Quantized electron states in nearly depleted hexagonal nanowires

The hexagonal quantum well (QW) is studied as a model for hexagonal nanowires, and the effects of donor impurities and geometrical deformations of the well are treated. By use of the Poisson equation the donor potential is calculated and the eigenspectrum of the hexagonal QW is shown to converge to that of a paraboloid quantum well with increasing donor density. Small deformations of the hexagon are shown to change the eigenspectrum significantly and give strong splittings of degenerate eigenvalues. Analytical approximations for the potential and eigenfunctions on the deformed hexagons are given.