Analytical calculation of the strain field of single and periodic misfitting polygonal wires in a half-space

Abstract

We calculate analytically the strain field induced by the coherent elastic relaxation of misfitting wires having an arbitrary polygonal section and buried in a half-space, assuming linear isotropic elasticity. The calculation applies in particular to semiconductor quantum wires both during and after epitaxial growth, and more generally to any polygonal wire or fibre lying close to a planar free surface. Our closed-form solutions apply both to isolated wires and to infinite periodic arrays of wires parallel to the free surface. Simple formulae are given for wires with trapezoidal and right-angled triangular sections and for semi-infinite slabs with vertical or oblique terminating facets. The calculations are illustrated in the important case of trapezoidal wires. In particular, we evaluate the effect of close and distant wires upon the strain in the vicinity of a given wire and show that the shape of the wire section has a substantial effect on the morphology and magnitude of the strain field.