A Strategy for Exploiting Self-Trapped Excitons in Semiconductor

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A Strategy for Exploiting Self-Trapped Excitons in Semiconductor Nanocrystals for White Light Generation Timothy G. Mack, Lakshay Jethi, and Patanjali Kambhampati ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.9b00212 • Publication Date (Web): 05 Apr 2019 Downloaded from http://pubs.acs.org on April 7, 2019

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A Strategy for Exploiting Self-Trapped Excitons in Semiconductor Nanocrystals for White Light Generation

Timothy G. Mack, Lakshay Jethi, Patanjali Kambhampati* Department of Chemistry, McGill University, Montreal, Quebec, H3A 0B8, Canada

Corresponding Author: *[email protected]

Abstract: 1 ACS Paragon Plus Environment

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Semiconductor nanocrystals have seen much use for their narrow emission linewidths for display and lighting applications. Recent progress on semiconductor nanocrystals has suggested the possibility of exploiting self-trapped excitons to create white light emitting materials. Specifically, charge carrier trapping at the surface or interface gives rise to broadened and redshifted bands that can support generation of white light. Most reported materials based on emission from self-trapped states suffer from poor intrinsic luminescent quantum yields at room temperature and have not considered the temperature dependence of the chromaticity. Here we show that such results stem from fundamental quantum considerations which can be easily visualized in terms of a simple, albeit microscopic electron transfer theory. We show the temperature dependent chromaticity trajectories and how one can design function. We rationalize the strong temperature dependence of the photoluminescence quantum yield. Our results identify potential paths towards tailoring surface structure of semiconductor nanocrystals for rational design of white light emitters. Specific implications for regarding efficiency limitations of the photoluminescence quantum yield for white light emitting CdSe nanocrystals are discussed.

KEYWORDS Photoluminescence, CdSe Nanocrystals, Chromaticity, Quantum Yield, ExcitonPhonon coupling, Perovskite

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Introduction: High-efficiency white light generation is of enormous contemporary interest, given that a large fraction of our global energy is used for lighting.1 It was recently estimated that lighting accounted for 7% of US electricity consumption.2 Currently, most white light emitting diodes (WLED) consist of InGaN blue dies coated by a yttrium aluminum garnet (YAG) phosphor such as YAG:Ce3+. These phosphors can possess intrinsic quantum yields exceeding 90%.3 The advantage of using such phosphors lies predominantly in their robustness and high temperature stability.4-5 Nevertheless, significant drawbacks remain. The high intrinsic quantum yields do not factor in losses due to scattering, since the phosphors consist of micron sized particles.6 There is also concern over the supply of YAG phosphor dopants, which consist of rare earth elements whose long-term economic accessibility is questionable.7 Also, conventional white light LEDs generated in this manner are also facing increased scrutiny as studies have reported adverse human health effects regarding blue light exposure.8-9 Recent articles have explored the ideal of turning to new white light emitting materials as a possible method to overcome these current technological limitations.10 White light materials consisting of coexistence of free and self-trapped excitons11-12 include bulk 2D lead halide ABX4 perovskites13-14, and II-VI semiconductor nanocrystals (NCs).10, 14-16 These materials are highly-scalable and cheap to synthesize, and thus provide a promising new path. There are two important figures of merit that should be considered for white light materials. The first is figure of merit whether the perceived spectral output of the material is suitably “white”, which can be quantified through standardized chromaticity coordinates, and the second figure of merit is the intrinsic quantum yield of the material. Often, these figures of merit are only reported at room temperature, and the reported intrinsic quantum yields of most 3 ACS Paragon Plus Environment

