## 2 Experimental and Analytical Procedure
### PR Measurements and Average Strain Determination  
Near-normal incidence PR measurements were collected in the energy range of interest (here typically 1.1-1.9 eV) with a spectral resolution of 1 meV. The probe beam of the standard experimental apparatus [31] was obtained from a 100 W halogen lamp, while the modulated excitation source was provided by the continuous output of a 20 mW Coherent HeNe laser (\(\lambda\) = 632.8 nm; 1-mm spot diameter) mechanically chopped at a frequency of 220 Hz. Typical PR spectra, obtained at room-temperature in the energy range of interest, are shown in Figure 2 for the multi-wires sample (panel a) and for the as-grown GaAsN reference sample (panel b). Despite the presence of the articulated and bulky spectral structures (near 1.42 eV), due to signals coming from the buffer/substrate region and related to the GaAs band gap [27], some PR features particularly interesting for determining the strain status of the GaAsN layer can be observed in both spectra. Figure 1: Schematic illustration of the hydrogenation process used to fabricate the GaAsN wires. View of a sample section near a GaAsN/GaAsN:H vertical interface (the actual wire is 10 \(\upmu\)m wide). The wires run perpendicularly to the figure plane and the Ti wire is sketched as a greyish rectangle on the top surface. The color map shows the effective N concentration (namely, N atoms not passivated by H atoms), as derived quantitatively by extending in two dimensions and in the presence of a Ti mask, the model reported in Ref. [28]. The corresponding effective N concentration value is shown in a false color scale on the right. Reproduced from [16] ([PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON], Appl. Phys. Lett. **101**, 191908 (2012). [[http://dx.doi.org/10.1063/1.4766285](http://dx.doi.org/10.1063/1.4766285)]([http://dx.doi.org/10.1063/1.4766285](http://dx.doi.org/10.1063/1.4766285))), with the permission of AIP Publishing. More in depth:  
1. In the multi-wires sample (Figure 1, panel a), the \"GaAs-like\" spectral structures of the band gap (E\({}_{0}\)') and of the split-off (SO) band (E\({}_{0}\)' + \(\Delta_{0}\)') are due to the optical response of the surface barriers between the GaAsN wires, that hydrogenation has turned into \"GaAs-like\" sections [9; 10; 11]. As previously observed [8; 10; 32], the broadening parameters of these features appear greatly enhanced and their energy position is systematically blueshifted with respect to the corresponding features, E\({}_{0}\) and E\({}_{0}\) + \(\Delta_{0}\), that can be found in the literature of GaAs materials. In particular, the SO blueshift of (\(9\pm 1\)) meV [16], obtained by fitting the spectral structure to the appropriate Aspnes line-shape model function [27], must be related to a sizeable expansion of the host lattice resulting from hydrogenation [10; 11] and can be used to determine the in-plane strain. An analytical procedure based on the deformation potential theory [25], and thoroughly described elsewhere [10], leads to a value of the average compressive in-plane strain \(\varepsilon_{//}\) (in the hydrogenated sections) roughly equal to \(-1.0\times 10^{-3}\). 2. In the low energy part of the same spectrum (Figure 1, panel a) one can see the contribution to the PR signal coming from the GaAsN sections (wires). It originates from the presence of the E-band [6; 7] at E-\({}^{w}\) = 1.265 eV, as determined by a best fit. This value is 11 meV higher than that (E-\({}^{u}\) = 1.254 eV) obtained for the same band in the untreated GaAsN sample (see Figure 2, panel b). One should note that the strain field produces shift and splitting of GaAsN valence bands [6; 7]. On the other hand, at room temperature, probably due to broadening effects, the doublet is unresolved in the optical response of both samples. For this reason, a single Aspnes model function [27] was used to derive the energy (E-) of the band gap of GaAsN.