Résumé
In contrast to epitaxial layers, single-crystalline GaN can be grown in the form of nanowires on Si substrates. In addition, the sub-wavelength diameter of nanowires facilitates light extraction, which is advantageous for the realization of efficient nanowire-based light emitting diodes. However, the ionization energies of dopants are different in nanostructures compared to the bulk. This effect may seriously affect the operation of nanowire-baseddevices relying on a controlled doping [1]. First, the combination of surface and dielectric mismatch effects results in a strong and non-monotonic variation of the donor binding energy, when going from the core to the surface of a nanostructure [2]. Second, surface states pin the Fermi level at the surface of the nanowire. This causes the formation of internal electric fields and the depletion of nanowires, as demonstrated by photoconductivity experiments [3]. We emphasize that this depletion is incomplete at low temperature, as donor bound exciton luminescence is observed even for GaN nanowires with a diameter of 30 nm [4].In this work, we investigate the impact of surface and internal electric fields on the binding energy of donor atoms in GaN nanowires. Using Monte-Carlo simulations, we first examine the validity of the assumption that depletion leads to a parabolic potential across the section of nanowires. For instance, we show that for nanowires with a doping of 2 x 1015 cm-3 and with a diameter and a length of 80 nm and 1.5 μm, respectively, the potential cannot be described by a parabola. In contrast, for a doping of the order of 1017 cm-3, the potential is nearly parabolic and is well described using the Poisson equation, where one assumes a spatially homogeneous distribution of dopants.Using envelope function calculations, we then compute the binding energy of donors in thin GaN slabs bounded by air. We take into account surface, confinement, and the dielectric mismatch, similarly to what has been reported in Refs. [2,5]. Based on the evolution of the spatial extent of the electron wave function as a function of the electric field at the nanowire surface, we deduce the magnitude of the electric field required for the ionization of surface donors. In particular, we show that surface donors are ionized for doping densities typically larger than 3 x 1016 cm-3, irrespectively of the nanowire diameter. Finally, the result of our calculations is compared with low-temperature photoluminescence experiments on ensemble of nanowires.[1] M. Pierre et al., Nature Nanotechnology 5, 133, (2010).[2] P. Corfdir and P. Lefebvre, J. Appl. Phys. 112, 106104 (2012).[3] R. Calarco et al., Nano Letters 5, 981 (2005).[4] P. Corfdir et al., J. Appl. Phys. 105, 013113 (2009).[5] P. Corfdir et al., Phys. Rev. B 80, 153309 (2009).