Photophysical Action Spectra of Emission from Semiconductor

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C: Physical Processes in Nanomaterials and Nanostructures

Photophysical Action Spectra of Emission from Semiconductor Nanocrystals Reveals Violations to Vavilov Rule Behavior from Hot Carrier Effects Bo Li, Patrick Brosseau, Dallas P. Strandell, Timothy G. Mack, and Patanjali Kambhampati J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11218 • Publication Date (Web): 06 Feb 2019 Downloaded from http://pubs.acs.org on February 7, 2019

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The Journal of Physical Chemistry

Photophysical Action Spectra of Emission from Semiconductor Nanocrystals Reveals Violations to Vavilov Rule Behavior from Hot Carrier Effects

Bo Li‡a, Patrick Brosseau†a, Dallas P. Strandell†, Timothy G. Mack†, and Patanjali Kambhampati†* †Department

of Chemistry, McGill University, Montreal, Quebec H3A 0B8, Canada

‡Department

of Physics, Harbin Institute of Technology, Harbin, 150001, China

a

Equal author contributions

* author to whom correspondence should be addressed, [email protected]

1

ACS Paragon Plus Environment

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Abstract Semiconductor nanocrystals are known to have properties of bulk semiconductors as well as molecules. Two rules that govern molecules are that there is not dual emission (Kasha) and there is not a spectrum to the emission quantum yield (Vavilov). We show that the latter rule of molecular spectroscopy is generally violated in semiconductor nanocrystals. Through experiments and theory on CdSe and perovskite nanocrystals, these violations are shown to arise via hot carrier effects. Experiments and simple phenomenology reveal that quantum yield spectra arise due to enhanced hot carrier trapping rates. A semi-classical electron transfer theory rationalizes a microscopic picture of the carrier kinetics. These effects are especially significant when quantifying syntheses of bright emitters such as perovskite nanocrystals. These effects are also a general approach to simple steady-state measurements of the action of hot carrier kinetics.

Keywords:

quantum

dot,

nanocrystal,

CdSe,

perovskite,

hot

carriers,

electron-transfer, surface trapping, quantum yield, photoluminescence, excitation energy dependence, Vavilov

2


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Introduction Semiconductor nanocrystals have seen widespread use in various forms of lighting applications based upon their unique properties. Some of the wellestablished areas for nanocrystals include light generation for white light displays1-5, lasers6, and optical sensing7. The specific properties of nanocrystals that are unique are their mixing of properties of bulk semiconductors and molecules, under the guise of quantum confinement effects. These effects are now well known, with the simplest aspects being quantized level structure for absorbing states, followed by carrier cooling to a manifold of emissive states8-11.In general, one sees narrowband emission from an effectively single, low energy state. One generally aims to characterize the emission process in terms of a single metric such as the photoluminescence quantum yield (PL QY) as one might for molecular chromophores. Unlike molecular systems, however, semiconductor nanocrystals have properties that include both bulk-like as well as molecular phenomena, based upon the size of the nanocrystal. A well studied aspect of nanocrystals that is unique are hot carrier effects12-15. In such situations, energetically excited carriers may undergo new processes not possible for low energy excitations. Such processes include carrier multiplication16, photoluminescence blinking17, optical gain bandwidth control18, and hot carrier photochemistry19. The rules of Kasha and Vavilov are classic propensity rules of spectroscopy. Violations to these rules were initially discovered in molecules, but the effects are general. Kasha’s rule20 describes the generalization that one only observes emission 3



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from a single electronic state, due to rapid electronic relaxation. Vavilov’s rule21 describes the generalization that there is no excitation energy dependence to emission quantum yield, also due to kinetic constraints. Since semiconductor nanocrystals retain properties of molecules as well as bulk semiconductors, these propensity rules may also be violated in these systems. In the case of Kasha’s rule, one sees dual emission from certain nanocrystals equilibration of states

4, 11, 25, 26.

22-24due

either to slow carrier cooling or thermal

In the face of Vavilov’s rule, one has an excitation

energy dependence to the photoluminescence quantum yield – a quantum yield spectrum

QY(E).

