Introduction of samples, theories and experimental setup
Since the first report of nanocrystals with quantum confinement effects in the early 1980s , semiconducting nanoparticles have been massively studied because of the increasing importance to understand the physics in nanoscale objects in the past decades. Colloidal nanocrystals, as one of the most important classes of semiconductor quantum dots, have been studied intensively for more than 30 years. Nowadays, the family of colloidal nanoparticles is not limited to the 0-dimensional quantum dots , but also expands to various structures, including 1-dimensional nano rods  and 2-dimensional nanoplatelets .
2-dimensional semiconducting nanoplatelets (NPLs), or to say colloidal quantum wells, have attracted considerable attention since the initial report by Ithurria and Dubertret in 2008 . Nanoplatelets have a well-controlled ultra-thin thickness consisted by a certain number of monolayers of atoms and have a controllable lateral expansion, resulting in unique optical characteristics, such as extraordinary narrow emission peak, low Stokes shift, large oscillator strength , and deterministic in-plane radiating dipoles .
Colloidal nanoplatelets present a strong natural tendency to aggregate because of their higher surface-to-volume ratio. By a choice of appropriate ligands and solvents, platelet stacking can be induced and one can obtain highly ordered complex structures. The first linear assembly of nanoplatelets was reported by Tessier et al. in 2013 . After that, Benjamin Abécassis from Laboratoire de Chimie de l’ENS de Lyon has been the pioneer for linear platelet self-assembly. He demonstrated a robust procedure to synthesize stable co-facially stacked platelet chains with controllable length as long as 4 micrometers .
Many efforts have been devoted to investigations of photo-physical properties of isolated nano-emitters, either as single emitters or ensembles, while the research on highly-ordered self-assembly of emitters, which constitutes attractive systems for studying interactions and couplings between neighbour emitters, is still lacking. The knowledge of collective photo-physical properties is crucial to improve the efficiency of optoelectronics employing a dense-packed layer of particles. Other potential applications may also be achieved once the collective behaviour of assembled particles is understood.
With this in mind, we collaborated during this thesis with Benjamin Abécassis and his PhD student Lilian Guillemeney, to investigate novel photo-physics on high-quality self-assembled chains of NPLs. As our expertise in the “Nanostructures et optique” group in Institut des NanoSciences de Paris, we used various optical analysis techniques, including micro-photoluminescence, time-correlated single photon counting, polarimetry, Fourier plane imaging and cryogenic photoluminescence, to analyse the fluorescence properties of different CdSe samples, from isolated single platelets, clusters of few platelets to self-assembled long chains. Our study involved various aspects of decay dynamics, blinking behaviours, dimensionality and directionality of transition dipoles, dipole-dipole interactions etc. The general goal was to reveal emerging collective effects in self-assembled samples, and to demonstrate that the properties of isolated single emitters will be drastically modified by the self-assembly.
Around the world, self-assembled chains of platelets have been achieved by very few other groups [9,10,11], while other assembly configurations have also been demonstrated, such as “face-down” or “edge-up” solid platelet films [12,13,14]. The previous research on assembled platelets involved non-radiative inter-NPL energy transitions , decay dynamics , and applications like light-emitting diodes  and lasing .
This thesis consists of 5 chapters.
In the first chapter, we will start with a general introduction of colloidal nanocrystals, nanoplatelets as well as self-assembled platelet chains. We will introduce a bit of history of the colloidal nanocrystals, their attractive optical properties and synthesis methods. We will also introduce the theoretical backgrounds involved in the studies in this thesis. Our homebuilt micro-photoluminescence setup will be briefly presented in the last section of this chapter.
In the 2nd chapter, we will report on excitonic energy transfer in self-assembled NPLs.
Excitonic energy transfer has been intensively studied in solid films of emitters, which is however limited by the insufficient control of the order of the building blocks. In this chapter, we will combine the highly-ordered linear assembly of NPL chains with the micro-photoluminescence to study inter-NPL excitonic energy diffusions. We will estimate the energy diffusion length by imaging analysis, from which we will then estimate the inter-NPL energy transfer rate by the development of a diffusion equation model, which relates the transfer rate to the diffusion length in the image. This knowledge is important for the fundamental study of collective photo-physics and also for the application significance, such as to improve the efficiency of light-emitting diode, photovoltaic solar cells, etc.
In the 3rd chapter, we will investigate the fluorescent behaviours of single NPLs, clusters and chains, including their blinking behaviours, decay dynamics and single photon emissions.
