Unified mechanical aberration theory of electrostatic focusing‐deflection systems

Abstract

AbstractAn axially symmetric electrostatic focusing‐deflection system is indispensable in forming a focused ion beam. This paper describes a general procedure for quantitatively evaluating the effect of the mechanical error existing in the electrode of the electrostatic optical system on the optical characteristics. From the perturbation theory, a rigorous formula is derived for evaluating the aberrations up to the third order due to the mechanical errors. It is shown that the well‐known static deflection trajectory appears in the first‐order trajectory component. It is shown that the higher‐order trajectories (aberrations) can be represented by five aberration coefficients for the second‐order components and by 28 for the third‐order components.The present method can analyze the effect due to mutual interactions in the case where mechanical errors exist both in the deflection system and the focusing system which has been neglected. Further, in the derived evaluation formula, static mechanical aberration correction systems such as aligners and stigmators are taken into consideration. Hence, the method can evaluate the situation after the main mechanical aberrations are removed by correcting devices.