Such

a

QY

spectrum

has

been

reported27-30,

without

phenomenological explanation or generalization. Early work31-32 revealed such an excitation energy dependence thereby resulting in a QY spectrum QY(E). Those early works were on poorly synthesized and characterized samples. Moreover, there was no explanation possible at that time. Since then, several groups have suggested the existence of a QY spectrum for NC: Chergui33; Loomis27; Kambhampati34; others28-30. While our prior works suggested a microscopic mechanism for such hot carrier effects, we were unsuccessful in observing those effects in CdSe NC. Other groups have seen these effects in CdSe, but without a theoretical basis31-33. Here, we report on the excitation energy dependence for the PL QY in model systems of CdSe NC and new systems of perovskite NC. We show that in a variety of CdSe model systems there is a clear excitation energy dependence to the PL QY in violation of the Vavilov rule of molecular systems. These effects can be significant, a 4


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factor of 2-3 variation across a bandwidth of ~1 eV. The results on perovskite nanocrystals show a similar response. But in the case of perovskites the impact is more significant. Specifically, we show fixed excitation energies can yield systematic errors in evaluating the quality of perovskite nanocrystals – redder NC will have more excess energy and will appear to have a smaller QY. These results are rationalized in terms of both phenomenological kinetic models as well as a microscopic electron-transfer theory. We show that a simple measurement of the PL QY can yield tremendous insight into hot carrier kinetics, resulting in a photo-action spectrum for carrier trapping.

Methods Lead(II) bromide (PbBr2, ≥98%), lead(II) iodide (PbI2, ≥99%), cesium carbonate (Cs2CO3, ≥99.9%), 1-octadecene (ODE, ≥70%), diisooctylphosphonic acid (DIOPA, ≥70%), oleylamine (OAm, ≥70%), cadmium oxide (CdO, ≥99%), trioctylphosphine oxide (TOPO, 99%), tetradecylphosphonic acid (TDPA, ≥99%), selenium(Se, ≥99.5%), trioctylphosphine (TOP, 97%) and methyl acetate (MeAc, 99%)were purchased from Sigma-Aldrich. Colloidal CdSe NCs were synthesized mainly following the work of Peng et. al35. CdO (0.0523 g), TOPO (3.94 g), and TDPA (0.220 g) were put into a three-necked flask and evacuated vacuum. The injection solution was made by dissolving 0.356 g Se in 2 g TOP in a glove box with argon filled, another vial containing 2 g TOP was prepared for rinsing the flask before reaction. The three-necked flask was heated to 5



120 ℃ until the reactants became liquid, the argon was then introduced. The flask was heated to 320 ℃ until the solution became colorless.The sides of the flask were thenrinsedwith TOP (2 g). After the temperature returned to ~320 ℃, the Se/TOP solution was quickly injected into the flask for reaction.The sizes of QDs are dependent on the reaction time,roughly40 s for the~2.8 nm NCs and 90 s for~3.8 nm NCs. The flask was then cooled down to about 70 ℃, the reaction mixture was transferred to a centrifuge vial, and MeAc was added until the mixture became totally cloudy.The vial was centrifuged at 10000 rpm for 10 min. At the end, the centrifuged NCs were thenredispersed in toluene. The Perovskite NCs were synthesized using a method modified from Protesescu et. al36 and Wang et. al37.The Cs-precursor was prepared in a three-neck flask with Cs2CO3 (0.6 mmol), DIOPA (1 mL) and ODE (5 mL). PbX2 (0.2 mmol), OAm (0.5 mL), DIOPA (0.5 mL) and 1-octadecene (5 mL) were added tothe reaction three-neck flask. Both mixtures were briefly degassed at room temperature. The temperature was increased to 150 ℃under argon until all solids weredissolved. The temperature was then decreased to 120 ℃. The flasks were then further degassed for 20 minutes under vacuum. Under argon, the temperature was increased to 140 ℃. 0.5 mL (0.1 mmol Cs) of the Cs-precursor was injected into the reaction flask, and the reaction was quickly quenched in an ice-water bath. 10-15 mL MeAc was added as an anti-solvent and the sample was centrifuged at 12000 rpm for 10 minutes. The PNCs were subsequently re-dispersed in toluene. A further centrifugation was done at 5000 rpm for 60s to remove large NCs from the sample. 6


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The absorption, PL and photoluminescence excitation (PLE) spectra were collected in 1 cm quartz cuvettes. The NC samples were dissolved in toluene and the solution was diluted(OD~0.05) to minimize self-absorption. Steady-state absorption measurements were performed on a Varian Cary 300 UV/Visible spectrophotometer. The PL and PLE spectra were measured on an Agilent CaryEclipsespectrofluorimeter.Jacobian correction was applied to spectra upon conversion from wavelength units to energy, following a previously described procedure38.

