Theory of semiconductor solid and hollow nano‐ and microwires with hexagonal cross‐section under torsion

Abstract

The effect of torsion on false[00.1false]‐oriented wurtzite and false[111false]‐oriented zincblende nanowires with hexagonal cross‐section is discussed. The stresses (and strains) are determined via calculation of Prantl's stress function. The spatial variation of the valence band structure in the cross‐section is evaluated in the framework of the 6×6 valence band Hamiltonian and deformation potential theory. The shear strain induced potential leads to additional localization of holes in the center of the facets. In wurtzite wires, torsion does not evoke piezoelectric charges or potentials and thus does not impact the signal in piezotronic sensors. In zincblende wires, the second order piezoelectric effect causes piezoelectric charges with threefold symmetry. The strain distribution in hexagonal nanowires with rounded corners depends on the curvature radius of the corners. For finite corner radius, the strain does no longer vanish at the corners. Also hexagonal nanotubes are discussed; here the inner and outer boundary exhibit different strain distributions. Visualization of the distribution of shear stress τ=σxz2+σyz2 in the hexagonal cross‐section of a false[00.1false]‐oriented wurtzite nanowire under torsion.