surface states is therefore: while the density of electrons trapped in the empty surface states is: D + s and D − s are the density of occupied and empty surface states, respectively (per unit surface and energy). The values of E + 1 , E + 2 , E − 1 and E − 2 used in this work are also reported in Table I. They are representative of ab initio calculations, 43–47 and reproduce the pinning of the Fermi level on non-polar GaN surfaces. 41 We have varied D + s = D − s between 5 × 10 12 cm − $^{2}$eV − 1 and 5 × 10 13 cm − $^{2}$eV − $^{1}$. Their effects will be discussed in paragraph III. We will show, in particular, that the electric field in the QD is weakly dependent on the model for the surface states up to large D + s and D − s . In practice, the carrier densities n ( r ) and p ( r ) are computed on each Ga, Al and N atom, while the surface state densities N + s ( r ) and N − s ( r ) are computed on each hydrogen atom. The charge on each atom is then transferred to the finite difference mesh, and Poisson’s equation for the total electrostatic potential V ( r ) is solved self-consistently with the Newton-Raphson method: 49 The chemical potential µ is adjusted to ensure overall charge neutrality of the nanowire. Finally, the electronic structure of the GaN QD in the potential V ( r ) is computed with a sp $^{3}$d$^{5}$s ∗ tight-binding model. 50–53 In order to access the relevant states directly, a slice containing the GaN QD and 4 nm of each AlN barrier is cut from the nanowire. The bonds broken by this operation are saturated with hydrogen atoms, and a few conduction and valence band states are computed with a Jacobi-Davidson algorithm. 54,55 The convergence of the electronic structure of the QD with respect to the thickness of the AlN barriers has been checked. The above methodology has been implemented in an in-house code called TB Sim . 7 κ$_{0}$ ∇$_{r}$ · κ ( r ) ∇$_{r}$ V ( r ) = ∇$_{r}$ · P ( r ) + [ n ( r ) − p ( r ) − N + d ( r ) + N − s ( r ) − N + s ( r ) ] e. (7) N − s ( r ) = kT D − s ln 1 + 2 e − β [ E − 1 − eV ( r ) − µ ] 1 + 2 e − β [ E − 2 − eV ( r ) − µ ] . (6) N + s ( r ) = kT D + s ln 1 + 1 $_{2}$e β [ E + 2 − eV ( r ) − µ ] 1 + 1 $_{2}$e β [ E + 1 − eV ( r ) − µ ] , (5)