Two-dimensional (2D) layered materials are integral to modern condensed matter research due to their remarkable electronic and optical properties. A key feature of these materials is that their properties can be adjusted bymaking small changes to their structure at the nano- and atomic scale. Understanding and linking these electronic and optical properties to structural features at the nanoscale is crucial for unlocking the full potential of 2D layered materials and maximizing their use in advanced devices. This thesis uses electron-based microscopy and spectroscopy to achieve the high spatial and energy resolution required for this goal. These techniques address the limitations of optical and X-ray spectroscopy, which, while offering excellent spectral resolution, lack the spatial precision needed to resolve nanoscale morphologies and atomic structures critical for understanding 2Dmaterials. To achieve this,we employ two advanced electron microscopy methodologies: probe corrected Scanning Transmission Electron Microscopy (STEM) and monochromated Electron Energy-Loss Spectroscopy (EELS). Together, these techniques enable the acquisition of high-quality Spectral Images (SIs) with both exceptional spatial and spectral resolution, providing a powerful platform for the detailed characterization of 2D layered materials. To further enhance the potential of STEM-EELS, we integrate Machine Learning (ML)-based approaches. These approaches introduce innovative solutions such as the removal of the dominant Zero Loss Peak (ZLP) background in the low-loss energy region, peak identification and multivariate techniques to separate overlapping signals and so fully leverage the rich information contained in STEM-EELS SIs Chapter 2 establishes the data processing methodology used in this work. It provides an overview of STEM-EELS SIs, detailing how they are acquired, interpreted, and the challenges involved in processing these high-dimensional datasets. A key focus is on ourML-based approach for image-wide subtraction of the ZLP in SIs. This step is crucial for isolating spatially localized information in the low-loss energy region, which would otherwise be obscured by the ZLP tail. The methodology incorporates ML techniques originally developed in high-energy physics for probing the interior structure of protons, demonstrating the adaptability of these methods to electron microscopy. This analysis framework, named EELSFITTER, serves as the foundation for the remainder of the thesis, where it is applied to the characterization of 2D layered materials. Developed in Python, the framework is open-source and freely available for use by the research community. In Chapter 3, the framework EELSFITTER is applied to investigate Indium Selenide (InSe) nanosheets and Tungsten Disulfide (WS2) flakes with mixed polytipism (2H/3R). The thickness and stacking order of layers are critical structural features that influence the optoelectronic properties of 2D materials, including their band gap. For InSe, the stacking order or crystalline phase determines whether the band gap is direct or indirect and affects its value. In the case of WS2, a member of the Transition Metal Dichalcogenides (TMDs) family, thickness plays a direct role in tuning the band gap, making it an ideal benchmark for validating the ML-based approach. Using robust ZLP subtraction in the SIs of these materials, we achieve nanoscale precision in spatially resolving their band gap and dielectric function. Additionally, we correlate the electronic properties to structural features, with a particular focus on local specimen thickness, demonstrating the effectiveness of this methodology. We extend the data processing techniques and analytical methods to tackle automated feature identification within the energy-loss and energy-gain region of EELS in Chapter 4. The first part of this chapter focuses on one-dimensional (1D) Molybdenum Disulfide (MoS2) nanostructures. As a TMD material similar to WS2, MoS2 in a 1D morphology allows us to study the effects of curvature-induced strain on its optoelectronic properties. We characterise excitonic and plasmonic resonances, revealing how these features are influenced by the 1D geometry. Additionally, we investigate excitonic behaviour and the band gap value in relation to localized curvature-induced strain, comparing the properties at the tips of the 1D structures with those at the body. The second part of the chapter examines the layered topological insulator Bismuth Telluride Bi2Te3. Here, we focus on the energy-gain region, applying ML-based techniques originally developed formodelling the loss region of the ZLP.Using this approach, we extract a well-defined collective excitation at -0.8 eV on the energy-loss axis. By relying on the energy-gain region, we avoid complications from multiple scattering, enabling the characterization of this excitation with enhanced spectral precision. This chapter highlights the versatility of our methods for analyzing diverse materials and morphologies. In Chapter 5, we focus on WS2 nanotriangles, examining localised plasmonic resonances that form along their edges. By employing non-negative matrix factorization (NMF), we identify the spatial distribution of these resonances and successfully separate them from signals originating from overlapping WS2 nanotriangles. The results of the NMF analysis are compared with electrodynamical simulations, which reveal strong agreement with the observed localized plasmonic resonances. Further,we quantify these resonances by analysing their dispersion relation through a 1D Fabry-Perot model. This analysis demonstrates a quadratic dispersion characteristic of surface plasmonic phenomena, offering deeper insights into the optical behaviour of WS2 nanotriangles. This thesis presents the development of novel strategies for processing and interpreting STEM-EELS SIs in both the low energy-loss and energy-gain regions. Through these advancements, we provide valuable insights into the relationship between structural and physical properties across various morphologies and material types of layered materials. Importantly, all computational frameworks developed during this work are open-source and freely available, ensuring that the methodologies and approaches can be easily adopted by other researchers...@en