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reported materials are currently too low to be of any practical use. Although, recently the perovskite material Cs2(Ag 0.60Na0.40)InCl6 was notably reported to possess intrinsic quantum yields of approximately 86%.17 This point will be readdressed later in the manuscript. In most realizations of WLED using nanostructures, one uses the narrowband emission from the cores, along with suitable multiplexing, to produce the appearance of white light. In contrast, several recent works have shown that broadband white light may be generated from a single nanoscale emitter10, 18-25. While most work has focused on the NCs themselves, there has been recent implementation of WLED using this scheme of white light from trapped excitons. Here, we provide detailed theoretical modeling to advance the rational design of nanoscale materials which exploit exciton self-trapping as a path towards white light emitters. We model the evolution of the International Commission on Illumination (CIE) chromaticity coordinates as a function of temperature for CdSe NCs whose photoluminescence consists of emission from both bulk and self-trapped excitonic states. Brief descriptions of CIE coordinates and CIE plots are provided in the S2 of the Supporting Information. Starting with a microscopic electron transfer theory, it is possible to qualitatively model changes to the chromaticity as a function of a few observables or material parameters. While often chromaticity coordinates are reported in papers as an additional measure of the suitability of the white light material at hand, the temperature dependence is not readily discussed. The challenges in employing self-trapped excitonic photoluminescence for the development of white light materials can be better understood through a study of the microscopic origins of the emission. Finally, the question of intrinsic quantum efficiency is also briefly considered. Thus far, these candidate materials have possessed low quantum yields at room temperature, and in general the intrinsic quantum yield has only become appreciable at cryogenic temperatures (~80K).10, 13, 26-27 Based on prior 4 ACS Paragon Plus Environment

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literature, we suggest that low quantum yield is a consequence of strong electron phonon coupling and can be explained within the context of the configuration coordinate representation. Methods: The experimental datasets in this work are adapted from our previously published work.15 These calculations were previously described in our prior works, in terms of the both lineshape16 and population analysis.15, 28 Briefly, the electronic system is described in terms of displaced harmonic oscillators. In a minimal picture, one has a ground state, a band edge exciton, and a surface state which is also a self-trapped exciton. In terms of electron transfer theory that is used here, the band edge exciton is considered the reactant state and the self-trapped surface exciton is considered the product state. The band edge exciton is weakly coupled to optical phonons whereas the trapped exciton is strongly coupled. In this first-order estimate, only the coupling to a single optical phonon is considered. The strength of the coupling is verified by experiments and is consistent with the degree of polarization of the exciton, which couples to polar optical phonons. 10, 15-16, 19, 29-32 Spectral lineshapes in this displaced harmonic oscillator picture can be simulated by calculating the Franck-Condon probabilities (Fnm) in terms of the equation33 2

∗ ―𝑆 𝑛 ― 𝑚 𝐹𝑚 𝑛 = |∫𝜓𝑚 𝜓𝑛𝑑𝑄| = 𝑒 𝑆

( )(𝐿𝑛𝑚― 𝑚(𝑆))2 𝑚! 𝑛!

(1)

Where S is the Huang-Rhys34 factor, and L(S) are the associated Laguerre polynomials. The Franck-Condon probabilities obtained in equation 1 is then multiplied by Boltzmann occupancy factors. The thermally averaged Franck-Condon probabilities are then broadened by a Gaussian function. Semiclassical Marcus-Jortner theory is usually written in terms of the expression35


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𝑘𝐶𝑇 = 𝐴

(

𝜋 2

ℏ 𝜆𝑚𝑘𝑏𝑇

1/2

)

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―(∆𝐺 + 𝜆𝑚 + 𝑛ℏ𝜔)2

𝑆

𝑛

𝑒 ―𝑆 × ∑𝑛𝑛!𝑒

4𝜆𝑚𝑘 𝑇 𝑏

(2)

Where A is a rate prefactor corresponding to the electron exchange matrix element between core and surface states, S is the Huang-Rhys factor, λm is the medium reorganization energy, ω is the energy of the longitudinal optical phonon (~208 cm-1 in CdSe), and ∆G is the free energy difference between core and surface states. Further details of the calculation have been described in prior publications by our group.28 Based upon the simulated spectra, one can compute CIE coordinates. We use the 1931 CIE color space, with associated color matching functions (CMFs) as shown in the Supporting Information. While we recognize that more advanced color appearance formalisms have been developed over the past few decades36, the 1931 CIE color space is the simplest formalism that has been commonly employed within the literature of white-light emitting materials.10, 13, 15, 23 It should be further stressed that one cannot accurately infer the impact of changes in human color perception simply based on differences in 1931 CIE chromaticity (x,y) coordinates.36 We also note that CIE integrals are done in units of wavelength (nm), whereas lineshape calculations are performed in units of energy (eV). Proper conversions of the intensities going from energy to wavelength axes are performed as described elsewhere.37-38

Results and Discussion: The photoluminescence spectrum of semiconductor nanocrystals is determined by several variables including composition, ligand passivation, the size and morphology of the nanocrystal, crystal structure, excitation energy and temperature. Here we focus specifically on the size and 6 ACS Paragon Plus Environment

