The strain configuration induced by the lattice mismatch in a core-shell nanowire is calculated analytically, taking into account the crystal anisotropy and the difference in stiffness constants of the two materials. The method is applied to nanowires with the wurtzite structure or the zinc-blende structure with the hexagonal / trigonal axis along the nanowire, and the results are compared to available numerical calculations and experimental data. It is also applied to multishell nanowires, and to core-shell nanowires grown along the $<001>$ axis of cubic semiconductors.
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