For example: Let us say we have GaAs as the substrate material and upon it is deposited a layer Al1-xGaxAs on that we have Al1-yGayAs. Of the last two materials, which one is strained and which one is relaxed? And how is the strain induced?
I'll start from the end.
The strain is caused by the lattice constant mismatch. If the layers are epitaxial and high quality, there is a competition between two energy terms: the elastic energy is increased by strain, and it can be relieved (fully or partially) by introducing dislocations (or other defects) at the interface - but this would result in an increase of the interface energy. As the strained layer becomes thicker, the elastic energy term increases, yet the surface energy 'cost' remains the same. Therefore, at some thickness, dubbed as the critical thickness, it is energetically more cost effective to form those dislocations to relieve the strain. This is true for equilibrium, whereas in practice kinetics can change this value considerably; there's also the issue of thermal strain etc. A dislocation-free interface is termed coherent, and it is often the desirable case, particularly for III-V semiconductors that are often used for EO applications.
As for the materials at hand, a quick google search should yield their lattice parameters. If you're having trouble with that I could refer you to the literature.
Strain, in thin films can be originated from various factors such as difference in lattice parameters, growth conditions, due to different thermal expansion coefficients etc.
Out of the above mentioned cases, strain due to lattice mismatch between substrate and film, and also between heterojunction can be dominant. The film can undergoes either in-plane tensile or compressive strain depending upon the lattice parameter of the substrate. If lattice parameter of the film>substrate (in-plane compressive) else opposite.
For compressive strained films:
The in-plane lattice parameters will get reduced whereas the out-of-plane lattice parameter will be increased to keep unit cell volume constant (most-of the cases) and can be determined by XRD. these changes in lattice parameters can be applied until the film is completely under strain. once it reaches critical thickness, as explained by Lior Kornblum, the lattice parameters will be exhibiting same as like bulk.
So, for your case, for the first examination, you can simply check the lattice parameters and from that, you can estimate the type strain in film if they are under critical thickness.
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