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temperature effects upon the photoluminescence spectrum in spherical wurtzite CdSe NCs capped by alkylphosphonic acids. These experimental variables are inputs to effects which contribute to the overall photoluminescence spectrum. Keeping in mind the danger of overparameterizing the model, we have attempted to minimize the number of effects to be ones that are well documented. The major factors which contribute to the overall emission color are the relative emissive intensities of free and self-trapped excitons dictated by energetic fine structure as well radiative and non-radiative kinetics, lineshape broadening /narrowing dictated by thermal occupation (statistical thermodynamics), ensemble sample inhomogeneity and bandgap-shifts due to temperature dependent lattice expansion/contraction. Moreover, unique to solid samples, the issue of background excitation scatter as a spectral artifact contributing to error in the calculated CIE coordinates is also considered (Figure S3, Supporting Information). The term “self-trapped exciton” has been defined in previous manuscripts, in terms of related terms such as large and small polarons.11-12 The definition of the self-trapped exciton is related to that of a polaron, which is a carrier (electron/hole) plus an associated strain and polarization they cause upon lattice. Small polarons are defined when the carrier causes a lattice distortion so large as to immobilize the carrier. A bound electron-hole pair involving such a carrier is a self-trapped exciton. Figure 1 shows a typical photoluminescence spectrum of a dual emitting white light CdSe NC (Radius=1.1nm) along with the corresponding CIE (x,y) coordinates on the chromaticity plane. There are two salient features present, which include a narrow peak at approximately 450 nm, and a broad feature centered at approximately 570 nm. These features are referred to as the core and surface emission, or alternatively the free and self-trapped excitonic emission respectively. The free exciton corresponds to the narrow emissive feature, whereas the self7 ACS Paragon Plus Environment

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trapped exciton corresponds to the broad feature. Panel (a) shows the spectral output of the NC along with core and surface fitted components. Panel (b) shows the three CIE components as separated in the panel above. The spectral output is analogous to the current approach to creating wLEDs, in terms of a narrow blue component along with a broad yellow one. White light emission therefore must include a spectral distribution that spans emission from the blue to the red. Unlike our previous publications, the photoluminescence data are reported here in terms of intensity vs wavelength, as the CIE coordinates are defined in terms of the integral in wavelength.10, 15-16, 28 Figure 2 shows representative data of three CdSe NCs with radii of 1.66 nm, 1.13 nm and 0.89 in panels (a), (b), and (c) respectively embedded in polystyrene films in the temperature range of 90K-295 K. The three sizes show remarkably different emission profiles. There are two main features of interest in the emission profile of these NCs. At low wavelengths, there is a narrow feature which is the commonly studied free exciton. The broader redshifted emissive feature is attributed to a self-trapped, or surface exciton, which is broadened due to strong exciton phonon coupling as we have described elsewhere. The largest dot (panel (a)) does not have appreciable surface emission at temperatures between 90 K -295 K, whereas the surface emission increases monotonically as a function of temperature for the smaller radii samples in panels (b) and (c). The results of each PL trace as a function of temperature is represented in terms of the CIE coordinates in panel (d). In order to gain more insight into the observed behavior of the chromaticity trajectories shown above, we calculated the CIE trajectories using our previously developed microscopic model.16, 28 Figure 3 illustrates the overall flow of the components, and we briefly summarize it here. Further details are provided in the Methods section and Supporting information. First, 8 ACS Paragon Plus Environment

