Particle Optical Corrector Eliminates Sixth-Order Axial Errors
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Solution Overview
Problem
Existing particle optical correctors for electron microscopes struggle to completely eliminate higher-order axial errors such as the sixth-order axial three-lobe error, which degrades image quality, and introduce additional errors that negate the improvement achieved.
Innovation Solution
A particle optical corrector design with a central hexapole field and two outer identical hexapole fields, carefully optimized to eliminate three-fold axial astigmatism, fourth-order axial three-lobe error, and six-fold axial astigmatism, ensuring the vectors representing these errors cancel each other out, thereby eliminating the sixth-order axial three-lobe error.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing particle optical correctors are used to correct aperture errors, then chromatic and spherical aberrations are compensated, but sixth-order axial three-lobe error and other higher-order axial errors are introduced or remain uncorrected
Solution Approach 1:
The corrector is divided into three separate multipole elements (first, second, and third multipole elements) that can independently generate hexapole fields. Each element contributes to correcting different components of the aberrations, allowing the system to eliminate sixth-order axial three-lobe error while maintaining correction of lower-order aberrations.
Solution Approach 2:
Each multipole element is positioned at a specific distance from the optical axis and has tailored field strength characteristics. The first and third multipole elements are positioned symmetrically at distance d1, while the second is at distance d2, creating localized field distributions that collectively eliminate higher-order axial errors without compromising overall image quality.
2Reliability
If correctors generate non-rotationally symmetric fields to correct aberrations, then chromatic and spherical aberrations are compensated, but additional intrinsic residual errors are introduced
Solution Approach 1:
The corrector employs non-rotationally symmetric hexapole fields generated by three multipole elements with specific spatial arrangements. The asymmetric field distribution is deliberately designed to counteract the symmetric aberration patterns, enabling cancellation of sixth-order axial three-lobe error while maintaining correction of lower-order aberrations through the specific geometric configuration.
Solution Approach 2:
The multipole elements generate opposing hexapole fields that act as counterweights to the aberration fields. The first and third multipole elements produce fields that counterbalance the errors introduced by the second multipole element, creating a net effect that eliminates higher-order axial errors while preserving the beneficial correction of chromatic and spherical aberrations.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This design enhances image quality by eliminating residual errors up to the sixth order, minimizing diffraction limitation, and maintaining optimal aperture angle, resulting in higher-resolution images without introducing new errors.
Implementation Method 1
a central multipole element of length L to generate a hexapole field in the plane of symmetry of the corrector as well as two external identical multipole elements of length L' for generating equally strong hexapole fields
Implementation Method 2
two round lens duplets with round lenses, wherein the round lenses closer to the plane of symmetry are arranged at a distance from the plane of symmetry equal to the focal lengths of the round lenses
Data Source
Figure 1
Figure 2a~2c
Figure 3a~3b
AI summary
The invention relates to a particle-optical corrector (5) for correcting imaging errors, wherein the corrector (5) has a central multipole element (2) of length L for generating a hexapole field (ΨHP2) in the plane of symmetry (6) of the corrector (5) as well as two outer identical multipole elements (1, 3) of length L' for generating equally strong hexapole fields (ψHP1, ψHP3) and two round lens doublets (7 and 8) with round lenses (7', 7", 8', 8"). In such a corrector, the sixth-order triple lobe error (D6) is avoided by selecting the strength of the central hexapole field (ΨHP2) relative to the strengths of the two equally strong outer hexapole fields (ΨHP1,3) such that the threefold axial astigmatism (A2) vanishes and the strengths (ΨHP1,3) of the latter are selected such that the corrector (5) has no sixfold axial astigmatism (A5) overall.that the distance of the multipole elements (1 and 3) from the circular lenses (7", 8") located further away from the plane of symmetry (6), whose focal length (f') corresponds to an additional distance (Δz) chosen such that the fourth-order axial trilobe error (D4) vanishes for the given lengths L and L', and that the length (L) of the central multipole element (2) is chosen in relation to the lengths (L') of the multipole elements (1 and 3) such that the sixth-order axial trilobe error (D6) vanishes for the given ratio (M = f / f') of the focal length (f') of the circular lenses (7', 8') closer to the plane of symmetry (6) to the focal length (f') of the circular lenses (7", 8") further away from the plane of symmetry (6).