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2.1. The challenge of stabilizing stoichiometric europium oxide 7 increase of Gibbs free energy, we can discriminate whether a reaction will proceed (dG 0). Its differential is given by dG = −S dT + V dp + μ dN, (2.1) where S is the entropy, V the volume, and μ the chemical potential. One recognizes that T , p, and N are the natural state variables of G. The Gibbs free energy is a suitable thermodynamic measure for chemical reactions at fixed pressure and fixed temperature. Thus, the Gibbs free energy is perfectly suited to describe the EuO growth by MBE, which is a quasi-equilibrium system. In thermodynamic equilibrium, there is no total transfer of entropy: ΔS = 0. This implies in terms of the variables for G for two subsystems A and B (e. g. two competitive EuO phases): T A = T B p A = p B μ A = μ B Since the temperature T and pressure p are constant, the only driving force out of the equilibrium is a possible difference in chemical potential Δμ = μ A − μ B . Provided a constant atomic flux dN in MBE, the Gibbs free energy (2.1) depends then only on the specific Δμ of materials. Those material-specific Gibbs free energies are tabulated in databases like the CRC Handbook or Landolt-Börnstein, 34,35 and a comparison allows for a prediction of quasiequilibrium reactions as during MBE synthesis. Ellingham diagrams Figure 2.2.: Ellingham diagram. Once the material-specific Gibbs free energies of formation and the gas lines are included, one can determine the principle thermodynamic stability (ΔG r ≷ 0) and regions of oxidation or separation of metal and oxygen. These regions are separated by equilibria at the intersections, which determine a set of oxygen partial pressure p(O 2 ) and temperature T . For oxide growth using MBE, we want to elucidate the question of oxidation reactions, which is conveniently achieved by Ellingham diagrams. An Ellingham diagram is a compilation of Gibbs free energies of oxide compounds of interest, with the addition of “gas lines”. One characteristic is the normalization of G f (T ) to one mole of gaseous oxygen O 2 ; this rule perfectly describes the adsorption-controlled EuO synthesis, in which the growth progress only depends on the limited and constant oxygen supply. This weighting of G f (T ) curves to one Further reading in the field of molecular thermodynamics is found in Dickerson (1969). 36
8 2. Theoretical background mole of O 2 makes all reactions immediately comparable among each other. The curves in an Ellingham diagram are G f (T )=H f − TS. (2.2) G gas (T )=−R gas T lnp(O 2 ). (2.3) Here, R gas denotes the gas constant, and p(O 2 ) is the oxygen partial pressure given in mbar. There are three main uses of the Ellingham diagram: 1. Determine the relative probability of reducing a given metallic oxide to metal, † 2. determine the partial pressure of oxygen that is in equilibrium with a metal oxide at a given temperature, and 3. determine the ratio of metal oxide phases (e. g. oxidation numbers II, III, or IV) at a given temperature. As a rule of thumb, if ΔG r is more negative than −60 kJ/mol, the reaction is considered to be completed in oxidation direction, and if more positive than +60 kJ/mol, it will not proceed at all. Reactions inside this interval around zero are considered to be reversible (shaded in Fig. 2.2). We note, that this approach is purely thermodynamic, and the predicted chemical products may form slowly or may even be prevailed by growth kinetics and activation energies. In this thesis, we use Ellingham diagrams to distinguish thermodynamic conditions, by which the EuO synthesis at elevated temperatures in direct contact with a Si (001) wafer will proceed to either higher oxides or silicon compounds. 2.2. Electronic structure of EuO The main properties of EuO investigated in this thesis, i. e. the chemical and magnetic properties, all rely on details of the electronic structure. First, we discuss the nature of the chemical bonding, then we proceed to the origin of ferromagnetism in EuO, which is the magnetic Eu 4f orbital. Finally, we elucidate the arrangement of valence level, band gap, and conduction bands. Their radial distribution is sketched in Fig. 2.3. Deep core-levels, as observed on photoemission experiments, are discussed in Ch. 2.5.2. Among the 61 electrons of the Eu(II) ion in EuO, 54 saturate orbitals giving the Xe configuration; the seven remaining ones are in the configuration 4f 7 (5d 6s) 0 . The Eu–O bonding is mainly of an ionic nature, which means that the two (5d 6s) 2 electrons are transferred to the p orbitals of oxygen. This explains why the europium chalcogenides are insulators, with the valence band built of the p states of the anion, and a conduction band composed of empty 6s and 5d states of the cation. A useful webtool for Ellingham diagram creation is available online. 220 † Technologically, the points 1) and 3) are used in the smelting industry, to reduce e. g. Fe from hematite (iron ore).
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 26 and 27: 2.2. Electronic structure of EuO 9
Page 28 and 29: 2.3. Magnetic properties of EuO 11
Page 36 and 37: 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
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Page 58 and 59: 3.2. In situ characterization techn
Page 60 and 61: 3.3. Experimental developments at t
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4. Results I: Single-crystalline ep
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59 Table 4.1.: Parameters for stoic
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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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