A new theoretical and practical approach to the multislice method

The multislice formulation of Cowley and Moodie for high-energy electron scattering is rederived from the Schrödinger equation, and the validity of the finite slice approach in practical computation is theoretically proved by the stationary-phase approximation. A set of computer programs for the multislice method is developed, where the convolution integral is carried out through the fast Fourier transform. The following conditions are required to obtain a sufficiently accurate result in multislice calculations: (1) the maximum slice thickness should be about kd², where k is the wavenumber of the incident electrons and d is the distance over which the potential does not change appreciably; (2) there must be a sufficient number of beams in the multislice iteration to prevent the aliasing effect of convolution. The multiple scattering masks the real specimen structure when the specimen thickness exceeds a certain value. This effect of multiple scattering is recognized from the probability distribution of the scattered electrons in addition to the scattering amplitudes obtained through the procedure developed in the present work.