An evaluation of the aberrations of focused beams of charged particles caused by space charge

Abstract

The aberrations, caused by the space charge, of both focused electron and ion beams, which prevent the attainment of highly resolved images in electron microscopy and which set a limit to the maximum current density in electron or ion beam machines are evaluated. Firstly, the aberrations caused by space-charge defects such as defocusing, change of magnification, as well as spherical aberration, coma, curvature of field, astigmatism and distortion analogous to Seidel's five aberrations, are deduced by means of the eiconal method by use of the potential distribution of the space charge of the beam itself in the focusing lens. It is found that, although the defocusing effect due to space charge is a most important defect, the other aberrations caused by space charge are rarely as severe as the defocusing, because all aberrations due to space charge act against the normal Seidel aberrations, i.e. so as to reduce them. According to the numerical examples, even in electron microscopy and electron beam devices with a high current, the resolving power or the minimum spot size is not yet limited by the space-charge effect, but by the spherical aberration and astigmatism caused by manufacturing inaccuracy or inhomogeneity of the material. The caustic patterns of focused ion beams are, in general, much more affected by space charge than those of electron beams of the same incident energy, because of the large mass of the ion. It is experimentally ascertained that, even though the increase of focal length is certainly caused by the defocusing effect due to space charge, a limit to the radius of least confusion of a focused ion beam with an accelerating potential of 30 kv and a beam current 500 μA is apparently not yet set by the space-charge effect, but by spherical aberration, because of the cancelling action of negative and positive aberrations.