n ( r ) = N$_{c}$F$_{1}$$_{/}$$_{2}$ [ − β ( E$_{c}$ − eV ( r ) − µ )] (3a) p ( r ) = N$_{v}$F$_{1}$$_{/}$$_{2}$ [+ β ( E$_{v}$ − eV ( r ) − µ )] , (3b) N + d ( r ) = N$_{d}$ 1 + 2 e − β [ E c − E b − eV ( r ) − µ ] , (4) where E$_{b}$ is the binding energy of the donor, which typically ranges from a few tens to a few hundreds of meV. As mentioned previously, surface states can play an important role in the electrostatics of nitride nanowires. They might act as a source 8–11 or as a trap 40,41 of carriers, effectively pinning the chemical potential in the band gap. Little is however known about the electronic structure of nitride surfaces. 42 On one hand, density functional theory (DFT) calculations on reconstructed GaN and AlN surfaces 43–47 suggest the existence of occupied (donor-like) surface states above the valence band edge and empty (acceptor-like) surface states below the conduction band edge (as expected from simple considerations). On the other hand, the extensive literature about 2D electron gases in [0001] GaN/GaAlN heterostructures 8–11 suggests the existence of dense ( ≃ 10 13 cm − $^{2}$eV − $^{1}$) surface donor states only ≃ 1 . 5 eV below the conduction band of Ga$_{1}$$_{−}$$_{x}$Al$_{x}$N alloys ( x ≃ 0 . 4). Although the nature of these surface donors is still debated, oxygen has often been put forward. 48 It is not clear however that the same picture holds for non-polar Ga(Al)N surfaces and for surfaces of pure AlN, where the oxide is not the same. The situation is particularly tricky in nanowires, which expose different (polar and non-polar) surfaces. For the sake of simplicity, we assume in this work the existence of a uniform density of occupied surface states in the [ E + 1 , E + 2 ] energy range above the valence band edge, and of a uniform density of empty surface states in the [ E − 1 , E − 2 ] energy range below the conduction band edge. The density of ionized occupied 6 where N$_{c}$ and N$_{v}$ are the effective conduction and valence band density of states of the material at point r , E$_{c}$ and E$_{v}$ are its conduction and valence band edge energies (see Table I), V ( r ) is the total electrostatic potential, and µ is the chemical potential or Fermi energy. F$_{1}$$_{/}$$_{2}$ is the Fermi integral of order one-half and β = 1 / ( kT ), where T = 300 K is the temperature. We have, additionally, assumed that the nanowires were non-intentionally n - doped, with a concentration of donor impurities (silicon, oxygen or vacancies) N$_{d}$ = 2 × 10 17 cm − $^{3}$. The density of ionized impurities is:39 holes, p ( r ) are calculated as: 39