Local structure of (Ga,Fe)N and (Ga,Fe)N:Si investigated by x-ray absorption fine structure spectroscopy

X-ray absorption fine-structure (XAFS) measurements supported by {\em ab initio} computations within the density functional theory (DFT) are employed to systematically characterize Fe-doped as well as Fe and Si-co-doped films grown by metalorganic vapour phase epitaxy. The analysis of extended-XAFS data shows that depending on the growth conditions, Fe atoms either occupy Ga substitutional sites in GaN or precipitate in the form of $\epsilon$-Fe$_3$N nanocrystals, which are ferromagnetic and metallic according to the DFT results. Precipitation can be hampered by reducing the Fe content, or by increasing the growth rate or by co-doping with Si. The near-edge region of the XAFS spectra provides information on the Fe charge state and shows its partial reduction from Fe$^{+3}$ to Fe$^{+2}$ upon Si co-doping, in agreement with the Fe electronic configurations expected within various implementations of DFT.