Different techniques are involved: a time-correlated single-photon counting (TCSPC) module is employed to record the blinking time traces and decay curves, and a Hanbury-Brown and Twiss (HBT) configuration is used to obtain the second order photon correlation function. We will study how assembly modifies the fluorescent behaviour, and will conclude respectively on the typical behaviours of non-assembled and assembled emitters. This is not only important for the study of self-assembly effects, but also a powerful tool to distinguish the cases between single NPLs and clusters, which cannot be resolved by optical microscope.
In chapter 4, we will investigate the dimensionality and directionality of dipoles in NPLs emitters, from single isolated NPLs to assembled NPL chains. For single NPLs, it has been both theoretically estimated by optical selection rules and experimentally demonstrated that they are supposed to have two in-plane dipoles contributing to the emission. However, the dipole’s dimensionality and orientation in co-facial assembly of NPL chains have never been fully investigated. Particularly, in assembled chains, all the NPLs are supposed to stand vertically on their edge, allowing for the deterministic vertical dipoles when deposited on a substrate, which is then of major interest for efficient surface plasmon couplings and emission optimization.
To study these questions, in our group, a polarimetric protocol for dipole orientation analysis of single emitters has been established, as well as the Fourier plane imaging, by which one can analytically probe the dipole components and orientations. In chapter 4, we will use a combination of polarimetry and Fourier plane imaging to probe the proportions of dipole components in both single and assembled emitters, with a record precision of ±3% thanks to the careful design of experimental configurations. By comparing the results of single NPLs and NPLs chains, we can study how stacked dielectric shape and other effects modify the transition dipoles, which will improve our understanding on collective photo-physics in self-assembled nanostructures.
In the last chapter, we will give conclusions of the works in this thesis and propose perspectives for future studies.
Introduction of colloidal nanoplatelets (NPLs)
With the development of nanoscience and nanotechnology, it has been of increasing importance to understand the physics in semiconducting materials with size reduced to the nanometer scale. This is motivated not only by its fundamental importance, but also by the practical significance as the size of electronics and optoelectronics has been reduced following Moore’s law in the past decades. To study this topic, semiconducting nanocrystals (NCs) with sizes less than 100 nm, which are sometimes referred to as artificial atoms, have been great research objects.
In this section, we will first introduce the basics of colloidal nanocrystals, including a bit of history, their optical properties and the methods for synthesis. Then we will introduce the more recent 2-dimensional nanoplatelets (NPLs), including their novel optical properties in comparison with spherical nanocrystals (quantum dots) and the engineering of their geometry. In the last section, we will review the self-assembly of NPLs and introduce our samples.
Semiconducting nanocrystals with quantum confinement effects were reported for the first time in the 1980s , opening a new area of fundamental studies in semiconductor nanomaterials and attracting considerable attention in the fabrications and applications of modern optoelectronics. In 1993, C. Murray, D. Norris and M. Bawendi synthesized and characterized monodisperse cadmium chalcogenide nanocrystals (quantum dots) , making the colloidal nanocrystals a subject of intense study in the past decades. At the same time, another class of nanocrystals, i.e. epitaxial quantum dots, was fabricated by L. Goldstein et al. in 1985 , which requires more complex fabrication techniques but can provide, at low temperature, coherent states of light and rich quantum-optical effects.
Nowadays, the family of colloidal nanoparticles is not limited to the 0-dimensional quantum dots (with 3 dimensional quantum confinement), but also expands to various structures, including nano rods (i.e. 1D nanocrystals with 2D confinement)  and 2D nanoplatelets (with 1D confinement) . In addition, there are other complex samples that have been synthesized and characterized with engineered dimensions and structures, such as tetrapods nanoribbons .
Nanocrystals are generally synthesized by II-VI or III-V materials, such as CdSe, CdS, InP, InAs, etc. High-quality nanocrystals should possess high luminescence quantum yields, good stabilities of luminescent properties, and compatibilities with desired solvents. All these properties rely on the proper passivation of dangling bonds present on the nanocrystal surface , which can be achieved by growing additional layers of appropriate materials outside of the emitting nanocrystal to form a “shell”. Thus, in addition to “core-only” nanocrystals, “core-shell” structure attracts considerable attention as well. By engineering sizes and materials of the shell, the optical performance of nanocrystals will be modified, as will be introduced later in the section on heterostructures.
