Abstract
Since the demonstration of nanowires utilization in optoelectronics [1], nano-objects have attracted a growing interest from the scientific community. In particular, GaN nanowires are strain- and defect-free UV light emitters that can be grown on Si substrates. However, as proposed recently in [2], the low-temperature donor-bound exciton emission from ensemble of narrow GaN nanowires is broad, due to the distribution of the distance between the donor nuclei and the surface. In this work, we study the influence of the surface and of the dielectric mismatch on the binding energy of donor atoms and, therefore, on the emission energy of donor bound excitons in GaN nanostructures. We compute by envelope function calculations, performed in the effective potential formalism, the binding energy of donor atoms in thin air/semiconductor/air slabs. We not only account for the Coulomb interaction between the electron and the donor nucleus, but also for the attraction between the electron and the image charges of the nucleus and for the repulsion between the electron and its images (i.e. the electron self-energy). We first consider the case of a donor nucleus located at the center of a nanostructure. Comparing our data with tight-binding calculations performed in Ref. [3], we show that the planar symmetry used here reproduces well the results obtained for cylindrical wires. Strikingly, the combination of the confinement and the dielectric mismatch in the narrowest nanostructures leads to donor binding energies exceeding four times the bulk Rydberg [4]. When the donor nucleus is located at the air/semiconductor interface, its binding energy is as expected reduced compared to the bulk case [5]. However, we obtain that this reduction is only by a factor of two, while a factor of four is computed when the dielectric mismatch is neglected [5]. Finally, we discuss the relative influence of the dielectric mismatch, surface and confinement on the donor binding energy with respect to the thickness of the nanostructure. [1] for a review, see C. M. Lieber et al., MRS Bulletin 32, 99 (2007). [2] P. Corfdir et al., JAP 105, 013113 (2009), O. Brandt et al. PRB 81, 045302 (2010). [3] M. Diarra et al., Phys. Rev. B 75, 045301 (2007). [4] G. Bastard, Phys. Rev. B 24, 4714 (1981). [5] S. Satpathy, Phys. Rev. B 28, 4585 (1983).