Advances in Imaging and Electron Physics (eBook)

Optics of Charged Particle Analyzers

eBook Download: PDF | EPUB

2010 | 1. Auflage
304 Seiten
Elsevier Science (Verlag)
978-0-12-381319-0 (ISBN)

Infos

Advances in Imaging and Electron Physics merges two long-running serials--Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. This series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains. - Contributions from leading international scholars and industry experts - Discusses hot topic areas and presents current and future research trends - Invaluable reference and guide for physicists, engineers and mathematicians

Inhalt

Front Cover 1
Advances in Imaging and Electron Physics 4
Copyright Page 5
Contents 6
Preface 10
Contributors 12
Future Contributions 14
Chapter 1: Principles of Dual-Beam Low-Energy Electron Microscopy 18
I. Introduction 19
2. Dual-Beam Approach 21
3. Electron-Optical Components 27
3.1. Magnetic Immersion Objective Lens 27
3.2. Magnetic Prism Array 30
3.3. Dual-Beam Gun and Illumination Optics 35
3.4. Illumination Optics with ‘‘Twist’’ Correctio 40
3.5. Illumination Optics with a Semitransparent Holey Mirror 50
4. Experimental Results 56
4.1. Semiconductor Substrates 57
4.2. Reticle Substrates: Nano-Imprint Lithography Masks 63
4.3. Experiments with a Tilted Illumination Beam 64
4.4. Magnetic Recording Media 65
5. Conclusions 68
Acknowledgments 69
References 69
Chapter 2: Determination of Adequate Parameters for Connected Morphological Contrast Mappings through Morphological Contrast Measures 72
1. Introduction 73
2. Background Definitions 75
2.1. Morphological Transformations 75
2.2. Connectivity 75
2.3. Transformations by Reconstruction 78
2.4. Morphological Contrast Mappings 79
2.5. Opening and Closing Size Determination 82
3. Morphological Contrast Measures 84
3.1. Morphological Contrast Measure Based on the Difference of Contrast 85
3.2. Morphological Contrast Measure Based on Image Edge Analysis 92
4. Magnetic Resonance Imaging Segmentation 95
4.1. Opening and Closing Size Determination on MRI Slices 95
4.2. Determination of Parameters a and ß on MRI Slices 97
4.3. White and Grey Matter in the Frontal Lobe 98
5. Enhancement of Images in the Presence of Noise 98
6. Contrast Measure Comparison 101
7. Conclusion 103
References 103
Chapter 3: Fractional Fourier Transforms and Geometrical Optics 106
1. Introduction 107
2. The ABCD Ray Transfer Matrix Method 108
2.1. Physical Meaning of the ABCD Elements 109
2.2. Basic Optical Components and Ray Transfer Matrices 111
2.3. Cardinal Elements of the Optical System 113
2.4. Lenses and Imaging 116
2.5. Self-Focusing Graded Index Ducts 119
3. Extension to Anamorphic Optical Systems 121
4. Wave Optics Properties of Geometrical Systems: Fourier Transform Systems 125
4.1. Connection between Wave and Ray Optics Formalisms 125
4.2. Exact Fourier Transform Optical System 126
4.3. Scale of the Optical Fourier Transform 127
4.4. Basic Fourier Transform Optical Lens Systems 129
4.5. Ray Transfer Matrix Factorizations 130
4.6. Anamorphic Optical Fourier Transformers 134
5. Cascading Multiple Equivalent Systems: The Fractional Fourier Transform 137
5.1. Heuristic Concept of the FRFT Optical System 137
5.2. Derivation of the Ray Transfer Matrix of an FRFT System 138
5.3. Propetries of the FRFT Operation 140
5.4. Basic FRFT Optical Systems 143
5.5. Symmetrical Lens Systems 144
5.6. Inexact Fractional Fourier Transformers 146
5.7. Fractional Fourier Transforms and Fresnel Diffraction 147
6. Cardinal Planes in Fractional Fourier Transform Lens Systems 148
6.1. Cardinal Planes in a Lohmann Type I FRFT System 148
6.2. Cardinal Planes in a Lohmann Type II FRFT System 149
7. Some Advanced FRFT Lens Systems 151
7.1. FRFT Lens System with Fixed Input and Output Planes 152
7.2. FRFT Lens System with Fixed Scaling Factor 155
7.3. Anamorphic FRFT Optical Systems 157
8. Conclusions 160
Acknowledgments 160
References 160
Chapter 4: Sparse Image Representation by Directionlets 164
1. Introduction 165
2. Asymmetric Wavelet Transforms 169
2.1. Fully Separable Decomposition 169
2.2. Asymmetric Wavelet Decomposition 172
3. Directional Wavelet Transforms 174
3.1. Discretization of Directions 175
3.2. Directional Interaction 176
3.3. Lattice-Based Filtering and Subsampling 178
3.4. Skewed Wavelet Transforms 180
3.5. Polyphase Representation 184
4. Nonlinear Image Approximation 185
5. Space-Frequency Quantization with Directionlets 190
5.1. Space-Frequency Quantization 191
5.2. Spatial Segmentation 194
5.3. Compression Algorithm 194
5.4. Deblocking 197
5.5. Computational Complexity 198
5.6. Results 200
6. Directional Image Interpolation 203
6.1. Locally Adaptive Wavelet-Based Interpolation 207
6.2. Directional Map 209
6.3. Interpolation Algorithm 209
6.4. Results 212
7. Conclusions 214
Appendix I. Proof of Theorem 1 215
Appendix II. Lagrangian Optimization 221
References 222
Chapter 5: Advances in Connectivity and Connected Attribute Filters 228
1. Introduction 229
2. Definitions 232
2.1. Basic Morphological Filters 232
3. Connected Filters 236
3.1. Reconstruction 237
3.2. Area Openings 239
3.3. Attribute Filters 241
3.4. Extensions to Grey Scale 242
4. Granulometries and Pattern Spectra 246
4.1. Shape Operators and Shape Granulomet 248
5. Set Connections, Partitions, and Operators 251
5.1. Set Connectivity 251
5.2. Partitions and Partition-Induced Connectivity 253
5.3. Second-Generation Connectivity 254
5.4. p-Connections Based on Masks 259
6. Multiscale Connectivity Analysis 260
7. Generalizations to Vector Images 266
7.1. Binary Partition Tree 266
7.2. Using Local Order 268
7.3. Global Order Methods 270
7.4. Alternatives to Strict Flat Zones 270
8. Algorithms 271
8.1. The Union-Find Approach 271
8.2. The Max-Tree Algorithm 274
8.3. Other Tree Struct 277
9. Beyond Connectivity 278
9.1. Hyperconnectivity 279
9.2. Attribute-Space Connectivity 283
10. Discussion and Conclusions 285
References 286
Contents of Volumes 151–160 294
Index 298
Color Plates 306

