electric field yields: E$_{QD}$ = − 8 . 15 MV / cm without electromechanical coupling (A3a) E$_{QD}$ = − 7 . 70 MV / cm with electromechanical coupling (A3b) in a 4 nm thick QD with t$_{inf}$ = 8 nm and t$_{sup}$ = 7 nm (experimental geometry). The elec- tromechanical coupling can therefore reduce the electric field by at most 5.75%. According to Fig. 8, a 0 . 45 MV/cm decrease of the electric field would account for a ≃ 120 meV increase of the bang gap. Additionally, the strains in the GaN layer are: Using the interband deformation potential a$_{z}$ = − 11 . 3 eV in GaN, 35 the strains in the coupled system would further increase the band gap by ≃ 19 meV. As a whole, the elec- tromechanical coupling can not, therefore, be expected to increase the band gap by more than ≃ 140 meV. The same order of magnitude is obtained assuming the heterostructure is biaxially strained onto AlN. ∗ Electronic address: yniquet@cea.fr 1 S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimoto, and H. Kiyoku, Appl. Phys. Lett. 69 , 4056 (1996). 2 F. A. Ponce and D. P. Bour, Nature 386 , 351 (1997). 3 A. J. Fischer, A. A. Allerman, M. H. Crawford, K. H. A. Bogart, S. R. Lee, R. J. Kaplar, W. W. Chow, S. R. Kurtz, K. W. Fullmer, and J. J. Figiel, Appl. Phys. Lett. 84 , 3394 (2004). 4 L. Nevou, N. Kheirodin, M. Tchernycheva, L. Meignien, P. Crozat, A. Lupu, E. Warde, F. H. Julien, G. Pozzovivo, S. Golka, G. Strasser, F. Guillot, E. Monroy, T. Remmele, and M. Al- brecht, Appl. Phys. Lett. 90 , 223511 (2007). 5 S. Kako, C. Santori, K. Hoshino, S. G¨ otzinger, Y. Yamamoto, and Y. Arakawa, Nature Mat. 5 , 887 (2006). 6 F. Bernardini, V. Fiorentini, and D. Vanderbilt, Phys. Rev. B 56 , R10024 (1997) ; A. Zoroddu, F. Bernardini, P. Ruggerone, and V. Fiorentini, Phys. Rev. B 64 , 045208 (2001). 22 ε$_{zz}$ = − 0 . 17% with electromechanical coupling . (A4b) ε$_{zz}$ = 0 without electromechanical coupling (A4a)