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

3.4 Challenges of Heteroepitaxial Growth of III-V on Silicon
Figure 3.6:
The bending of a grown-in threading dislocation to create a length of
mist dislocation at the interface between an epitaxial layer and its lattice-mismatched
substrate. Figure modied according to reference [44].
a result of this procedure, one can calculate the critical layer thickness h c (see
Eq. 3.14), according to the force balance model of Matthews and Blakeslee.
h c = b(1 − ν cos2 α)[ln(h/b) + 1]
8π|f|(1 + ν) cos λ
(3.14)
For layers with h < h c , the glide force is unable to overcome the line tension,
and grown-in dislocations are stable with respect to the proposed mechanism of
lattice relaxation. On the other hand, for layers thicker than the critical layer
thickness h > h c , threading dislocations will glide to create mist dislocations
at the interface and relieve the mismatch strain [31].
Equilibrium thermodynamics can be used to estimate the total density of
dislocations that will form for a mismatched semiconductor with a given mist
strain. For any strain state, the average spacing of an array of parallel mist
dislocation S can be estimated for a given amount of accommodated strain δ
[45], as described in Eq. 3.15.
S = b
2δ
(3.15)
This equation assumes that all strain-relieving dislocations have Burgers vectors
60 ◦ from the [110] dislocation direction. For GaAs grown directly on Si, the
complete relaxation of the 4.1% lattice mismatch would demand a dislocation
spacing S about 100 A ◦ [14]. However, equilibrium theory shows that some elastic
strain will remain in a mismatched lm after relaxation. Work by number
of authors has shown that the relaxation of a mismatched epitaxial lm can be
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