The real space method for dynamical electron diffraction calculations in high resolution electron microscopy: I. Principles of the method

Abstract

The real space method for dynamical electron diffraction calculations has been established on a more rigorous basis than in the original paper of 1980. First, the validity of the high energy approximation for deriving the high energy differential equation is critically examined. Then, the second-order slice expansion, which is the basis of the real space method, is compared with other existing slice methods, and it is shown why the originally proposed algorithm can lead to computational divergencies and how they can be avoided. Then the real space method is applied to calculate the wavefunction in Au, to show that, in the limit of small slice thickness and sampling distance, even for heavily scattering material, the results are identical with those obtained from the multislice and the iterative methods. Finally, it is shown that in the case of light scattering materials such as SiF 4 and foil thicknesses of the order of 10 to 20 nm, the accuracy obtained with the real space method can be several times better than that of the first-order multislice method, using the same slice thickness.