Excited State Phononic Processes in Semiconductor Nanocrystals

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C: Physical Processes in Nanomaterials and Nanostructures

Excited state phononic processes in semiconductor nanocrystals revealed by excitonic state-resolved pump/probe spectroscopy Brenna R Walsh, Colin Sonnichsen, Timothy G. Mack, Jonathan I Saari, Michael M Krause, Robert Nick, Seth Coe-Sullivan, and Patanjali Kambhampati J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11099 • Publication Date (Web): 23 Jan 2019 Downloaded from http://pubs.acs.org on January 29, 2019

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Excited State Phononic Processes in Semiconductor Nanocrystals Revealed by Excitonic State-Resolved Pump/Probe Spectroscopy Brenna R. Walsh1, Colin Sonnichsen1, Timothy G. Mack1, Jonathan I. Saari1, Michael M. Krause1, Robert Nick2, Seth Coe-Sullivan2, and Patanjali Kambhampati1* 1 Department

of Chemistry, McGill University, Montreal, QC, H3A 0B8 Canada 2 QD

Vision Inc., Watertown, MA, 02472, USA

*[email protected]

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Abstract. Semiconductor nanocrystals are being developed with increasingly complex shapes and geometries, often featuring complex shell structures. One aims to characterize these structures by different probes, beyond electronic spectroscopies. Vibrational spectroscopy is a useful tool to probe the phononic structure, but the commonly used frequency domain methods can be plagued by artifacts due to charge trapping dynamics. To circumvent these issues, coherent phonons may be measured in the time-domain via excitonic state-resolved pump/probe spectroscopy. These measurements reveal several new observations on phononic processes, focusing on model systems of radially graded alloys of core/shell nanocrystals: CdSeCdXZn1-XS. The main new observation is frequency changes to the longitudinal optical phonon at high energy due to electronic mixing. This new, softened phonon mode appears via previously unobserved. biexcitonic signals. The stateresolved measurements reveal insights into how the shelling process controls excitonic polarization, carrier trapping, and perturbations to sphericity.

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Introduction. Semiconductor nanocrystals are used for a wide variety of optoelectronic applications spanning light absorption and generation of charges for photovoltaics and photodetectors, to excitation followed by emission of light for light emitting diodes and lasers and imaging.1-3 New functionalities are aimed for via more complex nanostrucuring. Focusing upon light emission, one of the key paths towards improving performance has been to design new shell structures.4-8 The original CdSe semiconductor nanocrystals (NC) were passivated by organic ligands.9 These NC had low photoluminescence (PL) quantum yield (QY) for single excitons of ~ 10%. Subsequently inorganic shell structures were developed to increase QY to ~ 90%, typically using ZnS shells.10, 11

These shelling strategies are guided by maximining QY, with a rationale based upon lattice

mismatch which may generate interfacial defects which may cause non-radiative trap states. While these simple measurements of QY from a single exciton offer some measure of electronic properties as determined by physical interfacial structure, they have since been shown to be lacking. For example, single particle spectroscopy has revealed complex blinking phenomena that have enabled greater insight into how shelling can improve optical properties.12-17 In the same vein, time resolved spectroscopies from pump/probe to time resolved PL have revealed that multiexciton lifetimes offer additional measures of how the interface confers function for optical properties.18-25 In both cases, one aims to create shell systems to either minimize blinking or maximize multiexciton QY by slowing Auger recombination as a non-radiative effect. Based upon these more sophisticated measures of optical performance as dictated by interfacial structure, the nanocrystal community as developed more sophisticated shelling schemes than the original CdSe/ZnS system with an abrupt interface.20, 26-34 These shelling schemes have been discussed in detail by others and will not be elaborated upon here. The main point is that with 3 ACS Paragon Plus Environment

