Molecular beam epitaxial growth of III-V semiconductor ... - KOBRA

Heteroepitaxial Growth of III-V Semiconductor on Silicon Substrates
hand, epi-layers with lattices constant larger than the substrate lattice constant
(f< 0) will undergo compressive strain. In heteroepitaxial systems with a low
amount of mismatch (|f|< 1), the initial growth tends to be coherent, or pseudomorphic
as illustrated in Fig. 3.5(a). Therefore, a pseudomorphic (full strained)
layer exhibits an in-plane strain (ɛ || ) equal to the lattice mismatch (f) as described
in Eq. 3.9 [31].
ɛ || = f (P seudomorphic) (3.9)
The residual strain in highly strained materials is generally a function of the
mismatch and layer thickness. However, the strain can be calculated based on a
thermodynamic model, as long as the growth occurs near thermal equilibrium.
However, there are kinetic barriers to the lattice relaxation. These are associated
with the generation and movement of dislocations. Kinetic models have been
devised to explain and predict the lattice relaxation behavior in these situations
[31]. These models predict that the residual strain in the layer will depend on
the growth conditions and post growth thermal annealing (PGA) applied after
the growth, as well as the mismatch and layer thickness. However, with higher
amount of mismatch, or thicker epitaxial layers, the mist strain will increase until
it exceeds the elastic strength of the coherent semiconductor-substrate bonds. At
this point, the lm will undergo a plastic deformation resulting in the formation
of broken bonds and non-coherent growth fashion with mist dislocations at the
epitaxial lm-substrate interface as shown in Fig. 3.5(b). This mist dislocation
is associated with an extra half-plane of atoms in the substrate.
The pseudomorphic layer matches the substrate lattice constant in the plane
of the interface and therefore experiences in-plane biaxial compression. Beyond
the critical layer thickness, therefore, part of the mismatch is accommodated by
mist dislocations (plastic strain) and the balance by elastic strain. In this case,
using the denition for the mismatch adopted here, the in-plane strain (ɛ || ) is
expressed as in Eq. 3.10.
ɛ || = f − δ (P artially relaxed layer) (3.10)
Where δ is the lattice relaxation. In the pseudomorphic layer, for which no lattice
relaxation has occurred (δ=0), the result will be a fully strained system as
34