Molecular Nitrogen Formation in Nitrogen-Implanted (100) $\beta-Ga_2O_3$ Revealed by Temperature-Dependent $N$ $K$-edge XANES

The realization of $p$-type doping in wide-band-gap oxide semiconductors remains a major challenge, particularly in $\beta-Ga_2O_3$ where nitrogen has long been considered a potential acceptor dopant but has consistently failed to produce hole conductivity. Here we investigate the microscopic configuration of implanted nitrogen in (100) $\beta-Ga_2O_3$ using temperature-dependent $N$ $K$-edge x-ray absorption spectroscopy. The spectra reveal a pronounced $\pi^*$ resonance characteristic of molecular nitrogen, which becomes increasingly dominant upon thermal annealing. First-principles calculations and multiple-scattering simulations reveal a pronounced tendency for nitrogen atoms to form $N-N$ bonded configurations in the $Ga_2O_3$ matrix, particularly in defect-rich environments created by ion implantation, reproducing the characteristic spectral features observed in the $N$ $K$-edge XANES spectra. Structural analysis further indicates that implantation induces a defect-rich near-surface layer with local $\beta$-to-$\gamma$-like structural motifs, highlighting the strongly nonequilibrium structural environment in which nitrogen incorporation occurs. Reported results show that implanted nitrogen preferentially forms molecular $N_2$-like configurations rather than substitutional acceptors. Our results provide a microscopic explanation for the long-standing failure of nitrogen acceptor doping in $\beta-Ga_2O_3$ and reveal dopant molecularization as a previously overlooked pathway for impurity incorporation under strongly nonequilibrium implantation conditions.