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some combination of thick shells, designer shells with minimized stain, and radially graded shells via alloying, one has different means to design interfacial chemical and physical structure. With the strategies available for developing shell schemes, one aims for increased information richness in spectroscopic probes of these shelling schemes. Here, we perform excitonic state-resolved pump/probe spectroscopy 35-38 on CdSeCdXZn1XS

semiconductor nanocrystals with a radially graded shell. As expected, the resonance Raman

spectra reveal little information beyond broad spectral lines, without knowledge of the states to which the phonons couple. In contrast, these time-domain measurements reveal coherent optical and acoustic phonons which give fingerprint of phononic structure that is not observable by other means. By excitonic-state selectivity, these time domain experiments reveal couplings for each state, thereby the excitonic polarization for the manifold. The striking new observation is a bond softening at high photon energy. This softening is observed as a low frequency shoulder to longitudinal optical phonon. The shoulder is produced by previously unobserved biexcitonic signals, made possible by these time-domain methods. In addition to optical phonon processes, these measurements reveal coherent acoustic phonons which report on interfacial trapping and shape perturbations. These measurements show that time-domain measurements of coherent phonons when driven with excitonic state-selectivity uniquely enable new observations into the effects of shelling on the excitonics of nanocrystals.

Experiment The excitonic state-resolved pump/probe spectroscopy has also been described in detail elsewhere.39-43 Briefly, 70 fs pulses from a Ti:sapphire amplifier were used to drive optical

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parametric amplifiers of 50 fs duration for state-resolved excitation. The pump/probe signals were derived from a supercontinuum based spectrometer with dispersion compensation. The specific details of the pump and probe photon energies have been discussed in our prior works on the same system41-43. The same prior works discuss the samples, which are dispersed in toluene. The details of probing coherent phonons with pump/probe spectroscopy are discussed in our prior works37, 44, 45 The pump pulses are 40 +/- 5 meV in bandwidth. With these bandwidths the pump pulses span the bandwidth of coarse excitonic states. The probe was detected after the sample via a scanning monochromater. The probe pulse has a spectral center selected to be at the point of greatest slope in the linear absorption spectra in order to maximize the detected oscillations. This point of maximal slope is at the red edge at the half maximum of the band edge exciton. These CdSeCdXZn1-XS have described in detail elsewhere.41-43,

46

Additionally, an NC

system with a thinner shell was synthesized using published procedures47 for comparison of Raman spectra. Samples were prepared for Raman measurement by depositing ~100 μL of the concentrated NC solution onto on to clean p-doped Si wafer and dried under ambient conditions. Raman measurements were obtained using a Horiba LabRam HR800 microscope in conjunction with an external diode-pumped solid-state 473nm laser (Ciel, Laser Quantum). The source laser output power source was 12 mW. The external line was directed into a microscope through a series of pinholes and mirrors and directed into the microscope turret using a superholographic notch filter (Kaiser optical systems). A 100x objective (Olympus N Plan N, NA=0.9) was used, in conjunction with a grating 1800 lines/mm and the spot size was approximately ~1 um. Full spectra were acquired with stitching of 590 cm-1 windows in which the total acquisition time was 1.6 minutes (10s, 10 accumulations). No sample damage was apparent after laser exposure 5 ACS Paragon Plus Environment

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Results and Discussion. Fig. 1 provides an overview of interfacial structure in semiconductor nanocrystals. Fig. 1a illustrates the three primary types of interfaces. The core/ligand system represents the original NC and the most general case.9 In order to improve PL QY for single excitons, the core/shell system was developed. Initial work was done on CdSe/ZnS.10,

11

The shell is some wider gap

semiconductor for purposes of electronic passivation of interfacial states that may serve as nonradiative traps. The subtlety is in matching lattices. Minimally one aims to minimize strain by matching lattice parameters as given by bulk values. Since the realistic lattice structure on the nanoscale is not necessarily the same as the bulk, these interfacial effects of epitaxy may be affected by these structures being nanoscale. To mitigate these interfacial effects due to strain, various shelling approaches have been developed.20, 26-32 The graded alloy approach as shown here is a promising solution. By engineering radial composition gradients, one creates softer confinement potentials. These interfaces have been shown to improve nanocrystal performance, and result in changes in their electronic structure. One aims for measurements which inform on the interfacial structure. Fig. 1b shows representative linear spectra of graded shell CdSeCdXZn1-XS nanocrystals. These NC have been described in detail elsewhere, with emphasis on electronic processes for optical gain.41-43, 46, 48 These NC show the characteristic excitonic features in both the linear and the non-linear time-resolved spectra41-43. Fig. 1c shows a transmission electron microscopy (TEM) image of representative CdSeCdXZn1-XS nanocrystals. The outer shell of the nanocrystals is clearly non-spherical. The impact of this non-sphericity will have implications upon acoustic phonons, discussed later. As the growth of shells controls both the shape as well as the electronic properties 6 ACS Paragon Plus Environment

