Physical Principles of Electron Microscopy: An Introduction to TEM ...

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180 Chapter 7 7.2 Aberration Correction From analysis of the basic properties of electric and magnetic fields, the German scientist Otto Scherzer showed that a conventional electron lens (where the magnetic or electrostatic fields have axial symmetry) must suffer from spherical and chromatic aberration, with aberration coefficients that are always positive. Therefore, we cannot eliminate lens aberrations by careful shaping of the lens polepieces, unlike the situation in light optics where aspherical lenses can be fabricated with zero Cs. In addition, it is not possible (in electron optics) to design compound lenses in which axiallysymmetric lens elements have positive and negative aberration coefficients, so that they compensate for each other. Because of the practical incentive to achieve better resolution, physicists have for many years sought ways to circumvent Scherzer’s rule. One option is to employ mirror optics. An electrostatic mirror involves an electrode connected to a potential more negative than that of the electron source. Before reaching the electrode, electrons are brought to rest and their trajectory is reversed. As a result of this reversal of path, the mirror has negative aberration coefficients and can be used as a compensating element. By assembling an electron-optical system containing electrostatic lenses and an electrostatic mirror, Rempfer et al. (1997) showed that both spherical and chromatic aberrations can be corrected, for angles up to 40 mrad. Although no TEM or SEM has made use of this principle, it is being applied to the photoelectron microscope, in which electrons released from a specimen (exposed to ultraviolet or x-ray radiation) are accelerated and focused to form an image. It has also been known for many years that weak multipole lenses have the potential to correct for spherical aberration of an axially symmetric lens. Their construction is similar to that of a stigmator (Fig. 2-16), but in general there are n electrodes (n = 4 for a quadrupole, n = 6 for a sextupole, n = 8 for an octupole). A mixture of quadrupoles and octupoles (or sextupoles) is required, and accurate alignment of each element is critical. With careful design, accurate machining, and computer control of the lens excitations, such correction has recently become feasible, and transmission electron microscopes that incorporate this form of aberration correction are being built. In Fig. 7-1, the field-emission STEM has been fitted with four quadrupole and three octupole lenses, which correct the spherical aberration of the probe-forming lenses and generate a scanning probe with a width
Recent Developments 181 below 0.1 nm, as evidenced in Fig. 7-2b. A recent commercial design for an aberration-corrected dedicated STEM is shown in Fig. 7-3. Figure 7-3. Nion UltraSTEM. The rectangular base houses a 200-kV cold field-emission gun. The column (diameter 28 cm) includes two condenser lenses, a C3/C5 aberration corrector that uses 16 quadrupoles, and 3 combined quadrupole/octupoles to correct both third and fifth order spherical aberration, an objective lens, and two projector lenses. It incorporates an ADF detector, retractable bright-field detector, CCD Ronchigram camera, and a Gatan magneticprism spectrometer (located on top of the column). The large rectangular box attached to the side of the gun houses circuitry generating tip and anode voltages and a high-voltage sensing (feedback) resistor. Courtesy of Nion Co.
