Magnetic Electron Lenses

ISBN-13: 9783642815188 / Angielski / Miękka / 2011 / 464 str.

P. W. Hawkes

Opis

No single volume has been entirely devoted to the properties of magnetic lenses, so far as I am aware, although of course all the numerous textbooks on electron optics devote space to them. The absence of such a volume, bringing together in formation about the theory and practical design of these lenses, is surprising, for their introduction some fifty years ago has created an entirely new family of commercial instruments, ranging from the now traditional transmission electron microscope, through the reflection and transmission scanning microscopes, to co lumns for micromachining and microlithography, not to mention the host of experi mental devices not available commercially. It therefore seemed useful to prepare an account of the various aspects of mag netic lens studies. These divide naturally into the five chapters of this book: the theoretical background, in which the optical behaviour is described and formu lae given for the various aberration coefficients; numerical methods for calculat ing the field distribution and trajectory tracing; extensive discussion of the paraxial optical properties and aberration coefficients of practical lenses, il lustrated with curves from which numerical information can be obtained; a comple mentary account of the practical, engineering aspects of lens design, including permanent magnet lenses and the various types of superconducting lenses; and final ly, an up-to-date survey of several kinds of highly unconventional magnetic lens, which may well change the appearance of future electron optical instruments very considerably after they cease to be unconventional."

