Quantification of 3D atomic positions for nanoparticles using scanning transmission electron microscopy : statistical parameter estimation, dose-limited precision and optimal experimental design
27 June 2017
Campus Groenenborger, U0.24 - Groenenborgerlaan 171 - 2020 Antwerpen (route: UAntwerpen, Campus Groenenborger
Sandra Van Aert
PhD defence Marcos ALANIA - Faculty of Science, Department of Physics
Material properties are strongly connected to the atomic structure and chemical composition. For bulk materials, most of their properties can be measured and are well understood. However, for small particles such as nanoparticles or nanoclusters with sizes in the order of the nanometric scale (1 nm = m) these properties differ from both atoms (molecules) and bulk matter. Thanks to their unique properties and numerous applications in a wide range of materials and devices, these types of particles have attracted enormous attention from the scientific and industrial community during the last years.
It has been proven, both theoretically and experimentally, that the structure of such nanomaterials is connected to their characteristic properties. Therefore, in order to deeply understand their properties, a detailed structural characterization and chemical mapping at atomic level are required. High resolution (HR) scanning transmission electron microscopy (STEM) is established as one of the experimental techniques to determine the internal structure of materials at the atomic scale. Especially when using the high angle annular dark field detector (HAADF) allows one to acquire atomically resolved images of materials, which are sensitive to their structure and chemical composition. However, one should never forget that STEM images correspond to two-dimensional (2D) projections of a three-dimensional (3D) object and very often such images cannot be used for a detailed 3D structural and morphological characterization. In order to obtain reliable 3D information, electron tomography has evolved toward a standard technique, which when combined with advanced reconstruction algorithms, enables one to visualize atoms and even determine in some nanoparticles the chemical nature atom-by-atom. Once the atomic columns or individual atoms can be resolved in 2D or 3D, respectively, the next challenge is to refine their positions and composition in a quantitative manner in order to measure these structure parameters as precisely as possible. Although HR STEM is capable of reaching sub-Angstrom resolution, quantitative structural and chemical determination require both statistical parameter estimation and image simulations. Statistical parameter estimation theory allows us to estimate the parameters by fitting a parametric model to the experimental images, where parameters of the model are measured in an iterative manner by optimising a criterion of goodness of fit. Image simulations allow us to interpret the quantum mechanical nature of the electron-specimen interaction, and are used for comparison with the experimental images in order to validate the estimated parameters. In order to develop a method that allows us to quantify the theoretical limits with which atomic columns or atoms of a nanocluster can be located in 2D and 3D, respectively, from a STEM experiment, the combination of both statistical parameter estimation and image simulations is proposed.
The concept is explored from a theoretical point of view. This thesis can be divided into four parts. The first part consist of a general introduction where the motivation and the relevance of the research is described in chapter 1. The second part summarizes the theory about the physics of the image formation in the STEM and the basic principles of statistical parameter estimation theory, in chapters 2 and 3, respectively. The third part consists of the results of this work which are discussed in chapters 4, 5 and 6. In chapter 4, the reliability of two of the most popular methods used to perform STEM image simulation are compared in terms of the parameters that are commonly used for image quantification including the integrated intensity and the precision of the atomic columns. In chapter 5, the theoretical limit with which atoms of a nanocluster can be located in 3D based on the acquisition of a tilt series of annular dark field (ADF) STEM images is explored. This study is based on the concept of the Fisher information matrix that allows us to determine an expression for the highest attainable precision with which atoms can be located in 3D. Furthermore, using this criterion some of the experimental settings are optimized. In chapter 6, the same concept is used to investigate the attainable precision with which the depth location of atoms and the centre of mass of an isolated column can be measured from a focal-series of images acquired with HAADF STEM. In addition, a 3D reconstruction method based on a focal series of HAADF STEM images is developed. Finally, in the fourth part, the general conclusions and future perspectives are drawn in chapter 7.