Quantitative methods for electron energy loss spectroscopy

[spa] Este trabajo explora las posibilidades analíticas que ofrece la técnica de espectroscopia electrónica de bajas pérdidas (low-loss EELS), capaces de revelar la configuración estructural de los más avanzados dispositivos semiconductores. El uso de modernos microscopios electrónicos de transmisión-barrido (STEM) nos permite obtener información espectroscópica a partir de volúmenes reducidos, hasta llegar a resolución atómica. Por ello, EELS es cada vez mas popular para la observación de los dispositivos semiconductores, a medida que los tamaños característicos de sus estructuras constituyentes se miniaturiza. Los espectros de pérdida de energía contienen mucha información: dado que el haz de electrones sufre unos bien conocidos procesos de dispersión inelástica, podemos trazar relaciones entre estos espectros y excitaciones elementales en la configuración atómica de los elementos y compuestos constituyentes de cada material. Se describe un marco teórico para el estudio del low-loss EELS: el modelo dieléctrico de dispersión inelástica, que toma en consideración las propiedades electrodinámicas del haz de electrones y la descripción mecano-cuántica de los materiales. Adicionalmente, se describen en detalle las herramientas utilizadas en el análisis de datos experimentales o la simulación teórica de espectros. Monitorizando las energías de band gap y plasmon en los datos experimentales de low-loss EELS se obtiene información directa sobre propiedades electrónicas de los materiales. Además, usando análisis Kramers-Kronig en los espectros se obtiene información dieléctrica que puede ser comparada con las simulaciones o con otras técnicas (ópticas). Se demuestra el uso de estas herramientas con una serie de estudios sobre estructuras basadas en nitruros del grupo-III. Por otro lado, el uso de algoritmos para el análisis multivariante permite separar las contribuciones individuales que se miden mezcladas en espectros de estructuras complicadas. Hemos utilizado estas avanzadas herramientas para el análisis de estructuras basadas en silicio que contienen nano-cristales embebidos en matrices dieléctricas.[eng] This thesis explores the analytical capabilities of low-loss electron energy loss spectroscopy (EELS), applied to disentangle the intimate configuration of advanced semiconductor heterostructures. Modern aberration corrected scanning transmission electron microscopy (STEM) allows extracting spectroscopic information from extremely constrained areas, down to atomic resolution. Because of this, EELS is becoming increasingly popular for the examination of novel semiconductor devices, as the characteristic size of their constituent structures shrinks. Energy-loss spectra contain a high amount of information, and since the electron beam undergoes well-known inelastic scattering processes, we can trace the features in these spectra down to elementary excitations in the atomic electronic configuration. In Chapter 1, the general theoretical framework for low-loss EELS is described. This formulation, the dielectric model of inelastic scattering, takes into account the electrodynamic properties of the fast electron beam and the quantum mechanical description of the materials. Low-loss EELS features are originated both from collective mode (plasmons) and single electron excitations (e.g. band gap), that contain relevant chemical and structural information. The nature of these excitations and the inelastic processes involved has to be taken into account in order to analyze experimental data or to perform simulations. The computational tools required to perform these tasks are presented in Chapter 2. Among them, calibration, deconvolution and Kramers-Kronig analysis (KKA) of the spectrum constitute the most relevant procedures, that ultimately help obtain the dielectric information in the form of a complex dielectric function (CDF). This information may be then compared to the one obtained by optical techniques or with the results from simulations. Additional techniques are explained, focusing first on multivariate analysis (MVA) algorithms that exploit the hyperspectral acquisition of EELS, i.e. spectrum imaging (SI) modes. Finally, an introduction to the density functional theory (DFT) simulations of the energy-loss spectrum is given. In Chapter 3, DFT simulations concerning (Al, Ga, In)N binary and ternary compounds are introduced. The prediction of properties observed in low-loss EELS of these semiconductor materials, such as the band gap energy, is improved in these calculations. Moreover, a super-cell approach allows to obtain the composition dependence of both band gap and plasmon energies from the theoretical dielectric response coefficients of ternary alloys. These results are exploited in the two following chapters, in which we experimentally probe structures based on group-III nitride binary and ternary compounds. In Chapter 4, two distributed Bragg reflector structures are examined (based upon AlN/GaN and InAlN/GaN multilayers, respectively) through different strategies for the characterization of composition from plasmon energy shift. Moreover; HAADF image simulation is used to corroborate he obtained results; plasmon width, band gap energy and other features are measured; and, KKA is performed to obtain the CDF of GaN. In Chapter 5, a multiple InGaN quantum well (QW) structure is examined. In these QWs (indium rich layers of a few nanometers in width), we carry out an analysis of the energy-loss spectrum taking into account delocalization and quantum confinement effects. We propose useful alternatives complementary to the study of plasmon energy, using KKA of the spectrum. Chapters 6 and 7 deal with the analysis of structures that present pure silicon-nanocrystals (Si-NCs) embedded in silicon-based dielectric matrices. Our aim is to study the properties of these nanoparticles individually, but the measured low-loss spectrum always contains mixed signatures from the embedding matrix as well. In this scenario, Chapter 6 proposes the most straightforward solution; using a model-based fit that contains two peaks. Using this strategy, the Si-NCs embedded in an Er-doped SiO2 layer are characterized. Another strategy, presented in Chapter 7, uses computer-vision tools and MVA algorithms in low-loss EELS-SIs to separate the signature spectra of the Si-NCs. The advantages and drawbacks of this technique are revealed through its application to three different matrices (SiO2, Si3N4 and SiC). Moreover, the application of KKA to the MVA results is demonstrated, which allows to extract CDFs for the Si-NCs and surrounding matrices

