Accurate multislice theory for elastic electron scattering in transmission electron microscopy

Combining the concept of the slice-transmission-operator matrix with the transfer matrix technique, the complete Schrِdinger equation for elastic electron scattering in solids is rigorously solved within the framework of the multislice scheme. This new approach extends the range in which the multislice theory is accurate. It is shown that the multislice theory can in principle be as accurate as the Bloch wave theory and the Green function theory in all cases of elastic electron scattering. It is pointed out that in some cases such as the calculation of high-order Laue zone (HOLZ) reflections, more accurate corrections should be made for the conventional high-energy approximation and therefore the conventional multislice method (CMS). A new multislice formula is developed for calculating the transmitted wave. This formula takes back-scattering effects into account and may therefore be accurate for large beam tilt. It is also shown that the new multislice approach keeps all the advantages of the CMS with respect to the Bloch wave method.