On the residual six-fold astigmatism in DCOR/ASCOR

Abstract After the introduction of the hexapole Cs-correctors for scanning transmission electron microscopes (STEM), the next big step forward was the strong reduction of the six-fold astigmatism A5 by means of an advanced hexapole design (DCOR/ASCOR). As a result all axial aberrations up to fifth order are sufficiently small to allow for large semi-aperture angles beyond 40 mrad for electron energies in the range of 30 to 300 kV without deterioration of the STEM resolution. In this paper we derive simple expressions for the optimum hexapole strength for minimum A5 and the size of the residual A5. Both quantities are intrinsic properties of the hexapoles and the transfer lens doublet in between. The optimum hexapole strength scales with the inverse of the electron wavelength, while the residual A5 does not depend on the electron energy directly, but on the spherical aberration Cs of the pole piece. With the given properties of the DCOR/ASCOR and typical values of Cs in the range of 0.5 to 2.7 mm, at all acceleration voltages A5 remains in the range from 0.03 to 0.4 mm, the latter even for a large-gap pole piece.