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.

This report focuses on the process of aberration coefficient retrieval for measurements of a
Scanning Electron Microscope (SEM). The main goal is the verification of a modified aberration coefficient retrieval method described in an article by Uno et al. (2005) [1]. This method
first extracts spot profiles, represented by Point Spread Functions (PSFs), from a through-focus
series of SEM images using Fourier analysis. The size and shape of a PSF characterize the
performance of a SEM. Afterward, it determines characteristics from these PSFs to obtain
aberration coefficients.
The process consisted of three parts: probe shape extraction, PSF analysis, and aberration coefficient calculation, which included a consistency test. The original method was changed to
include clarification for the use of complex conjugates of functions in the Fourier domain, the
proper statistical definition of standard deviation as characteristic of the width of a PSF, the
curvature definition used in the method, and contour tracing around a PSF to exclude points
outside the contour. These adaptations were made to clarify the methods described in the reference article.
This modified method was tested against generated PSFs that used the wave-optical description
of five different aberrations. By increasing the value of these individual simulated aberration
coefficients C
′
n with factors s ∈ [1, S], S ∈ N, the consistency of this retrieval method could be
determined by calculating the ratio Q between simulated and retrieved aberration coefficients
as a function of the factor s.
The spot shape extraction method was implemented and assessed successfully, as the shapes of
the generated PSFs were successfully retrieved, and the use of complex conjugates of functions
in the Fourier domain resulted in rotated spot shapes.
Contour tracing around the retrieved PSFs had mixed results. For all aberrations, it presented
a good measure of the spot shape. The implementation of an algorithm that excluded points
pj outside the contour was not accurate for one test aberration: two-fold astigmatism A2. The
contour tracing algorithm excludes important parts of the shapes of the PSFs. From research
into the characteristics asymmetry µ, width σ, and curvature ρ it could be inferred that the first
two characteristics µ and σ represent the mean and standard deviation of discrete probability
mass functions. Curvature ρ has no such direct statistical equivalent, it was concluded however
that this characteristic presented a good measure for the effect of third-order spherical aberration in a PSF.
Results could not indicate that this wave-optical description of aberrations is consistent with
all of the coefficients retrieved using the modified method of aberration coefficient retrieval
as the ratio Q remained consistent for defocus Cdf , three-fold astigmatism A2 and third-order
spherical aberration Cs as a function of the factors s.
Continued research into this method of aberration retrieval is recommended, specifically in the
definitions of the characteristic curvature ρ, more advanced contour tracing, and the digitizations of aberration coefficients. More assessment and modification of this method of aberration
coefficient retrieval can allow for a more comprehensive understanding of the method, which
will eventually contribute to an automatic aberration corrector that could speed up SEM measurements significantly.