a distribution of surface states which act as a source or trap of carriers. We show i ) that the piezoelectric component of the field can be significantly reduced by the efficient strain relaxation in the nanowire geometry ; ii ) that the spontaneous and piezoelectric polariza- tions create an electron gas at the lower GaN/AlN interface and are likely large enough to create a hole gas in the upper AlN barrier. These electron and hole gases screen the electric field in the GaN QD and reduce the Stark shift ; iii ) that for carefully chosen dot and bar- rier thicknesses (realized experimentally) the GaN QD is empty at equilibrium, consistent with the observation of exciton and biexciton transitions. We discuss the magnitude of the electric field and the electronic stucture of the QDs as a function of the dimensions of the heterostructure. The paper is organized as follows: We review the methods in section II, then discuss the electric field in GaN/AlN nanowire heterostructures in section III. We introduce a simple 1D model for the pyro- and piezoelectric field that reproduces the main trends. We finally discuss the electronic structure of the GaN QDs and compare our calculations with the available experimental data in section IV. We analyze the dependence of the electronic and optical properties of the QDs on the geometry of the heterostructures. In this section, we introduce the methods used to compute the structural and electronic properties of the GaN/AlN heterostructures. Each nanowire is modeled as a 30 nm diameter and 150 nm long 30 cylindrical GaN pillar oriented along [0001], with the heterostructure on top (we assume metal-face polarity – the case of N-face polarity will be briefly discussed at the end of paragraph IV). The heterostructure consists of a lower AlN barrier with thickness t$_{inf}$ , a GaN quantum disk with thickness t$_{QD}$ and a upper AlN barrier with thickness t$_{sup}$ (see Fig. 1). The dangling bonds at the surface of the nanowire are saturated with hydrogen atoms. The strains in the nanowire are computed with Keating’s valence field model. 31 This model provides an atomistic description of the elasticity of tetrahedrally bonded semicon- ductors. It was originally designed for zinc-blende and “ideal” wurtzite materials with equal bond lengths and angles, 32 and has been recently adapted to arbitrary wurtzite materials such as GaN and AlN. 29 The elastic energy of the nanowire is minimized with respect to the 3 II. METHODOLOGY