan-tized, the equivalent of intraband absorption is intraexcitonicabsorption. These transitions are typically in the mid-infrared(1000�5000 nm) and hence are far outside the visible probewindow. In addition to creating a more highly excited singleexcitation (e.g., X1 f X4), the quantum dot can support multipleexcitations per dot. This multiple excitation is minimally thebiexciton (XX) but is generally a multiexciton (MX) state. MXprocesses are very important to the processes of multiexcitonrecombination (MER), multiple exciton generation (MEG), opticalgain, and correlated photon emission. At the field level, the first twofield�matter interactions arise from the pump pulse, therebyproducing an excited state population. The third interaction is withthe probe fieldwhichmonitors absorption fromX intoXX. ProvidedEXX 6¼ 2EX, therewill be a photoinduced absorption (PA). ThePA isdue to the fact that exciton�exciton interactions stabilize thebiexciton and lower its energy. Hence, absorption into the biexcitonis typically red-shifted with respect to absorption into the singleexciton.The discussion of ESA and biexciton formation warrants

further mention due to inconsistent usage in the literature. Inthe early literature, the induced absorptions were described interms of a Stark shifting picture.3 In the Stark approach, a trappedcarrier creates a Stark field similar to a laboratory frame externalStark field.3,110,111 The Stark spectrum approximately follows thesecond derivative of the absorption spectrum. Since the early TAspectra without excitonic state selectivity resembled the secondderivative of the absorption spectrum,3,92 the Stark approachappeared reasonable. In recent years, it has emerged that thebiexciton picture (more generallyMX) enablesmore insight.6,66,74,78

The experimental TA spectra are clearly quite different from theStark-like derivative spectrum (Figure 8a). In short, the biexciton isthe simplest way to describe the relevant signals, a topic that we havebeen investigating6,66,74,78 in parallel with these relaxation dynamicsexperiments.Having established the general features of the source of optical

nonlinearities in quantum dots, we relate these signals to specificprocesses such as probing nonequilibrium electron/hole popula-tions. This disentangling of the signals was discussed at length in ourinitial work66 and will only be briefly reviewed here. The B1 spectralfeature was argued by Klimov tomonitor only the population of the1S electron due to the small degeneracy of the electronmanifold andthe large degeneracy of the hole manifold at these energies.3,92 Weconfirm this prediction in Figure 8d and e.66 OPA pulses are tunedinto X1 and X2 initial excitonic states, while the probe is tuned to theB1 spectral feature. X1 and X2 share a common 1S state for theelectron and differ only by the state of the hole, 1S vs 2S. The B1bleaching signal is identical under both pumping conditions, verify-ing that the B1 feature monitors the electron population but isinsensitive to the hole population. This method of analysis will beexpanded below to further connect to specific hot electron and hothole relaxation processes.3.2. Unraveling Electron and Hole Processes from the

Signals.The objective of this work is a precisionmeasurement ofcarrier relaxation (i.e., cooling) processes in quantum dots. Sincethe term “cooling” itself is imprecise, it is preferable to considermeasurement of an excitonic state-to-state transition rate.6,66,68,69

To measure such a transition rate, there must be specificity in theinitial excitonic state prepared by the pump pulse as well asspecificity in whether the electron or the hole is monitored by theprobe pulse. Figure 9 outlines the approach which was discussedin detail in our prior works.6,66,68,69

Figure 8. Decomposing the TA signals into the contributions fromground state bleaching (GSB), stimulated emission (SE), and excitedstate 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 edgeexciton, and X4 is a 1P type hot exciton. The features are noted as A/Bbased upon whether that spectral region produces an induced absorp-tion or a bleach. The TA spectra at 50 fs, prior to cooling, reveal cleardifferences based upon the pump-induced populations. The TA spectraare shown to be distinct from the Stark spectrum, which is approximatelythe second derivative of the absorption spectrum. (b) The bleachingsignals arise fromGSB and SE. (c) The absorptive signals arise from ESAdue to biexciton formation. (d) Two pumps are shown in the electron/hole picture such that they are resonant with X1 and X2. (e) When theprobe is tuned to the B1 feature, the ΔOD transients are identical. Thisobservation confirms that the B1 feature probes the electron state and isinsensitive to holes, with their larger degeneracy.



Figure 8a shows a linear absorption spectrum as well as fourOPA pump spectra used to perform these state-resolved mea-surements. 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 thatmight be used for probing hot carrier processes in QDs.66 Wecontrast this suite of observables with the commonly usedapproach of arbitrary pumping at 400 nm combined with only aB1 probe. The 400 nmpump/B1 probe enables a qualitative estimateof electron cooling; however, it does not enable a quantitativemeasure of a well-specified transition rate for electrons, and it doesnot 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 thesecombinations 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 initiallyproposed by Klimov and subsequently confirmed by us, the B1feature in the TA spectrum is only sensitive to the electronpopulation. Hence pumping directly into X1 (1Se�1S3/2 in EMA)will instantaneously produce a B1 bleach without any ensuingdynamics.6,66,68,69 The experimental data in Figure 9b confirm thisexpectation. Pumping directly into X4 (1Pe�1P3/2) should producea bleach that builds up exponentially due to the 1Pf1S electronrelaxation process. The difference between the X4 and X1 pumped

transients (ΔΔOD(t)) will then directly monitor the hot electronrelaxationprocess (P1Se(t)) with state specificity (Figure 9d).