Results& Discussion The processes of absorption and PL, as predicted by the Kasha-Vavilov rules, are illustrated in Fig. 1(a).Electrons and holes are excited by absorbing a photon withhigher energy than the band edge. The entire population of hot carriers then relaxes to the lowest excited state. The carriers at the band edge then recombine non-radiatively througha process such as surface trapping or recombine radiativelyby emitting a photon (PL)38.Linear absorption, PL and PLEof CdSe NCs are shown in Fig. 1(b). The PL and PLE demonstrate expected behavior: the PL spectrum shows a ~50 meVstokes shift compared to absorption and the PLE spectrum shows line narrowing near the band edge from inhomogeneous broadening. Calculation of the QY requires an accurate representation of the number of photons absorbed and emitted at a given energy. In order to correct for previously reported anomalies at high energy, the spectra were corrected by Jacobian conversion38. The absorbance, A, is only proportional to the number of photons 7



absorbed when the A < 0.133. For the case of CdSe NCs, A increases with increasing energy and may exceed the range of A < 0.1. A is therefore converted to 1 - 𝑇 through the equivalence 1 - 𝑇 = 1 - 10 -𝐴. This gives a more accurate representation of the number of photons absorbed as a function of energy33. The linear spectra of several representative CdSe NC samples with different sizes and ligands are shown in Fig. 2 (a),(b),(c). The 1 - 𝑇 and PLE spectra of each sample follow the same qualitative trends seen in Fig. 1b. The relative quantum yield, QY(δE), is calculated from the linear spectra following equation (1). The excess energy,δE = E – EB, is defined as the difference between the spectral energy and the energy of the first absorption peak in each sample. QY(δE) spectra for the CdSe NCs are plotted in Fig. 2(d),(e),(f). PLE(δ𝐸)

QY(δ𝐸) = (1 ― 𝑇)(δ𝐸)

(1)

The QY spectra vary microscopically depending on the size and the nature of the ligand shell though all three spectra decrease as a function of excess energy. The overall trend of decreasing QY is consistent with previous results27. The QY measured at δE = 1.0 eV is 1.5x to 2x smaller than the QY at the band edge (δE = 0 eV). Here, the band edge refers to the lowest excited state, labeled X1 in Fig.4. Due to this energy dependence, absolute QY measurements made at the band edge (or any single energy) may not fully represent the QY of an NC system. The QY energy dependence seen in CdSe NCs may be a characteristic of nanocrystals in general28-30. The linear spectra and QY spectra of perovskite NCs are shown in Fig. 3(a), (c) for CsPbI3 and Fig. 3(b),(d) for CsPbBr3. The decreasing 8


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QY(δE) trends observed in perovskite NCs qualitatively resemble those seen in CdSe NCs. The effect is however dependent on the NC composition as the slope of the QY(δE)is steeper in CsPbI3 NCs than in CsPbBr3. The energy dependence seen in both CdSe and perovskite NCs contradicts Vavilov’s rule and is not explained by the model presented in Fig.(1), which assumes that 100% of hot carriers relax to the band edge before undergoing recombination. Hot carrier trapping could account for the QY spectra28-30. Some proportion of hot carriers could undergo trapping processes rather than relaxing directly to the band edge and the competition between hot carrier trapping and relaxation as a function of excess energy may define the relative QY spectra.

While steady state spectra fundamentally lack time resolution, they can still enable extraction of kinetics. These kinetics may be simulated with a kinetic model where hot carriers relax through the manifold of hot states to the band edge, or undergo surface trapping from hot states directly to the surface11. Fig.4(a) shows a phenomenological model with competing radiative and non-radiative pathways for hot carriers, where kr and knrrepresent radiative and non-radiative rates. Surface trapping may occur from any of the excited states, X1 – X5, while de-trapping only occurs from the surface to the band edge state, X1. The relative competition between these pathways defines the QY spectrum. The relative QY is calculated by dividing the number of excitons recombining through radiative pathways (Nradiative) by the total number of excitons recombining 9



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through both radiative and non-radiative pathways (Nradiative + Nnon-radiative), as in equation 2:

𝑄𝑌 =

∫𝑛1(𝑡)𝑑𝑡

𝑁𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑣𝑒 𝑁𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑣𝑒 +

𝑁𝑛𝑜𝑛 ― 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑣𝑒 = ∫𝑛 (𝑡) 𝑑𝑡 1

+ ∫𝑛𝑠(𝑡)𝑑𝑡

(2)

Here, n1 is the population in state X1 and ns is the population in state Xs and it is assumed that the radiative and non-radiative pathways decay with the same rate constant. The energy structure is governed by a system of time dependent differential equations taking into account the transfer of charges in and out of every state. These equations are provided in the supporting information. The populations n1 and ns are found by solving the system of equations. Thus, Nradiativeis calculated by integrating n1 over time and Nnon-radiative is calculated by integrating ns over time. The energy dependence is found by varying the initial values in the ODEs to reflect excitation into different excited states. If the trapping rate increases with excess energy, as in Fig. 5(a), the manifold of states will equilibrate on a different time scale depending on the initial excited state. Fig. 5(b) shows population dynamics of the X1 state and the Xs state over time. Two situations are presented to show that the dynamics change considerably if the initial excited state is changed. (i) If the sample is directly excited into the X1 state, then no hot carrier trapping occurs and the Xs state is populated on a slow timescale. (ii) If the sample is initially excited into the X3 state, then hot carriers quickly trap directly to Xs, decreasing the X1 population at early time. According to equation 2, the QY is proportional to the population of the X1 state. Hot carrier trapping decreases the X1 population and therefore decreases the QY. 10


