## 2 Experimental and Analytical Procedure
### Data Reduction  
We devised a data reduction method which allows to isolate the LO mode frequency shift produced by strain components other than the biaxial strain [38] associated with the lattice parameter mismatch between the GaAs buffer and the pseudomorphic materials GaAsN and GaAsN:H in the planar heterostructure. To this aim, we assume a linear relation between the isotropic biaxial in-plane strain and the LO phonon frequency. Near the wire-barrier interfaces we also assume a linear relation between the anisotropic components of the strain and the phonon frequency.  
Figure 4: (**a**) GaAs-like LO phonon frequency along a direction perpendicular to 10\(-\)um wide wire (see section “Experimental and analytical procedure”). In-plane strain values in the hydrogenated barriers and in the untreated GaAsN reference sample obtained by PR measurements are also reported as described in section “PR measurements and average strain determination”. (**b**) Ga-N mode Raman integrated intensity at the same positions of panel (a). (**c**) Full dots: Same data reported in panel (a) after the data reduction procedure described in section “Data reduction”. Shift with respect to the frequency measured in barriers far from interfaces is proportional to uniaxial stress \(X_{xx}\) (right axis scale). Empty dots: GaAs-like LO phonon frequency profile in the wire before data reduction. Dashed vertical lines indicate wire-barrier interfaces, as derived from data in panel (b). 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))) and from ([38] [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON], [PERSON]. **116**, 245304 (2014). [[http://dx.doi.org/10.1063/1.4905097](http://dx.doi.org/10.1063/1.4905097)]([http://dx.doi.org/10.1063/1.4905097](http://dx.doi.org/10.1063/1.4905097))), with the permission of AIP Publishing.  
These local strain components, in turn, are linearly related to X\({}_{\rm xx}\), the diagonal component of the stress acting perpendicularly to the wire/barrier interfaces. It follows that a linear relationship holds between the phonon frequency and the X\({}_{\rm xx}\) stress component. Figure 4, panel (c) illustrates the data reduction method. Inside the wire, the LO phonon frequency data have been incremented by +1.0 cm\({}^{-1}\). This amount corresponds to double the shift between the LO frequency in the hydrogenated barrier far from the interface and at the interface. The procedure follows from two assumptions: (i) The elastic constants are equal in the untreated and in the hydrogenated GaAs\({}_{0.991}\)N\({}_{0.009}\) alloy, and (ii) they are in accordance with symmetry considerations in the proximity of the interface local uniaxial stress in the wire and in the barrier with equal intensity and the opposite sign. Finite element method (FEM) simulations [11] were made using the same parameters of the sample under experimental investigation. It turns out that the reduced data from Raman experiments favorably compare with the results of simulations, i.e., the uniaxial strain component \(\varepsilon_{\rm xx}\) (linearly related to the diagonal X\({}_{\rm xx}\) stress component) in wires and barriers oriented in the [110] direction (see Figure 5). Both experiments and simulations, in particular, suggest that nonzero uniaxial stress exists even at wire axis, in accordance with the lack of a frequency plateau within the wire.