and band bending into account in the calculation of the pyro- and piezoelectric field. We have shown that strain relaxation reduces the piezoelectric polarization, and that the electric field pulls out electrons from the occupied states of the top surface. These electrons accumulate in the GaN pillar below the heterostructure, thereby screening the pyro- and piezoelectric field. We suggest that the electric field is likely strong enough to pin the Fermi level in or close to the valence band edge of AlN at the top surface. As a consequence, the electric field is significantly reduced with respect to GaN/AlN quantum wells or Stranski-Krastanov quantum dots. This is in agreement with recent experimental data on GaN/AlN nanowire heterostructures. 20 The calculation however overestimates the electric field in thick quantum dots, which calls for further experiments with different geometries and detailed polarity measurements. We have, for this purpose, provided a simple 1D model for the electric field to help the design of such heterostructures. We thank B. Daudin, B. Gayral, J. Renard and C. Bougerol for fruitful discussions. In this appendix, we give an estimate of the electromechanical coupling and of its effect on the optical band gap of the nanowire heterostructures. We assume that the heterostructures are biaxially strained onto GaN. According to Fig. 7b, this should provide an upper bound to the electric field, hence to the electromechanical coupling. The in-plane strains ε$_{xx}$ = ε$_{yy}$ = ε$_{‖}$ in the GaN QD and AlN barrier are then: Following Ref. 57, the vertical strain ε$_{zz}$ reads in each material: where c$_{13}$ and c$_{33}$ are the macroscopic elastic constants. 35 The first term is the “uncoupled” elastic strain while the second one describes the feedback of the electric field E$_{z}$ on the structure (electromechanical coupling). Solving Eq. (A2) with Eqs. (11)–(13) for the ε$_{zz}$ = − 2 c$_{13}$ c$_{33}$ ε$_{‖}$ + e$_{33}$ c$_{33}$ E$_{z}$ (A2) ε$_{‖}$ = 2 . 47% in AlN . (A1b) ε$_{‖}$ = 0 in GaN (A1a) 21 Appendix A: Electromechanical coupling