6,66,68,69

A similar approach was used to directly monitor holedynamics.6,66,68,69 Recognizing that X1 and X2 (1Se�2S3/2) sharea common 1S state for the electron, the only difference is the stateof the hole. Since the electron does not undergo any dynamics onthis time scale when in its 1S state (surface trapping is muchslower74), the only dynamics in the signals will be hot holerelaxation from 2Sf 1S. Precisely because both excitons share acommon electron state, both pumping conditions produceidentical B1 signals (Figure 8d and e). However, other signalsin the TA spectra remain useful. In particular, the A1 signalreflects the magnitude of the biexciton-based level shift (ΔXX)(Figure 8).6,66,74,78 The A1 transients under these two pumpingconditions are shown in Figure 9c. It is worth noting that the A1

signal for the X1 pump is actually not absorptive as the labelsuggests. Instead, it is an attenuated bleach due to a small ΔXX.The induced absorption develops as ΔXX becomes larger, as wehave previously shown. In this case, the difference between the A1

transients directly monitors the hot hole population relaxationfrom 2S f 1S (Figure 9e).The spectroscopic methods summarized here reveal that there

is a rich spectroscopy to these QDs. Themany signals available ina TA spectrum along with the capacity for direct excitonicpumping enable a tremendous increase in the precision with

Figure 9. Judicious combinations of pump/probe wavelengths can be prescribed to reveal specific cooling processes with excitonic state-to-statespecificity. (a) A linear absorption spectrum of CdSe quantum dots. The main features are noted in the exciton and the electron/hole picture. Theelectron/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 electronsurvival probability for 1Pf 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.



which one can monitor hot electron dynamics and a new windowinto monitoring hot hole dynamics. The results of this approachare summarized below.3.3. Breaking the Phonon Bottleneck for Electrons and

Holes in Quantum Dots. Due to the importance of hot excitonrelaxation in a wide variety of applications, it is essential to have adetailed map of the time scales and pathways of relaxation. Priorwork on high-quality colloidal CdSe quantum dots by Klimov hasconfirmed the Auger relaxation path for electrons.3,91,92 By spatiallydecoupling the electron and the hole, Guyot�Sionnest22,94,101 andKlimov102 have both shown that the surface ligands can play a strongrole in electron relaxation. Finally, terahertz experiments by Bonnhave provided the first direct measure of the electron to hole Augerscattering process in QDs.104 What is missing in all cases is ameasure of electron and hole transition rates (rather than cooling)with excitonic state specificity. Such a level of precision is required tocleanlymeasure the processes of interest and to furthermore offer anexperimental benchmark for comparison to theory. For example,theories by Efros99 and Zunger55 both suggest rapid Auger-basedelectron relaxation, but the absolute values and the functional formsof 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 thatare 100�200 fs in duration).3,91,92 By measuring state-to-statetransition rates for electron relaxation rather than a qualitativeestimate of cooling, we recover the pulsewidth-limited timingprecision of a simple two-level system (Figure 9d and e). Thesize-dependent transition rates for electrons and holes are shownin Figure 10.These data confirm the early work by Klimov3,91,92 that

electron relaxation (in the presence of a hole) is very fast andgets faster for smaller dots (Figure 10a). This result is consistentwith the Auger scattering picture of hot electron relaxation in theQD. The main new result is that we obtain such a measure withspecificity and precision ((10 fs) to enable a rigorous measure of

the absolute value as well as the functional form of this hot electrontransition rate.6,66,68,69 We find that the electron transition ratefollows a R�1(0.1 functional form, which can be comparedagainst benchmark calculations, e.g., the recent ab initio work byPrezhdo.59�64

The more interesting result is that the lifetime of the hot hole(2S) is completely size independent (Figure 10b).68,69 Thisresult is completely at odds with the prevailing picture of hotexciton relaxation. In the recent view, electrons will relax via anAuger channel (holes present), thereby breaking the phononbottleneck for electrons. In contrast, the holes should still begoverned by a phonon bottleneck since the Auger channel isunidirectional for CdSe. The directionality arises from therelative sparseness of the CB vs VB manifolds. We contrast theseresults to earlier work by Klimov93 and Bonn104 which measurehole cooling. In those works, the hole cooling was estimated fordynamics throughout the entire VB manifold. In both cases, awell-specified transition rate between fixed initial/final states wasnot measured as we show here. These results are not inconsistentwith the prior work. Rather, they afford a more precise measureof 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, onecan plot the energy dissipation rate vs the energy gap of thesespecific state-to-state transition processes. Figure 10c and dshows that both electrons and hole have energy relaxation ratesthat increase with smaller dots and furthermore increase withenergy gap. Hence, there is a breaking of the phonon bottleneckfor both electrons and holes for excitons in these colloidalquantum dots. This result suggests that the phonon-basedrelaxation pathway and the very search for the “phonon bottle-neck” was simply an early theory that needs to be extended tocreate a more complete picture of hot exciton relaxation path-ways in quantum dots.

4. WHAT IS THE MECHANISM OF HOT EXCITONRELAXATION IN QUANTUM DOTS?

4.1. Overview of Relaxation Pathways in NanocrystalQuantum Dots. The topic of hot carrier relaxation in quantumdots 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 coordinatefor this process. The early theory proposed phonon emission asthe channel, and later theory proposed an electron/hole Augerscattering process for electron relaxation. Subsequent theoriesthat have been inspired by experiment now include coupling toligands via differing schemes such as Forster energy transfer(FRET)101 or electron vibration energy transfer (EVET),112 aswell as nonadiabatic coupling between ligands and excitonic statesvia the breakdown of the Born�Oppenheimer approximation.68,69

Figure 11 schematically illustrates these possible transition path-ways. The aim of experiments has been to verify the proposedchannels and establish the pathway for hot exciton relaxation.Due tothe divergence in the experimental literature, the controversies havelargely remained.The value of these precisionmeasurements66,68,69 is to provide

precisely the feedback to enable the original question to beanswered. Given the presence of multiple possible pathways forrelaxation as well as the presence of both electrons and hole torelax, disentangling of the relative contributions to the totalmeasured relaxation process is essential. While it is qualitatively

Figure 10. State-resolved femtosecond pump/probe measurementsreveal the lifetimes of the first excited state of the electron (1P) andhole (2S3/2) states with excitonic state-to-state selectivity. (a) The hotelectron lifetime as a function of particle size reveals that smaller particleshave shorter lifetimes. The spectroscopic method produces experimen-tal uncertainties that are sufficiently small to enable quantitativemeasurement of the functional form of hot electron cooling for the firsttime. (b) The first excited state of the hole shows a lifetime which iscompletely size independent. The energy dissipation rate for electrons(c) and holes (d) shows a complete absence of a relaxation (phonon)bottleneck for either.



obvious that the phonon-based channel cannot explain theseresults, an independent verification of the strength of exciton�phonon coupling would be an important point in assessing thecontribution of phonons to the cooling process.4.2. PhononContributions to Relaxation: Exciton�Phonon