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Physical Principles of Electron Mic
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Ray F. Egerton Department of Physic
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Contents Preface xi 1. An Introduct
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Contents ix 7. Recent Developments
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xii Preface textbooks, such as Will
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2 1.1 Limitations of the Human Eye
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4 Chapter 1 parallel beam of light
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6 Chapter 1 Figure 1-3. One of the
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8 Chapter 1 Figure 1-5. Light-micro
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10 Chapter 1 Figure 1-7. Scanning t
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12 Chapter 1 Figure 1-8. Early phot
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14 Chapter 1 Figure 1-10. JEOL tran
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16 Chapter 1 hydrated. But high-ene
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18 Chapter 1 Figure 1-14. Scanning
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20 Chapter 1 Figure 1-16. Photograp
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22 Chapter 1 visible-light photons
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24 Chapter 1 Typically, the STM hea
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Chapter 2 ELECTRON OPTICS Chapter 1
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Electron Optics 29 a c b object len
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Electron Optics 31 � a n 2 ~1.5
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Electron Optics 33 We can define im
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Electron Optics 35 electron source
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Electron Optics 37 symmetry and use
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Electron Optics 39 As we said earli
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Electron Optics 41 2.4 Focusing Pro
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Electron Optics 43 � = [e/(8mE0)
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Electron Optics 45 image plane. Whe
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Electron Optics 47 procedure that i
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Electron Optics 49 The basic physic
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Electron Optics 51 From Eq. (2.7),
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Electron Optics 53 y +V 1 +V 2 -V 2
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Electron Optics 55 point from the o
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58 Chapter 3 3.1 The Electron Gun T
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60 Chapter 3 The rate of electron e
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62 Chapter 3 electron emission curr
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64 Chapter 3 As seen from the right
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66 Chapter 3 � r r s r � (a) (b
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68 Chapter 3 Table 3-2. Speed v and
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70 Chapter 3 where G is a large amp
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72 Chapter 3 The second condenser (
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74 Chapter 3 Figure 3-9 summarizes
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76 Chapter 3 resolution (especially
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78 Chapter 3 The major advantage of
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80 Chapter 3 contrast (for a given
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82 Chapter 3 A more correct procedu
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84 Chapter 3 diffraction pattern (s
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86 Chapter 3 Nowadays, photographic
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88 Chapter 3 A related concept is d
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90 Chapter 3 molecules, imparting a
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92 Chapter 3 Frequently, liquid nit
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94 Chapter 4 -e -e -e -e +Ze Figure
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96 Chapter 4 � (a) elastic z x m
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98 Chapter 4 � b a (a) (b) Figure
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100 Chapter 4 fraction of electrons
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102 Chapter 4 whose composition or
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104 Chapter 4 replica crystallites
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106 Chapter 4 4.5 Diffraction Contr
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108 Chapter 4 remain undiffracted (
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110 Chapter 4 Close examination of
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112 Chapter 4 Unfortunately, the va
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114 Chapter 4 Crystals can also con
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116 Chapter 4 A simple example of p
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118 Chapter 4 High-magnification ph
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120 Chapter 4 At this stage it is c
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122 Chapter 4 All of the above meth
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124 Chapter 4 The procedures outlin
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126 Chapter 5 specimen scan coils o
Page 136 and 137: 128 Chapter 5 functions with m and
Page 138 and 139: 130 Chapter 5 inelastic collisions
Page 140 and 141: 132 Chapter 5 Figure 5-5. Dependenc
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Page 146 and 147: 138 Chapter 5 Backscattered electro
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Page 150 and 151: 142 Chapter 5 Figure 5-14. Red, gre
Page 152 and 153: 144 Chapter 5 the SE2 and SE3 compo
Page 154 and 155: 146 Chapter 5 just-observable loss
Page 156 and 157: 148 Chapter 5 Section 4-10. Films o
Page 158 and 159: 150 Chapter 5 A backscattered-elect
Page 160 and 161: 152 Chapter 5 One example of this p
Page 162 and 163: Chapter 6 ANALYTICAL ELECTRON MICRO
Page 164 and 165: Analytical Electron Microscopy 157
Page 184 and 185: 178 Chapter 7 Figure 7-1. Modified
Page 188 and 189: 182 Chapter 7 Besides decreasing th
Page 190 and 191: 184 Chapter 7 7.4 Electron Holograp
Page 192 and 193: 186 Chapter 7 There are now many al
Page 194 and 195: 188 Chapter 7 holography could ther
Page 196 and 197: Appendix MATHEMATICAL DERIVATIONS A
Page 198 and 199: Mathematical Derivations 193 A.2 Im
Page 200 and 201: REFERENCES Binnig, G., Rohrer, H.,
Page 202 and 203: INDEX Aberrations, 3, 28 axial, 44
Page 204 and 205: Index 199 EELS, 172 Electromagnetic
Page 206 and 207: Index 201 Principal plane, 32, 80 P
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