Piezoelectric fields in one- and two-dimensional heterostructures fabricated on high-index surfaces

We present a theoretical study of the strain-induced piezoelectric fields which may occur in one- and two-dimensional III-V compound semiconductor heterostructures on high-index surfaces. The strain tensor components of the low-dimensional structures are calculated by minimization of the strain-energy density and by imposing appropriate constraints at the heterointerfaces. We obtain a tetragonal deformation for two-dimensional heterostructures grown on the high symmetry surfaces, while in the case of high-index surface orientations a monoclinic lattice deformation is obtained. For the one-dimensional heterostructures, which are fabricated from superlattices grown on thick substrate crystals and are laterally confined by air, a lower symmetry lattice deformation than a tetragonal one may also occur for the [001]-substrate orientation, as a result of the anisotropic elastic lattice relaxation. In zincblende heterostructure, these particular strain fields can generate high internal electric fields. In two-dimensional heterostructures, these piezoelectric fields appear for the [111] or for higher-index interface orientations. However, in one-dimensional heterostructures the strain fields can generate high piezoelectric fields even for the high-symmetry [001]-interface orientation.