Long range energy transfer in self assembled nanoplatelets 

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Micro-photoluminescence

We use a homebuilt inverted fluorescence microscope, combined with different detection components, to conduct the optical measurements on single NPLs or single assembled NPL chains.
This setup was initiated in 2013 by Feng Fu during his thesis directed by Laurent Coolen. It uses a diode laser and a mercury lamp as excitation sources, and a same objective to focus the excitation beam on the sample and collect its emission. The objective is mounted on a piezo-electronic stage, which can be controlled by software to scan the laser on the demanded area of the sample. As for the detectors, a monochromator (Triax 190 @Horiba) can work either in image plane mode or Fourier plane mode in cooperation with a flip Fourier lens. A time-correlated single photon counting (TCSPC) system (which will be introduced in chapter 3) of two avalanche photodiodes combined with a PicoHarp acquisition card, is also established for decay curve measurements with 500 ps characteristic time of the total system response function.
During this thesis, this setup was further improved:
1) Polarization microscopy: the polarization effects induced by the optical elements in the setup were characterized and corrected, in order to maintain the intrinsic polarization property of the emission from samples. We found that the dominant sources of diattenuation (different attenuation along the x and y axes) and dephasing (phase difference between the x and y axes) are respectively the beam splitter and the prisms, and we managed to correct these effects by adding proper compensation elements (note that here we use prisms instead of mirrors because practically we find it is easier to achieve satisfactory compensation). This development draws on the PhD work of Nguyen Thu Loan (advisor Agnès Maître) in our group on polarization corrections on a similar setup [94]. More details of setup characterization will be given in appendix A.
To evaluate the performance of the polarization-effect-corrected setup, fluorescent polymer spheres (Thermo Fisher, 200nm, 580-605 nm emission) were used as a reference emitter, the emission of which is non-polarized. As a result, a degree of linear polarization of 0.03 was measured for the microsphere emission, while an average degree of circular polarization of 0 was measured, with fluctuation in the range of ±0.02. Besides, when introducing a polarizer below the objective to fully polarize the emission, a 0.99 degree of linear polarization was obtained. We thus conclude that the emission polarization was preserved by the setup with 1-3 % precision.
In this thesis, the degree of linear polarization of NPL’s emission will be analysed in chapter 4. Linear and circular polarization analyses can be performed by introducing a polarizer before the detector (spectrometer or EMCCD) and respectively rotating a half-wave plate or comparing the +45° and -45°positions of a quarter-wave plate before the polarizer.
2) Fourier plane imaging: to investigate the radiating transition dipole, Fourier plane imaging is a powerful tool, which allows access to angular resolved information (radiation diagrams) of the emitter. In addition to the Fourier imaging mode of the spectrometer established by Feng Fu, here we also implemented a Fourier imaging system by conjugating the back focal plane of the objective onto an EMCCD to record the Fourier plane image with better resolution and better efficiency, so that the precise analysis can be achieved on single nano emitters. More technical details and analytical calculations will be elaborated in chapter 4.
3) The imaging system was also improved to achieve a larger magnification on the CCD camera by modifying the lens system on the setup. Larger imaging magnification provides better resolution in imaging-based studies of energy transfer (exciton diffusion) in self-assembled chains of NPLs, which will be demonstrated in chapter 2.

Hetero-FRET and homo-FRET.

Hetero-FRET, as has been shown in the above-presented schematic, is the case in which the acceptor and the donor belong to two distinct populations of emitters. The donor’s emission spectrum must overlap with the acceptor’s absorption spectrum so that energy can be transferred from the donor to the acceptor (but not the reverse). Hetero-FRET has been investigated more widely than homo-FRET, because the former case is straightforward and convenient to be verified and analysed in assistance of optical filters, thanks to the different emission wavelengths of the donor and the acceptor.
There are many ways to evidence hetero-FRET. One of the simple methods is to analyse the sensitized emission (SE) spectrum, in which the donors are pumped and the emission of both the donors and the acceptors are detected. As a result, the emission intensity of the donor (resp. acceptor) will decrease (resp. increase) in the donor-acceptor mixture comparing to the case without the presence of acceptors (resp. donors). Similarly, one can achieve the same purpose by swiping the excitation wavelength at the range in which the donor has a strong absorption. It is expected that the PLE spectrum of the acceptor emission is similar to the donor’s absorption spectrum. Another widely employed technique to analyse hetero-FRET effect is time-resolved fluorescence emission measurements: the decay rate of the donor will be accelerated in donor-acceptor mixture, because the presence of the acceptor opens an additional decay channel. Unlike hetero-FRET, homo-FRET involves the donor and the acceptor which belong to the same emitter population with their absorption spectrum overlapping with their own emission spectrum thanks to a small Stokes shift. Thus, when these emitters are located very closely or get assembled, it is possible to have energy transfer between them, similar to hetero-FRET but the energy transfer is reversible. Figure 2-3 presents the homo-FRET process in a simple model of 1-dimensional chain of particles, with an energy transfer rate of and a diffusion length (i.e. the excitonic energy migration length) .

