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

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62 5. Local Anisotropy Control by Strain Engineering Figure 5.1: (a) microscope image of patterned 4 × 4 mm stripe array containing fields of 251 parallel stripes. (b) SEM image of border region between two stripe fields. The width of the stripes is 200 nm. defects caused by plastic deformation. In pattering the layer into strips as introduced in the previous chapter, we allow the stripe material to relieve strain by expanding its lattice perpendicular to the stripe axis. This deformation is purely elastic and does not cause the formation of lattice defects. Since the lattice constant along the stripe direction is unaffected, we refer to this case as uniaxial relaxation. 5.1 Patterning and Structural Characterization Table 5.1 provides a list of all samples which will be discussed in this chapter. All samples were grown following the general procedure described in Chapter 3. The (In,Ga)As stressor layer was grown at a temperature of 500 ◦ C. For this layer, it is critical to avoid crossing the critical layer thickness and therefore the onset of plastic strain relaxation through lattice defect formation. The critical layer thickness can be estimated according to [Cohe 94]. Verification that indeed no relaxation takes place before pattering is achieved by HRXRD measurements. After growth, electron beam lithography and chemically assisted ion beam etching are used to pattern the samples into the desired stripe structures. For most samples, a total area of 4 × 4 mm is covered by arrays of stripes, see Fig. 5.1. Each field in the array contains 251 parallel stripes, with each individual stripe measuring nominally 200 nm × 100 µm. The separating distance between the stripes is 200 nm. A total etch depth of about 200 nm was chosen to avoid influence from insufficient GaAs pillar height (see Section 4.3.2).
5.1. Patterning and Structural Characterization 63 Table 5.1: List of (Ga,Mn)As stripe samples. Layer thickness and material content as determined by HRXRD measurements. All strains are simulation values in units of 10 −3 , averaged over a cross section of the respective layer. sample (Ga,Mn)As (In,Ga)As stripe (Ga,Mn)As strain (In,Ga)As strain name thickness [Mn] thickness [In] alignment ex ey ez exy ex ey ez exy A (S366) 70 nm 2.5% – – [100] 0.21 -1.50 0.56 0.00 – – – – B (S336) 70 nm 2.5% 80 nm 7.4% [100] 1.47 -1.50 -0.27 0.00 0.08 -5.30 1.58 0.00 C (S336) 70 nm 2.5% 80 nm 7.4% [1¯10] -0.42 -0.42 -0.06 1.09 -3.10 -3.10 3.55 2.16 D (S464) 19 nm 4.4% 11 nm 12.8% [100] 1.87 -2.30 0.21 0.00 -5.31 -9.20 6.50 0.00 E (S464) 19 nm 4.4% 11 nm 12.8% [1¯10] -0.64 -0.64 0.60 1.65 -7.59 -7.59 6.83 1.59 F (S469) 19 nm 5.4% 14 nm 19.0% [100] 3.60 -2.60 -0.44 0.00 -7.29 -13.60 9.36 0.00 G (S469) 19 nm 5.4% 14 nm 19.0% [1¯10] -0.15 -0.15 0.16 2.45 -11.10 -11.10 9.93 2.52 H (S470) 18 nm 4.4% 15 nm 22.6% [100] 4.78 -2.30 -1.09 0.00 -8.81 -16.20 11.20 0.00 I (S470) 18 nm 4.4% 15 nm 22.6% [1¯10] 0.47 0.47 -0.41 2.78 -13.20 -13.20 11.90 3.02
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 and 38: 3.5. X-Ray Diffraction 37 between t
Page 39 and 40: 3.5. X-Ray Diffraction 39 lattice d
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: Chapter 5 Local Anisotropy Control
Page 65 and 66: 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 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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