Ferromagnetic (Ga,Mn)As Layers and ... - OPUS Würzburg

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38 3. MBE Growth of Ferromagnetic (Ga,Mn)As Layers Figure 3.9: Reciprocal lattice for a cubic substrate (black), a pseudomorphic layer (red) and a fully relaxed cubic layer (blue). The lower half shows a combination of the above three cases, the zoomed section corresponds to the (044) reflection with the triangle of relaxation.
3.5. X-Ray Diffraction 39 lattice direction by measuring a reflection that is sensitive to only one in-plane lattice direction, such as for example (206). A map of the reciprocal space is assembled by a number of line scans along a scan axis. Each such scan is offset by a small step in a second axis, called the area axis. Possible choices for these axes are ω, 2Θ, and ω-2Θ. The best choice of axes depends on the specific reflection and the area which needs to be measured. Usually it is a pair of axes which most efficiently spans a reciprocal space area containing the whole region of interest. Reciprocal Lattice Units A RSM is usually depicted as a 2D cut plane in reciprocal space. The coordinates in a RSM have a component perpendicular to the sample surface q ⊥ and a component parallel to the surface q ‖ . For the scaling of RSMs, we use reciprocal lattice units (r.l.u.), a dimensionless representation of rational Miller indices (hkl) with respect to the Miller indices of the substrate. For a layer where both in-plane directions h and k are equal, the conversion between the reciprocal lattice constant q and the real space lattice constant a is given by: ⎛ ⎞ ⎛ ⎞ ⎛ q ‖ h ⎝q ‖ ⎠ = ⎝k⎠ ⎜ · ⎝ q ⊥ l a sub ⎞ a ‖ a sub ⎟ a ‖ a sub a ⊥ ⎠ (3.8) With this equation it is immediately possible to relate a reciprocal space peak position measured in r.l.u. with a real space in-plane and perpendicular-to-plane lattice constant for a given reflection. With this relation and the information from Fig. 3.9, it is also easy to calculate the corners of the relaxation triangle, see table 3.1. Table 3.1: Reciprocal space coordinates for the corner points of a relaxation triangle of an epitaxial layer. For a GaAs substrate, a sub = 5.6533 Å. position real space reciprocal space (q ‖ , q ⊥ ) substrate a ‖ = a ⊥ = a sub (h, l) pseudomorphic a ‖ = a sub , a ⊥ = a vert (h, l · asub relaxed a ‖ = a ⊥ = a layer a (h · sub a layer , l · a vert ) a sub a layer ) Example of RSM To illustrate the application of a RSM, we present the measurement on a GaAs/ (In,Ga)As/(Ga,Mn)As structure. The goal of this sample was to achieve an out of plane easy axis of the magnetization, as described in Chapter 1, by growing (Ga,Mn)As under tensile strain. To achieve this strain situation, the (In,Ga)As layer was grown to a thickness of 1 µm, to allow plastic relaxation of the layer, and thereby forming a substrate for the (Ga,Mn)As layer with a larger lattice constant than the relaxed lattice constant of (Ga,Mn)As.
Page 1 and 2: Ferromagnetic (Ga,Mn)As Layers and
Page 3 and 4: Contents Zusammenfassung 5 Summary
Page 5 and 6: Zusammenfassung Ferromagnetische Ha
Page 7 and 8: Anisotropiekontrolle in (Ga,Mn)As i
Page 9 and 10: Summary The great promise of ferrom
Page 11 and 12: Chapter 1 Introduction The event co
Page 13 and 14: 13 investigated with SQUID and magn
Page 15 and 16: Chapter 2 The (Ga,Mn)As Material Sy
Page 17 and 18: 2.1. Ferromagnetism in (Ga,Mn)As 17
Page 19 and 20: 2.2. Band Structure Calculations in
Page 21 and 22: 2.3. Magnetic Anisotropy 21 growth
Page 23 and 24: 2.3. Magnetic Anisotropy 23 E n e r
Page 25 and 26: 2.3. Magnetic Anisotropy 25 Figure
Page 27 and 28: Chapter 3 MBE Growth of Ferromagnet
Page 29 and 30: 3.2. Epitaxial Growth of (Ga,Mn)As
Page 31 and 32: 3.3. Crystal Defects 31 lead to a d
Page 33 and 34: 3.4. RHEED 33 Figure 3.5: (a) Ewald
Page 35 and 36: 3.5. X-Ray Diffraction 35 1 0 7 1 0
Page 37: 3.5. X-Ray Diffraction 37 between t
Page 41 and 42: 3.5. X-Ray Diffraction 41 substrate
Page 43 and 44: Chapter 4 Finite Element Simulation
Page 45 and 46: 4.1. Derivation of the Equation Sys
Page 47 and 48: 4.2. The FlexPDE Software 47 4.2 Th
Page 49 and 50: 4.3. Simulation Results - Physical
Page 55 and 56: 4.4. Simulation Results - (In,Ga)As
Page 57 and 58: 4.5. Stripes Along [1¯10] 57 Figur
Page 59 and 60: 4.5. Stripes Along [1¯10] 59 in-pl
Page 61 and 62: Chapter 5 Local Anisotropy Control
Page 63 and 64: 5.1. Patterning and Structural Char
Page 73 and 74: 5.2. Magnetic Characterization 73 p
Page 75 and 76: 5.2. Magnetic Characterization 75 1
Page 77 and 78: 5.2. Magnetic Characterization 77 8
Page 79 and 80: 5.3. Shape Anisotropy 79 ∼ 0.2 k
Page 81 and 82: 5.4. A Model for Anisotropy Orienta
Page 83 and 84: 5.4. A Model for Anisotropy Orienta
Page 85 and 86: Chapter 6 Device Application As sta
Page 87 and 88: 6.2. The Role of the Constriction 8
Page 89 and 90:
6.2. The Role of the Constriction 8
Page 91 and 92:
6.2. The Role of the Constriction 9
Page 93 and 94:
Chapter 7 Conclusion and Outlook Th
Page 95 and 96:
Appendix A Band Structure Hamiltoni
Page 97 and 98:
Appendix B Sample FlexPDE Input Fil
Page 99 and 100:
99 BOUNDARIES s u r f a c e ’ s u
Page 101 and 102:
Bibliography [Abol 01] M. Abolfath,
Page 103 and 104:
103 [McGu 75] T. R. McGuire and R.
Page 105 and 106:
Publications • J. Wenisch, C. Gou
Page 107:
Acknowledgements There is a number
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Ferromagnetic (Ga,Mn)As Layers and ... - OPUS Würzburg

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