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equation (1) is employed calculate the thermally averaged Franck Codon factors. From this, the linewidth and energy mesh are selected. Secondary corrections come in the form of lattice contraction as a function of temperature, and the relative intensity ratios can be calculated either from semiclassical Marcus Jortner theory if ∆G, A and radiative rates are estimated. In the simple two state model, Marcus Jortner theory rate theory is used to calculate the relative populations of core and surface, denoted as AC and AS. AT refers to the sum of the populations, AC + AS. These populations can be experimentally determined at a given temperature by the ratio of the integrated photoluminescence intensities of fitted core and surface peaks. Alternatively, instead of employing Marcus-Jortner theory, a fitted polynomial to experimentally determined ratios of AS and AT as a function of temperature can also be employed. With the spectrum calculated in the energy/frequency domain, the transformation can be made to wavelength domain, and then the CIE chromaticity integrals can be performed. Figure 4 show the influence of microscopic parameters of ∆G ((a) and (b)) and ∆S ((c) and (d)) on the chromaticity coordinate trajectories in the range of 100 K-300K. The calculations held all other parameters fixed while sweeping the single parameter in order to study its effect. The impact of increasing the value of ∆G favors much higher surface emission, which in turn shifts the chromaticity to the red. The surface to total ratio, AS/AT, lowers as the magnitude of the Huang-Rhys factor increases. The displacement ∆ between the core and surface parabolas is directly related to the value of the Huang-Rhys parameter. In addition, since the curvature of the core and surface parabolas is assumed to be the same, the net effect is to increase the barrier height between the core and surface states. Figure 5 (a) shows the size dependence chromaticity coordinates of a set of CdSe NCs of radii 0.89 nm to 1.66 nm at 300K. The chromaticity coordinates of the overall emission (circles) 9 ACS Paragon Plus Environment

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along with the chromaticity coordinates of the fitted core emission (triangles) are plotted. The narrow core emissions fall outside the periphery of the spectral locus, whereas the combined emission for smaller samples fall into the center of the spectral locus. The core and total emission chromaticity coordinates diverge for smaller NCs given the more significant contribution of the surface emission. The red curve shows the simulated chromaticity trajectory using the basic model discussed above. Figure 5 (b) shows the results of the same analysis done for 100K and 200K. At these lower temperatures, the chromaticity trajectories monotonically narrow both in width and are reduced in amplitude, which is fully consistent with a higher surface/core ratio. Figure 6 (a) shows the integrated photoluminescence intensity for the case of the 1.13 nm radius sample. For high temperatures, the integrated intensity stems mostly from the core, whereas at low temperatures the emission is dominated by the surface. These observations can be rationalized in the configuration coordinate model in the following manner. First, within the equilibrium picture that our group has previously proposed, the fractional population of surface emitters is inversely proportional to temperature and tied to the value of the energetic separation between core and surface states (∆G). However, this does not consider the overall rise in quantum yield. The basic expression given for the quantum yield (η) can be written in terms of the radiative rate constant krad and non-radiative rate constant knonrad. The former is taken to be temperature independent whereas the latter term is temperature dependent. In our previous work, we noted that the lifetime of the core emission did not change appreciably in the range from 70 K-300 K, while the quantum yield decreased monotonically.27 In order to explain this


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observation, our group previously suggested a modified quantum yield (η) expression for CdSe NCs, incorporating the fractional subset of bright emitters, n(T)27 𝑘𝑟

𝜂 = 𝑘𝑟 + 𝑘𝑛𝑟𝑛(𝑇)

(4)

However, this proposed expression was not substantiated by any other direct evidence. The second major omission is that such an expression does not reconcile differences between the core and surface states. For example, the lifetimes of both the core and surface states were recently measured as function of temperature in 3.7 nm - 4.7 nm CdS NCs.39 The lifetime of the core state decreases slightly whereas the surface states increases with temperature. This implies that the knr is increasing in the case of the core with temperature whereas knr is decreasing in the case of the surface state. The first instance is understood in terms of greater decay pathway into the surface. What this points to is that the quantum yield cannot be determined solely based on the core even in the case of larger CdSe NCs where the observed surface emission is negligible. Non-radiative decay pathways of the surface are present by the very fact that quantum yields are low for core-only NCs. Moreover, expressions for quantum yields for states involving strong electron-phonon coupling as in the case of the surface have been proposed several decades ago.40-42 Figure 6b illustrates the non-radiative decay pathway of the surface state with strongelectron phonon coupling within the configuration coordinate model feature as discussed elsewhere.40-42 The salient point described here is that the ground and surface state parabolas intersect. The temperature dependence is thus made explicit, as there is an activation energy barrier in direct analogy to the core to surface transition. Expressions for quantum yields for states involving strong electron-phonon coupling are also given. In the simplest case only


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considering the quantum yield of the surface, the classical phenomenological expression (ignoring quantum tunneling rate) can be written as:41

{

(

𝐸𝐴

𝜂 = 1 + 𝑐𝑒𝑥𝑝 ― 𝑘𝑇

)}

―1

(5)

