Quantitative methods for electron energy loss spectroscopy

Abstract

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.

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.