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Regardless of the initial excitation energy, the X1 and Xs states reach the same equilibrium value around 4 ns (shown by the red and blue lines converging in Fig. 5(b)). This long equilibration time between the core and surface states would give rise to a multi-exponential photoluminescence decay, as typically seen in nanoscrytals27. Although hot carrier processes occur on a sub-picosecond timescale, they may affect the nanosecond timescale equilibration between core and surface states. The shape and magnitude of the QY spectrum is defined by competition between hot carrier relaxation and hot carrier trapping. Fig. 5(c) shows QY spectra derived from the population dynamics in Fig. 5(b) overlaid with the measured QY spectrum for CdSe. If relaxation occurs on a much faster time scale than trapping (kTkR), the excited states become quickly depopulated and few carriers relax to the band edge. This results in a steep drop off in relative QY as excess energy increases. The spectral shape seen in CdSe is formed when trapping and relaxation are on a competitive time scale. If hot carriers trap to the surface then immediately de-trap back to the X1 state, then hot carrier trapping will not significantly alter QY. Fig. 5(d) shows the effect of changing the de-trapping rate, kDT, between the X1 and Xs states. When de-trapping occurs an order of magnitude faster than the PL decay, equilibrium is reached quickly and the effect of hot carrier trapping is minimized. Conversely, a long de-trapping time increases the QY drop-off. Therefore, the system must be out of equilibrium on a 11



time scale concurrent with PL in order to significantly affect the PL QY.

In our previous work we used a steady state model based on Marcus-Jortner electron transfer theory to explain the temperature dependence of the QY34. The modeling showed that hot carrier trapping would occur but kDTwas large enough at room temperature to nullify the effect, as in Fig. 5(d). It was determined that the QY developed energy dependence as the temperature decreased as surface trapped carriers would not have enough thermal energy to de-trap. However, this was a steady state model that did not take into account non-equilibrium dynamics. The phenomenological model assumes that trapping rates increase with excess energy, but Marcus-Jortner theory can provide a functional form to the trapping rate as a function of excess energy33. Fig.4(b)presents a microscopic model following semi-classical Marcus-Jortner electron transfer theory. The system of differential equations governing the system is identical to the phenomenological model, though the surface trapping rates 𝑘Tfollow a functional form determined by equation 3:

𝑘T(δ𝐸) =

(

2𝜋𝐻𝑟𝑝

𝜋

ħ

ħ2𝜆𝑘𝐵𝑇

)

1/2

𝑒 -𝑆 ∑

2 𝑆𝑛 -(Δ𝐺0 + δE + + 𝑛 𝜆 ħ𝜔) /4𝜆𝑘𝐵𝑇(3) 𝑒 𝑛 𝑛!

In equation 3, 𝐻𝑟𝑝 represents the electron exchange matrix element, S represents the Huang-Rhys factor, 𝜆 defines the coupling between core and surface states,𝜔 is the mean phonon frequency and Δ𝐺0 is the energy difference between the first core state and the surface state.Fig. 6(a) shows the trapping rate,𝑘T, resulting from equation 3 as a function of excess energy,δ𝐸.The rest of the variables in the equationare kept constant. As the excess energy increases, the trapping rate becomes faster as predicted 12


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by the phenomenological model. The spacing between the X1 and Xsstates is defined by Δ𝐺0, where Δ𝐺0= 5 meV would represent a shallow surface trap and Δ𝐺0=100 meV would represent a relatively deep surface trap. Fig. 6(b)shows the resulting QY spectra for these trapping rates. Marcus-Jortner theory confirms that the QY decreases with excess energy and the slope of the spectrum increases for deeper surface traps. The dependence of QY on Δ𝐺0 is shown in detail in Fig. 6(c). In this case, the drop off in QY from δE=0 eV to δE=0.8 eV is shown by the ratio QY(δE=0 eV)/QY(δE=0.8 eV). Thisdrop off increases sharply as Δ𝐺0 grows and the surface trap becomes deeper.

