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Theory

Strain effects

Strain effects in a heterostructure can be divided on internal and external. The internal strain is a result of lattice constant mismatch. The grown on substrate layers copy the in-plane substrate lattice constant if the thickness of layers is below critical one. In that case, the heterostructure layer has a biaxial tensile strain if the layer lattice constant is smaller than substrate one. In other case, when the layer lattice constant is larger than substrate one, the heterostructure layer has a compressive strain. For the lattice matched strain the strain tensor has the following nonzero components:
(43)
where a0 and a are the lattice constant of the substrate and the layer material, C11 and C12 are the elastic stiffness constant.

A layer material with a lattice constant a to be grown on a substrate with a lattice constant a0: (a) unstrained; (b) strained [7].

The nonzero strain terms for uniaxial external strain in [110], [100] and [001] directions are:
(44)
where S11, S12 and S44 are compliance constants. The final strain is the sum of (43) and (44).

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