Evaluation of residual aberration in fifth-order geometrical aberration correctors

Higher order geometrical aberration correctors for transmission electron microscopes are essential for atomic-resolution imaging, especially at low-accelerating voltages. We quantitatively calculated the residual aberrations of fifth-order aberration correctors to determine the dominant aberrations. The calculations showed that the sixth-order three-lobe aberration was dominant when fifth-order aberrations were corrected by using the double-hexapole or delta types of aberration correctors. It was also deduced that the sixth-order three-lobe aberration was generally smaller in the delta corrector than in the double-hexapole corrector. The sixth-order three-lobe aberration was counterbalanced with a finite amount of the fourth-order three-lobe aberration and 3-fold astigmatism. In the experiments, we used a low-voltage microscope equipped with delta correctors for probe- and image-forming systems. Residual aberrations in each system were evaluated using Ronchigrams and diffractogram tableaux, respectively. The counterbalanced aberration correction was applied to obtain high-resolution transmission electron microscopy images of graphene and WS2 samples at 60 and 15 kV, respectively.