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Seeing multiexcitons through sample inhomogeneity: bandedge biexciton stucture in CdSe nanocrystals revealed by 2D electronic spectroscopy Helene Seiler, Samuel Palato, Colin Sonnichsen, Harry Baker, and Patanjali Kambhampati Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b00470 • Publication Date (Web): 28 Mar 2018 Downloaded from http://pubs.acs.org on March 28, 2018
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Nano Letters
Seeing multiexcitons through sample inhomogeneity: bandedge biexciton stucture in CdSe nanocrystals revealed by 2D electronic spectroscopy Hélène Seiler, Samuel Palato, Colin Sonnichsen , Harry Baker, Patanjali Kambhampati*. Department of Chemistry, McGill University, Montreal, Quebec H3A 0B8, Canada
*Email:
[email protected] / Phone: +1 514 398 7228
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ABSTRACT:
The electronic structure of multiexcitons significantly impacts the performance of nanostructures in lasing and light-emitting applications. Yet these multiexcitons remain poorly understood due to their complexity arising from many-body physics. Standard transient-absorption and photoluminescence spectroscopies are unable to unambiguously distinguish effects of sample inhomogeneity from exciton-biexciton interactions. Here we exploit the energy and time resolution of two-dimensional electronic spectroscopy to access the electronic structure of the bandedge biexciton in colloidal CdSe quantum dots. By removing effects of inhomogeneities, we show that the bandedge biexciton structure must consist of a discrete manifold of electronic states. Furthermore, the biexciton states within the manifold feature distinctive binding energies. Our findings have direct implications for optical gain thresholds and efficiency droop in lightemitting devices, and provide experimental measures of many-body physics in nanostructures.
KEYWORDS: nanocrystal, quantum dots, CdSe, multiexcitons, two-dimensional electronic spectroscopy
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Quantum confinement of the electron and the hole in semiconductor colloidal nanocrystals famously yields a manifold of excitonic states. The physics of the core exciton (X) is now well understood and exploited in various applications, ranging from lighting and display to photovoltaics1–3. One of the most fascinating aspects of semiconductor nanocrystals is their ability to host multiple excitations per particle. When multiple excitons are created in the same nanocrystal, bound quasi-particles called multiexcitons (MXs) form. In contrast to the single exciton, the structural and dynamic properties of MXs remain, to this day, relatively poorly understood due to their complexity as well as the difficulty in observing them4–7. Yet despite the fact that MXs are higher-order excitations, they significantly impact the performance of practical applications. In lasing applications, gain performance hinges on both the structure of MXs, which dictate optical gain threshold and spectral bandwidth, as well as the dynamics of MXs, which controls gain lifetime. In light-emitting device (LED) applications, Auger processes in MXs are responsible for the observed efficiency droop
8,9
. At the more fundamental level, MXs
also provide an ideal experimental test ground for many-body effects in spherically quantum confined structures 10,11. Because of the large contribution of MXs to the optical response, gaining an understanding of their structure and dynamics is therefore essential. A variety of spectroscopic probes are sensitive to the formation and evolution of MXs. Upon increasing pump fluence, MXs are easily observed in time-resolved or continuous wave photoluminescence (PL) studies
12–14
. However, such
experiments are unable to capture sub-picosecond dynamics. In addition, they are limited to the observation of the emissive states of the bandedge biexciton (XX). Femtosecond transientabsorption (TA) spectroscopy can provide a more detailed picture of XX structure4,15–17. In a TA experiment, the pump pulse creates a population of single excitons. The probe pulse then
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monitors the absorption from X into XX. This translates into a photoinduced absorption (PA) signal. The biexciton transition can be either redshifted or, in rarer instances, blueshifted with respect to X18,19. The value of the binding energy determines how far redshifted (or blueshifted) this peak appears. While insightful, the binding energy extracted from the PA signals only provides an average over all quantum dots within the spectral bandwidth of the laser pulse. This means that TA methods are unable to unambiguously distinguish effects of sample inhomogeneity from exciton-biexciton interactions. Effects of inhomogeneity can be removed by employing single-molecule spectroscopic probes 5,20–24
. Single-molecule photon-correlation experiments have been used to directly access the
ratio of the biexciton to the single exciton fluorescence quantum yields5,23. Such experiments are not subject to trapping artifacts25 and do not require modelling of multi-exponential decays as in TA or ensemble PL measurements. Recently, a method to measure the average single biexciton dynamics was also demonstrated24. However, just like ensemble PL measurements, singlemolecule measurements are not sensitive to the absorptive structure of multi-excitons and lack the temporal resolution by orders of magnitude. Because the absorptive structure plays an important role in dictating gain thresholds in lasing applications, a spectroscopic technique which can directly access the optical response while retaining the sensitivity to inhomogeneities is desirable. Coherent multi-dimensional spectroscopies can complement and overcome many of the limitations faced by these one-dimensional approaches, be they ensemble or single-molecule methods. Two-dimensional electronic spectroscopy (2DES) directly accesses the absorptive structure of XX. The 2DES method has already demonstrated its power in the context of XX studies on InAs and GaAs samples11,26–31. By spreading the optical response along two