Spis treści

1. Magnetic Lens Theory.- 1.1 Derivation of the Equations of Motion of Electrons in Rotationally Symmetric Magnetic Fields.- 1.2 Paraxial Properties.- 1.2.1 General Remarks.- 1.2.2 Real Cardinal Elements.- 1.2.3 Asymptotic Cardinal Elements.- 1.3 Methods of Calculating Aberration Coefficients.- 1.3.1 Characteristic Functions.- 1.3.2 The Trajectory Method.- 1.4 Aberration Coefficients.- 1.4.1 Real (Objective) Aberration Coefficients.- a) Geometrical Aberrations.- b) Chromatic Aberrations.- 1.4.2 Asymptotic (Projector) Aberration Coefficients.- a) Geometrical Aberrations.- b) Chromatic Aberrations.- 1.4.3 Aberration Matrices and the Aberrations of Lens Combinations.- 1.5 Parasitic Aberrations.- References.- 2. Magnetic Field Calculation and the Determination of Electron Trajectories.- 2.1 Basic Concepts.- 2.1.1 General Field Equations.- 2.1.2 Fourier Series Expansions of the Scalar Potential.- 2.1.3 Paraxial Expansions.- 2.1.4 Circular Vector Potentials and Related Fields.- 2.2 Methods of Discretization.- 2.2.1 The Finite-Difference Method.- 2.2.1a The Taylor Series Method.- 2.2.1b The Integral Method.- 2.2.1c Application to a Simple Magnetic Lens.- 2.2.2 Improvement of the Finite-Difference Method.- 2.2.2a Different Mesh Grids.- 2.2.2b Nine-Point Formulae.- 2.2.2c Fields in Regions with Variable Material Coefficients.- 2.2.2d Irregular Mesh Grids.- 2.2.3 The Finite-Element Method.- 2.2.3a Application to Circular Vector Potentials.- 2.2.3b Application to Saturated Magnetic Lenses.- 2.2.3c The Computation of Scalar Potential Fields.- 2.2.3d Comparison of the Finite-Element Method with the Finite-Difference Method.- 2.3 Solution of the Discretized Equations.- 2.3.1 The General Structure of the Discretized Equations.- 2.3.2 The Successive Overrelaxation Method.- 2.3.3 Survey of Other Methods.- 2.4 Differentiation and Interpolation in Mesh Grids.- 2.4.1 The Calculation of the Axial Flux Density.- 2.4.2 Interpolation in Square-Shaped Grids.- 2.5 Analytical Field Calculation.- 2.5.1 Superposition of Aperture Fields.- 2.5.2 Additional Superposition of the Fields of Charged Rings.- 2.5.3 Linear Superposition of Magnetic Ring Fields.- 2.5.4 The Integral Equation Method.- 2.5.4a Solution of Boundary-Value Problems.- 2.5.4b Solution of Problems with Interface Conditions.- 2.5.4c Integral Equations Containing the Magnetization.- 2.6 Field Calculation in Systems Without Rotational Symmetry.- 2.6.1 Lenses with Small Perturbations of the Rotational Symmetry.- 2.6.2 Toroidal Deflection Systems.- 2.6.3 Magnetic Multipole Systems.- 2.7 The Calculation of Electron Trajectories.- 2.7.1 Solution of the Paraxial Ray Equation.- 2.7.1a Initial-Value Problems.- 2.7.1b Boundary-Value Problems.- 2.7.1c Numerical Differentiation.- 2.7.1d Calculation of Aberration Coefficients and Optimization.- 2.7.2 Solution of the Lorentz Equation.- 2.7.2a The Runge-Kutta Method.- 2.7.2b A Predictor-Corrector Method.- 2.8 Concluding Remarks.- References.- 3. Properties of Electron Lenses.- 3.1 Concepts and Definitions.- 3.1.1 Definition of Lenses and Their Properties.- 3.1.2 Saturated and Unsaturated Lenses.- 3.1.3 Lens Strength Parameters.- 3.1.4 Field-Form Factor.- 3.1.5 Scaling of the Field.- 3.1.6 Scaling of Trajectories.- 3.2 Field Distribution in Unsaturated Lenses.- 3.2.1 Symmetrical Lenses.- 3.2.2 Asymmetrical Lenses.- 3.3 Analytical Field Models.- 3.3.1 Glaser’s Bell-Shaped Field.- 3.3.2 Analytical Models for a Symmetrical Lens with S ? D.- 3.3.3 Analytical Models for Symmetrical Lenses with Finite S/D ratios.- 3.3.4 Analytical Models for Asymmetrical Lenses.- 3.3.5 Analytical Solutions of the Paraxial Trajectory Equation.- 3.4 Paraxial Properties.- 3.4.1 Weak Lens Approximation.- 3.4.2 Strong Lens Approximation.- 3.4.3 Focal Length and Focal Position.- 3.4.4 Chromatic Aberration.- 3.4.5 Unified Representations.- 3.5 Third-Order Aberrations.- 3.5.1 Classification of Third-Order Aberrations.- 3.5.2 Unified Representation in the Aperture-Free System.- 3.5.3 Unified Representation of the Asymptotic Aberration Coefficients.- References.- 4. Practical Lens Design.- 4.1 Introduction.- 4.2 General Rules for the Electron Optical Design of the Magnetic Lens.- 4.2.1 Objective Lenses.- 4.2.1a Objective Lens Aberrations, Optimum Apertures.- 4.2.1b Electron Optical Properties Fundamental for Objective Lens Design.- 4.2.1c Optimizing the Objective Lens with Regard to CS and CC.- 4.2.1d Basic Objective Lens Operating Modes.- 4.2.1e The Pin-Hole Objective Lens.- 4.2.2 Projector Lenses.- 4.2.2a Basic Design Considerations for Projector Lenses.- 4.2.2b Optimization of Projector Lenses.- 4.2.2c Practical Realization of a Large Magnification Range for Projector Lenses.- 4.2.3 Condenser Lenses.- 4.3 Design of the Magnetic Circuit.- 4.3.1 Magnetic Design of the Pole-Piece System.- 4.3.1a Calculation of the Magnetic Flux Density Distribution Within the Pole-Piece System.- 4.3.1b Applications and Comparison with Experimental Results.- 4.3.2 The Magnetic Design of the Lens Core.- 4.3.2a Some General Considerations.- 4.3.2b The Hildebrandt-Schiske Procedure for the Calculation of the Magnetic Flux Density in the Lens Core.- 4.3.2c A Perturbation Method for Obtaining the Magnetic Flux Distribution in the Core and Casing of a Magnetic Electron Lens.- 4.3.2d Determination of the Cross-Sectional Area of the Lens Core by Means of the Perturbation Method.- 4.3.3 Magnetic Design of the Lens Casing.- 4.3.4 Comments on Lenses with Highly Saturated Pole-Piece Tips.- 4.4 Other Aspects of Magnetic Lens Design.- 4.4.1 The Lens Coil and Its Cooling System.- 4.4.2 Stigmators.- 4.4.3 Apertures and Their Alignment.- 4.4.4 Special Aspects of Specimen Stages Relevant for the Optical Performance of the Magnetic Lens.- 4.4.5 Mechanical Lens Alignment Devices.- 4.5 Measures for Reducing the Sensitivity of the Magnetic Electron Lens to Environmental Disturbances.- 4.5.1 Design Considerations for Protecting the Lens Against Low Frequency Environmental Vibrations.- 4.5.2 Protective Measures in the Lens Design Against Stray Magnetic Field Disturbances.- 4.6 Permanent Magnet Lenses.- 4.6.1 The General Layout of Electron Optical Lens Systems with Permanent Magnet Lenses.- 4.6.2 Special Design Aspects for Permanent Magnet Lenses.- 4.6.2a Means for Changing the Focal Length of Permanent Magnet Lenses.- 4.6.2b The Permanent Magnet and Its Design.- 4.7 Superconducting Electron Lenses.- 4.7.1 Superconducting Electron Lenses with Ferromagnetic Pole Pieces.- 4.7.2 The Superconducting Shielding Lens.- References.- 5. Unconventional Lens Design.- 5.1 Introduction.- 5.1.1 High Voltage Electron Microscopy.- 5.1.2 Conventional Lenses.- 5.1.3 Electrical Power Requirements.- 5.1.4 Heat Transfer in Lens Windings.- 5.1.5 Tape Windings.- 5.2 Boiling-Water Cooling Systems.- 5.3 Miniature Rotation-Free Magnetic Electron Lenses.- 5.3.1 The Distortion-Free Mode.- 5.4 Iron-Free or Partly Shrouded Magnetic Lenses.- 5.4.1 Conical Lenses.- 5.4.2 Thin Helical (Pancake) Lenses.- 5.4.3 The Ultimate Performance of Pancake Lenses.- 5.4.4 Minimization of Chromatic Aberration.- 5.5 Iron-Shrouded Pancake Lenses.- 5.5.1 The Exponential Field Model.- 5.5.2 The Single Pole-Piece Lens.- 5.5.3 The Magnetized Iron Sphere Model.- 5.5.4 Aberrations of the Uniformly Magnetized Sphere Model.- 5.5.5 The Preferred Form of Single Pole-Piece Lenses.- 5.6 Improved Image Viewing Systems.- 5.7 Correction of Spiral Distortion.- 5.8 Concluding Remarks.- References.- Appendix A Some Earlier Sets of Curves Representing Lens Properties.- Appendix B Bibliography of Publications on Magnetic Electron Lens Properties.