Unlike bulk semiconductor materials, nanocrystals possess optical properties determined not only by the intrinsic property of the materials, but also by the size of the nanocrystal due to quantum confinements. Briefly, this effect can be observed when the size of the crystal is much smaller than the wavelength of the wavefunction of the electron and the hole, so that the motion of the electron and the hole are “confined” in the crystal, leading to a transition from continuous to discrete energy levels. Basics of semiconductor physics and more theoretical backgrounds will be introduced later in section 1.2.
Figure 1-1. (a) Potential profile of a CdSe/ZnS core-shell nanocrystal. The energy levels of the excited carriers (electrons and holes) become quantized because of the quantum confinement effect originating from the limited size of the semiconductor nanocrystal. (b) UV-vis absorption (black solid line) and fluorescence (red dashed line) spectra of CdSe/ZnS QDs in solution, adapted from ref. .
To intuitively show the fluorescence mechanism and the quantum confinement effect, as an example, we consider a nanocrystal with a CdSe core and a ZnS shell (figure 1-1 (a)), which is one of the most successful nanocrystal systems having been synthesized in high quality and extensively studied. The pumping energy ℎ is absorbed by the nanocrystal, promoting an electron to the conduction band and leaving a hole in the valence band. Then the electron-hole pair will relax to the lowest energy levels and recombine either radiatively by emitting a fluorescence photon or non-radiatively if defects are present. Due to the limited volume of the nanocrystal, the wavefunction of the electron and the hole are strongly confined. Thus, as shown in figure 1-1 (b), the absorption spectrum of the nanocrystal is close to a continuum at higher energies but at lower energies shows peaks indicative of quantum confinement, while the emission spectrum displays a single peak which can shift as a function of the NC size.
Colloidal synthesis method
The favorable and promising optical properties of nanocrystals are affected by their size, as depicted in figure 1-2, which then can be controlled precisely during the fabrication procedure. Various synthetic methods (one can refer to ref. ) have been developed for the growth of nanostructures and here we will briefly introduce the colloidal synthesis method related to the samples that will be studied in this thesis.
Figure 1-2. Tuning the mission wavelength of nanocrystals by modifying their size.
Colloidal synthesis has two main types, i.e. hot-injection and one-pot method. Here we take the hot-injection method as an example to briefly present the preparation processes in figure 1-3. First, a surfactant (e.g. oleic acid) solution and the precursor (e.g. cadmium precursor) are mixed in a three-neck flask equipped with a heater. Then, the reactive reactant is injected into the flask at a specific moment. By careful control of the temperature and the reaction atmosphere (e.g. inert gas), the desired nanocrystals will be obtained in the mixed solutions at a certain time. Most importantly, by modifying the temperature and the reaction time, the colloidal synthesis method allows for controlled synthesis of colloidal hybrid nanostructures with excellent monodispersity, uniform size and shape, and high purity.
Compared to the epitaxial quantum dots obtained by vacuum deposition, which are particularly good for making high-quality (low-defect, highly stable) semiconductor crystals from a compound or from a number of different elements, the colloidal nanocrystal has its own advantages: low cost, high yield, solution processability, precise control in shapes and sizes, good compatibility with versatile substrates, etc.
Colloidal nanoplatelets (NPLs)
The nanoplatelets (NPLs) of II-VI semiconducting materials have attracted considerable attention since the pathbreaking report by S. Ithurria and B. Dubertret in 2008 . A colloidal NPL is a 2-dimensional nanocrystal, or to say a colloidal quantum well, with a strong 1D quantum confinement in the direction vertical to the NPL’s flat plane. Thanks to the atomic layer precision in colloidal synthesis, NPLs are essentially monodisperse in thickness, while the lateral dimension can be extended on an order of tens of nanometers or even larger with a shape control over the aspect ratio .
NPLs have attractive optical properties as compared to spherical nanocrystals:
1) Their photoluminescence peak is extraordinary narrow (typically of 12 nm) (yellow dotted line in figure 1-4) and tunable according to their thickness;
2) NPL ensembles have negligible inhomogeneous broadening in their emission spectra (green dashed line in figure 1-4), indicating the perfect uniformity in their thickness;
3) Their transition dipoles present large oscillator strength resulting from increased exciton center-of-mass extension [5,27], which will then significantly enhance the absorption cross-section 
and accelerate the decay of excitons;
4) They have two in-plane emitting dipoles parallel to the platelet plane and can be deterministically deposited on a substrate with a horizontal orientation [6,29].
