Quantitative Electron Energy-loss Spectrum Data Processing for Hyperspectral Imaging in Analytical Transmission Electron Microscopy

In this thesis, a comprehensive automated quantification process of some of the features in electron energy-loss spectroscopy (EELS) is described. For high-loss spectra, two algorithms have been proposed for automated ionization core-loss edge onset detection and quantification. The robustness of the edge detection by estimated exponent method is tested with respect to various parameters for different values of such size of the detection window, specimen thickness and an average white Gaussian noise. For quantification, the pre-edge regions and the integration ranges are automatically chosen based on the edges detected and elemental maps are calculated. A novel way of modelling background in post-edge regions is explored for GaAs high-loss spectra. However, simple post-edge background extrapolation tends to give an overestimation of the net core-loss. Hence, an optimum background is calculated from the error bars of the Poissonian statistics of net core-losses subtended by backgrounds modelled from pre- and post-edge regions. The Richardson-Lucy deconvolution method is explored at high-loss spectra to iteratively reconstruct the single scattering distribution. The ringing artefacts are studied with respect to number of iterations. A baseline correction to conventional linear least-squares method of core-loss quantification is proposed. An example of a high-loss spectrum image (SI) from a Ge based solar cell is used to test the relative quantification of Ga, As and Cu. The improvement from ~ &plusmn 8% to less than &#8818 &plusmn 3% in the quantification of Cu, Ga and As compared to other least-squares fit models are noticed. In some regions due to overlapping of core-losses, the large errors produced by standard leastsquares methods was reduced from ~ &plusmn 15% to &#8818 &plusmn 9%. The thesis also explores the joint fitting of bulk plasmons (InN, GaN and In_xGa_1-xN) and core-losses of 4d and 3d transitions of In and Ga respectively in the low-loss range < 50 eV. The effective In content in phase separated In_xGa_1-xN is quantified from two different fit ranges. A correction factor is proposed to correct the effects of a limited fit range arising due to inclusion of a truncated In reference spectrum in joint fitting. In both short and truncation corrected extended fit ranges the values of effective In content has been quantified ~ &#8818 10% with both bulk plasmons and core-losses. Chemical profiling of different regions in an EELS SI is done by mapping the positions of bulk plasmons. The full width at half maximum (FWHM) of bulk plasmon, W_p, is also studied by fitting a Lorentzian function. Regions with (surface) oxide formation or imperfection in the crystal structures due to formation of Tb–O complexes revealed an increase in W_p. The blind measurement of bandgap for a wide-bandgap material, GaN, has also been studied. The bandgap onset detection is compared for different methods such as by fitting a square-root function, derivative method and a novel approach based on the centroids of clusters identified when fit ranges are systematically varied. The square-root fitting and derivative method was applied to density of state (DOS) region between 0 eV to 12 eV to variously modelled backgrounds such as exponential tail extrapolation of ZLP, Richardson-Lucy and Fourier-log deconvolutions etc. The blind measurement of bandgap with square-root fitting to ZLP subtracted GaN spectrum was found to be at 3.28 eV with an R² of 0.91 and for derivative method it was at 3.31 eV which is in agreement with the literature. The square-root fit applied to different DOS background modelling was able to determine bandgap at 3.52 &plusmn 0.91 eV where as from derivative method it was 3.52 &plusmn 0.41 eV. The bandgap measured using centroid of the highest R² in the clusters detected using k-means clustering analysis was found to be at 3.52 &plusmn 0.91 eV which is comparable to square-root fits. The blind measurement of bandgap was applied to test for GaAs spectrum. The determined values with derivative and k-means cluster analysis was found to be at 1.40 eV and 1.20 eV, respectively. The precise measurement of bandgaps from EELS for an unknown material is found to be difficult (&#8818 &plusmn 0.41 eV) when compared to optical spectroscopy.

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Recommended citation: V. C. Angadi (2018), "Quantitative Electron Energy-loss Spectrum Data Processing for Hyperspectral Imaging in Analytical Transmission Electron Microscopy", Doctoral Thesis, University of Sheffield, UK.