The importance of backscattering in high‐energy electron diffraction calculations

The Schrödinger equation, describing the motion of a high‐energy electron in a crystal foil, can be solved exactly with appropriate boundary conditions. The formal analytical solution in matrix form however is not suitable for numerical calculations but can be expanded in a series of terms proportional to subsequent powers of the electron wavelength. In the case of fast electron scattering, the electron wavelength decreases so that, to a good approximation, the series can be cut off after the low order terms, yielding a relatively simple expression. This expression reveals two corrections to the dynamical solution of Howie and Whelan, which was obtained by neglecting second order derivative terms in the Schrüdinger equation. From an analysis of these corrections, an investigation of the validity of the Howie‐Whelan solntion could be performed as function of the cqwtal thickness and an estimation for the thickness limit could be derived.