In addition to unique optical properties, NPLs have a large and flat surface, which makes them promising building blocks in self-assembly (as will be presented later in this section). When stacked co-facially, the center-to-center separation distance between adjacent NPLs is short, with very well controlled orientation and thus the orientation of their transition dipoles is matched, resulting in an efficient dipole-dipole interaction. Thanks to the perfect thickness monodispersity in stacked NPLs, their inhomogeneous line width is negligible with a very low Stokes shift . Therefore, their emission and absorption spectra overlap, allowing a picosecond scale exciton diffusion (FRET) between neighbour NPLs in an assembly .
Thus, colloidal NPLs inherit the advantages of colloidal nanocrystals while possessing many emerging superior properties as compared to quantum dots, which make NPLs excellent candidates for versatile applications, such as lasing [32,33,34,35,36], light-emitting diodes [37,38,39], photovoltaics , single photon sources  and field-effect transistors .
Figure 1-4. Absorption spectrum (blue) of single NPLs in solution, and emission spectra of a single NPL (yellow) or an assembled NPL chain (green).
Besides, NPLs can serve as a good platform of 2D materials for many fundamental studies, such as magnetic circular dichroism (MCD) , exciton mobility , dark exciton emission , etc.
Commonly, CdSe NPLs with respectively 3, 4, 5, 6 monolayers in thickness have corresponding emission wavelengths at around 462, 513, 553, and 585 nm . S. Delikanli et al. demonstrated the synthesis of ultrathin 2-monolayer CdSe NPLs  and found on them a lower luminescence quality similar to the spherical QDs with diameter less than 2 nm : the optical properties start to be dominated by surface-induced effects, which yield a broad Stokes-shifted emission with lower quantum efficiency. As a summary, structural and spectroscopic characteristics of zinc-blende CdSe NPLs are presented in table 1-1. Note that there is a dispersion in the meaning of the “n-ML” denomination in early papers, here in this thesis we are using the now-common denomination.
In addition to CdSe NPLs, other II-VI semiconductor core-only NPLs were also reported, such as CdS and CdTe , PbS  or PbSe NPL , etc.
In terms of crystalline structures, both wurtzite and zinc-blende NPL can be synthesized depending on the fabrication conditions (ligand, reaction temperature etc.) [4,50]. Generally, zinc blende NPLs are obtained using carboxylic acid ligands with temperatures in the range of 150-240 °C, while amines and lower temperatures yield NPLs in the wurtzite structure. In this thesis, all the considered NPLs have a zinc-blende structure.
Heterostructured nanocrystals can provide an additional degree of freedom and therefore improve the performance of the hybrid system. One can modify the optoelectronic properties by using nanocrystals with heterostructure, such as the core-shell nanocrystals shown in figure 1-1 (a). Depending on the materials used in the heterostructure, different electron-hole localization regimes can be obtained in excited emitters:
1) Type-I structure (figure 1-5 (a)): a narrow band gap material is used as the core, covered by a wide band gap material as the shell; the wide band gap shell works as a passivator of surface states, increasing the efficiency and stability of photoluminescence. In the type-I regime, the electron and the hole are confined within the narrow band-gap core material and form a direct exciton. The opposite situation, i.e. the “inverted type- I structure”, is also possible, in which a wide band gap material is used in the core and a narrow band gap material forms the shell.
2) Type-II regime (figure 1-5 (c)): the materials of the core and the shell have their band gaps misaligned so that the core has the lowest electron band edge but the highest hole band edge or vice versa, so that the electron and hole are separated in different parts of the heterostructure, resulting in an indirect exciton.
3) Quasi type-II structure (figure 1-5 (b)): in some cases, the narrow band gap in the core material is displaced and reach a similar level as a band edge of the wide band gap shell. For quasi type-II case, one of the carriers (i.e. the hole) is confined in the core while the wavefunction of the other carrier can spread over a large area of the heterostructure.
In NPLs, heterostructures can be formed by sandwiching a core by shells (“core-shell” structure), or by growing a “crown” laterally around the core and forming a so-called “core-crown structure” as shown in figure 1-6. Various heterostructured NPLs have been reported in the literature, such as:
1) Core-crown NPLs, including type-I CdSe/CdS NPLs [52,53], inverted type-I NPLs , type-II CdSe/CdTe NPLs [55,56], type-II CdTe–CdSe NPLs , Type-II CdS/ZnSe NPLs  and composition tuneable CdSe/CdSe1−xTex core/crown NPLs ;
2) Core-shell NPLs: CdSe/CdS and CdSe/CdZnS heterostructures , CdSe/ZnS NPLs , CdSe/CdS/ZnS NPLs , etc.
3) More complicated structures, such as the CdSe/CdS core/crown@shell samples .
Figure 1-6. Schematics of core-only, core/crown, core/shell, and core/crown@shell NPLs. Adapted from ref. .