Returning to the context of developing white light emitters, this may rationalize why the quantum yields of most reported materials have are poor at room temperature but become appreciable at low temperatures(~80K). Recalling the notable exception of Furthermore, this also brings into question how to best optimize the quantum yield through the parameters of the microscopic model. Broad emission of the surface state is a direct consequence of the large magnitude of the Huang-Rhys factor, but this same coupling may have a negligible impact on the quantum yield if it lowers the activation energy EA between surface and ground states. Simply put, if the reasoning is correct, it may well be practically unfeasible to obtain both high photoluminescence quantum yields as well as broad lineshapes in CdSe NCs, limiting the strategy of harnessing strong-exciton phonon coupling in lighting technologies. It also underlines the importance of considering the surface in future temperature dependent time resolved fluorescence studies.

Conclusion: We show via microscopic quantum mechanical theory that trapping of charges can be rationally exploited for the design of white light emitters for light emitting diodes. Following the initial observation of these effects, one aims to generalize the effect in order to predict a broad range of optical responses over a range of material parameters. This work shows that the emission from two states, one featuring very strong exciton-phonon coupling will lead to significant changes to 12 ACS Paragon Plus Environment

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both the chromaticity and quantum yield as a function of temperature. Chromaticity coordinates can be simulated starting from a set of parameters employed in a configuration coordinate model. The influence of these parameters on the photometric output of the white light material can be more easily understood in this manner. The issue of the quantum yield temperature dependence is attributed to self-trapped excitonic state non-radiative decay pathways, and not a fractional subset of emitters as previously thought.

Acknowledgements: TM acknowledges scholarship support from Hydro Quebec. Dr. Jonathan Mooney and Dr. Michael Krause are thanked for helpful discussions. Funding Sources: We gratefully acknowledge financial support from NSERC. Supporting Information: Details of model calculations, Details of CIE integrals, Additional spectra and CIE plots, Polynomial fits to experimental data, Parameters used in model calculations, CIE temperature dependence of the linewidth and lattice contraction parameters are provided. This material is available free of charge via the Internet at http://pubs.acs.org.”


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Figure 1: How self-trapped excitons give rise to chromaticity changes. Representative photoluminescence spectra for CdSe NCs (Radius = 1.1 nm) in toluene (a). The dual emission spectra are fit to two bands, arising from the excitonic core and the self-trapped surface. The spectra are represented in terms of CIE chromaticity coordinates for the two bands as well as for the sum (b).


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Figure 2: Representative photoluminescence data of three sizes of CdSe NCs embedded in polystyrene films between 90 K – 295 K (a,b,c) and represented in terms of CIE chromaticity coordinates (d). The direction of the arrows corresponds to a monotonically decreasing temperature from 295K (red) to 90K (blue). The chromaticity changes as function of temperature are most pronounced for the smaller radii samples in which two emissive states contribute to the overall emission.


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Figure 3: Model flowchart used in this work. In order to compute spectral lineshapes three elements are required: the thermally averaged Franck-Condon probabilities, the relative intensities of core and surface emission (estimated via semiclassical Marcus -Jortner theory or emipiracally obtained) and an estimate of the extent of spectral blueshift as a function of temperature due to semiconductor lattice contraction. Once the Spectral lineshapes are obtained and calculated in units of energy, the lineshape is converted to units of energy, and the CIE integrals can be performed.


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Figure 4: The magnitude of the Gibbs free energy (∆G) and Huang-Rhys (S) parameters of the microscopic model on the changes to the (x,y) chromaticity coordinates as a function of temperature. AS/AT corresponds to the fractional population of the surface state. Panels (a) and (b) show the effect of varying the Gibbs free energy on the surface to total area and chromaticity coordinates. Panels (c) and (d) show the effect of changing the Huang-Rhys parameter energy on the surface to total area and chromaticity coordinates.


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Figure 5: The CIE coordinates change as a function of dot size. Panel (a) shows the model as compared with range of sizes collected in suspension at 300K. Panel (b) shows the predicted differences in CIE trajectories. The extent of FC line narrowing increases with greater S:C ratio.


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Figure 6: Integrated intensity dependence of the white light NC (Radius=1.13 nm) emission (a) and 3 parabola model illustrating the proposed non-radiative decay pathway within the configuration coordinate model (b). The photoluminescence intensity increases monotonically with decreasing temperature for both Core (black squares) and Surface (red circles).


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A Strategy for Exploiting Self-Trapped Excitons in Semiconductor

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