Phonon scattering: how does it affect the image contrast in high-resolution transmission electron microscopy?

In quantitative high-resolution transmission electron microscopy (HRTEM), the theoretically calculated images usually give better contrast than the experimentally observed images although all the factors have been accounted for. It is suggested that this discrepancy is due to thermal diffusely scattered electrons, which were not included in the image calculation. The question is: how do they affect the image contrast? In this paper, under the weak-phase object approximation, it is shown that the contribution of the thermal diffusely scattered electrons to the image is of the same order as the cross-interference terms for the Bragg reflected beams in the dark-field HRTEM imaging. Indirect experimental measurements showed that thermal diffuse scattering (TDS) is not a small effect; rather it is the dominant scattering at large angles. The TDS absorption is measured and the result indicates that about 12% of the incident electrons have been diffusely scattered to angles larger than 15.6 degrees (the column angle of the transmission electron microscope) by a Si foil as thin as 15-20 nm. The data clearly show the magnitude and importance of TDS in HRTEM. It is therefore mandatory to include this component in image calculation.