Self-consistent electronic structure of a cylindrical quantum wire

The self-consistent subband electronic structure, potential profile, and charge distribution of a GaAs quantum wire with cylindrical symmetry has been obtained by a numerical solution of the coupled Schro¨dinger and Poisson equations (within the Hartree approximation). The potential profile is exactly (nearly) parabolic when there are no (few) free carriers inside the wire, but approximates a stretched harmonic oscillator as charge accumulates in the cylindrical quantum wire. The dependence of the results on physical parameters such as the wire radius and concentration of surface states is analyzed.