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Strain and piezoelectric fields in arbitrarily oriented semiconductor heterostructures. II. Quantum wires.

In this paper, we investigate the strain and piezoelectric fields of semiconductor quantum-wire heterostructures. The quantum-wire structures considered here are those which are fabricated from superlattices grown on a thick substrate crystal and are laterally confined by vacuum or air. The strain-tensor components are calculated by minimization of the strain-energy density and by imposing the commensurability constraint at the wire/substrate interface only along the wire direction. In fact, due to the finite lateral dimension of the structure, a relaxation of the crystal lattice perpendicular to the wire occurs until the minimum of the strain energy is reached. A detailed study of the symmetry of the distorted crystallographic unit cell as a function of the substrate orientation and the wire direction is presented. We find that due to the anisotropic elastic lattice relaxation of the quantum wires a lower-symmetry lattice deformation than a tetragonal one can occur also for the [001]-substrate orientation. We show that, for zinc-blende heterostructure quantum wires, these strain fields can generate high piezoelectric fields that can be different from zero even for the high-symmetry [001]-interface orientation. Due to the presence of these high piezoelectric fields in quantum-wire structures, a one-dimensional electron gas can be produced.