Textauszug

Chapter 1

Principles of Dual-Beam Low-Energy Electron Microscopy

Marian Mankos*,1; Vassil Spasov*; Eric Munro†    * KLA-Tencor, 160 Rio Robles, San Jose, CA 94301, USA
† MEBS Ltd., 14 Cornwall Gardens, London SW7 4AN, UK
1 Current address: Electron Optica, Palo Alto, CA, USA

1 INTRODUCTION

The continuing trend toward smaller features in the semiconductor industry poses a formidable problem for scanning electron beam tools because of their relatively low throughput. The throughput of an electron beam tool is determined by the time required to deliver the electron dose needed to provide a useful signal with sufficient signal-to-noise ratio, so it is proportional to the maximum total electron beam current. However, the large current required to deliver the necessary throughput results in increased electron-electron (e-e) interactions, which blur the image and result in loss of resolution. As the features and pixel sizes become smaller, the beam current must be reduced to maintain the resolution, while the number of pixels to be examined on a wafer increases, resulting in inspection times that exceed practical limits.

One possible approach to circumvent this problem is to replace the serial acquisition process of scanning electron microscopes (SEMs) with a parallel scheme, where all the image pixels of interest on the surface are acquired in parallel on a scintillating screen and further processed on a computer. A low-energy electron microscope (LEEM; Telieps and Bauer, 1985; Tromp and Reuter, 1993) optimized for high throughput (i.e., large beam currents and field sizes) is ideally suited for this application. In a LEEM, a flood beam illuminates the sample with electrons with energies ranging from a few hundred electron volts to near zero electron volts, depending on the substrate bias. The fact that electrons reflect back and travel along the path of the incident beam poses a major challenge in the design of an electron microscope. Since independent control of the illumination and projection is required, the optical axis is split by a magnetic sector field, a nonradially symmetric optical element. This requires a departure from the traditional design with a straight optical axis, resulting in a more complex optical design. We have adopted a design with a straight gun-to-screen axis, which significantly eases column alignment. The four subsystems of the electron-optical column—the magnetic prism array, the illumination, objective, and projective optics—are shown in Figure 1. The illuminating electrons are emitted from the surface of a flat cathode and accelerated to their final beam energy, forming a crossover inside the electron gun. The cathode temperature and extraction field determine the total beam emitted from the gun. The adjacent condensor lenses form a zoom lens that maintains a focused image of the gun crossover at the illumination shape aperture and allows the current illuminating the wafer to be varied and therefore determines the number of electrons/pixel reaching the detector. An additional set of lenses is used to vary the current density at the wafer and therefore determines the size of the illuminated area. The magnetic prism array deflects the electron beam from the illumination optics into the objective optics. Below the magnetic prism array, the electron-optical components of the objective optics are common to the illumination and projection optics. The immersion cathode objective lens decelerates the electrons before they reach the substrate and illuminates the wafer surface with a nearly uniform beam. The electrostatic part of the objective lens creates an electric field of ~5 kV/mm at the substrate surface. In the opposite direction (i.e., upward from the substrate), the objective lens simultaneously forms a magnified image of the substrate. As the electrons reenter the prism array, they are deflected into the projection optics. The magnetic prism array is followed by a diffraction lens, which forms an image of the objective lens back focal plane in the pupil aperture plane and simultaneously forms a magnified image of the wafer in the object plane of the projection zoom optics. The projection zoom section is followed by the final magnifying element of the projection optics, the final projector lens. The electron image formed at the scintillating screen is then viewed by a charge-coupled device camera and further processed on a computer.

