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

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60 4. Finite Element Simulations of Strain Relaxation
Chapter 5 Local Anisotropy Control by Strain Engineering As discussed in the previous chapter, finite element simulations of the strain relaxation in stripe-shaped nanostructures predict a significant anisotropy in strain for the directions parallel and perpendicular to a long stripe axis. Theoretical band structure calculations and the Zener model indicate that lattice strain plays a significant role in determination of the magnetic anisotropy of (Ga,Mn)As. To investigate the interplay between lattice strain and magnetic anisotropy, we have produced a series of samples. Their main characterizing properties, aside from Mn content and layer thicknesses, are twofold: the inclusion of a stressor layer and the alignment direction of the stripe pattern. Therefore the series contains samples • consisting solely of a (Ga,Mn)As layer on a GaAs substrate. • containing an additional (In,Ga)As stressor layer between the substrate and the (Ga,Mn)As layer to increase lattice strain. • with stripe structures aligned along the [100] crystal direction. • with stripes aligned along the [1¯10] direction. In the first section of this chapter, we will describe the fabrication process of the samples and provide detailed XRD studies which investigate the strain situation in the parent and structured layers. The second section focuses on the magnetic characterization by SQUID and transport measurements. At this point it is important to emphasize the difference between the two mechanisms of relaxation which are important in the context of this work. One is the relieving of accumulated growth strain during fabrication of an epitaxial layer. This effect takes place after a critical layer thickness is reached during growth of a layer with a lattice mismatch to its substrate. Stress relief is achieved via plastic relaxation of the crystal, through formation of lattice defects, which leads to degradation of the layer quality. During this process, the lattice constant will increase in both in-plane directions, which is why we will refer to this phenomenon as biaxial relaxation. The strain relaxation discussed in this chapter is induced by the removal of constricting material in parts of the layer. The initial condition of the layer, which is below its critical thickness, is still completely pseudomorphic, with a crystal devoid of lattice 61
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: 4.5. Stripes Along [1¯10] 59 in-pl
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 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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