Excitations in cubic BaSnO3_{3}: a consistent picture revealed by combining theory and experiment

Among the transparent conducting oxides, the perovskite barium stannate is most promising for various electronic applications due to its outstanding carrier mobility achieved at room temperature. Most important characteristics however, $i.e.$, its band gap, effective masses, and absorption edge remain controversial. Here, we provide a fully consistent picture by combining state-of-the-art $ab~initio$ methodology with forefront electron energy-loss spectroscopy (EELS) and optical absorption measurements. On- and off-axis valence EELS spectra, featuring signals originating from band gap transitions, are acquired on defect-free sample regions of a BaSnO$_{3}$ single crystal. These high-energy-resolution measurements are able to capture also very weak excitations below the optical gap, attributed to indirect transitions. By temperature-dependent optical absorption measurements, we assess band-gap renormalization effects induced by electron-phonon coupling. Overall, we find for the effective electronic mass, the direct and the indirect gap, the optical gap as well as the absorption onsets and spectra excellent agreement between both experimental techniques and the theoretical many-body results, supporting also the picture of a phonon-mediated mechanism where indirect transitions are activated by phonon-induced symmetry lowering. This work demonstrates a fruitful connection between different high-level theoretical and experimental methods for exploring the characteristics of advanced materials

Insight into the compositional and structural nano features of AlN/GaN DBRs by EELS-HAADF

: III-V nitride ~AlGa!N distributed Bragg reflector devices are characterized by combined high-angle annular dark-field ~HAADF! and electron energy loss spectroscopy ~EELS! in the scanning transmission electron microscope. Besides the complete structural characterization of the AlN and GaN layers, the formation of AlGaN transient layers is revealed using Vegard law on profiles of the position of the bulk plasmon peak maximum. This result is confirmed by comparison of experimental and simulated HAADF intensities. In addition, we present an advantageous method for the characterization of nano-feature structures using low-loss EELS spectrum image ~EEL-SI! analysis. Information from the materials in the sample is extracted from these EEL-SI at high spatial resolution.The log-ratio formula is used to calculate the relative thickness, related to the electron inelastic mean free path. Fitting of the bulk plasmon is performed using a damped plasmon model ~DPM! equation. The maximum of this peak is related to the chemical composition variation using the previous Vegard law analysis. In addition, within the context of the DPM, information regarding the structural properties of the material can be obtained from the lifetime of the oscillation. Three anomalous segregation regions are characterized, revealing formation of metallic Al islands

Quantitative parameters for the examination of InGaN QW multilayers by low-loss EELS

