Bloch-wave-based STEM image simulation with layer-by-layer representation

In a dynamical STEM image simulation by the Bloch-wave method, Allen et al. formulated a framework for calculating the cross-section for any incoherent scattering process from the inelastic scattering coefficients: thermal diffuse scattering (TDS) for high-angle annular dark-field (HAADF) and back-scattered electron (BSE) STEM, and ionization for electron energy-loss spectroscopy (EELS) and energy-dispersive X-ray spectroscopy (EDX) STEM. Furthermore, their method employed a skillfull approach for deriving the excitation amplitude and block diagonalization in the eigenvalue equation. In the present work, we extend their scheme to a layer-by-layer representation for application to inhomogeneous crystals that include precipitates, defects and atomic displacement. Calculations for a multi-layer sample of Si-Sb-Si were performed by multiplying Allen et al.'s block-diagonalized matrices. Electron intensities within the sample and EDX STEM images, as an example of the inelastic scattering, were calculated at various conditions. From the calculations, 3-dimensional STEM analysis was considered.