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independent frequency coordinates, the technique enables to directly observe how the transition from G to X correlates with the transition from X to XX. Unlike in a TA experiment, inhomogeneous and homogenous linewidths are separated on a 2D correlation map, thereby enabling a clearer assignment of exciton correlations effects. The 2DES method has previously been employed for the study of ensembles of colloidal nanocrystals in other contexts32–45, such as for the study of inter-excitonic coherences 32,35 or to unravel linewidth contributions36,39. Here we exploit the 2DES method to directly reveal the structure of the bandedge biexciton in an ensemble of semiconductor colloidal CdSe quantum dots. Thanks to the increased temporal and energy resolution afforded by the 2DES method compared to standard TA spectroscopy, we are able to capture glimpses of the XX structure following the birth of the hot exciton. Our results offer a direct measure of the absorptive electronic structure of the bandedge biexciton. We show that the XX structure must consist of a manifold of states. This finding informs the rational design of similar semiconductor nanostructures for lasing and LED applications, and offers an experimental measure of many-body physics in quantum-confined structures. Before showing the benefits of the 2DES method in the context of XX studies, we recall the strengths and limitations of one-dimensional ensemble methods. Panels (b) and (c) of Figure 1 show a series of one-dimensional spectra yielding information about the exciton and biexciton structure of the nanocrystals. From the linear spectrum represented in black in panel (b), one can observe a manifold of excitonic states. The linear PL peak, redshifted from the core absorption peak, displays a Stokes shift of around 30 meV. While significant insights have been gained into the structure of the single exciton owing to simple linear methods46,47, probing the structure of multi-excitons requires the use of nonlinear spectroscopic probes. One-dimensional signatures of the bandedge biexciton can be observed in time-resolved PL studies12,13. As an example, a non-
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linear PL spectrum acquired using a streak camera is shown in dark orange on Figure 1(b). This spectrum was obtained following high fluence excitation of the nanocrystals with 400 nm, 100 fs pulses. As can be seen on this panel, the entire PL trace is redshifted with respect to the PL of the core exciton, consistent with prior studies12,13. This shift is a clear manifestation of bound MXs. As was stated in the introduction, the weakness of PL-based methods is that they only probe the emissive states of MXs. Figure 1(c) shows an example TA spectrum obtained on an ensemble of CdSe nanocrystals. Using an optical parametric amplifier (OPA), the pump pulses of ≈ 70 fs duration were tuned resonant with the bandedge exciton, thereby specifying the initial excited state population. The probe consisted in a white light continuum derived from self-phase modulation in a Sapphire window. While a TA experiment can probe the absorptive XX, the one-dimensional spectroscopic signatures always bear ambiguities when measuring the electronic structure of complex systems due to overlapping contributions. A 2DES experiment is conceptually analogous to a multi-dimensional nuclear magnetic resonance (NMR) experiment. In a 2DES experiment, a series of three electric fields interact with the sample. Most commonly, femtosecond laser pulses are employed to generate the three fields. The first pulse instigates a coherent superposition of excitonic states in the sample, which oscillates and dephases during time period t1. Subsequently, the second pulse hits the sample and converts this coherence into an excitonic population. Following this second field-matter interaction, the hot excitons undergo relaxation during time period t2 as in a standard TA experiment. A third and last interaction converts the population into another coherence state, which dephases during time period t3. Following this last interaction, a nonlinear polarization P(3)(t1, t2, t3) is created in the sample. This polarization contains the sum of the signals arising from the various light-matter interaction pathways. By varying the time delays t1 and t3, a 2D
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energy correlation map can be obtained at a given t2 by Fourier transforming (FT) the signal along the t1 and t3 dimensions. An example 2D correlation map is shown in Figure 2(a). We point the interested reader to reference textbooks for further details about the method48,49. Details about the instrument are provided in the methods section. Relevant to the present study, the key point is that this correlation map contains XX contributions. Similar to a TA experiment, the present 2DES experiment is sensitive to three physical processes at play in the nanocrystals: Ground State Bleach (GSB), Stimulated Emission (SE) and Excited State Absorption (ESA). Each of these processes contribute to the observed spectra. The various biexcitonic states are accessed through a subset of the ESA pathways. Specifically, the first pulse creates a coherence between the ground state G and the excitonic state X. This coherence oscillates at frequency ωX. The second pulse creates an excited population X. The third pulse then accesses the biexciton states by creating a coherence between X and XX. This new coherence now oscillates with a frequency of ωXX - ωX. Because of the binding energy of the biexciton ∆XX, the frequency of XX is given by ωXX = 2ωX – ∆XX. Thus the frequency of the oscillation during t3 is ωX – ∆XX. In other words, the X to XX transition is detuned from the exciton frequency by the binding energy. Upon FT, the biexcitonic contribution will show at ωX along the E1 axis, while it will show at ωX – ∆XX along the E3 axis. Comparing the one-dimensional projections shown in Figure 1(c) with the example 2D spectrum shown in Figure 2(a) readily illustrates the advantage of spreading the optical response along two independent energy coordinates. Each slice along the E3 axis for a given value of E1 corresponds to a separate pump-probe experiment, with the difference that additional coherent pathways contribute in a 2D experiment. However, these coherent pathways are found to be
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small for the particular case of our sample. The 2DES method can thus be seen as an extension of pump-probe spectroscopy, where the pump is spectrally resolved. Like in dynamic hole burning experiments50, 2DES enables the separation of inhomogeneous and homogenous contributions to the linewidth. Importantly, the energy resolution of the E1 axis – corresponding to the pump energy – is dictated by the coherence time range (t1) in the experiments. Thus, the 2DES method is also exempt of the limiting trade-off between time and energy resolution faced in TA experiments. In a TA experiment, time resolution can typically reach