This effect is closely tied to the de-trapping rate, 𝑘DT, defined

in the microscopic model by equation (4): 0

(4)

𝑘DT = 𝑘T𝑒Δ𝐺 /𝑘𝑏𝑇

The dependence of 𝑘DT on Δ𝐺0, also plotted in Fig. 6(c), follows the same trend as the QY ratio. When Δ𝐺0 is small, the de-trapping barrier is shallow and X1 and Xs quickly equilibrate so the effect on QY is small. When Δ𝐺0 is large, the de-trapping rate is slow so the effect on the QY is more significant. Given that the spectra in figures 2 and 3 show relative QY ratios of 1.5 to 3, this leads one to believe that Δ𝐺0 is relatively shallow, likely less than 100 meV. Previous work34 has shown that the QY spectrum becomes steeper at lower temperatures, since kDT decreases as a function of temperature. This is consistent with the current modelling, which shows that the relative QY ratio is strongly defined by the de-trapping rate. 13



There is a wealth of atomistic level theory describing surface states and defects in nanocrystals39, 40 that present a variety of trapping processes occurring on time scales from picoseconds to nanoseconds. Experimental data is required to validate these theories and offer further input. Our modeling is theoretical and not system specificand is therefore applicable to many nanocrystal structures. We hope that these results and modeling will enable advances in new atomistic and ab initio theories of trapping processes in realistic nanocrystals.

Action spectra, defined as the efficiency of a physical process as a function of the energy of incident light, have been used to characterize many photochemical processes in materials such as photocatalysis41, photocurrents42and internal quantum efficiency43.An action spectrum may therefore be defined to quantify the amount of hot carrier trapping in a nanocrystal sample as a function of excess energy. Fig. 7a shows the hot carrier trapping action spectrum of CsPbBr3, defined asS(𝛿𝐸) = |QY(𝛿𝐸) ― QY(𝛿𝐸 = 0)|. The spectrum is normalized to S(δE) = 0 at δE=0, to reflect the lack of hot carrier trapping at δE=0. The action spectrum increases with excess energy, reflecting the number of carriers relaxing non-radiatively due to hot carrier trapping. Action spectra simulated with the phenomenological model are plotted in Fig. 7(a). Increasing the ratio of trapping, kT, to relaxation, kR, increases the slope of the action spectrum. This reflects the number of hot carriers trapping to the surface versus relaxing directly to the band edge. The simulation approximately recreates the 14


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behavior of the CsPbBr3 action spectrum when kT/kR = 0.4, though the simulation deviates from the experiment at high energy. Allowing the ratio kT/kR to vary as energy increases allows the simulation to recreate the behavior seen in the CsPbBr3 action spectrum at high excess energy. Fig. 7(b) shows that ifkT/kR decreases at as energy increases, then the simulated action spectrum levels out and follows the experimental spectra. However, if the ratio kT/kRincreases with excess energy, the magnitude of the action spectrum increases due to competitive surface trapping. Therefore, by isolating hot carrier effects, action spectra enable one to study ultrafast hot carrier processes using steady state spectroscopy techniques.

Conclusion In summary, we find that PL QY decreases as excitation energy increases in CdSe and perovskite NCs. The results are explained by both a phenomenological model and a Marcus-Jortner electron transfer model. The decreasing PL QY is caused by the increasing hot carrier trapping rate at higher energy states. The competition between hot carrier trapping and cooling processes influences the magnitude of the QY energydependence.The depth of surface traps (Δ𝐺0) have a significant influence on surface trapping rates and QY spectra, and the effect of hot carrier trapping can be well explained by action spectra. Local variations between different samples may reveal

further

information

about

the

nature

of

hot

carrier

trapping

processes.Ultimately, this work provides further insight on complex hot carrier 15



processes with simple experimental methods.

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Figure 1. Overview of the excitation energy dependence to photoluminescence. (a) Schematic illustration of photon absorption and emission, involving different electronic states. The kinetic processes are carrier cooling, trapping, and radiative recombination. (b) Linear spectroscopy of a representative CdSe NC. Shown are the spectra for linear absorption, 1-T, PL and PLE.

17



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Figure 2.Linear spectra of CdSe NC reveal PL quantum yield spectra, QY(E). The top row shows the linear spectra for three different sizes and passivations, (a-c). The bottom row shows the PL QY spectra, QY(E), for the same samples, (d-f). Normalizing the PL QY spectra at δE = 1.0 eV emphasizes that the relative QY can differ by as much as a factor of 2 near the band edge (δE = 0 eV). The samples are: CdSe/OA,

X1=2.30

eV,

D=2.85nm;

CdSe/TDPA,

nm;CdSe/TDPA, X1=2.14 eV, D=3.82 nm.

18


X1=2.31

eV,

D=2.80

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Figure 3. Linear spectra of Perovskite NC reveal PL quantum yield spectra, QY(E). The top row shows the linear spectra for(a) CsPbI3 and (b) CsPbBr3. The bottom row shows the PL QY spectra, QY(E) for the same samples (c) (d).