Coupling. 4.2.1. Overview. Much like hot carrier relaxation dy-namics, the problem of exciton�phonon coupling in quantumdots has seenmuch divergence in the experimental and theoreticalliterature.72,73,113,114 The problem of exciton�phonon coupling iscentral to quantum dot science in that it is a key parameter in thefactors that determine linewidths for optical nonlinearities, for itsthermal and electrical resistance properties, and for its role in hotcarrier relaxation—the topic of this review. One aims to obtain anindependentmeasure of the strength of exciton�phonon couplingto reconcile the experimental observations of the relevance ofphonon-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 long-itudinal optical mode (LO) which is coupled via the polarFr€ohlich interaction. The relevant acoustic phonon is the con-fined radial breathing mode which is coupled via the deformationpotential as well as via piezoelectric effects.The coupling between the electronic and vibrational (phonon)

degrees of freedom can be represented in the standard displacedharmonic oscillator approach (Figure 12a). The potentials betweenthe various states may involve nuclear displacements, Δ, in dimen-sionless normal coordinates. This displacement is related to theHuang�Rhys coupling constant, S, via S = Δ2/2. The couplingstrength is pωphononS.The strength of exciton�phonon coupling has itself seen

considerable controversy as illustrated by the wide variance inthe computed115�121 andmeasured113,122�136 coupling strengthsfor both optical and acoustic modes. In colloidal CdSe quantum

dots, nearly all early experiments have observed either the opticalor the acoustic modes but not both.72,73,114 As a result there istremendous divergence in the experimental literature. The theo-retical work has seen similar divergence with up to 3 orders ofmagnitude difference in the computed coupling strengths.72,73,114

This divergence in the theoretical results indicates the difficulty inobtaining realistic wave functions for theQD aswell as reveals thatexciton phonon coupling is itself a tremendously sensitive probeof the excitonic state.We have measured the exciton�phonon coupling in colloidal

CdSe quantum dots using this state-resolved femtosecondpump/probe approach.6,72,73 In a femtosecond pump/probetransient, oscillations are readily apparent (Figure 12b). Appro-priate experimental considerations must be taken such that thepump pulses are vibrationally impulsive (∼50 fs), the probepulse is tuned to the point of maximum slope in the absorptionspectrum, and experiments are done with sufficient care as toresolve these weak oscillations. Subtraction of the slowly varyingexcitonic contribution more clearly reveals the oscillations due towavepacket motion of coherent optical and acoustic phonons(Figure 12c). Fourier transform of these oscillations reveals thespectra of the phonon modes which are coupled to this excitonictransition (X1 pump in the case of Figure 12). Notably, this was thefirst observation of coupling to both phonon modes in these high-quality colloidal CdSe quantum dots.6,72,73 As described below,these oscillatory signals can be used to extract the exciton�phononcoupling strength in a straightforward manner. Doing so enablessimulation of the relevant frequency domain spectra such as PL andresonance 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 vibrationallyimpulsive pump pulse creates a phonon wavepacket via coherentsuperposition of phonon eigenstates.109 Two field�matter interac-tions with the pump pulse can produce an excited state electronicpopulation with a vibrational coherence (Figure 13a). This vibra-tional coherence will generate an excited state wavepacket and isreferred to as displacive excitation of coherent phonons (DECP).Alternatively, the first interaction with the pump pulse can create anelectronic coherence. This coherence then evolves, followed bystimulated emission back to the ground state to create a ground stateelectronic population and vibrational coherence from the secondinteraction. This pathway is referred to as resonance impulsivestimulated Raman scattering (RISRS). Both terms generally con-tribute to the wavepacket motion that results in the experimentallyobserved coherent oscillations in the pump/probe signals.109

When the system undergoes wavepacket dynamics, the co-herent phonons modulate the dynamic absorption spectrum—the transient absorption spectrum of the pumped sample. As thewavepacket oscillates on the potential(s), the energy gap ismodulated (Figure 13c). It is also possible for the wavepacketmotion to modulate the oscillator strength via non-Condoneffects (Figure 13d). Modulation in the energy gap can be viewedas frequency modulation (FM) of the transient spectrum whichwill result in a π/2 phase shift when probing at the peak or therising edge of the spectrum. In contrast, modulation in theoscillator strength can be viewed as amplitude modulation(AM) of the transient spectrum which will not result in a phaseshift. Hence, measurement of the phase shift at different probewavelengths reveals the relative contributions of the AM and FMterms 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

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



modulation of the dynamic absorption spectrum. Since theoscillations are purely due to energy gap modulation, one obtainsa simple result that the amplitude of the oscillation is directlyproportional to the coupling strength via Aosc = (dOD/dω)Δω.Here, Aosc is experimental oscillation amplitude; dOD/dω is thederivative of the absorption spectrum; and Δω is the couplingstrength in energy units.4.2.2. State-Resolved Exciton�Phonon Coupling: Intrinsic vs

Extrinsic Coupling. This method of obtaining exciton�phononcoupling strengths can be used to measure the coupling for anygiven excitonic state as well as to measure the size dependence ofthe coupling. This information will be used to reconcile thepresence or absence of phonon-based relaxation pathways. Theresults 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 thecontinuum at 400 nm (3.1 eV), whereas Xsurface corresponds toan exciton with surface-trapped charges. Themain trends are that asthe exciton cools to lower energy the coupling strength increasesand that the process of surface trapping tremendously increases thecoupling strengths. As these are the first measurements of thiscoupling with excitonic state specificity, insight is immediatelyobtained into the nature of the excitonic states as well as the originof the experimental divergence.6,72,73

Since the polar optical phonons are coupled via the polariza-tion-based Fr€ohlich interaction, the data show that the excitonic

polarization increases for the lower states. The acoustic modesshow a similar dependence, albeit less pronounced. Since thecoupling is proportional to the polarization of the excitonic wavefunction, these results indicate that the lower excitonic statesshow a larger electron�hole polarization than the higher states.This state-dependent polarization might be exploited for appli-cations based upon quantum dot polarization effects.These data enable reconciliation of many of the prior experi-

mental divergences based upon knowledge of how strongly eachexcitonic state couples to each mode. For example, the com-monly used 400 nm excitation will not generate either optical oracoustic phonons due to weak coupling, rather than due to timeresolution. Typical 400 nm pulses are∼100 fs in duration, whichis vibrationally impulsive for the acoustic modes and close toimpulsive for the optical modes. The near universal absence ofeither mode in 400 nm pumping experiments (including ours) ispurely due to coupling effects—the excitonic continuum is muchless polar than, e.g., the band edge exciton. This question ofpolarization of the excitonic wave functions was previouslydiscussed byGuyot-Sionnest94,137�139 and suggests the atomisticorigin50,140 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) experi-ments. This result also bears connection to the recent multipleexciton generation controversy, discussed in Section 5.

