Finite-size effects in one-dimensional strained semiconductor heterostructures

The elastic lattice deformation of strained one-dimensional (1D) semiconductor heterostructures (quantum wires) is investigated theoretically. We consider the case of lattice-mismatched [100]-oriented superlattices made of cubic symmetry materials with a finite lateral dimension along the [011]- or the [001]-crystallographic direction. Due to the small lateral dimension of the quantum wires, an elastic stress relaxation occurs near the free surfaces. The theoretical evaluation of strain fields in these 1D heterostructures is made with a Fourier series treatment and by using the elasticity theory and the condition of zero total stress on the free surfaces. We also investigate the effect of strain on the confinement potentials. In the case of 1D heterostructures made by materials with zinc-blende symmetry, the nonuniform lattice deformations can induce polarization charges due to the piezoelectric effect. Large band-gap and valence-band-splitting energy modulations of several tens of meV can be obtained near the free surfaces, inducing strong variations in the confinement potentials, which could cause red-shifted electron-hole transitions. Our analytical expressions for the nonuniform strain and stress fields, piezoelectric fields, and confinement potentials are valid for any zinc-blende heterostructure made of III-V and II-VI semiconductor compounds. Our results clearly demonstrate that, in addition to the 1D confinement that is caused by the reduced geometrical lateral dimension, the elastic strain relaxation and the piezoelectric fields on the free surfaces of the quantum wires must be considered in order to understand and describe correctly the electronic properties of 1D heterostructures.