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

Heteroepitaxial Growth of III-V Semiconductor on Silicon Substrates
with respect to their substrates. In highly mismatched material systems, gross
misorientations are sometimes observed, due to the close matching in the atomic
spacings for the substrate and the epitaxial layers in dierent crystallographic
directions [31]. However, as noted before, the strain energy will grow as the overlayer
thickness increase. As result, it will eventually be favorable for the overlayer
to generate dislocations. In simplistic theories this occur at an overlayer thickness
called critical thickness (d c ), which is approximately given by Eq. 3.11 [21].
d c
∼ a s
= (3.11)
2|ɛ|
The most widely used theoretical model for the critical layer thickness is the
force balance model of Matthews and Blakeslee [43].
• Matthews and Blakeslee Force Balance Model :
The Matthews and Blakeslee model is used most often to calculate the critical
layer thickness for heteroepitaxy. Here it is considered that a pre-existing
threading dislocation in the substrate replicates in the growing epi-layer and can
bend over to create a chain of mist dislocations at the interface, once the critical
layer thickness is reached. This process is shown schematically in Fig. 3.6. The
glide force F G acting on the dislocation is dened by Eq. 3.12.
2Gbfh(1 + ν) cos λ
F G = (3.12)
(1 − ν)
Where λ is the angle between the Burgers vector b and the line in the interface
plane that is perpendicular to the intersection of the glide plane with the interface,
G is the shear modulus, ν is the Poisson ratio, b is the length of the Burgers vector
for the threading dislocation and h is the lm thickness. On the other hand, the
line tension of the mist segment of the dislocation F L expressed in Eq. 3.13 is
acting with force in the opposite direction of the glide force F G [31].
F L = Gb(1 − ν cos2 α)
[ln(h/b) + 1] (3.13)
4π(1 − ν)
By equating the glide force F G in (see Eq. 3.12) to the line tension for the mist
segment of the dislocation F L (see Eq. 3.13) and solve for the thickness. As
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