Abstract ........................................................ i
1 Introduction ................................................. 3
1.1 The system Vanadium:Silicon ............................. 3
1.2 Conditioning of the system Vanadium:Silicon ............. 6
1.3 Work structure .......................................... 8
2 Electron structure calculations ............................. 11
2.1 Schrodinger equation of many body systems .............. 11
2.2 Time-independent Schrodinger equation .................. 12
2.2.1 Necessary approximations ........................ 12
2.3 Density functional theory .............................. 14
2.3.1 Hohenberg-Kohn theorem .......................... 14
2.3.2 Kohn-Sham equations ............................. 15
2.3.3 Exchange-and-correlation functional ............. 16
3 Calculation methods and codes ............................... 19
3.1 Crystallographic representations ....................... 19
3.2 Basis sets ............................................. 19
3.3 DFT- methods and codes ................................. 20
3.3.1 Pseudopotential plane wave method ............... 21
3.3.2 Projector augmented waves method ................ 23
3.3.3 Full-potential local-orbital minimum-basis
method .......................................... 23
3.4 Common output .......................................... 24
4 Optimized program input parameters .......................... 27
4.1 Pseudopotentials ....................................... 27
4.2 Occupation scheme ...................................... 33
4.3 Energy cutoff of the basis set ......................... 33
4.4 Real space projection .................................. 33
5 System conditions ........................................... 35
5.1 Vanadium implantation and defect generation ............ 35
5.2 Subsequent sample preparations ......................... 36
5.3 Crystal morphology and depth profile ................... 36
5.4 Crystal structure ...................................... 38
5.5 Magnetic properties .................................... 40
5.6 Conclusion - schematic depth profile ................... 41
6 Diffusion of Vanadium in Silicon ............................ 43
6.1 Methodical details ..................................... 44
6.2 Structure optimization, lattice parameter and
stability .............................................. 44
6.3 Activation energy ...................................... 45
6.4 Limitations ............................................ 46
7 Point defects of Vanadium in Silicon ........................ 47
7.1 Defect structures ...................................... 47
7.2 Methodical details ..................................... 48
7.3 Structure optimization, lattice parameter and
stability .............................................. 49
7.4 Local defect results and the magnetic moment ........... 49
7.5 Electronic properties of the local defects ............. 50
7.6 Energy barrier from interstitial to substitutional
Vanadium ............................................... 52
7.7 Interaction of interstitial Vanadium with
self-interstitials ..................................... 53
7.8 Determination of complex concentrations ................ 54
7.9 The charged interstitial Vanadium defect ............... 56
7.10 Connection distance of magnetic Moments of
interstitial Vanadium .................................. 60
8 Vanadium clusters in Silicon ................................ 63
8.1 Methodical details ..................................... 64
8.2 Structure optimization, lattice parameter and
stability .............................................. 64
8.3 Cluster results and the magnetic moment ................ 64
8.4 Meta stable silicide structures ........................ 65
9 Vanadium silicide ........................................... 67
9.1 Methodical details ..................................... 69
9.2 Structure optimization, lattice parameters and
stability .............................................. 69
9.3 Formation enthalpy ..................................... 71
9.4 Bulk modulus ........................................... 72
9.5 Electronic properties .................................. 75
9.6 Special case: hexagonal structure of V5Si3 .............. 75
10 Conclusions ................................................. 79
A Details of calculation parameters ............................ 85
List of Figures ................................................ 86
List of Tables ................................................. 90
Bibliography ................................................... 92
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