Figure 12. Evaluating the coupling of excitons to phonons. (a) The exciton�phonon coupling can be understood in terms of the displaced harmonicoscillator picture. The displacements yield the coupling strength. (b) Experimental observation of coherent phonons in CdSe dots enables measurementof the exciton�phonon coupling. The transient here is for the X1 pump and A1 probe. (c) Subtraction of the slow population decay reveals the residualoscillations which reveal wavepacket motion of the coherent optical and acoustic phonons. (d) FFT of the residuals recovers the spectra of the coupledmodes 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. Graylines are experimental data, and red lines are fits/simulations.



It was initially proposed by Krauss andWise113,123,124 and alsoEfros141 that the time integrated CW experiments probe the

coupling of a dot with accumulated charges created during thecourse of the experiment. Hence CW experiments will measurethe coupling of this photoproduct, whereas ultrafast time domainexperiments can in principle measure the intrinsic coupling.Much like the seminal work by Krauss and Wise,113,123,124 ourCW Raman results on colloidal CdSe quantum dots revealextremely strong coupling to the optical phonons and weakcoupling in the ultrafast time domain experiments.6,72,73 Essen-tially, the time domain experiments tend to measure the intrinsiccoupling of the delocalized excitonic states of interest. In con-trast, the frequency domain (continuous wave) experimentsmeasure the average coupling which is dominated by surfacestates. Hence, the CW experiments do not measure theintrinsic exciton�phonon coupling, precisely as proposedby Krauss, Wise, and Efros.The subtlety in the time domain experiments is that they still

can produce a photoproduct consisting of a surface-trappedexciton. Hence, if experiments are performed at high pumpfluences or with insufficient sample flow rate, the oscillations andthe extracted coupling can be much larger.79,129,132,142 Thesubtlety arises from the time scale of the surface trapping process,discussed in detail in Section 5. If the surface trapping rate is notvibrationally impulsive, there will be no effect on the measuredoscillations. Since the surface trapping rates are vibrationallyimpulsive for the acoustic modes but not impulsive for the opticalmodes, only the acoustic modes grow in amplitude basedupon the accumulation of a surface-trapped (i.e., excitonicallypolarized) photoproduct.42,79 Typical surface trapping timescales for these CdSe nanocrystals passivated with organic ligands(amines) are ca. 10 ps from the band edge exciton (X1)

74 and canincrease to 1 ps for X2

74 and rise to 0.1 ps for higher lyingexcitons.42,79 These rates are in principle tunable by chemicalcontrol of the surface ligands. These experiments on exciton�phonon coupling provide independent verification of weakcoupling to both optical and acoustic phonons, confirming thatphonons do not strongly control the time scales and pathways ofhot exciton relaxation. These phonon results also provide aperspective on the nature of the multiple exciton generationcontroversy, discussed in Section 5.

Figure 13. Relating the observed coherent phonons to the underlyingwavepacket dynamics and to the extraction of exciton�phonon couplingconstants. The coherent phonons can be generated by excited state wavepack-ets (a) or ground state wavepackets (b). The excited state wavepacket washistorically called Displacive Excitation of Coherent Phonons (DECP), andtheground statemechanismwas calledResonant ImpulsiveStimulatedRamanscattering. Both generally contribute to the observed oscillations. (c) Thewavepacket motion can modulate the energy gap which yields frequencymodulation of the dynamic absorption spectrum with an associate π/2 phaseshift going from the B1 to A1 probe. (d) The wavepacket motion can alsomodulate the transition moment with no associated phase shift. (e) Repre-sentative probe spectra, chosen tomonitor the phase shift. (f) The data show aperfectπ/2phase shiftwhich indicatedpure frequencymodulation and simpleextraction of the exciton�phonon coupling constants.

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



4.3. Multipath Picture Which Unifies Hot Exciton Relaxa-tion Dynamics. Following the early literature on hot electronrelaxation, the experimental and theoretical work at that timesuggested the presence of an alternative relaxation channel for hotelectrons—the electron/hole Auger relaxation channel.55,99,100 Thismost recent work, along with the simple energy mismatch argu-ments, clearly suggest that phonon-based pathways are not respon-sible for controlling the rate of hot electron relaxation in thesestrongly confined quantum dots. Our independent measurement ofweak exciton�phonon coupling6,73,74,79 further corroborates thisview that phonons are of minor importance in controlling hotexciton dynamics. In contrast, experiments by Guyot-Sionnest werethe first to demonstrate the importance of surface ligands incontrolling hot electron relaxation.94,101 In these experiments, theelectronwas spatially decoupled from the hole to better focus on theinfluence of the surface ligands. Hence, some confusion arose as tothe pathway by which hot electrons relax. In addition to theseexperiments on hot electron relaxation, our experiments summar-ized here have shown that there is an absence of a phononbottleneck for holes as well.68,69 These seemingly disparate observa-tions can be unified provided one views the process of hot excitonrelaxation 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 earliestwork, e.g., doped glasses. In the case of colloidal CdSe quantumdots, the majority of attention was placed upon measurement ofhot electron relaxation rather than hot hole relaxation. Thecontroversy in the literature largely arose due to differentexperiments measuring different processes. In the simplestexperiment, a hot exciton is optically generated, followed byhot electron relaxation—among amanifold of other processes. Ina related experiment, the hole may be spatially decoupled,enabling measurement of a relaxing hot electron—not the sameas a hot exciton.22,94,101,102 The geometric and functional differ-ence between the two situations is in the extent of electron/holeinteraction. It is specifically this interaction which is responsiblefor the Auger relaxation process. Hence hot electron relaxationin the excitonic configuration is designed to measure the Auger

process, whereas hot electron relaxation with a spatially de-coupled hole is designed to measure all non-Auger-based relaxa-tion paths for the excited electron.This identification of differences in available relaxation path-