The quest to miniaturize optical and electronic devices has driven significant interest in transition metal dichalcogenides (TMDs) like molybdenum disulfide (MoS₂) due to their remarkable optoelectronic properties. This thesis explores the synthesis, structural control, and advanced characterization of MoS₂, with a focus on vertically-aligned nanosheets for enhanced non-linear optical applications. A novel 4D-STEM framework, StrainMAPPER, is developed to map strain at atomic resolution, revealing critical insights into bandgap modulation. Additionally, convergent beam electron diffraction (CBED) techniques are used to identify crystal domains and grain boundaries. These findings contribute to advancing the fabrication and characterization of TMD nanomaterials, enabling new platforms for tunable nanoelectronics and nanophotonics.@en

Electron energy-loss spectroscopy (EELS) is a powerful analytical technique used in transmission electron microscopy (TEM) to investigate the energy loss of electrons as they interact with a specimen. EELS provides valuable information about the electronic structure, composition, and bonding properties of materials at the nanoscale. Despite its tremendous potential, EELS techniques often face challenges related to spectral resolution and signal-to-noise ratio. In this context, the present project aims to significantly enhance the EELS spectra resolution by innovatively designing and fabricating a specialized Transmission Electron Microscope (TEM) holder. By leveraging advances in photonics and micro-resonator technology, this project seeks to revolutionize the quality and accuracy of EELS measurements, opening new avenues for high-resolution material characterization. The motivation behind this project lies in the critical need to overcome existing limitations in EELS techniques and push the boundaries of nanoscale material analysis. Traditional EELS setups, while offering valuable insights, often suffer from challenges associated with background noise, limited energy resolution, and compromised signal quality due to multiple scattering events. These factors hinder the ability to extract precise information about material properties, impeding progress in various scientific and technological fields. Motivated by these challenges, the central aim of this project is to design and develop a TEM holder that incorporates cutting-edge photonic micro-resonator technology. This combi- nation is expected to improve EELS abilities. The proposed holder will enable controlled interactions between the electron beam and the photonic micro-resonator, exploiting quantum optical phenom- ena to enhance the energy-loss signal and reduce unwanted noise. This approach aligns with recent advancements in Photon Induced Near-field Electron Microscopy (PINEM), quantum optics and electron-photon interactions, paving the way for unprecedented sensitivity and resolution in EELS measurements. The outcomes of this project hold immense promise for diverse scientific disciplines. In materials science, researchers will gain deeper insights into the electronic behavior and properties of nanoma- terials, facilitating the design and optimization of advanced materials with tailored functionalities. Additionally, the improved EELS resolution will impact fields such as catalysis, nanoelectronics, and biological imaging, where precise characterization at the nanoscale is essential. To achieve our objectives, we will address the following key research questions: • What are the optimal design parameters for the micro-resonator, facilitating efficient electronphoton interactions and maximal photon generation per electron? • What strategies can be employed to mitigate potential sources of photon loss within the integrated TEM holder, such as losses in coupling, transmission, and detection, thereby maximizing the efficiency of photon collection and measurement? • How do the characteristics of the micro-resonator, such as its size, shape, and material properties, impact the generation and propagation of cavity photons, and how can these parameters be tailored for optimal EELS performance? We expect that the results of this project will revolutionize the field of material characterization by enabling unprecedented high-resolution EELS measurements, poised to impact diverse scientific and technological domains.

In the last decades there has been an increasing interest in computing the local strain at the atomic scale of materials. By knowing aspects of the local strain in a lattice, one has information about measurements of distortions of lattice parameters concerning shifts, deformations and defects computed with respect to a smooth, defect-free reference region. Multiple methods have been implemented so far in order to map the strain of two-dimensional lattice patterns, which are obtained through means of a High Resolution Electron Microscope (HRTEM). The functioning of a HRTEM is based on the same principles as an optical microscope, but it uses a beam of electrons instead of visible light. One of the computational methods which then processes the obtained two-dimensional images is called the Geometrical Phase Analysis (GPA) and makes use of a very important mathematical tool, the Fourier transform. The GPA method lies at the center of this project and consists of several steps. First, the Fourier transform of the lattice image is plotted and two Bragg peaks corresponding to two linearly independent frequency vectors in the power spectrum are chosen. Next, a mask is applied around these peaks, separately. In my project I have chosen to apply the Hann smoothing filter. Then, the inverse Fourier transform is applied to the masked image and the phase (also called the raw phase) is plotted. The next step is to compute the reduced phase, which is defined at a local pixel as being the raw phase from which the following product is subtracted: 2𝜋 ⃗𝑔 ⋅ ⃗𝑟, where ⃗𝑟 is the vector corresponding to a pixel in the real space and ⃗𝑔 the frequency vector corresponding to the Bragg peak around which one has applied the mask. At this point the reference region is computed by choosing a smooth, homogeneous area in the reduced phase image. In order to obtain the strain, one needs an optimal frequency vector ⃗𝑔 defined at every pixel of lattice. In order to do so, a minimization process defined in the context of a computer algorithm in the programming language Python has been implemented. These computations should lead to obtaining the lattice strain, which is calculated by taking the symmetric part of the derivation of the displacement obtained from the two linearly independent Fourier components, which is in turn called the distortion. The antisymmetric part of the distortion is the rotation component and serves as a check for the correctness of the computational method. The goal of my project is not only to provide a solid theoretical background for the GPA method and to discuss the strain at atomic level in several lattice patterns, but to also provide a rigorous computer algorithm that makes these computations reality. This algorithm, opposed to pre-existing software, facilitates the reader’s process immensely by the large amount of detail which is given at every step, detail which easily motivates and supports the reader in potential side-steps they would want to take in order to make the method their own.