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2.4. Hard X-ray photoemission spectroscopy 19 was interpreted by the quantum nature of light in which the “light particles” possess an energy hν dependent on frequency, 78 a discovery for which Albert Einstein was honored with the Nobel Prize in 1921. After a continuous development of theoretical and experimental techniques, photoemission spectroscopy is nowadays the most important experimental technique for studying the electronic structure of occupied electronic states in a solid. 79 The high-energy variant of photoemission, HAXPES, is employed to investigate the electronic properties of buried layers and interfaces of EuO heterostructures in this thesis. In order to interpret the core-level photoemission spectra, we discuss the basic photoemission theory in the framework of the three-step model. Later, spectral features besides the main core-level lines are discussed by means of intra-atomic interactions. Finally, we discuss the characteristics of hard X-ray excitation including the important benefit of increased information depth. 2.4.1. The three-step model of photoemission (a) E E f E i (b) E f E E i solid 0 z solid 0 z Figure 2.11.: The three step model of photoemission (a). It connects Bloch states (plane waves) of the photoelectron in three independent steps. For comparison, the one-step model (in b) includes the electronic waves of the initial state, and the (eventually damped) final state, and matches with the wave departed from the solid in one formalism. 80 An intuitive, yet simplified approach to the photoemission process is the three-step model, introduced by Berglund and Spicer (1964). 81 This model divides the photoemission process into three independent events and assumes Bloch functions in a one-electron picture for both the initial and final states of the photoelectron. The successive events are discussed in the following 82 and schematically sketched in Fig. 2.11a. Finally, we briefly mention the exhaustive description of photoemission by the one-step theory, which uses the inverse LEED state as final state, as sketched in Fig. 2.11b. 1. Excitation of the electron into unoccupied states The interaction of the electron with a time-dependent electromagnetic field A(r,t) (from the plane wave of the incoming light) in
20 2. Theoretical background the single-electron picture is expressed as H = H 0 + H S = 1 ( ) 2 2m i ∇−e c A(r) + V (r), (2.12) here, H 0 is the Hamiltonian of the unperturbed system, H S is the perturbation operator, p = /i ∇ denotes the momentum operator, and V (r) is the potential within the solid from the ionic cores. The single Hamiltonians are written as H 0 = − 2 2m ∇2 + V (r), H S = 1 ( − e ) e2 (2A∇ +(∇A)) + 2m ic c 2 |A|2 . (2.13) Here, we approximate |A| 2 ≈ 0 for small electromagnetic field strengths, and the gradient ∇A ≈ 0, because the field changes within the crystal only very slowly (X-ray penetration of the crystal). The ansatz for A is a plane wave with wave vector k γ , the amplitude A 0 , and r is the unit vector in direction of the electric field: A(r,t)=A 0 e ik γ r ⇒ H S = − e mc A 0e ik γ r p. (2.14) The wave vector k γ = 2π λ is small with respect to the size of a typical Brillouin zone up to the XPS regime, therefore e ik γ r ≈ 1, which simplifies the perturbation Hamiltonian in the dipole approximation as H S = − e mc A 0 ·p. (2.15) We remark that for high-energetic photons (HAXPES), the dipole approximation may be insufficient and higher order transitions (electric quadrupole E2, or magnetic dipole M1) are emerging. The Hamiltonian (2.15) depends only on the momentum transfer p between the plane wave (light) and the electron, which is to be determined now. It is used in Fermi’s golden rule, which expresses the probability per time that the system is excited by a photon of the energy hν, w i→f = 2π 〈 ∣ ∣ f ∣∣H ∣ S 〉 ∣ 2 ∣i ∣∣∣ ·δ(E f − E i − hν) (2.16) Here, |i〉 denotes the electron’s initial state with the energy eigenvalue E i , and |f 〉 is the final state in the single particle model with energy E f , as depicted in Fig. 2.11a. The δ-function ensures the energy conservation. The transition matrix element in Fermi’s golden rule, M if , depends on the symmetries of the final and initial state as M if = 〈 f ∣ ∣ ∣H S ∣ ∣ ∣i 〉 ∝〈f |p|i〉. (2.17) Besides the energy conservation, also the conservation of the momentum (∝ k, the wave The E2 or M1 distributions occur for very short wavelength photons (hν ≫ 1 keV) and for the ejection of electrons in very large orbits. However, these distortions only alter the angular dependence of photoemission. Since we conduct angle-integrated HAXPES only at fixed emission angles, the inclusion of higher order transitions is negligible in this thesis.
Page 1 and 2: Member of the Helmholtz Association
Page 4 and 5: Forschungszentrum Jülich GmbH Pete
Page 6: Zusammenfassung In dieser Doktorarb
Page 10 and 11: Contents 1. Introduction 1 2. Theor
Page 12 and 13: List of Figures 2.1. Phase diagram
Page 14: List of Figures xi 5.12. Resulting
Page 18 and 19: 1. Introduction Smart and powerful
Page 20 and 21: 3 In the thesis at ha
Page 22 and 23: 2. Theoretical background . . . The
Page 24 and 25: 2.1. The challenge of stabilizing s
Page 26 and 27: 2.2. Electronic structure of EuO 9
Page 28 and 29: 2.3. Magnetic properties of EuO 11
Page 38 and 39: 2.4. Hard X-ray photoemission spect
Page 46 and 47: 2.5. Magnetic circular dichroism in
Page 52 and 53: 3. Experimental details Die Pläne
Page 54 and 55: 3.1. Molecular beam epitaxy for oxi
Page 56 and 57: 3.2. In situ characterization techn
Page 58 and 59: 3.2. In situ characterization techn
Page 60 and 61: 3.3. Experimental developments at t
Page 62 and 63: 3.4. Ex situ characterization techn
Page 74 and 75: 4. Results I: Single-crystalline ep
Page 76 and 77: 59 Table 4.1.: Parameters for stoic
Page 78 and 79: 4.1. Coherent growth: EuO on YSZ (1
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4.1. Coherent growth: EuO on YSZ (1
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4.2. Lateral tensile strain: EuO on
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4.2. Lateral tensile strain: EuO on
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4.3. Lateral compressive strain: Eu
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5. Results II: The integration of t
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5.1. Chemical stabilization of bulk
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5.2. Thermodynamic analysis of the
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5.3. Interface engineering I: Hydro
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5.4. Interface engineering II: Eu p
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5.5. Interface engineering III: SiO
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5.5. Interface engineering III: SiO
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5.6. Summary 121
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6. Conclusion and Outlook In the th
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125 Outlook and perspectives In the
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A.1. EuO-related phases and cubic o
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A.1. EuO-related phases and cubic o
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A.2. In situ analysis of the Si (00
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Bibliography 133 [13] S. S. P. Park
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Bibliography 135 [36] R. E. Dickers
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Bibliography 137 [65] R. Sutarto, S
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Bibliography 139 [91] P. Braun, M.
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Bibliography 141 [116] S. Hüfner.
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Bibliography 143 [144] R. Feder and
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Bibliography 145 [171] H. Miyazaki,
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Bibliography 147 [197] J. Qi, T. Ma
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Software and Internet Resources [21
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List of own publications 151 [10] R
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List of conference contributions 15
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Schriften des Forschungszentrums J
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Schlüsseltechnologien / Key Techno
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