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20 To derive the change of the beam amplitude the two-beam approximation is applied. This means that only one diffracted beam is strong. This condition can also be reached in a real TEM by tilting the sample until only one beam besides the (000) reflex is strong. The other spots can then be neglected. If one writes now this equation in terms of the change of the amplitudes when the beam passes through the specimen along the z direction, one obtains the Howlie - Wehlan equations (eqn. 3.11, eqn. 3.12,) [32]. dφ g πi −2 πisz = φ 0e dz ξ g πi + φ ξ dφ0 πi πi 2πisz = φ0 + φge dz ξ0 ξg This pair of coupled differential equations can be used to derive the amplitude of the scattered beam. This gives the intensity of a diffracted beam Whereas seff is the effective excitation error and is given by φ g 2 ⎛ t ⎞ ⎜ π = ⎟ ⎜ ⎟ ⎝ ξg ⎠ s is the excitation error and expresses the deviation from the exact Laue condition and is also a vector in reciprocal space. Many diffraction spots can be seen even if the Laue condition is not exactly fulfilled, which is then expressed as K=kD-kI+s. The intensity of the scattered electron beam is a periodic function of the specimen thickness t. The period of the oscillations is πseff. seff differs for different diffraction spots (hkl) and approaches s for very large values of s and becomes ξg -2 if s equals zero. The periodic behaviour of the electron beams plays an important role in the interpretability of the lattice fringes in HRTEM images (see section 3.4). s eff 2 = 0 g ( ) ( ) 2 2 πts eff πts sin s 2 eff + 1 ξg 2 (3.11) (3.12) (3.13) (3.14)
3.3 Contrast Enhancement with Bright and Dark Field Imaging To get sufficient information from a TEM image it is important to know what the origin of contrast in the image is and how one can use these mechanisms to enhance it. The term of contrast itself is defined as a difference in intensity between to areas (egn. 3.15), [32]. Therefore, it is not possible to increase contrast by increasing the intensity of the electron beam. Rather one will decrease the contrast and the best condition to record high contrast images is to do it with low intensity. 3.3.1 Contrast Mechanism There are three main contrast mechanisms that are important for TEM imaging. The mass-thickness (ρt, density×thickness) contrast is caused by incoherent elastic electron scattering. The Rutherford cross section depends strongly on the atomic number Z (eqn. 3.3). Thicker samples cause more scattering events due to the mean free path remains constant. In a specimen region with a higher mass-thickness more electrons are scattered, thus less electrons are collected by the objective lens in the image plane (see Fig. 3.4), [32]. On the other hand, coherent elastic scattering causes the diffraction contrast. This contrast is a form of amplitude contrast, because diffraction peaks appear at the Bragg angles. The intensity of the diffraction peaks depends on the unit cell structure factor and can be used to produce contrast between materials with different structure. The mass thickness effect and the diffraction contrast compete. Given that Rutherford scattering in a thin specimen is strongly forward peaked, the primary spot of the DP contains most of the mass thickness contrast. This spot can be used to form a real image which is called bright field image (BF). On the other hand, collecting the electrons of any diffraction spot with dominant diffraction contrast for imaging is called Dark field (DF) imaging. I C = 2 − I I 1 1 ΔI = I 1 21 (3.15)
Page 1: Transmission Electron Microscopy of
Page 5: Kurzfassung Nanostrukturierung erla
Page 9 and 10: Contents Preface i Eidesstattliche
Page 11 and 12: Chapter 1 Introduction 1.1 Material
Page 13 and 14: 1.2 Quantum Dot precipitation in so
Page 15 and 16: Chapter 2 The material system and i
Page 17 and 18: of PbTe is one order of magnitude s
Page 19 and 20: an intermediate case with a strain
Page 21 and 22: therefore it can be Te or Cd termin
Page 23 and 24: Chapter 3 The Transmission Electron
Page 25 and 26: screen. These are the two basic mod
Page 27 and 28: This leads with Cs = 1mm and λ = 2
Page 29: F(θ) is the structure factor of th
Page 33 and 34: kind of imaging is called Dark fiel
Page 35 and 36: Centred Dark Field One disadvantage
Page 37 and 38: Whereas A 2 and B 2 are the intensi
Page 39 and 40: Figure 3.9: Plots of the sin x(u) t
Page 41 and 42: Chapter 4 Shape and size of the PbT
Page 43 and 44: 4.2 Precipitation steps TEM images
Page 45 and 46: lines approaches the diameter of th
Page 47 and 48: Figure 4.6: The distribution of the
Page 49 and 50: Figure 4.8: The image at the top sh
Page 51 and 52: Figure 4.10: Length of the {111} in
Page 53 and 54: Figure 4.12: Different shapes of cu
Page 55 and 56: (Centre Interdisciplinare de Micros
Page 57 and 58: 5.1.2 Simulation Procedure The stan
Page 59 and 60: The DP of the materials is very hel
Page 61 and 62: interface through the whole specime
Page 63 and 64: Figure 6.1: A schematic sketch of t
Page 65 and 66: Figure 6.3: Two HRTEM examples of d
Page 67 and 68: PbTe and CdTe, respectively, are co
Page 69 and 70: simulation a continuous Te matrix.
Page 71 and 72: Figure 6.8: HR simulation of the (0
Page 73 and 74: Figure 6.10: The images on the righ
Page 75 and 76: 6.2.4 The (110) interface The main
Page 77 and 78: Figure 6.14: Two example of the (11
Page 79 and 80: Figure 6.15c and 6.16b show example
Page 81 and 82:
figure 6.15. This displacement can
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6.2.5 The (111) interface It is dif
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Figure 6.20: HR-map of the model co
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Chapter 7 Conclusions and Outlook C
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Figure 7.1: (a) QDs interfaces stit
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segregate at the surface, build lat
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A1 CdTe structure factor CdTe has z
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Figure B2: HR-map for the Te termin
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B2 The (110) interface The tree HR-
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Figure B8: HR-map of the (110) inte
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References [1] R.C. Ashoori, Nature
Page 105 and 106:
Curriculum Vitae 1 March 1979 born
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Contributed talks: “The coherent
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All member of the institute for the
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