We assume that the polarization is homogeneous in the lower AlN barrier ( P$_{z}$ = P$_{inf}$ ), GaN quantum disk ( P$_{z}$ = P$_{QD}$ ) and upper AlN barrier ( P$_{z}$ = P$_{sup}$ , see Fig. 5). This polarization is equivalent to a charge density σ$_{sup}$ = Δ P$_{sup}$ = P$_{QD}$ − P$_{sup}$ on the upper QD interface and σ$_{inf}$ = − Δ P$_{inf}$ = − ( P$_{QD}$ − P$_{inf}$ ) on the lower QD interface. We also assume that the difference of potential Δ V across the heterostructure is set by band structure effects [Eq. (9) or equivalent if other pinning of the Fermi level]. The electric field is then homogeneous in each layer and fulfill the continuity and integral equations: We therefore get: where: is an average polarization discontinuity at the interfaces of the QD. Additionally, the electric field in the barriers is: The above equations hold as long as the QD is empty – which is also often desired experimentally. Neglecting quantum confinement in a first approximation, the QD is empty as long as the conduction band edge is above the Fermi energy, and the valence band edge below the Fermi energy throughout the dot. Assuming E$_{QD}$ < 0 (which is the case here), the QD is therefore free from holes if E$_{v}$ (GaN) − eV ( z = − t$_{sup}$ − t$_{QD}$ ) < µ , and free from electrons if E$_{c}$ (GaN) − eV ( z = − t$_{sup}$ ) > µ . Using Eqs. (8), (9) and (13), these conditions respectively translate into the following constraints on t$_{inf}$ and t$_{sup}$ : t$_{sup}$ < Δ V E$_{sup}$ . (14b) t$_{inf}$ < E$_{g}$ (GaN) eE$_{inf}$ (14a) E$_{sup}$ = 1 κ$_{0}$κ [ Δ P$_{sup}$ − t$_{inf}$ + t$_{sup}$ t$_{het}$ Δ ¯ P ] + Δ V t$_{het}$ . (13b) E$_{inf}$ = 1 κ$_{0}$κ [ Δ P$_{inf}$ − t$_{inf}$ + t$_{sup}$ t$_{het}$ Δ ¯ P ] + Δ V t$_{het}$ (13a) Δ ¯ P = t$_{inf}$ Δ P$_{inf}$ + t$_{sup}$ Δ P$_{sup}$ t$_{inf}$ + t$_{sup}$ (12) E$_{QD}$ = − 1 κ$_{0}$κ t$_{inf}$ + t$_{sup}$ t$_{het}$ Δ ¯ P + Δ V t$_{het}$ (11) t$_{inf}$E$_{inf}$ + t$_{QD}$E$_{QD}$ + t$_{sup}$E$_{sup}$ = Δ V . (10c) κ$_{0}$κ ( E$_{sup}$ − E$_{QD}$ ) = Δ P$_{sup}$ (10b) κ$_{0}$κ ( E$_{inf}$ − E$_{QD}$ ) = Δ P$_{inf}$ (10a) 12