Elastic lattice deformation in quantum-wire heterostructures

We report on the lattice deformation of quantum-wire heterostructures with cubic symmetry deposited on arbitrarily oriented substrate surfaces. The elasic strain and the stress-tensor components are calculated by using Hooke’s law and applying the appropriate boundary conditions at the wire-substrate interface. We assume that the lattice coherence at the wire-substrate interface is achieved only along the wire direction, due to the limted lateral extension of the wires. We show that either a tetragonal or an orthorhombic or a lower-symmetry lattice deformation of the quantum-wire structure may occur depending on the coherence direction and substrate orientation. In some particular cases, even for high-symmetry substrate orientations ([001] and [110]), it is possible to obtain one shear strain element different from zero, leading to a monoclinic lattice deformation. Moreover, for the [111] or low-symmetry substrate orientations a triclinic lattice deformation can also be obtained. In the case of an orthorhombic lattice deformation our theoretical results are found to be in good agreement with the few experimental data available.