State of the arts: FRET and other transfer mechanisms

In the literature, various methods were developed for the delicate characterization of FRET exciton migration [100] and the migration length has been reported to 20-30 nm for dense films [101,102] as well as clusters [103] of nanocrystals. Theoretical calculation of FRET length based on lifetime analysis is reported to be 133 nm [16] for nanoplatelets.
In other systems like in molecular or polymer, migration by FRET hopping was generally demonstrated over a few tens of nanometers [104,105,106]. Longer energy transfers distances of hundreds of nanometers or several microns have been reported by many groups under different mechanisms other than FRET, such as 1) Dexter hopping and coherent exciton motion combination of coherent and incoherent exciton motion in the case of J- and H-aggregates [109,110]; 3) plasmon-mediated transfer along metal nanowires [111,112].
Many researchers have studied FRET rate both experimentally and theoretically in systems of semiconducting nanocrystals and yielded hopping rates ranged from tens of picosecond scale [113,114] to nanosecond scale [100]. The fastest observation of FRET rate is reported by Rowland et al., who demonstrated hetero-FRET times of 6−23 ps [15] in binary (i.e. mixture of 4-monolayer and 5-monolayer) nanoplatelet films. Guzelturk et al. developed a model of stacked NPLs with the presence of trapping sites and estimated theoretically that the FRET rate is in the range of (23.8 ps)−1 and (3.0 ps)−1 [115], in good agreement with Rowland’s observation.
Energy transfer between nanoplatelets and other materials have also been studied. As an example, in ref. [116], it is shown the energy transfer rate from CdSe/CdS nanoplatelets to MoS2 could be as fast as ~ (4 ps)-1. In ref. [117], Hernández et al. showed theoretically that the distance dependence of the FRET rate depends on the geometry and dimensionality of the acceptor and on the effective dielectric constant of the donor. For NPLs, the distance dependence is calculated to be 1⁄ 4 instead of 1⁄ 6 for point-like quantum dots.
Besides, temperature dependent FRET behaviour has also been studied in the literature [118]: FRET efficiency is reported to linearly increase as temperature is decreased which is attributed to the increasing photoluminescence and quantum yield of the donor QDs at low temperatures.

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Imaging studies of energy migrations in NPLs chain

In this section, we will present the result of imaging of self-assembled chains of nanoplatelets under localized excitation by a focused laser beam. We will characterize the imaging system to analyse the excitation distribution and the point spread function, in order to reveal the system-response-corrected fluorescence pattern of single nanoplatelet chains.

Demonstrations of elongated fluorescence in CCD images

Experiments are performed on a homebuilt inverted fluorescence microscope, equipped with a laser scanning system (as shown in figure 1-20 in chapter 1). The excitation source could be either a mercury lamp (with bandpass filter at 330-480 nm) for wide field excitation, or a 470 nm diode laser (PDL 800-D @PicoQuant) for localized excitation, which provides 70-ps pulses at variable repetition rate. Combined with a piezo controlled stage, the laser spot can scan on samples or excite specifically the site of interest, which enables the study of individual emitters.
In the image measurement, the laser provides excitation with power of about 5 nW, which ensures the linear excitation regime (details will be given in the later section). A same objective (Olympus super-corrected apochromat 100X 1.4 N.A.) is used to focus the excitation beam on the sample and to collect the fluorescence. A set of Semrock filters (488 nm long-pass and 562/40 nm bandpass filters) are employed to remove the excitation in the collected beam. The detection is conducted by a QImaging Retiga EXi CCD camera, with a pixel size of 6.45×6.45 µm2. The imaging magnification was about 90X so that the size of each pixel on the camera image corresponds to 72 nm on the actual sample plane.
In figure 2-5, upper and lower panels show the CCD images for three different NPL chains excited by mercury lamp (wide field excitation) and laser spot (localized excitation), respectively. Under wide field excitation, the fluorescence pattern from these different chains are about 1.5-2 μm in length, in agreement with the electron microscopy image figure 1-10 (b) in chapter 1, showing that the spin coating deposition preserved the chain structure. In the laser excitation images, the laser spot is positioned in the middle of the chains and the size of the laser spot, which will be carefully characterized later, is represented by the white circles. Thus, if no energy migration occurs within the NPL stacks, only a limited area of laser-spot-size would be luminescent. However, we detected, for all the chains considered, fluorescence from an elongated 1-µm to 1.5-µm portion that extended far beyond the spot of the excitation laser.