ways enables a simple reconciliation of an earlier controversy aswell as suggesting a unified picture of the larger problem of hotexciton relaxation. We proposed that there are multiple compet-ing pathways in hot exciton relaxation.6,68,69 In this picture, thequestion at hand is no longer one of establishing the mechanismof relaxation but to understand and ultimately control the relativecontributions of themanifold of pathways. Hence there should bea phonon-based path for both electrons and holes. There shouldalso be a surface ligand based path, and finally there should be anAuger-based path for the case of electrons. There will not be anAuger path for holes due to larger level spacings in the VBmanifold. In our multichannel approach, the aim is to unravel thecontributions for the total rate as illustrated by

keðRÞ ¼ kphononðRÞ þ kligandðRÞ þ kAugerðRÞ ð3Þand

khðRÞ ¼ kphononðRÞ þ kligandðRÞ ð4ÞThe total rate corresponds to the experimentally measured ratewhich corresponds to an electron or hole which has someexperimentally determined size dependence. This total rate isideally an excitonic state-to-state transition rate as measuredhere. The value of a state-to-state transition rate is initially that itenables greater precision in the specific process measured. Theprecision as well as control in the specific process (i.e., manifoldof available pathways) is what uniquely enables assessment of therelative contributions of each path, e.g., phonons vs Auger. Theseindividual paths need not have the same size dependence.The results of this multichannel approach to hot exciton

relaxation are summarized in Figure 15. The experimentallymeasured state-to-state transition rate for hole relaxation is nearlysize independent and is well reproduced by a relaxation pathwaythat is largely dictated by ligands, with minor contributions from

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 ofelectrons (b) there are three paths. There is no phonon bottleneck in energy dissipation for either holes (c) or electrons (d) due to the presence ofadditional transition paths to carrier cooling. The presence of multiple transition paths suggests that each transition path might have a unique sizedependence and might further be controlled by materials design to control the relaxation rate.



phonons. In contrast, the electrons show a strong size dependencewith a major contribution from the Auger pathway, a minorcontribution from surface ligands, and negligible contribution fromphonons.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 onlytwo possible relaxation paths: phonon and ligands.While there are avariety of sophisticated phonon-based theories of carrier relaxation,they all point to the relative unimportance of this path.Hencewe usea simple functional form for phonon-based hot carrier relaxationfrom Nozik.69,143 This functional form reproduces the expectedphonon bottleneck for electrons and hole (Figure 15). We theninvoked the existence of a nonphonon-based relaxation path forholes—the surface ligands. We note that the term phonon isused only for the optical and acoustic normal modes of thenanocrystal, and ligands are used to denote the molecularvibrations of the adsorbed surfactants and proximal solventmolecules. However, these terms may be used somewhatinterchangeably.The initial proposal of the influence of surface ligands was

from Guyot-Sionnest.101 They proposed an energy transferbased scheme, wherein the electronic energy from the carriersis transferred to molecular vibrations of adsorbed molecules. Asimilar approach was invoked by Banin and Rabani.112 We haveinvoked the existence of a nonadiabatic pathway wherein theligand vibrations induce electronic transitions via a breakdown ofthe Born�Oppenheimer approximation.68,69

Nonadiabatic processes are well-known in quantummoleculardynamics and frequently drive ultrafast electronic processes, e.g.,the dynamics of the solvated electron.144�153 In this process, thecoupling of the electronic and vibrational degrees of freedomenables energy exchange. Hence, vibrational motion can mediateelectronic transitions as well as electronic transitions creatingmolecular vibrations as is the case here. We evaluated thenonadiabatic transition rate in a golden rule form, utilizingthe Hellman�Feynman theorem to simplify the functionalform.68,69,154 This analysis shows that the relevant matrix ele-ment is a quotient of the Hellman�Feynman force and therelevant energy gap. For transitions driven by surface ligands, theforce is proportional to the fraction of the hot carrier that tunnelsinto the ligands and solvent matrix. Smaller dots will have a largerfraction which couples to the surface. These smaller dots will alsohave a larger energy gap. The energy gap in the case of holescorresponds to E(2S3/2)� E(1S3/2) or E(X2)� E(X1), directlyobtained from the linear absorption spectra. The force and theenergy gap have nearly the same functional form, resulting in aquotient (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 nonadiabatictransition rate. We are not able to compute the absolute value.Nonetheless, with one adjustable parameter (the prefactorswhich scale the computed functional form), we are able toreproduce these precision measurements (Figure 15a). In thisapproach, we computed the kphonon(R) as well as the functionalform for kligand(R). We then adjusted the amplitude of kligand(R)so the total rate fits the experimental rate. Notably, recent abinitio work by Prezhdo has shown the importance of thesenonadiabatic processes,59,61,63 thereby confirming our initialproposal of mechanism(s). This proposal may be further testedvia chemical control of the surface ligands, distance dependence

via tunneling barriers, and via comparison to atomistic quantumdynamics calculations.We then use this approach to unravel the pathway(s) by which

hot electrons relax (Figure 15b). The same phonon-based rate isused for electrons, with the appropriate 1P�1S electron energygap, E(X4) � E(X1). The ligand-based rate is computed in thesame manner, replacing the hole energy gap with the electronenergy gap and using the functional form of the fraction of thehot electron in contact with ligands. These pathways are muchless significant for electrons than holes mainly due to the largerelectron energy gap. The Auger path is then taken to be thedifference between the experimentally determined transition rateand 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 relaxa-tion pathways in semiconductor quantum dots. The broaderpoint is that the relaxation pathways may be controlled bysuitable materials design. The earliest such example was byGuyot-Sionnest, in which the surface ligands were chosen tomatch or mismatch the electron energy gaps.101 In the non-excitonic case of hot electron relaxation, this ligand controlenabled control of the hot electron relaxation time. We have simplyattenuated the strength of the ligand channels by spatially decou-pling the ligands. This decoupling is achieved by passivating theCdSe dots with a ZnS layer, onto which the ligands are now bound.Doing so results in hole relaxation rates that are measurably longerand electron relaxation rates that are completely unchanged.69

These results are entirely consistent with our multichannel picturefor both holes and electrons. In the case of holes, attenuating theligand channel increases the relative contribution fromphonons andreduces the total rate, precisely as observed. In the case of electrons,decoupling of the ligands produces no measurable effect on thetransition rate. This observation is reconciled by considering that allmeasurable contribution to the total electron transition rate arisesfrom the electron/hole Auger channel. Hence, attenuating theligand channel has no effect.69

