## I. INTRODUCTION 

Wide band gap nitride semiconductors are now widely used for light emission in the blue and ultraviolet range. 1–3 Thanks to large band offsets, GaN/AlN heterostructures are also promising candidates for fast telecommunication devices based on intersubband transitions 4 or for high-temperature single photon emitters. 5 One of the specifics of nitride heterostruc- tures is the existence of large internal electric fields due to spontaneous polarization and strains (piezoelectricity). 6 These built-in fields might transfer charges in the devices, leading for example to the formation of two dimensional (2D) electron gases at the interfaces be- tween GaN and (Ga)AlN layers. 7–11 They might also separate the electrons from the holes in GaN quantum wells and Stranski-Krastanov (SK) quantum dots, thereby reducing the band gap and oscillator strength (quantum confined Stark effect). 12–14,16 It is therefore essential to understand and tailor the electric field in nitride heterostructures to suit a particular application. 

Whereas 2D layers usually feature a large density of dislocations, nitride nanowires offer the opportunity to make defect-free heterostructures thanks to the efficient strain relaxation. 17,18 Single GaN quantum disks (QDs) between two AlN barriers have for exam- ple been grown on top of GaN pillars (20–50 nm diameter) with plasma-assisted molecular beam epitaxy (see Fig. 1). 19 The exciton and biexciton luminescence of 1 nm thick GaN QDs has been observed, showing the potential of such heterostructures for nitride optoelec- tronic devices. 19 A strong red shift (below the bulk GaN band gap) has been subsequently observed for larger disk thickness, a signature of the quantum confined Stark effect. 20 The apparent electric field is however smaller than expected from a comparison with GaN/AlN quantum wells. 14 The effects of strain relaxation (decrease of the piezoelectricity) and finite lateral size on the electric field, 15 as well as the screening mechanisms are still unclear. 

Nitride SK dots have been modeled before with k · p or tight-binding approaches. 15,21–26 The key role played by the charges transferred by band bending, which screen the elec- tric field, has been emphasized in 2D GaN/GaAlN layers. 7–11 In this paper, we model the electronic properties of [0001]-oriented GaN/AlN nanowire heterostructures in an atomistic tight-binding framework. 27,28 We compute strains with a valence force field method, 29 then the pyro- and piezoelectric field. We account for band bending with a semi-classical Debye- H¨ uckel approach, making no assumption about the pinning of the Fermi level, but including 

