COMPUTATIONAL COMPARISONS BETWEEN THE CONVENTIONAL MULTISLICE METHOD AND THE 3RD-ORDER MULTISLICE METHOD FOR CALCULATING HIGH-ENERGY ELECTRON-DIFFRACTION AND IMAGING

The third-order multislice method (TOMS) for the calculation of high-e nergy electron microscopic diffraction patterns and images, as propose d by Van Dyck, is tested by detailed computations. Results calculated by the TOMS and the conventional multislice method (CMS) with differen t slice thicknesses and dynamical apertures (g(max) values) are compar ed 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 intri nsic error imposed by the order of the method in slice thickness, whic h appears as the pseudo HOLZ (high-order Laue zone) effect in the diff raction 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 disappe arance of the numerical error, as long as the dynamical aperture is la rge enough to cover all the ZOLZ reflections. It is also shown that th e TOMS has much smaller intrinsic error than the CMS for a large slice thickness and therefore is superior to the CMS with respect to accura cy vs. computational time for ZOLZ calculations. Nevertheless, the nor malisation of the total intensity, as an error criterion, is more reli able for the TOMS than for the CMS. Hence, TOMS is a feasible and comp etitive procedure for dynamical calculations in high-energy electron d iffraction (HEED). Possible error sources of practical multislice proc edures are thoroughly discussed.