Table of contents :

Chapter 1. Introduction of samples, theories and the experimental setup
1.1 Introduction of colloidal nanoplatelets (NPLs)
1.1.1 Colloidal nanocrystals
1.1.2 Colloidal nanoplatelets
1.1.3 Self assembled ch ai n s of CdSe nanoplatelets
1.2 Theoretical backgrounds
1.3 Micro-photoluminescence
Chapter 2. Long range energy transfer in self assembled nanoplatelets 
2.1 Introduction of FRET
2.1.1 FRE T e ffects
2.1.2 State of the arts: FRET and other transfer mechanisms
2.1.3 Motivations
2.2. Imaging studies of energy migrations in NPLs chain
2.2.1 Demonstrations of elongated fluorescence in CCD images
2.2.2 Characterization of the imaging system
2.2.3 Studies of th e energy migration length
2.2.4 Exclusion of n o n linear effects
2.3 Studies of waveguiding efficiency
2.3.1 Experimental analysis of waveguiding of the excitation beam
2.3.2 FDTD simulations of excitation and emission beam
2.3.3 Conclusion
2.4. Diffusion model for FRET rate deduction
2.4.1 Diffusion model
2.4.2 FRET r ate deduction
2.4.3 Theoretical FRET rate calculation from Förster’s theory
2.4.4 Discussion
2.5 Conclusion and perspectives
Chapter 3. Blinking, decay and single photon emission
3.1 Introduction: blinking, decay and antibunching
3.1.1 Exponential decay and principles of TCSPC
3.1.2 Blinking: mechanisms and analytical methods
3.1.3 Antibunching and HBT measurements
3.2 Blinking and decay in single NPLs
3.2.1 Bl i nking in single NPLs
3.2.2 Decay in single NPLS
3.2.3 Conclusion
3.3 Blinking and decay in clusters and chains
3.3.1 Blinking and decay in clusters
3.3.2 Blinking and decay in chains
3.4 Assembly-induced effects and interpretations
3.5 Antibunching in CdSe NPLs
3.6 Conclusion and perspectives
Chapter 4. Analyses of transition dipole componentsapter 4. Analyses of transition dipole components
4.1 Protocols of dipoles analysis
4.1.1 Polarization analysis
4.1.1 Polarization analysis
4.1.2 FourFourier plane analysisier plane analysis
4.1.3 Choice of experimental configurations
4.1.3 Choice of experimental configurations
4.1.4 State of the art of dipole analysis
4.1.4 State of the art of dipole analysis
4.2 Reference: dipole analysis on single nanoplatelets
4.2.1 Polarization analysis
4.2.1 Polarization analysis
4.2.2 Fourier plane image analysis.
4.2.2 Fourier plane image analysis.
4.2.3 Dipole analysis under reflection configuration
4.2.3 Dipole analysis under reflection configuration
4.2.4 Summary and discussion
4.2.4 Summary and discussion
4.3 Dipole analysis of self-assembled NPLs chains
4.3.1 Polarization analysis of single chains
4.3.1 Polarization analysis of single chains
4.3.2 Fourier plane image analysis of sing
4.3.2 Fourier plane image analysis of singlele chainschains
4.3.3 Dipole analysis of NPLs chains with different configurations
4.3.3 Dipole analysis of NPLs chains with different configurations
4.3.4 Summary and discussion
4.3.4 Summary and discussion
4.4 Dipole analysis on clusters as intermediate cases
4.5 Evolution of the novel dipole as a function of the number of NPLs
4.6 FDTD simulations: antenna effect
4.6.1 Numerical calculation of antenna eff
4.6.1 Numerical calculation of antenna effects.ects.
4.6.2 Comparisons: analytical calculation vs numerical simulation
4.6.2 Comparisons: analytical calculation vs numerical simulation
4.6.3 Dielectric effects in single NPLs and NPLs chain
4.6.3 Dielectric effects in single NPLs and NPLs chainss
4.6.4 Summary and Discussion
4.6.4 Summary and Discussion
4.7 Hypothesis on the origin of the out-of-plane dipole in NPLs
4.7.1 Effects of disorde
4.7.1 Effects of disorder r iin assembly: TEM image studyn assembly: TEM image study
4.7.2 Analysis of new transition states
4.7.2 Analysis of new transition states
4.7.3 Local electric field induced by trapped ions/ch
4.7.3 Local electric field induced by trapped ions/charargges in defected siteses in defected sites
4.7.4 Strain
4.7.4 Strain–induced effectsinduced effects
4.8 Conclusion
Chapter 5. Conclusion and perspectives
Appendix A. Compensation of polarizing effects of the setup
Appendix B. Circucullar polarization measurements of chiral Dy ar polarization measurements of chiral Dy crystalscrystals
Reference

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