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of nanocrystals, one aims for interfacial information in addition to the commonly employed electronic spectroscopies. The mechanical properties of the interface on the microscopic level may be gleaned by vibrational spectroscopy. In the case of nanocrystals one has optical and confined acoustic phonons.49-51 Each type of phonon is highly sensitive to the interface. The optical phonons reflect interfacial strain and the presence of interfacial modes.34,

52-58

The acoustic phonons reflect

physical boundary itself.37, 59, 60 There are a number of means by which one can measure phonon spectra in nanocrystals. Resonance Raman spectroscopy is among the most common, due to its simplicity and information content. Fig. 2a shows resonance Raman spectra of two different graded shell nanocrystals. We focus on the previously discussed core/shell system which we denote NC1. Since resonance Raman is a vibrationally resolved electronic spectroscopy, one has issues of sample photoluminescence (PL). These PL backgrounds render measurements challenging due to signal to noise. Hence it is common to quench the PL via ligands so as to optimize the system for Raman measurements. Here, one cannot remove these backgrounds as normally done in Raman studies due to the shells. The PL will always be present as a large background. In this NC1, only the modes of the CdZnS based shell are observable. This mode appears at 294 cm-1. But the CdSe LO mode is not visible due to volume effects. Excitation was at a photon energy resonant with the shell, hence the core modes are below detection limits. In order to reduce the effect of shell volume, we synthesized a control graded alloy NC, denoted NC2. NC2 was designed with a thinner shell, revealing the core CdSe peak at 202 cm-1 as well as a shell peak at 287 cm-1. The resonance Raman spectra reveal the challenge of even observing core modes in core/shell nanocrystals, let alone gleaning insight. 7 ACS Paragon Plus Environment

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While PL backgrounds and shell thickness pose a simple set of challenges for obtaining vibrational information, there are additional effects fundamental to gleaning insight from resonance Raman in semiconductor nanocrystals. Our group has previously shown that time domain and frequency domain Raman measurements do not obtain the same results for a number of reasons.36-38, 61 Time domain measurements of coherent phonons yield narrower linewidths and excitonic state-resolved measurements of exciton-phonon couplings. Fig. 2b shows Raman spectra of CdSe/ligands nanocrystals using both frequency domain resonance Raman and time domain state-resolved pump/probe measurements of the same. The time domain measurements of the 208 cm-1 LO phonon reveal narrower linewidths, and smaller couplings than their frequency domain counterpart. These points have been discussed in detail elsewhere as arising from surface trapping effects.38 In order to obtain vibrationally resolved information on complex interfaces of graded shell nanocrystals, we performed excitonic state-resolved pump/probe spectroscopy. These methods have been discussed in detail elsewhere.35-38 Briefly, a femtosecond pump pulse creates vibrational wavepackets that are monitored in the time domain as coherent phonons which modulate the pump/probe signals. These wavepackets may derive from optical or confined acoustic phonons.50, 51

By pumping into specific excitonic states, this approach yields exciton-phonon couplings for

specific states. Fig. 3 shows excitonic state-resolved TA data on these NC. The inset of Fig. 3a shows the idea of state-resolved exciton-phonon interactions. Each excitonic state is coupled to a phonon as described by a displaced harmonic oscillator picture for a two electronic state system. This idea is generalized to multiple electronic states by having a different coupling or frequency for each state. In the case of nanocrystals, these are the excitonic states that one probes.