19



Figure 4.Schematic illustrations of minimal models to rationalize excitation energy dependence. (a) A phenomenological kinetic model. Energy dependence arises due to competition between carrier cooling and trapping. (b) A microscopic model based upon semi-classical electron-transfer theory. The microscopic model rationalizes the phenomenological model. The term Δ𝐺0represents the difference in free energy between the minimum of the core (X1) and surface (XS) states and λ denotes the coupling between the core states and the surface.

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Figure 5.The phenomenological model reveals the kinetic parameters which result in the QY spectra. (a)Trapping, kT, and relaxation, kR, rates as a function of excess energy. (b) Population kinetics of surface (Xs) and core (X1) states. The X1population kinetics over the first 5 nanoseconds depend on the excitation state. By 5 nanoseconds equilibrium is reached and the population is independent of excitation state. (c) Competition kinetics between hot carrier trapping and relaxation. If the hot carrier trapping occurs on a faster time scale than the hot carrier trapping, then the slope on the spectrum is steeper. (d) QY spectra for different de-trapping rates, kDT. Increasing kDT results in a weaker energy dependence as the hot carriers trap to the surface then quickly detrap. Decreasing kDT results in a stronger energy dependence as the system takes longer to equilibrate.

21



Figure 6.The microscopic model rationalizes the QY spectra in terms of thermodynamic free energies. (a) The trapping rates derived from the Marcus-Jortner rate equation, for a variety of ΔG0 values. (b) Simulated QY spectra derived from trapping rates in panel (a). (c) Theratio between the QY at δE = 0 eV and δE = 0.8 eV as a function of ΔG0. As ΔG0 increases, the QY ratio grows exponentially. This is explained by the de-trapping time, 1/kDT, which grows proportionately.

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Figure 7.The QY spectra reflect an action spectrum, S(E) for surface trapping. The action is hot carrier surface trapping, as a function of excess energy. (a) Action spectrum of CsPbBr3, overlaid with simulated action spectra created with a phenomenological model. The ratio of trapping to relaxation, kT/kR, is set to a constant and defines the slope of the action spectra. (b) Phenomenological action spectra simulated by letting kT/kR remain constant, increase or decrease with excess energy. If kT/kR decreases as energy increases, then the experimental data may be qualitatively recreated.

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Supporting information Sample information and details of kinetic model calculations. Table S1. Equation S1.

Acknowledgement We acknowledge the financial support of NSERC. LB acknowledges financial support from China Scholarship Council (CSC number: 201706120202).

References: 1. Lee, K.; Han, C.; Kang, H.; Ko, H.; Lee, C.; Lee, J.; Myoung, N.; Yim, S.; Yang, H. Highly Efficient, Color-ReproducibleFull-Color Electroluminescent DevicesBased on Red/Green/Blue QuantumDot-Mixed Multilayer.ACS Nano2015, 9, 10941-10949. 2. Supran, G. J.; Shirasaki, Y.; Song, K. W.; Caruge, J.; Kazlas, P. T.; Coe-Sullivan, S.; Andrew, T. L.; Bawendi, M. G.; Bulović, V. QLEDs for Displays and Solid-State Lighting.MRS Bulletin2013, 38, 703-711. 3. Jang, E.; Jun, S.; Jang, H.; Lim, J.; Kim, B.; Kim, Y. White-Light-Emitting Diodes with Quantum Dot Color Converters for Display Backlights.Adv. Mater.2010, 22, 3076-3080. 4. Jethi, L.; Krause, M. M.; Kambhampati, P. Toward RatiometricNanothermometry via Intrinsic Dual Emissionfrom Semiconductor Nanocrystals.J.Phys. Chem. Lett.2015, 6, 718-721. 5. Shirasaki, Y.; Supran, G. J.; Bawendi, M. G.; Bulović, V. Emergence of Colloidal Quantum-Dot Light-Emitting Technologies.Nat. Photonics2013, 7, 13-23. 6. Diroll, B. T.; Talapin, D. V.; Schaller, R. D. Violet-to-Blue Gain and Lasing from Colloidal CdS Nanoplatelets: Low-Threshold Stimulated Emission Despite Low PhotoluminescenceQuantum Yield.ACS Photonics2017, 4, 576-583. 7. Wang, X. D.; Wolfbeis, O. S.; Meier, R. J. Luminescent Probes and Sensors for Temperature.Chem. Soc. Rev.2013, 42, 7834-7869. 8. Klimov, V. I. Optical Nonlinearities and Ultrafast Carrier Dynamics in Semiconductor Nanocrystals.J.Phys. Chem. B2000, 104, 6112-6123. 9. Klimov, V. I. Spectral and Dynamical Properties of Multiexcitons in Semiconductor Nanocrystals.Annu. Rev. Phys. Chem.2007, 58, 635-673. 10. Kambhampati, P. Unraveling the Structure and Dynamics of Excitons in Semiconductor Quantum Dots.Accounts Chem. Res.2011, 44, 1-13. 11. Kambhampati,

P.

