  Determining the types and concentrations of vacancies present in
intentionally doped GaN is a notoriously difficult and long-debated problem.
Here we use an unconventional approach, based on thermal transport modeling, to
determine the prevalence of vacancies in previous measurements. This allows us
to provide conclusive evidence of the recent hypothesis that gallium vacancies
in ammonothermally grown samples can be complexed with hydrogen. Our
calculations for O-doped and Mg-O co-doped samples yield a consistent picture
interlinking dopant and vacancy concentration, carrier density, and thermal
conductivity, in excellent agreement with experimental measurements. These
results also highlight the predictive power of ab initio phonon transport
modeling, and its value for understanding and quantifying defects in
semiconductors.
