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List of Tables

1.1 The lattice constants (in Å) for GaN, AlN, InN  [53], and for Si and Ge  [19]. The lattice constants of AlxGa1-xN/GaN, InxGa1-xN/GaN and Si1-xGex/Si are calculated using Vegard’s law with the data in the table.
1.2 The stiffness constants (in GPa) for GaN, AlN, InN  [61], for Si  [29], for Ge  [19] . The stiffness constants of the systems AlxGa1-xN/GaN, InxGa1-xN/GaN and Si1-xGex/Si are calculated using Vegard’s law with the data in the table.
3.1 Pre-logarithmic coefficients for some alloys according to the isotropic and anisotropic models. Data from atomistic simulations are included whenever available.
3.2 Parameters of the dislocation cores from atomistic simulations. 0.43 eV/Å is equal to 0.64 nJ/m.
3.3 Angle α minimizing the dislocation energy for each kind of dislocation within isotropic elasticity.
3.4 Angle α minimizing the dislocation energy for each kind of dislocation in monocrystals (0001) oriented with (0001) free surface (planar growth mode).
3.5 Angle α minimizing the dislocation energy for each kind of dislocation in monocrystals (0001) oriented with (1100) free surface (island growth mode).
3.6 Angle α minimizing the dislocation energy for each kind of dislocation in monocrystals (0001) oriented with (1122) free surface (island growth mode).
4.1 An overview of different assumptions for evaluating misfit dislocation energy, and equilibrium critical thickness .
4.2 Critical thickness values (in nm) of the studied systems.
5.1 Reaction table  [49] for threading dislocations (TDs) in GaN with hexagonal symmetry. Reactions which are not possible either due to the Frank’s criterion or for geometric reasons are indicated with a “—” while reactions which are possible are indicated with their designated number. Reactions producing two dislocations are denoted with two numbers corresponding to their products. Annihilation reactions are denoted by “A”.
5.2 Inclination angle γ of threading dislocations (TDs) with respect to the [1122] direction.
5.3 Ratios of the three threading dislocation (TD) types (in %) used as initial conditions.

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