Hot

Exciton

Relaxation

Dynamics

in

Semiconductor

Quantum

Dots:Radiationless Transitions on the Nanoscale.J. Phys. Chem. C2011, 115, 22089 - 22109. 12. Tyagi, P.; Kambhampati, P. False Multiple Exciton Recombination and Multiple Exciton GenerationSignals in Semiconductor Quantum Dots Arise from Surface Charge Trapping.J. Chem. Phys.2011, 134, 094706. 13. Sewall, S. L.; Cooney, R. R.; Anderson, K. E. H.; Dias, E. A.; Sagar, D. M.; Kambhampati, P. State-Resolved Studies of Biexcitons and Surface Trapping Dynamics in Semiconductor Quantum 24


Page 25 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Dots.J. Chem. Phys.2008, 129, 084701. 14. Chung, H.; Choi, H.; Kim, D.; Jeong, S.; Kim, J. Size Dependence of Excitation-Energy-Related Surface TrappingDynamics in PbS Quantum Dots.J.Phys. Chem. C2015, 119, 7517-7524. 15. Saari, J. I.; Dias, E. A.; Reifsnyder, D.; Krause, M. M.; Walsh, B. R.; Murray, C. B.; Kambhampati, P. Ultrafast Electron Trapping at the Surface of SemiconductorNanocrystals: Excitonic and Biexcitonic Processes.J. Phys. Chem. B2012, 117, 4412-4421. 16. Schaller, R. D.; Klimov, V. I.; Agranovich, V. M. High-Efficiency Carrier Multiplicationthrough Direct Photogeneration of Multi-Excitons via Virtual Single-Exciton States.Nat.Phys.2005, 1, 189 194. 17. Galland, C.; Ghosh, Y.; Steinbruck, A.; Sykora, M.; Hollingsworth, J. A.; Klimov, V. I.; Htoon, H. Two Types of Luminescence Blinking Revealed bySpectroelectrochemistry of Single Quantum Dots.Nature2011, 479, 203-207. 18. Cooney, R. R.; Sewall, S. L.; Sagar, D. M.; Kambhampati, P. Gain Control in Semiconductor Quantum Dots via State-Resolved Optical Pumping. Phys. Rev. Lett.2009, 102, 127404. 19. Wu, K.; Lim, J.; Klimov, V. I. Superposition Principle in AugerRecombination of Charged and NeutralMulticarrier States in Semiconductor QuantumDots.ACS Nano2017, 11, 8437-8447. 20. Kasha, M. Characterizationof Electronic Transitionsin Complex Molecules.Discuss. Faraday soc.1950,14-19. 21. Timmerman, D.; Valenta, J.; Dohnalová, K.; de Boer, W. D. A. M.; Gregorkiewicz, T. Step-Like Enhancement of Luminescence QuantumYield of Silicon Nanocrystals.Nat.Nanotechnol.2011, 6, 710-713. 22. Battaglia, D.; Blackman, B.; Peng, X. Coupled and Decoupled Dual Quantum Systems in OneSemiconductor Nanocrystal.J. Am. Chem. Soc.2005, 127, 10889-10897. 23. Dias, E. A.; Sewall, S. L.; Kambhampati, P. Light Harvesting and Carrier Transport in Core/Barrier/Shell Semiconductor Nanocrystals.J. Phys. Chem. C2007, 111, 708-713. 24. Choi, C. L.; Li, H.; Olson, A. C.; Jain, P. K.; Sivasankar, S.; Alivisatos, A. P.Spatially Indirect Emission in a Luminescent Nanocrystal Molecule.Nano Lett.2011, 11, 2358-2362. 25. Krause, M. M.; Kambhampati, P. Linking Surface Chemistry to Optical Properties of Semiconductor Nanocrystals.Phys. Chem. Chem. Phys.2015, 17, 18882-18894. 26. Vlaskin, V. A.; Janssen, N.; van Rijssel, J.; Beaulac, R.; Gamelin, D. R. Tunable Dual Emission in DopedSemiconductor Nanocrystals.Nano Lett.2010, 10, 3670-3674. 27. Hoy, J.; Morrison, P. J.; Steinberg, L. K.; Buhro, W. E.; Loomis, R. A. Excitation Energy Dependence of the Photoluminescence QuantumYields of Core and Core/Shell Quantum Dots.J. Phys. Chem. Lett.2013, 4, 2053-2060. 28. Geißler, D.; Würth, C.; Wolter, C.; Weller, H.; Resch-Genger, U. Excitation Wavelength Dependence of the Photoluminescence Quantum Yield and Decay Behavior of CdSe/CdSQuantum Dot/Quantum Rodswith Different Aspect Ratios.Phys. Chem. Chem. Phys.2017, 19, 12509-12516. 29. De, C. K.; Routh, T.; Roy, D.; Mandal, S.; Mandal, P. K. Highly Photoluminescent InP Based Core