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The data in Fig. 3a shows behavior qualitatively consistent with prior work on CdSe NC.38 Pumping into the band edge exciton, X1, yields an instrument limited bleach, a DC offset. In addition to this bleach, there are intensity oscillations, an AC signal. The AC / DC ratio of these signals reflects the frequency and strength of electronic coupling to specific phonon modes. Pumping into higher excitonic states, X2, X3, and at 3.1 eV yield different bleach signals, qualitatively consistent with CdSe NC. The details of these DC signals have been discussed elsewhere. Focusing upon the AC signals, one sees a strong dependence upon excitonic state Fig. 3b. Fig. 3c shows the FFT power spectra of the residual oscillations, corresponding to the Raman spectra in the frequency domain. The excitonic state-resolved measurements reveal information on both optical modes, ~ 200 cm-1, and confined acoustic modes, 20 cm-1. The X1 pump data recovers the well-known longitudinal optical (LO) phonon mode. This linewidth is narrower than in Raman, as was previously discussed in CdSe. With higher excitonic state, the optical mode becomes weaker, and spectral density in the 20 cm-1 region becomes stronger. In the case of CdSe NC, one can observe coherent acoustic phonons, with a size dependence. Observation of these modes, however, is very sensitive to the interface due to their mechanical nature. It is the mechanical contrast at the interface which confines the acoustic wave thereby yielding its spectrum.59 In the case of CdSe/ligands one can observe well resolved LA modes, whether in the time domain or via frequency domain measurements of single dot PL. In these graded shell NC, the spherical core is overcoated by a shell that is non-spherical, hence the confinement is non-spherical. As such, one observes a spectral density rather than a peak. This spectral density shows some excitonic statedependence, suggesting that the mechanical contrast at the interface dependence upon the electronic structure of the state. 9 ACS Paragon Plus Environment

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Fig. 4 shows the pump power dependence to these signals. The TA data in Fig. 4a shows a DC response that has been discussed in detail elsewhere. These bleaching signals reflect a statistical distribution of X or XX generated by the pump pulse. The multiexciton multiplicity is limited by the degeneracy of the state into which one pumps. Assuming the core is spherical, the X1 state would be doubly degenerate due to 1S symmetry as in the case of CdSe NC. Fig. 4b shows the residual oscillations, the AC response. Fig. 4c shows the FFT power spectra. The main observation is that a low energy shoulder arises at higher fluence. The appearance of the high energy shoulder reflects that the excitonic state also controls the frequency of the coupled LO phonon. The shoulder grows in with fluence. The inset of Fig. 4c shows that the amplitude ratio for the two peaks is linear to pulse energy and has a low energy intercept with zero amplitude. At higher fluence there is a higher fraction of XX states relative to X states. Since the XX states are at near twice the total energy of X, the electronic and phonon structure may be very different. In particular at 4 eV vs 2 eV, the vibrational frequencies of optical modes can change. These data suggest that picture. It is worth noting that that one can see biexciton-phonon coupling for states near 4 eV but one cannot detect exciton-phonon coupling for states near 3 eV. These observations suggest differences between a biexciton state and a high energy single exciton state of the same energy. The observation of biexciton-phonon coupling in this system is a first, to the best of our knowledge. It is made possible by the difference in LO phonon frequency for higher energy states. Fig. 5 shows the pulse energy dependence to the TA data with 3.1 eV pump. Fig. 5a shows the TA data for different pulse energies. Fig. 5b shows the residual oscillations and Fig. 5c shows the FFT power spectra of those oscillations. The data show a low energy spectral density in the

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regime of confined acoustic phonons. There is no measurable pulse energy dependence to these data. While the LO phonons probe aspects of local physical structure, electronic covalency, and excitonic polarization, the confined longitudinal acoustic (LA) phonons probe aspects of larger spatial structure and material contrast. In the case of CdSe spherical NC, one observes discrete confined LA modes by various means. As recently shown, the ability to observe LA modes can even depend upon ligand choice, illustrating the issue of material contrast. Since it is the physical boundary that gives rise to the confined acoustic phonon spectrum, perturbations will have effects. Specifically, realistic non-spherical shells will result in perturbing a single LA mode into some spectral density. The mean frequency of this spectral density should be consistent with a resolved LA mode. Based upon size dependence for CdSe, the peak should be 15 – 25 cm-1. This is precisely as observed here. In contrast to the pulse energy dependence for X1 pump, there is no energy dependence for 3.1 eV pump. In the case of LA phonon they arise different coupling mechanism than LO phonons, with some common ones also. The LA modes are coupled via the deformation potential, which was shown to be excitonically state-specific. But for higher excitonic states one has a large amount of excess electronic energy to dissipate. This dissipation process may also impulsively generate coherent LA phonons. We have previously shown in NC that these effects arise from impulsive charge trapping rather than impulsive heating. The present data shows minimal effect, in contrast to CdSe NC. The observation of LA modes and their dependence upon excitonic state and pulse energy reflects the quality of the interface in light of interfacial charge trapping. Insight into the nature of the low frequency shoulder for the LO phonon may be obtained via fluence dependent measurements, Fig. 6. Fig. 6a shows the LO spectral region is comprised of 11 ACS Paragon Plus Environment