Strategies for tuning the emission color
NPL’s emission peak can be tuned by different strategies. The most straightforward method is to change the thickness of NPLs as shown in table 1-1, which will directly modify the quantum confinement and consequently change the corresponding emission wavelength. However, controlling the emission of NPLs by thickness is limited by the discrete wavelengths corresponding to the number of monolayers. In the meantime, other methods have been proposed to fabricate NPLs with different wavelengths. One approach is to engineer the heterostructures by growing quasi type-II band structure, in which the change in emission color can be attributed to reduced confinement by exciton delocalization into the shell . In addition to changing the thickness or structure of the NPLs, Y. Kelestemur et al. synthesised CdSe/CdSe1-xTex core/crown hetero-nanoplatelets and demonstrated that by changing the composition the emission color can vary from green to red . Besides, S. Delikanli et al. prepared CdS/CdSe core/crown NPLs with inverted type-I band alignment and their emitting wavelength range covers all visible range by growing the CdSe crown around the CdS core with different thickness .
Apart from emission colors, other optical properties, such as emission rates and blinking, are also drastically influenced by the structure of NPLs. Generally, compared to core-only NPLs, heterostructured NPLs have 1) slower recombination lifetime, which is commonly attributed to the decreasing electron and hole exciton wave function overlap; and 2) fewer blinking events, because of better passivation of nonradiative surface defects by the shell. More properties of blinking and decay dynamics will be discussed in chapter 3.
To modify the optical properties of NPLs, doping is another strategy that has been commonly used in nanocrystals. By doping metal ions in semiconductor materials, new energy levels can be created and result in different fluorescent behaviours. Various types of metal-ion doping in NPLs have been reported, such as Mn2+ doping in CdSe NPLs nanoribbons  or CdSe/CdS core shell NPLs , Cu2+ doping in CdSe NPLs  and Ag2+ doping in CdSe NPLs .
Synthesis of our CdSe NPL samples
The colloidal CdSe NPL samples used in this thesis were synthesized by Lilian Guillemeney under the supervision of Benjamin Abécassis from Laboratoire de Chimie de l’ENS de Lyon. Briefly, the first step was to prepare cadmium oleate from a mixture of dissolved sodium oleate and cadmium nitrate tetrahydrate through a careful washing and drying process. Then the cadmium oleate was introduced with selenium powder and ODE in a three-neck flask equipped with a septum, a temperature controller and an air condenser. The temperature and the reaction atmosphere were carefully controlled and cadmium acetate dihydrate and oleic acid were successively added. After cooling the flask, a mixture containing 5-ML CdSe NPL, 3ML-CdSe NPL and quantum dots were obtained in solution, from which the 5-ML CdSe NPLs were separated by centrifugation. More details about the synthesis and assembly protocol can be found in ref. .
CdSe nanoplatelets with a 1.5-nm thickness (6 layers of Cd and 5 layers of Se) were synthesized corresponding to a fluorescence wavelength of 550 nm. The lateral dimensions were 7 x 20 nm²(with 2-nm width dispersion and 4-nm length dispersion) as measured using transmission electron microscopy (TEM) in figure 1-7.
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
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
2.2. 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
2.4. Diffusion model for FRET rate deduction
2.4.1 Diffusion model
2.4.2 FRET rate deduction
2.4.3 Theoretical FRET rate calculation from Förster’s theory
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
3.2.1Blinking in single NPLs
3.2.2 Decay in single NPLS
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
4.1.2 FourFourier plane analysisier plane analysis
4.1.3 Choice of experimental configurations
4.1.4 State of the art of dipole analysis
4.2 Reference: dipole analysis on single nanoplatelets
4.2.1 Polarization analysis
4.2.2 Fourier plane image analysis.
4.2.3 Dipole analysis under reflection configuration
4.2.4 Summary and discussion
4.3 Dipole analysis of self-assembled NPLs chains
4.3.1 Polarization analysis of single chains
4.3.2 Fourier plane image analysis of sing
4.3.3 Dipole analysis of NPLs chains with different configurations
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.
4.6.2 Comparisons: analytical calculation vs numerical simulation
4.6.3 Dielectric effects in single NPLs and NPLs chain
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 disorder r iin assembly: TEM image studyn assembly: TEM image study
4.7.2 Analysis of new transition states
4.7.3 Local electric field induced by trapped ions/charargges in defected siteses in defected sites
4.7.4 Strain–induced effectsinduced effects
Chapter 5. Conclusion and perspectives