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

3.4 Challenges of Heteroepitaxial Growth of III-V on Silicon
this work, has been done to study and ensure that the dislocations generated stay
near the overlayer-substrate interface and do not propagate into the overlayer as
shown in Fig. 3.7(a).
3.4.3 Large Thermal-Mismatch
In lattice-mismatched heteroepitaxial layers, most of the mismatch may be accommodated
by mist dislocations during growth, even if kinetic factors are important.
Therefore, the grown layer will be nearly relaxed at the growth temperature.
However, the strain measured at room temperature may be quite dierent if the
epitaxial layer and substrate have dierent thermal expansion coecients like in
the case of III-V epitaxy on silicon (see Table 3.1). Therefore, a thermal strain
will be introduced during the cool down to room temperature. The thermal expansion
coecient of a given material is related to the expansion or contraction of
the crystal lattice as the material's temperature changes. Commonly, the lattice
expands under increased temperature, and returns to its original dimensions as
the temperature is reduced. Moreover, thermal cycling during device operation
will result in a temperature dependence of the built-in strain [31].
At room temperature conditions, the mismatch between GaP and Si is 0.37 %,
while at a typical MBE growth temperature of 550 ◦ C, the mismatch is increased
to 0.48 %, due to the fact that the GaP with higher thermal expansion coecient
will expands more than the Si substrate. This change in lattice mismatch
increases the mist strain, reducing the critical thickness of the GaP epilayer at
growth temperature, and must be taken into account [49]. On the other hand,
the thermal expansion coecient of GaAs is almost 60 % larger than Si expansion
coecient at room temperature. After the relaxation process at the growth
temperature during MBE epitaxy, the GaAs layer will shrink much more than
the Si substrate during the cooling down after the growth. Assuming that the
mismatched GaAs layer has completely relaxed at the growth temperature, a tensile
strain ɛ t will thus be developed during the cooling process in the layer, which
will be proportional to the total change in temperature of the system:
ɛ t =
∫ T
T 0
[α S − α L ] dT (3.16)
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