The potential actually rises the occupied surface states of the upper AlN barrier above the Fermi energy. They therefore empty, leaving positive charges at the surface and releasing electrons in the GaN pillar. At moderate electric field, the surface states would be able to provide enough charge to reach equilibrium, and the chemical potential would lie in the band gap at the top AlN surface. Here the electric field is however large enough to empty the N + tot = D + s ( E + 2 − E + 1 ) = 2 × 10 13 cm − 2 occupied surface states. The chemical potential then sinks into the valence band; a gas of holes forms at the top surface and provides the missing charges. According to this picture, the charge in the system is mostly distributed at the top AlN surface and at the GaN/AlN interfaces. As a consequence, the electric field is typical of a series of parallel plate capacitors, being almost homogeneous in the GaN QD and AlN barriers. This is further emphasized in Fig. 4, which represents the electrostatic potential V ( r ) in a ( xz ) plane containing the axis of the nanowire. The equipotential lines are indeed parallel to the interfaces. The electrostatic corrections due to the finite cross section of the nanowire are therefore limited in the GaN QD and barriers in this range of dimensions. The effective density of states in the conduction and valence bands of GaN and AlN FIG. 4: (Color online) The electrostatic potential V ( r ) in the ( xz ) plane containing the axis of the nanowire ( t$_{QD}$ = 4 nm, t$_{inf}$ = t$_{sup}$ = 8 nm). The GaN and AlN layers are delimited by dotted lines. 10