We evaluate the robustness of this picture by further compar-ison to recent experiments by Guyot-Sionnest on recovery of thephonon bottleneck.22 The initial observation of the phononbottleneckmay have been byNorris in epitaxial quantum dots.103

In those dots, there are no ligands to provide an alternativerelaxation channel. Those experiments isolated dots whichcontained only electrons from dots which contained electronsand hole (excitons) via geminate carrier capture. In this situation,a fraction of the dots would have no Auger channel and therebyrevealed the phonon bottleneck. To further explore this situa-tion, in the high-quality colloidal quantum dots widely studied,Guyot-Sionnest found that full isolation of the electron from thehole and surface ligands enabled realization of extremely slowelectron cooling (nanosecond rather than picosecond orfemtosecond) and finally revealed the existence of the phononbottleneck in these colloidal quantum dots. While the phononbottleneck remains more of a historical artifact today, the mainpoint here is the ability to control relaxation processes—a point ofconsiderable 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 ratherthan the more qualitative approach of carrier cooling. This idea isillustrated in Figure 16a. The pump pulse creates some initialexcitonic population, e.g., X4. The primary transition process forX4 is Auger-based relaxation for the 1P electron which then



creates an energetic (hot) hole. This hot hole then relaxesthrough the VB manifold to yield the band edge exciton, X1.This band edge exciton can either radiatively recombine (notshown) or undergo surface trapping for either holes (shown) orelectrons (not shown). The time scales for each of thesetransition processes are shown in Figure 16a, based upon ourmeasurements summarized here.In addition to identifying excitonic transition processes, we are

now able to identify the path(s) by which each of these transitionprocesses takes place (Figure 16b and c). Since the totaltransition rate is now viewed as the sum of all possible transitionpaths, the carrier-specific transition process can be decomposedinto the respective contributions. Figure 16b shows the pathwaysby which the electron relaxes: primarily via Auger relaxation withminor contributions from ligand channels and negligible con-tribution from phonons. The hole relaxes primarily via ligandswith minor contribution from phonons. The relative contribu-tions from the two leading pathways are noted in Figure 16c.Beyond providing a detailed picture of energy relaxation in thesequantum dots, this picture enables rational design of the dot andits environment to control energy relaxation for specific applica-tions such as quantum dot lasers or photovoltaics.

5. PHOTOINDUCED CHARGING AND SURFACE TRAP-PING PROCESSES

5.1. Hot Exciton Surface Trapping.The hot carrier relaxationprocesses discussed above can be considered more broadly toinclude related processes such as charge trapping into surfacestates42,74,79 and alsomulticarrier/exciton recombination.3,4,42,155,156

The multiexciton recombination (MER) process is much slowerthan these relaxation processes and can involve similar pathwayssuch as Auger recombination—related but not identical to theAuger relaxation process discussed here. The MER process is alsorelated to the complementary process ofmultiple exciton generation(MEG). Neither MER nor MEG will be further discussed to focuson relaxation processes that take place at conditions which generatemean occupancies of fewer than one exciton per dot. In thissituation, the final relaxation process involves trapping of carriersfrom 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 surfacetrapping.42,74,79 The very same process has seen recent interest inlight of the MEG controversy. In that context, the surface trappingprocess is referred to as photocharging.29,32,108,157 We have referredto this surface-trapped state as a polarized state rather than a chargedstate based upon the TA signals.42,79 We use the term “surfacetrapping” in the absence of clear evidence of photoionization whichproduces a charged dot. Nonetheless, there are a variety of termsused to describe the same process. At present, the nature of surface-related 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 eitherelectron or hole traps. The nature of the surface states in theseQDs is a topic unto itself and is beyond the scope of this Review.Without mention of the microscopic nature of the surface statesin QDs, we will identify the importance of these surface statesand how they connect to the topic of hot exciton relaxation. Adetailed treatment of the nature of these surface states will bepresented elsewhere.The lowest delocalized excitonic state of the quantum dot is

the band edge exciton, X1, comprised of electrons and holes in 1Sorbitals. For the ideal QD, X1 is the lowest energy state. In thecase of real QD, surface states are present at lower energy. Thesestates can be seen in the spontaneous PL spectra, typically atlower temperatures. The excitonic PL is of narrow bandwidth(100meV) and slightly Stokes shifted with respect to X1 (50meV).In contrast, the PL from the surface states is broadband (300meV)and much further red-shifted, consistent with its designation asa midgap state.These state-resolved measurements of exciton relaxation

enable observation of the time scales and pathways by whichexcitons undergo surface trapping.42,74,79 A working knowledge ofthe signal origins in the TA spectra enables identification of thepresence of electron and/or hole traps in these QDs. For example,pumping directly into X1 implies that no exciton cooling can takeplace. The only processes are radiative recombination on thenanosecond time scale and surface trapping. Our measurementson CdSe QDs reveal that under those material conditions holes aretrapped at the surface, whereas electrons are not.74 This point wasestablished by noting that the B1 transients (sensitive to electron 1Spopulation) show no change in the first 100 ps. Hence electronsremain in their delocalized 1S state for CdSe QDs that are wellpassivated. In contrast, the A1 signal (sensitive to exciton chargedistribution) changes dramatically over this time scale. Since the

Figure 16. Schematic of the transition processes and a unified picture ofexciton relaxation processes. (a) This excitonic state-resolved approachto transition processes enables measurement of state-to-state dynamicsgoing from Auger heating of the holes, to hole cooling, to hole trappingat the surface. (b) The transition process is unified by considering thepresence of multiple pathways which are controllable. (c) The differentpathways do not have the same dependence upon particle size.



electron remains in the initially pumped state, the changes in the A1signal can only arise from hole dynamics, i.e., hole trapping at thesurface of the QD.We use the case of CdSe merely to illustrate howthe TA signals can be used to identify specific trapping processes. Inprinciple, either carrier may be trapped. Furthermore, this carrier-specific trapping process may be chemically controlled via surfaceligands.158�164