Figure 1 Basic layout of LEEM optics.

When the wafer is biased positively with respect to the electron source, the electrons scatter at or near the surface and either reflect back from the sample, undergoing low-energy electron diffraction, or generate secondary electrons, provided the bias and therefore kinetic energy of the illuminating electrons is large enough (few tens to hundreds of electron volts). When the substrate is biased slightly negative (~1 V) with respect to the electron source, the illuminating electrons are reflected above the surface without hitting the surface. This imaging mode is also known as mirror electron microscopy (MEM). When the substrate is illuminated by a source of ultraviolet (UV) or shorter-wavelength light, photoelectrons are emitted, resulting in the well-known photoelectron emission microscopy mode.

However, when a conventional LEEM instrument is used to image substrates with a variety of insulating materials at the surface, the imbalance of the electron flux results in charging effects that can significantly reduce the imaging quality. In this review, we show how the need for imaging of insulating surfaces at high throughput affects the electron-optical design of a LEEM and present experimental results from several types of substrates used in the semiconductor industry.

2 DUAL-BEAM APPROACH

The dual-beam approach is driven by the difficulties encountered when electron microscopes are used to image insulating surfaces. The imbalance between the arriving and outgoing flux of electrons causes the surface to charge up, resulting in increased blur and distortions. On a homogeneous insulator surface, the charging can be suppressed by operating at a landing energy resulting in a net secondary yield of 1. However, this approach restricts the landing energy and typically does not work when different insulating materials are present on the surface. We have developed a dual-beam approach that mitigates the charging effect when either two electron beams with different landing energies or an electron and photon beam are used for imaging (Adler and Marcus, 2005; Mankos et al., 2007; Veneklasen and Adler, 2003).

The basic principle of dual-beam charge control is shown in Figure 2. When an insulating substrate is illuminated with a single electron beam, the surface charges either negatively (i.e., in mirror mode when the landing energy is very low, and electrons are absorbed) or positively (electron yield >1, landing energy greater than a few hundreds of electron volts). In the case of UV photon illumination, the surface charges positively as electrons are emitted. However, when two beams with opposite charging characteristics—that is, a mirror beam and either a higher-energy electron beam or UV photon beam—are superimposed on the substrate, charging effects can be neutralized.

Figure 2 Basic principles of dual-beam charge control.

A more detailed description of this charge balance for the case of two illuminating electron beams is given in Figure 3. The energy spectrum of the illuminating electrons approaching the substrate surface and signal electrons leaving the surface is shown in Figure 3a. Typically the electron energy of illumination has a Maxwell–Boltzmann distribution peaked at 0.25 eV with a full width half maximum of approximately 0.5 eV. The first beam is partially mirrored and its high-energy tail is absorbed, which charges the surface negatively. The second beam, frequently referred to as the charge control beam, strikes the wafer with energies of typically a few hundred electron volts, which results in a total (secondary and backscattered) yield σ (=δ+η) larger than 1 that charges the surface positively. The portion of the mirror beam current Im that is absorbed equals αIm, and the second charge control beam current equals Icc, so the condition for charge equilibrium then can be written as

Im=(σ-1)Icc.

  (1.1)

Figure 3 Energy spectra for dual-beam charge control. (a) Energy spectrum of illuminating electrons approaching the substrate surface and signal electrons leaving the surface. Ucb, relative cathode bias. (b) Energy spectrum of electrons for two different charge control currents. See text for details. (c) Energy spectrum of illuminating electrons and photons approaching the substrate surface and signal electrons leaving the surface. See text for details.

This state of charge control is a dynamic quasi-equilibrium, and the surface is at a potential that is slightly (<1 eV) more negative than the cathode potential (0 V), depending on the fraction of absorbed mirror electrons. This scenario is demonstrated in Figure 3a. When the charge control beam current (or total yield σ) slightly increases to Icc1, the surface begins to charge...

Produkt-Details

• Erscheint lt. Verlag: 10.3.2010
• Mitarbeit: Herausgeber (Serie): Peter W. Hawkes
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Angewandte Physik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Elektrodynamik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-12-381319-0 / 0123813190
• ISBN-13: 978-0-12-381319-0 / 9780123813190