An accurate multislice method for low-energy transmission electron microscopy

The conventional multislice method (CMS), originally proposed by Cowley and Moodie (1957), is an important algorithm for image and electron diffraction calculations in transmission electron microscopy. Nevertheless, this method is based on the so-called high-energy approximation, which neglects the second differential term ∂2φ(r)/∂z2 to greatly simplify the calculation without severe loss of accuracy. In the current study, we show that for low-energy transmission electron microscopy (LE-TEM) (<100 kV), the high-energy approximation error becomes large and the accurate multislice method, proposed by Chen and Van Dyck (1997), can be used as an alternative method to obtain more accurate calculations. The accurate multislice method, called the revised real space method (RRS) in this paper, can be realized by treating the propagation and scattering as an entirety in real space. A detailed comparison of the numerical results of the RRS and CMS at different accelerating voltages, Debye–Waller factors, and beam tilts is performed. Results show that for image and diffraction simulations in LE-TEM, CMS is no longer sufficiently accurate and the RRS procedure can be used as an alternative method with reasonable computing time.

► We have shown that in low-energy transmission electron microscopy (<100 kV), the conventional multislice method is not sufficiently accurate owing to the conventional high-energy approximation.
► We have obtained an accurate multislice solution as a numerical alternative for low-energy transmission electron microscopy.