The simplest picture of surface trapping is that it is the finalstage in relaxation following hot exciton cooling (Figure 16a).The complicating point is that surface trapping can compete withexciton cooling.42,74,79 Essentially a simple competition kineticsanalysis shows the yield of surface trapping from excited states(Figure 17). The pump pulse creates an initial hot exciton. Inaddition to cooling within the excitonic manifold, each of thesehot exciton states may directly trap to the surface, provided thesurface trapping rate can compete effectively with the hot excitoncooling rate(s). Since exciton cooling is completed within 1�2ps, the excited state (hot carrier) surface trapping time scaleshould be at least 10�20 ps to compete. This competitionbetween cooling and trapping may be controlled by the degreeof 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 trap-ping/charging processes in real time is essential to establish thepathways by which these photoproducts are created and ulti-mately managed. The premise is illustrated by a simple three-level system, not including the ground state. We omit considera-tion of the ground state since it is populated on the nanosecondor slower time scale, too slow to be relevant here. We consider ahot exciton, a cold exciton, and a surface-trapped exciton. Each istaken to have a unique value of the A1 signal due to biexcitoninteractions. The hot exciton produces a strongly bound biexci-ton (Xhot + Xcold) and therefore has a large, positive ΔOD signalin the A1 region. The cold exciton produces a strongly boundbiexciton (Xcold + Xcold) and therefore has an attenuated bleachin the A1 region. Finally, the trapped exciton produces a moderatelybound biexciton (Xsurface + Xcold) and thus has a small, positiveΔOD signal in the A1 region. The qualitative nature of these signalshas been discussed in our prior work42,66,74,78,79 and will bequantitatively discussed below. Pumping directly into Xcold means

only cold (relaxed) exciton surface trapping takes place on a slowtime scale. Pumping into Xhot without hot exciton trapping yields asignal which is clearly distinct from the case of a hot exciton trappingchannel that competes with hot exciton cooling. Without hotexciton trapping, the processes of cooling and trapping are sequen-tial and result in a clear production of Xcold as illustrated by anegative ΔOD. In contrast, the presence of hot exciton trappingcreates a small, positive ΔOD due to a mixture of Xcold and Xsurface

produced during the course of cooling. This schematic qualitativelyillustrates how the A1 signal reflects hot exciton trapping, uponcomparing the transient with different initial excitonic states pre-pared by the pump pulse.The process of excited state surface trapping (or hot carrier

photocharging) is quantitatively illustrated in Figure 19 basedupon our state-resolved measurements of surface trappingprocesses.6,42,66,68,69,74�76,78,79 Figure 19a shows pump/probetransients in this key A1 spectral region upon pumping into fourinitial excitonic states, one cold exciton and three hot excitons ofincreasing excess electronic energy. The fact that the signals donotmeet upon completion of cooling (t < 2 ps) quantifies the aboveschematic illustration of excited state surface trapping. Essentially,the signals only meet after surface trapping is complete since somefraction of the hot excitons directly populates the surface excitonicstate. While surface trapping from X1 is on the 50 ps time scale,surface trapping directly from X2 can compete with hot excitonrelaxation from X2 to X1. This process extends to higher energy,ultimately creating a quantum yield spectrum70,75,76 or photoactionspectrum for surface trapping/charging/polarizing (Figure 19b).The process of hot exciton surface trapping is quantitativelyanalyzed for the simplest case of trapping from X1 vs X2, inFigure 19c and d. The experimental data can only be reproducedby some fraction of the hot excitons undergoing prompt, excitedstate surface trapping.5.2. Relating Hot Exciton Surface Trapping to Exciton�

Phonon Coupling, Optical Gain, Multiexciton Recombina-tion, Multiple Exciton Generation, and Single Dot Blinking.The idea of surface trapping connects with hot exciton relaxationin that trapping can be considered a relaxation process and thattrapping 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 photo-product can obscure measurements of interest.Historically, the first discussion of surface trapping creating

artifactual signals was discussed by Wise113 and Efros141 as describedin Section 4.2.Wise andEfros had independently proposed that a verylong-lived photoproduct is created by illumination. This photopro-duct was invoked to reconcile the enormous differences in timedomain and time integrated measurements of exciton�phononcoupling. Our measurements72,73 summarized above verify the pre-dictions ofWise and Efros. This photoproduct consisting of a surface-trapped exciton in CW experiments also reconciles surprising ob-servations by Bawendi using single dot PL measurements.134,165�167

The early PL measurements revealed very strong coupling to LOphonons, surprisingly with a coupling that fluctuated for an individualdot. The fact that an ideally intrinsicmeasurement (coupling strength)fluctuates in time for a single particle clearly indicates that themeasurement is either contaminated or not an intrinsic couplingmeasurement. The most recent experiments by Chilla et al. haveconverged upon our time domain results with very small couplingto LO phonons.136 This convergence is presumably enabled bydot quality in the case of the time integrated experiments, e.g., Raman,PL, hole burning. Hence, frequency domain time integrated

Figure 17. In addition to relaxation/cooling, the excitons can experi-ence surface trapping. This trapping process can proceed via the bandedge exciton (X1). However, there can also be direct hot exciton surfacetrapping. The condition for hot carrier trapping is a surface trapping ratewhich competes effectively with carrier cooling. The population of thesesurface states is effectively a photoproduct which can obscure cleanmeasurement of nearly all processes in quantum dots.



measurements of exciton�phonon coupling should be interpretedwith caution inmuch the sameway thatMEG experiments are nowunderstood 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 andBawendi showed that the development of optical gain was dependent

upon the surface properties of the dot.19,168 Upon the basis of thepassivation of the dot and the host matrix, the performance metricsfor optical gain showed tremendous variance. These gain metricsinclude the threshold and the size dependence. Our work on state-resolved studies of optical gain75,76 and multiexcitons74,78 hasrevealed the underlying cause of this response, as well as measures

Figure 18. Schematic illustration of real time observation of hot exciton surface trapping. The A1 spectral feature is monitored in the experimentaltransients. This feature reflects the excitonic charge distribution via the biexciton induced energy shift. In the illustrative example here, we consider aminimal 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 sequentiallyby cold exciton trapping, has the two signals (Xhot vs Xcold pumping) meeting after cooling is complete (center). Excitation into the hot exciton, withdirect-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 referredto as excited state surface trapping, hot carrier trapping, and recently hot electron photocharging. The process involves direct excited state to surface statetransitions 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 photoluminescenceexcitation (PLE) spectra. The PLE spectra deviate from the Abs spectra at higher energy. The normalized quantum yield (QY) spectrum is PLE/A. ThisQY spectrum can be considered a photoaction spectrum for surface trapping. See text for details. (c) The process of excited state surface trapping isillustrated for the simplest case of trapping directly from X2. (d) Direct surface trapping from X2 is reflected in the slow component of the ΔΔODtransients.



