K. Scheerschmdit and V. Kuhlmann
The quantitative analysis of electron microscope images require image simulations of the object wave function (exit wave) based on well relaxed structure models and a suitable description of the electron scattering. The elastic interaction between electrons and an object can be simulated with good accuracy using the multi-slice formulation of the dynamical theory of electron interferences. Thereby the concept of structure factors is applied or the scattering potential V(r) is given by solving the Poisson equation for the charge density.
Calculations of V(r) on the first principle level may include quantum effects properly and describe electronic properties completely, however, they are computationally too expensive for large systems because the diagonalization of the Hamiltonian scales as O(N3). Empirical MD enable larger structure relaxations, but the inter-atomic forces used are accurate only if the influence of the local environment according to the electronic structure is included. The analytic BOP achieves O(N) scaling by diagonalizing the orthogonal TB-Hamiltonian approximately and is recognized as a fast and accurate model for atomic interaction especially in higher order approximation as BOP4+. The Figure shows as an example 4 hydrogen atoms in a Si-lattice colored with the electron density calculated by DFT (left) and the resulting phase grating map (right) scanned from BOP4+ of the central slice which may be used as V(r) in HREM simulations.