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two modes, the parent LO phonon and a sideband. Often sidebands to optical phonons are inferred from deconvolution of broad resonance Raman spectra which cannot resolve distinct peaks. Sidebands have previously been interpreted as arising from surface phonons62. More information rich ultrafast time-domain echoes experiments has recently revealed LO phonon energy shifts due to specific excitonic states63. In these state-resolved pump/probe experiments, two peaks are clearly visible. Fig 6b shows the fluence dependence of the peak areas. The area of the sideband relative to the parent LO mode is linear to fluence, with an intercept at zero fluence, upon pumping into X1. This linearity of relative areas is consistent with two-photon absorption. At low fluence, the pump pulse prepares a single exciton in the X1 state which couples to the LO phonon. At higher fluences there is an increasing population of biexcitons formed by multi-photon absorption. Since the band edge exciton is two-fold degenerate there can only be single or biexcitons formed upon pumping into X1. The linearity of the ratio illustrates the sideband is associated with biexciton signals. To the best of our knowledge, this is the first observation of specific biexciton-phonon coupling, made possible by the presence of a frequency shift. Fig6c schematically illustrates the phononic processes which arise and the observation of these new processes for biexcitons. The standard method of analysis is given by the displaced harmonic oscillator model in which there is one excited state. Other excited states are characterized by additional parabolas at higher energy. We have used this approach previously to probe phononics in the low fluence single exciton regime44. What is new in here is the presence of a sideband for the case of a biexciton. The biexciton has approximately twice the energy of the single exciton, albeit dressed by a small binding energy of 10 meV 24, 64-66. Since the displacement of the XX parabola give rise to the coupling and amplitude of the oscillation, but the curvature gives rise 12 ACS Paragon Plus Environment

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to the frequency, these results show that the LO phonon has a bond softening for the energy corresponding to the biexciton. At this energy, the excitation samples the core and the shell and reveals that the bond frequency reflects the mixing in these phases.

Conclusions. These excitonic state-resolved pump/probe experiments provide new observations on excited state phononic processes in semiconductor nanocrystals. Pump/probe spectroscopy has previously been shown to be useful in observing coherent phonons in the time domain which can reveal further information beyond frequency domain resonance Raman spectroscopy. Here, we apply those methods to a core/shell nanocrystal which reveals new LO phonon sidebands upon direct excitation into the biexciton. These experiments reveal new methods to obtain excited state properties of nanocrystals.

Acknowledgements Financial support from CFI and NSERC is gratefully acknowledged.

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Fig. 1. Overview of structure and spectroscopy of the interface of semiconductor nanocrystals. a) Schematic illustration of the three main classes over interface: core/ligands, core/shell with a hard interface, and core/shell with a radially graded interface. b) Linear absorption, photoluminescence, and photoluminescence excitation spectra of CdSeCdXZn1-XS nanocrystals. Arrows denote the excitonic transitions and the pump photon energies used in state-resolved excitation. c) Transmission electron microscope image of these nanocrystals. 14 ACS Paragon Plus Environment

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Fig 2. Evaluating phonon modes in nanocrystals. a) Resonance Raman spectra of two different CdSeCdXZn1-XS nanocrystals. NC 1 is the focus of this work, while NC 2 is a control. b) Comparison of longitudinal optical (LO) phonon lineshapes as revealed by time domain (pump/probe) vs frequency domain (resonance Raman) in a model CdSe/ligands nanocrystal system.

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Fig. 3. Excitonic state-resolved pump/probe spectroscopy reveals coherent phonons. a) pump/probe signals with pumping into denoted excitonic states and probing to the red of the band edge exciton. See text for details. The inset shows a schematic illustration of specific exciton-phonon processes probed via state-resolved pumping. b) Residual oscillations from the pump/probe signals reveal coherent phonons. c) FFT of residual oscillations yields spectra of optical and acoustic phonons.

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Fig. 4. Fluence dependence of pump/probe signals with pumping into band edge exciton, X1. a) pump/probe signals. b) Residual oscillations. c) FFT spectra.

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Fig. 5. Fluence dependence of pump/probe signals with pumping into the continuum at 3.1 eV, X1. a) pump/probe signals. b) Residual oscillations. c) FFT spectra.

