or from the pillar. Eqs. (3)–(7) do not, however, properly take quantum confinement into account. We have therefore refined the assessment of the charge state of the QDs with the tight-binding model: we have tentatively assumed that the QDs were empty (setting N$_{v}$ = N$_{c}$ = 0 in the dots so that they are free of carriers), and checked the position of the tight-binding band edges with respect to the Fermi energy. We find that all the QDs of Fig. 7 are actually empty, except those with t$_{sup}$ = 4 nm and t$_{inf}$ ≥ 8 nm, which are filled with holes. As expected from Eq. (19b), the total charge density in the AlN barriers increases with t$_{het}$ , from n$_{s}$ = 2 . 39 × 10 13 cm − 2 for t$_{inf}$ = t$_{sup}$ = 4 nm, to n$_{s}$ = 3 . 54 × 10 13 cm − 2 for t$_{inf}$ = t$_{sup}$ = 8 nm, and n$_{s}$ = 4 . 25 × 10 13 cm − 2 for t$_{inf}$ = t$_{sup}$ = 16 nm. The Fermi energy is therefore pinned in the valence band of AlN at the top surface in all heterostructures considered here ( n$_{s}$ > N + tot = 2 × 10 13 cm − $^{2}$). We would finally like to discuss the role of the lateral surface states. The top surface states play a key role by releasing electrons in the GaN pillar, thereby screening the pyro- and piezo-electric field. The occupied lateral surface states of the upper and lower AlN barrier also act as a (secondary) source of electrons. Most of these extra electrons (as well as the donor electrons) are, however, trapped by the empty lateral surface states of the GaN pillar. As a consequence, the GaN pillar is effectively depleted far away from the heterostructure, and the Fermi level is pinned ≃ 1 . 25 eV below the conduction band edge (see Fig. 2). 41 This does not, however, have significant influence on the physics of the heterostructure. We now discuss the electronic and optical properties of the GaN/AlN nanowire het- erostructures, and compare our results with experimental data. The tight-binding band gap energy E$_{g}$ of empty 4 nm thick GaN QDs is plotted as a function of the electric field E$_{QD}$ in Fig. 8. The corresponding values of t$_{inf}$ and t$_{sup}$ are reported between parenthesis. The excitonic correction is not included in this calculation and should further decrease the optical band gap by at most ≃ 25 meV. The band gap energy is strongly red-shifted (below the bulk value) by the electric field (Stark effect). It depends almost linearly on E$_{QD}$ and spans around 1 eV in the investigated range of t$_{inf}$ and t$_{sup}$ . The ground-state electron and hole wave functions of a particular QD ( t$_{inf}$ = t$_{sup}$ = 8 IV. ELECTRONIC PROPERTIES OF GAN/ALN NANOWIRE HETEROSTRUC- TURES 17