to optimize gain in quantumdots. The idea is quite simple: onemustminimize excited state absorptions in the gain (stimulated emission)spectral region. The excited state (photoinduced) absorptions arisefrom multiexcitons which are typically lower in energy than theirsingle exciton building blocks due to Coulomb interactions. Ourwork showed that the surface-trapped exciton results in largephotoinduced absorptions (loss) due to strongly bound biexcitonsthat are comprised of a surface exciton and a core exciton.6,74�76,78

The connection between optical gain and the relaxation processes ofcooling and trapping arises from the excitonic state dependence tothese processes. The surface state photoproduct is produced athigher yield and with much faster rates for higher energyexcitons.42,74�76,79 The problem is most severe excitation into thecontinuum at 400 nm.42,79 Hence, the process of direct excited statesurface trapping can explain much of the observed optical gainphenomena.This photoproduct consisting of a surface-trapped exciton

is finally central to the recombination processes which guidethe analysis of multiple exciton generation (MEG),4,12,26�42

multiexciton recombination (MER),3,42,43,156,169 and singledot blinking.42,71,170�180 The presence or absence of photo-product-related artifacts inMEG experiments has garnered muchrecent attention. We discuss MEG, MER, and blinking together asthey are all related to the process of nonradiative recombination ofmultiexcitons. Hence, the photoproduct can strongly affect notjust exciton�phonon coupling and multiexciton interactionstrengths but the rates of multiexciton recombination.TheMER rate is of direct importance to several applications in

that it can govern the lifetime of optical gain in quantum dots aswell as determine the time scale for charge extraction of multi-excitons in a solar cell. The MER rate is furthermore of indirectimportance to the controversial MEG and blinking experiments.In the case ofMEG, the standardmethods ofMER analysis are usedto report on theMEGyield, a topic of recent importance in quantumdot photovoltaic research. In the case of single dot blinking, it wasproposed that the same MER mechanism of Auger recombinationwas responsible for the blinking process.181 Recent experiments havechallenged this Auger recombination picture due to inconsistenciesof the MER rates of a biexciton as compared to the implicitnonradiative decay of the dark/off state of the dot.170,171,182 Recentsingle dot PL experiments have shown that a charge accumulationprocess is at play in blinking,176,177,180 much like the chargeaccumulation problem in exciton�phonon coupling.72,73

Our recent work has shown that this photoproduct creates MERrates that can be an order ofmagnitude faster than theMER rate of abiexciton.42 This fast decay is only present when a photoproduct ispresent. The photoproduct can be spectroscopically identified, forthe first time, by virtue of the TA signals discussed here. Ourexperiments have shown that under these trapping/charging/polarizing conditions the MER rates are fast and yield false positiveMEG signals.42 For the case of blinking, our experiments show thatthe MER rate for this photoproduct is identical to the predictionsfrom the recent single dot PL experiments,171 points that arediscussed in detail elsewhere.42 In short, the creation of a photo-product comprised of a surface-trapped exciton can compete withhot exciton relaxation and can dramatically influence the interpreta-tion of a wide variety of processes central to quantum dot science.

6. SUMMARY

This Review presents an overview of the processes whichgovern relaxation of hot excitons in semiconductor quantum

dots. The process of relaxation or cooling has been extensivelyinvestigated since the first discovery of the quantum dot, nearlytwo decades ago. The topic is important in that it is one of themain dynamical processes that govern function of these materialsand serve to illustrate the extent to which quantum confinementeffects on the nanoscale are truly well understood. This processof exciton relaxation is also of great importance to nanoscaledevices such as quantum dot lasers and quantum dot photo-voltaics. Despite clear motivation and long-standing experimen-tal and theoretical investigations, the topic of hot excitonrelaxation has been challenging for the community.

This Review identifies some of the sources of these difficultiesand provides a reconciliation in light of a multichannel approach toexciton relaxation dynamics. We have found that the vague processof carrier cooling can be replaced with a more precise description interms of excitonic state-to-state transitions. We summarize here ourexperiments which provided the first measure of hot excitonrelaxation processes with excitonic state specificity. This precisionin measurement enabled disentangling of all possible processes withelectron and hole specificity, as well as unification of hot carrierprocesses in terms of a multichannel or multipath picture. Thesemeasurements of hot exciton relaxation processes are connected tomeasurements of exciton phonon coupling, which independentlyconfirm the picture established from the relaxation dynamicsexperiments. Finally, the process of hot exciton relaxation isextended to include hot exciton surface trapping, a process thathas seen much recent interest in light of photoproducts that arise inmeasurements of optical gain, exciton�phonon coupling, single dotblinking, and multiple exciton generation.

’AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected].

’BIOGRAPHY

Patanjali Kambhampati received a B.A. in Chemistry fromCarleton College in 1992 and a Ph.D. in Chemistry from theUniversity of Texas at Austin in 1998. His doctoral work focusedon ultrahigh vacuum surface studies of adsorbate�substratecharge transfer excitations and surface-enhanced Raman scatter-ing under the supervision of Alan Campion. From 1999 to 2001he was a Postdoctoral Associate with Paul Barbara, also at theUniversity of Texas at Austin. His postdoctoral work focused onfemtosecond laser spectroscopy of condensed phase chemicaldynamics of the solvated electron and intramolecular electron



transfer. From 2001 to 2003 he was involved in early phase workin a fiber optic startup based in Los Angeles. At McGillUniversity, where his group focuses on ultrafast dynamics inquantum dots, he was an Assistant Professor from 2003 to 2009and is presently an Associate Professor.

’ACKNOWLEDGMENT

I would like to thank the current and past members for theircontributions to the work summarized here. In particular, Igratefully acknowledge the contributions from Ryan Cooney,Samuel Sewall, Kevin Anderson, and D. M. Sagar, who per-formed the first generation of experiments in my lab. I also thankEva Dias, Pooja Tyagi, Jon Saari, and Jonathan Mooney who arecurrently performing the next generation of experiments tofurther explore the topics discussed here. Financial support fromCFI, NSERC, FQRNT, and McGill University is acknowledged.

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