11 FIG. 5: The 1D model used for the analysis of the electric field in the GaN QD. are large enough to “lock” the potential at the interface with the GaN pillar and at the top surface (as a small variation of potential leads to exponential variations of the charge densities once the Fermi energy is in the bands). Hence, at the top surface, and at the interface z = − t$_{het}$ = − ( t$_{inf}$ + t$_{QD}$ + t$_{sup}$ ) with the GaN pillar. The voltage drop Δ V = V ( z = − t$_{het}$ ) − V ( z = 0) across the heterostructure is therefore: The voltage drop across the heterostructure is thus primarily defined by the band gap E$_{g}$ (GaN) of GaN and the valence band offset between GaN and AlN once the Fermi energy is pinned in the valence band of AlN at the top surface. The validity of this assumption will be discussed in the next paragraphs. We can derive a simple 1D model for the electric field E$_{QD}$ in the GaN QD from the above observations. For that purpose, we neglect finite size effects ( R → ∞ ) and doping. B. A simple 1D model e Δ V ≃ E$_{c}$ (GaN) − E$_{v}$ (AlN) ≃ E$_{g}$ (GaN) + E$_{v}$ (GaN) − E$_{v}$ (AlN) . (9) µ ≃ E$_{c}$ (GaN) − eV ( z = − t$_{het}$ ) (8b) µ ≃ E$_{v}$ (AlN) − eV ( z = 0) (8a)