Alloy

Shell

QDs

from

AirStable

Precursors:

Excitation

Wavelength

DependentPhotoluminescence Quantum Yield, Photoluminescence DecayDynamics, and Single Particle Blinking Dynamics.J. Phys. Chem. C2017, 122, 964-973. 30. Martynenko, I. V.; Baimuratov, A. S.; Osipova, V. A.; Kuznetsova, V. A.; Purcell-Milton, F.; Rukhlenko, I. D.; Fedorov, A. V.; Gun Ko, Y. K.; Resch-Genger, U.; Baranov, A. V. Excitation Energy Dependence of the Photoluminescence QuantumYield of Core/Shell CdSe/CdS Quantum Dots and 25



Correlation withCircular Dichroism.Chem. Mater.2018, 30, 465-471. 31. Rumbles, G.; Selmarten, D. C.; Ellingson, R. J.; Blackburn, J. L.; Yu, P.; Smith, B. B.; Mićić, O. I.; Nozik, A. J. J. Photoch. Photobio. A2001, 142, 187-195. 32. Hoheisel, W.; Colvin, V. L.; Johnson, C. S.; Alivisatos, A. P. Threshold for quasicontinuum absorption and reduced luminescence efficiency in CdSe nanocrystals. J. Chem. Phys.1994, 101, 8455-8460. 33. Tonti, D.; van Mourik, F.; Chergui, M. On the Excitation WavelengthDependence of the Luminescence Yieldof Colloidal CdSe Quantum Dots.Nano Lett.2004, 4, 2483-2487. 34. Mooney, J.; Krause, M. M.; Kambhampati, P. Connecting the Dots: The Kinetics and Thermodynamics of Hot, Cold,and Surface-Trapped Excitons in Semiconductor Nanocrystals. J. Phys. Chem. C2014, 118, 7730-7739. 35. Peng, Z. A.; Peng, X. Formation of High-Quality CdTe, CdSe, and CdSNanocrystals Using CdO as Precursor.J. Am. Chem. Soc.2001, 123, 183-184. 36. Protesescu, L.; Yakunin, S.; Bodnarchuk, M. I.; Krieg, F.; Caputo, R.; Hendon, C. H.; Yang, R. X.; Walsh, A.; Kovalenko, M. V. Nanocrystals of Cesium Lead Halide Perovskites (CsPbX3, X = Cl, Br,and I): Novel Optoelectronic Materials Showing Bright Emission withWide Color Gamut.Nano Lett.2015, 15, 3692-3696. 37. Chujie Wang, A. S. R. C. Stabilizing the Cubic Perovskite Phase of CsPbI3 Nanocrystals by Using an Alkyl PhosphinicAcid.Chem.Commun.2017, 53, 232-235. 38. Mooney, J.; Kambhampati, P. Get the Basics Right: Jacobian Conversion of Wavelength and EnergyScales for Quantitative Analysis of Emission Spectra.J. Phys. Chem. Lett.2013,4, 3316-3318. 39. Califano, M.; Gomez-Campos, F. M. Universal Trapping Mechanism in Semiconductor Nanocrystals.Nano Lett.2013, 13, 2047-2052. 40. Jain, A.; Voznyy, O.; Korkusinski, M.; Hawrylak, P.; Sargent, E. H. Ultrafast Carrier Trapping in Thick-Shell Colloidal Quantum Dots.J. Phys. Chem. Lett.2017, 8, 3179-3184. 41. Lee, S. K.; Mills, A.; O'Rourke, C. Action Spectra in Semiconductor Photocatalysis.Chem. Soc. Rev.2017, 46, 4877-4894. 42. Harrison, M. G.; Grüner, J.; Spencer, G. C. W. Analysis of the Photocurrent Action Spectra of MEH-PPV Polymer Photodiodes.Phys. Rev. B1997, 55, 7831 - 7849. 43. Kojima, A.; Teshima, K.; Shirai, Y.; Miyasaka, T. Organometal Halide Perovskites as Visible-Light Sensitizers for PhotovoltaicCells.J. Am. Chem. Soc.2009, 131, 6050-1.

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Photophysical Action Spectra of Emission from Semiconductor

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