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## III. THE ELECTRIC FIELD IN GAN/ALN NANOWIRE HETEROSTRUC- TURES 

In this section, we discuss the electric field in GaN/AlN nanowire heterostructures. We first analyze a particular case as an example. We then show that the electric field can be reproduced by a simple 1D model in a wide range of dimensions. We finally discuss the main trends as a function of the geometry of the heterostructures. 

## A. Example 

We focus as an illustration on a 30 nm diameter nanowire with a t$_{QD}$ = 4 nm thick GaN QD and t$_{inf}$ = t$_{sup}$ = 8 nm thick AlN barriers. We set D + s = D − s = 10 13 cm − $^{2}$eV − $^{1}$. 

The conduction band edge energy ε$_{c}$ ( r ) = E$_{c}$ − eV ( r ) and the valence band edge energy ε$_{v}$ ( r ) = E$_{v}$ − eV ( r ) are plotted along the axis of the nanowire in Fig. 2. The reference of energy for this plot is the chemical potential µ = 0. The top of the nanowire is located at 

