Third-order spherical aberration correction using multistage self-aligned quadrupole correction-lens systems

New multistage self-aligned quadrupole correction-lens systems are proposed for correcting the spherical aberration of a rotationally symmetrical lens in a probe-forming system such as electron beam lithography and focused ion beam. These multistage correction-lens systems consist of six- or eight-stage electrostatic quadrupole and aperture electrodes placed between the quadrupoles. An octupole field for the correction of aperture aberration is automatically created and aligned with a quadrupole field by supplying a voltage to the aperture electrode. The optical properties of the self-aligned quadrupole correction-lens systems are precisely simulated using the potential functions approximated from the calculated three-dimensional potential distributions. The lens components of the correction-lens systems are symmetric with respect to the mid-plane of the correction system, and the quadrupole excitations are anti-symmetric to the mid-plane. The simulated optical properties of the six- and eight-stage self-aligned quadrupole correction-lens systems are compared with a four-stage self-aligned quadrupole correction-lens system. Aperture aberration coefficients of the six- or eight-stage quadrupole system under non-excitation of the aperture electrodes become much smaller than those of the four-stage quadrupole system. It is found that the correction of spherical aberration using the six- or eight-stage self-aligned quadrupole correction-lens system can be easily achieved under the condition of considerably lower excitation of lens elements in comparison to the four-stage self-aligned quadrupole correction-lens system.