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26 • Stability of the acceleration and lens currents • On-axis alignment of the electron beam and the voltage centre of lens current • Low spherical aberration coefficient of the objective lens • Parallel beam for good spatial coherence • Low energy spread and low chromatic aberration coefficient • Well aligned stigmators of the intermediate and objective lens to avoid lens astigmatism Figure 3.8: (a) Diffraction pattern of a CdTe specimen, recorded along the (110) zone axis. The most important spots that cause the phase contrast of the lattice planes in the real image, are indicated. The circle indicates the size of the aperture that was used for real image recording. (b) Real image that shows phase contrast. The {002} and {220} diffraction spots are strong for the PbTe rs structure, the {111} are strong for the CdTe zb structure. The two materials can be distinguished by the corresponding lattice planes in the real image. The lattice planes are indicated. 3.4.2 Origin of Lattice Fringes The origin of the lattice fringes are the different phase factor of the scattered beams. This can be easily shown by the solution of the Howlie - Wehlan equations. The intensity of the solution is given for the two-beam approximation by [32] 2 2 2 I = ψT = A + B + 2AB sin( 2πg′ x − πst) (3.16)
Whereas A 2 and B 2 are the intensities of the primary and scattered beam and the term 2AB is the interference part. This equation also implements the assumption that the specimen is thin enough to set sg equal to s. The intensity of the two beams is a sinusoidal function of g´ (g´ = g+sg). If the term πst is a constant, one will see this variations as lattice fringes with a periodicity of x = 1/g. If the excitation error s = 0 it is the exact lattice plane spacing of the scattering planes. If the excitation error is not zero and there are no variations of the thickness t it will be still the same case. For a not entirely flat specimen the lattice fringes will be shifted as a function of πst, but the periodicity will not change drastically. 3.4.3 Transferfunction and Scherzer Defocus As image formation in a microscope is described in terms of a specimen function f(x,y), the image function g(x,y) can be written as the convolution of f(x,y) with a so called impulse response function h(x,y) (eqn. 3.17), [32]. h(x) describes the properties of the optical system. g( r) = ∫ f ( r′ ) h( r − r′ ) dr′ = f ( r) ⊗ h( r) A Fourier transform of a convolution results in a multiplication of the fourier transformed terms in the reciprocal space. This terms are the contrast transfer function H(u), the specimen function F(u) and the image function G(u). G( u ) = H( u) F( u) H(u) contains the properties of the optical system of the microscope as the aperture function A(u), the envelope function E(u) and the aberration function B(u). H( u ) = A( u) E( u) B( u) A(u) and E(u) restrict the spatial frequency range, whereas A(u) depends on the aperture size and E(u) is a fixed property of the lens system. Depending on the chosen aperture, A(u) can be more or less restrictive. B(u) is usually given by eqn. 3.20 and eqn. 3.21, the phase-distortion function χ(u). A point like object is imaged as disk due 27 (3.17) (3.18) (3.19)
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 and 30: F(θ) is the structure factor of th
Page 31 and 32: 3.3 Contrast Enhancement with Brigh
Page 33 and 34: kind of imaging is called Dark fiel
Page 35: Centred Dark Field One disadvantage
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
Page 83 and 84: 6.2.5 The (111) interface It is dif
Page 85 and 86: Figure 6.20: HR-map of the model co
Page 87 and 88:
Chapter 7 Conclusions and Outlook C
Page 89 and 90:
Figure 7.1: (a) QDs interfaces stit
Page 91 and 92:
segregate at the surface, build lat
Page 93 and 94:
A1 CdTe structure factor CdTe has z
Page 95 and 96:
Figure B2: HR-map for the Te termin
Page 97 and 98:
B2 The (110) interface The tree HR-
Page 99 and 100:
Figure B8: HR-map of the (110) inte
Page 101 and 102:
References [1] R.C. Ashoori, Nature
Page 105 and 106:
Curriculum Vitae 1 March 1979 born
Page 107 and 108:
Contributed talks: “The coherent
Page 109:
All member of the institute for the
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Diplomarbeit Diplom-Ingenieur - Institut für Halbleiter

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