Fast STEM image simulation in low-energy transmission electron microscopy by the accurate Chen-van-Dyck multislice method

The Chen-van-Dyck (CVD) formulation as a rigorous numerical solution to the Schrödinger equation has been demonstrated being the only accurate multislice method for calculating diffraction and imaging in low-energy transmission electron microscopy. The CVD formulation not only considers the forward scattering effects but also includes the backscattering effects. However, since its numerical computation has to be performed in real-space, the CVD method may suffer from divergence and inefficiency in computing time, especially when used for low-energy scanning transmission electron microscopy (STEM) image simulation. The present study investigates the influence of cutoff value and slice thickness on the accuracy and efficiency of STEM image simulation using this formula. The results show that a small cutoff value is required in the low-energy regime to ensure accuracy, especially for thick specimens. The optimal slice thickness can be predicted approximately by a simple equation. To speed up STEM imaging simulation by up to 17 times using the CVD formulation, a hybrid computation model incorporating multiple graphic process units (GPUs) is suggested, which is of great significance for quantitative STEM imaging in low-energy transmission electron microscopy. The significance of including backscattering effect in STEM image simulation is estimated in comparison with forward-scattering effect.