Computational comparisons between the conventional multislice method and the third-order multislice method for calculating high-energy electron diffraction and imaging

Abstract The third-order multislice method (TOMS) for the calculation of high-energy electron microscopic diffraction patterns and images, as proposed by Van Dyck, is tested by detailed computations. Results calculated by the TOMS and the conventional multislice method (CMS) with different slice thicknesses and dynamical apertures ( g max values) are compared with the accurate results. It is pointed out that for both the TOMS and the CMS there are basically two types of errors. One is the intrinsic error imposed by the order of the method in slice thickness, which appears as the pseudo HOLZ (high-order Laue zone) effect in the diffraction patterns, Another is the numerical error caused by the finite dynamical aperture, such as the aliasing error and the intensity-loss error. For zero-order Laue zone (ZOLZ) calculations, it is shown that the intrinsic errors are the dominant errors for both the TOMS and the CMS since the elimination of the intrinsic error leads to the disappearance of the numerical error, as long as the dynamical aperture is large enough to cover all the ZOLZ reflections. It is also shown that the TOMS has much smaller intrinsic error than the CMS for a large slice thickness and therefore is superior to the CMS with respect to accuracy vs. computational time for ZOLZ calculations. Nevertheless, the normalisation of the total intensity, as an error criterion, is more reliable for the TOMS than for the CMS. Hence, TOMS is a feasible and competitive procedure for dynamical calculations in high-energy electron diffraction (HEED). Possible error sources of practical multislice procedures are thoroughly discussed.