We present a detailed examination of a multiple InxGa1−xN quantum well (QW) structure for optoelectronic applications. The characterization is carried out using scanning transmission electron microscopy (STEM), combining high-angle annular dark field (HAADF) imaging and electron energy loss spectroscopy (EELS). Fluctuations in the QW thickness and composition are observed in atomic resolution images. The impact of these small changes on the electronic properties of the semiconductor material is measured through spatially localized low-loss EELS, obtaining band gap and plasmon energy values. Because of the small size of the InGaN QW layers additional effects hinder the analysis. Hence, additional parameters were explored, which can be assessed using the same EELS data and give further information. For instance, plasmon width was studied using a model-based fit approach to the plasmon peak; observing a broadening of this peak can be related to the chemical and structural inhomogeneity in the InGaN QW layers. Additionally, Kramers-Kronig analysis (KKA) was used to calculate the complex dielectric function (CDF) from the EELS spectrum images (SIs). After this analysis, the electron effective mass and the sample absolute thickness were obtained, and an alternative method for the assessment of plasmon energy was demonstrated. Also after KKA, the normalization of the energy-loss spectrum allows us to analyze the Ga 3d transition, which provides additional chemical information at great spatial resolution. Each one of these methods is presented in this work together with a critical discussion of their advantages and drawbacks

EEL spectroscopic tomography: Towards a new dimension in nanomaterials analysis

Electron tomography is a widely spread technique for recovering the three dimensional (3D) shape of nanostructured materials. Using a spectroscopic signal to achieve a reconstruction adds a fourth chemical dimension to the 3D structure. Up to date, energy filtering of the images in the transmission electron microscope (EFTEM) is the usual spectroscopic method even if most of the information in the spectrum is lost. Unlike EFTEM tomography, the use of electron energy-loss spectroscopy (EELS) spectrum images (SI) for tomographic reconstruction retains all chemical information, and the possibilities of this new approach still remain to be fully exploited. In this article we prove the feasibility of EEL spectroscopic tomography at low voltages (80kV) and short acquisition times from data acquired using an aberration corrected instrument and data treatment by Multivariate Analysis (MVA), applied to FexCo(3-x)O4@Co3O4 mesoporous materials. This approach provides a new scope into materials; the recovery of full EELS signal in 3D

Electron energy-loss spectroscopic tomography of FexCo(3-x)O4 impregnated Co3O4 mesoporous particles: unraveling the chemical information in three dimensions

Electron energy-loss spectroscopy-spectrum image (EELS-SI) tomography is a powerful tool to investigate the three dimensional chemical configuration in nanostructures. Here, we demonstrate, for the first time, the possibility to characterize the spatial distribution of Fe and Co cations in a complex FexCo(3-x)O4/Co3O4 ordered mesoporous system. This hybrid material is relevant because of the ferrimagnetic/antiferromagnetic coupling and high surface area. We unambiguously prove that the EELS-SI tomography shows a sufficiently high resolution to simultaneously unravel the pore structure and the chemical signal

3D Visualization of the Iron Oxidation State in FeO/Fe3O4 Core-Shell Nanocubes from Electron Energy Loss Tomography.

Left panel shows the explained variance ratio of the principal component analysis (PCA) decomposition. The six first components, which are enough to explain the whole data set, are plotted in the right panel. Components 0, 3 and 5 show no remarkable features in the Fe L2,3 ionization energy and seem rather related to the background of the spectra due to their power-law behaviour, while component 1 is almost constant and therefore could be related to the dark noise in the detector

3D Visualization of the Iron Oxidation State in FeO/Fe3O4 Core-Shell Nanocubes from Electron Energy Loss Tomography

The physicochemical properties used in numerous advanced nanostructured devices are directly controlled by the oxidation states of their constituents. In this work we combine electron energy-loss spectroscopy, blind source separation, and computed tomography to reconstruct in three dimensions the distribution of Fe and Fe ions in a FeO/FeO core/shell cube-shaped nanoparticle with nanometric resolution. The results highlight the sharpness of the interface between both oxides and provide an average shell thickness, core volume, and average cube edge length measurements in agreement with the magnetic characterization of the sample