were quantified by comparison to a standard reference sample containing [$\mathrm{N_{s}^{0}}$]{} and were performed below microwave power saturation. Ultraviolet-visible (UV-vis) and IR absorption measurements were performed in PerkinElmer Lambda 1050 and Spectrum GX spectrometers, respectively.

   Sample               Dopants            Growth run    Annealing temp ()
  -------- -- --------------------------- ------------ -------------------
     A         [$^{15}\mathrm{N}$]{}, Si       1                  As-grown
     B         [$^{15}\mathrm{N}$]{}, Si       1                      1600
     C         [$^{15}\mathrm{N}$]{}, Si       1                      1800
     D         [$^{15}\mathrm{N}$]{}, Si       1                      2000
     E         [$^{15}\mathrm{N}$]{}, Si       1                      2200
     F         [$^{15}\mathrm{N}$]{}, Si       1                      2400
     G                   N, Si                 2                      1800

  : Summary of the samples employed in this study. All post-growth anneals were performed under stabilizing pressure and for , except for [Sample G]{}which was annealed for . Dopants without explicit isotopes are natural abundance.[]{data-label="tab:sample_summary"}

Computational method
--------------------

Density functional theory within the supercell approach was employed using the AIMPRO software package[@rayson2009highly]. We have used a generalized gradient approximation (GGA)[@perdew1996generalized] for the exchange and correlation and the pseudo-potential approximation[@hartwigsen1998relativistic] to remove the core electrons from explicit determination. Kohn-Sham functions were expanded in a basis of atom-centered Gaussian functions[@Goss2007] using four d-type functions resulting in 40 functions per atom. The charge density was Fourier transformed using plane waves with a cutoff of 300Ha, which results in total energy convergence 