A critical-dimension scanning electron microscope (CD-SEM) is widely used for measuring the most important semiconductor device pattern geometries, known as critical dimensions (CDs). Radiation damage by the electron beam to patterns of materials, such as an extreme ultraviolet lithography (EUVL) resist, is a serious issue. A low-voltage SEM (LV-SEM) provides a gentler metrology tool for patterns. However, both spherical and chromatic aberrations of the objective lens increase, and thus the beam spot size becomes larger for lower landing energy beam. Aberration correction is necessary to improve the resolution of LV-SEMs. One of the typical corrector is an electron mirror with a large angle bending magnet, typically bending the beam over 90 degrees. Such large-angle deflection causes significant deflection aberrations. As a result, special complicated designs and precise machining and assembly have been implemented to suppress these aberrations. The technology of micro-electro-mechanical systems (MEMS) has advanced considerably. MEMS technology should, therefore, make it possible to realize miniature-scale mirrors as well. It will be possible to reduce the deflection angle of the electron beam further, sufficiently suppressing undesirable aberrations. This would drastically reduce not only manufacturing costs but also the size of the corrector unit. The goal of this dissertation is to suggest a conceptual design of a low-voltage aberration-corrected scanning electron microscope using a novel miniature electron mirror corrector and small-angle deflectors. By referring to prior research, we start by investigating perturbation theory for mirrors and deflectors to derive formulae for aberration coefficients.
First, we derive the aberration theory of electron mirrors. For the electron mirror, the incident electron must be reflected by the electrostatic field, and the slope of the trajectory, with respect to the optic axis, becomes divergent. To avoid it, time is taken as a parameter. Integral aberration formulae for both on- and off-axis path deviation and aberration coefficients up to second rank and third order for the system of rotationally symmetric electrostatic and magnetic fields, which overlap with each other, are derived.
Second, we derive the deflection aberration theory for standard lenses and deflectors. By applying perturbation theory to a system of round symmetric electrostatic and magnetic lenses and electrostatic and magnetic deflectors, relativistic deflection trajectory formulae and aberration coefficient formulae for deflection up to second rank and third order are derived for two independent deflectors in three types of configurations.
Third, we derive the deflection aberration theory for systems that include electron mirrors. A non-relativistic time-dependent deflection theory is developed based on the consideration of non-relativistic time-dependent aberration theory for round symmetric electrostatic and magnetic fields and on the deflection aberration theory of standard electron optics. The time-dependent deflection theory of mirrors and small angle deflectors up to second rank and third order is derived.
Forth, we propose a miniature aberration corrector consisting of double magnetic deflectors and double electrostatic mirrors, named the S-corrector. The optical properties of an SEM equipped with the proposed S-corrector with 50-mrad magnetic deflection are analyzed. Design examples of miniature mirrors and deflectors, as well as a possible configuration for an SEM with the post-deflection S-corrector, with a deflection angle of 50 mrad, are presented. Numerical calculations of aberration properties for a miniature electron mirror and double deflectors are performed using the formulae derived. The estimation method for higher-rank combination aberrations up to fourth rank and fifth order was considered. The estimated results of deflection aberrations and combination aberrations are, at their largest, 0.2 nm, which is negligible compared with target spot sizes of 1 nm for a landing voltage of 1000 V and 1.5 nm for a landing voltage of 100 V, except for fourth-rank chromatic spherical aberration and fifth-order spherical aberration. Numerical calculations based on wave optics are performed, accounting for all combination aberrations and residual deflection aberrations. The calculated spot sizes are 0.976 nm and 1.367 nm for landing voltages of 1000 V and 100 V, respectively. The potential of an aberration-corrected LV-SEM by miniature mirrors with small angle deflectors is demonstrated.

Time-dependent perturbation theory was originally studied for analyzing the aberration properties of electrostatic mirrors. The describing parameter of the theory is time and the perturbation is constructed based on the velocity of electrons, instead of slope of trajectories with respect to the optic axis, to avoid divergence at the reflection. This article gives a detailed review and further investigation on the time-dependent theory of the system of electron mirrors, composed of both rotationally symmetric electrostatic and magnetic fields. We review everything from the concept of the time-dependent theory to the procedure of perturbation method. Then, the second-rank aberration coefficients, the third-order geometrical aberration coefficients, and the aberration coefficients induced by variation in voltages and currents, including the off-axis aberrations, are derived. We give the time-dependent small-angle deflection aberration theory up to the third order, for a system composed not only of rationally symmetric fields but also of small angle deflection fields, such as a few degrees.