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

5.4 Self-Assembled InAs QDs Embedded in Si Matrix
negligible strain relaxation (Eq. 5.10) and negligible crystal rotation. However,
by direct substitution of the approximation in Eq. 5.10 into Eq. 5.11, the relation
between material strain and GPA strain is obtained and expressed by Eq. 5.12:
d bulk
Si
d measured
Si
= 1 (approximation) (5.10)
ε GP A − f
1 + f
=
d measured
InAs (
d bulk
Si
d measured
Si
d bulk
InAs
) − d bulk
Si
(5.11)
ε InAs = εGP A − f
1 + f
(5.12)
The material strain analysis of dierent shape and size InAs QDs is shown in
Fig. 5.27. The direction and magnitude of tensile and compressive strain is clearly
shown with the color map. The color scale indicates the type and magnitude of
the strain.
The tensile strain has positive sign values (marked in red to yellow colors
in Fig. 5.27) and is pointing to outward directions (highlighted by red arrows).
Fig. 5.27(a) shows an example of tensile strain in y direction (ε yy ). On the other
hand, the compressive strain has negative sign values and marked in green to
dark blue colors with direction (highlighted by red arrows) pointing to inward
direction as illustrated in Fig. 5.27(b). The structure of 4 MLs InAs embedded in
Si matrix proved to have high degree of relaxation and low residual strain values.
The bulk lattice mismatch of 11.55 % is relieved by dislocation loops along the
interface consisting of perfect 60 ◦ -type dislocations and partial dislocation with
stacking faults inside the InAs clusters, which is in agreement with the literature
[1]. By two-dimensional strain mapping derived from high-resolution TEM
structure images, no strain gradients in the Si matrix around InAs clusters are
detectable (Fig. 5.26). Therefore, it has been observed that the strain relaxation
eects is mostly relieved by defects formation inside InAs QDs such as (SFs and
MTs) and mist dislocation (MD) array at the InAs/Si interface, as it was shown
in Fig. 5.27. On the other hand, anisotropic distortion of InAs lattice constant
is another indication of strain relaxation. The residual strain is discussed based
on the thermal mismatch between InAs and Si. However, the deformation force
93