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Fig. 6. Sideband reveal high energy phonon processes. a) With X1 pump, a sideband is observed, redshifted from the parent LO phonon mode. b) The ratio of the area of the sideband relative to the parent peak as a function of pump fluence. c) Schematic illustration of possible high energy phonon processes of frequencies and couplings.

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53. Kelley, A. M. Resonance Raman Overtone Intensities and Electron-Phonon Coupling Strengths in Semiconductor Nanocrystals, J. Phys. Chem. A 2013, 117, (29), 6143-6149. 54. Dzhagan, V. M.; Valakh, M. Y.; Milekhin, A. G.; Yeryukov, N. A.; Zahn, D. R. T.; Cassette, E.; Pons, T.; Dubertret, B. Raman- and IR-Active Phonons in CdSe/CdS Core/Shell Nanocrystals in the Presence of Interface Alloying and Strain, J. Phys. Chem. C 2013, 117, (35), 18225-18233. 55. Beecher, A. N.; Dziatko, R. A.; Steigerwald, M. L.; Owen, J. S.; Crowther, A. C. Transition from Molecular Vibrations to Phonons in Atomically Precise Cadmium Selenide Quantum Dots, J. Am. Chem. Soc. 2016, 138, (51), 16754-16763. 56. Mukherjee, P.; Lim, S. J.; Wrobel, T. P.; Bhargava, R.; Smith, A. M. Measuring and Predicting the Internal Structure of Semiconductor Nanocrystals through Raman Spectroscopy, J. Am. Chem. Soc. 2016, 138, (34), 10887-10896. 57. Tschirner, N.; Lange, H.; Schliwa, A.; Biermann, A.; Thomsen, C.; Lambert, K.; Gomes, R.; Hens, Z. Interfacial Alloying in CdSe/CdS Heteronanocrystals: A Raman Spectroscopy Analysis, Chem. Mater. 2012, 24, (2), 311-318. 58. Lin, C.; Gong, K.; Kelley, D. F.; Kelley, A. M. Electron–Phonon Coupling in CdSe/CdS Core/Shell Quantum Dots, ACS Nano 2015, 9, (8), 8131-8141. 59. Schnitzenbaumer, K. J.; Dukovic, G. Comparison of Phonon Damping Behavior in Quantum Dots Capped with Organic and Inorganic Ligands, Nano Lett. 2018, 18, (6), 3667-3674. 60. Salvador, M. R.; Hines, M. A.; Scholes, G. D. Exciton-bath coupling and inhomogeneous broadening in the optical spectroscopy of semiconductor quantum dots, J. Chem. Phys. 2003, 118, (20), 9380-9388. 61. Kambhampati, P. Hot Exciton Relaxation Dynamics in Semiconductor Quantum Dots: Radiationless Transitions on the Nanoscale, J. Phys. Chem. C 2011, 115, (45), 22089-22109. 62. Lin, C.; Kelley, D. F.; Rico, M.; Kelley, A. M. The “Surface Optical” Phonon in CdSe Nanocrystals, ACS Nano 2014, 8, (4), 3928-3938. 63. Spencer, A. P.; Hutson, W. O.; Irgen-Gioro, S.; Harel, E. Exciton–Phonon Spectroscopy of Quantum Dots Below the Single-Particle Homogeneous Line Width, The Journal of Physical Chemistry Letters 2018, 9, (7), 1503-1508. 64. Sewall, S. L.; Cooney, R. R.; Anderson, K. E. H.; Dias, E. A.; Sagar, D. M.; Kambhampati, P. Stateresolved studies of biexcitons and surface trapping dynamics in semiconductor quantum dots, J. Chem. Phys. 2008, 129, (8), 8. 65. Sewall, S. L.; Franceschetti, A.; Cooney, R. R.; Zunger, A.; Kambhampati, P. Direct observation of the structure of band-edge biexcitons in colloidal semiconductor CdSe quantum dots, Phys. Rev. B 2009, 80, (8), 4. 66. Sewall, S. L.; Cooney, R. R.; Dias, E. A.; Tyagi, P.; Kambhampati, P. State-resolved observation in real time of the structural dynamics of multiexcitons in semiconductor nanocrystals, Phys. Rev. B 2011, 84, (23), 8.

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