  Using hybrid density functional theory, we address point defects susceptible
to cause charge compensation upon Mg doping of GaN. We determine the free
energy of formation of the nitrogen vacancy and of several Mg-related defects.
The entropic contribution as a function of temperature is determined within the
quasiharmonic approximation. We find that the Mg interstitial shows a
noticeably lower free energy of formation than the Mg substitutional to Ga in
p-type conditions. Therefore, the Mg impurity is amphoteric behaving like an
acceptor when substitutional to Ga and like a double donor when accommodated in
an interstitial position. The hybrid-functional results are then linked to
experimental observations by solving the charge neutrality equations for
semiconductor dominated by impurities. We show that a thermodynamic equilibrium
model is unable to account for the experimental hole concentration as a
function of Mg doping density, due to nitrogen vacancies and Mg interstitials
acting as compensating donors. To explain the experimental result, which
includes a dropoff of the hole concentration at high Mg densities, we thus
resort to nonequilibrium models. We show that either nitrogen vacancies or Mg
interstitials could be at the origin of the self-compensation mechanism.
However, only the model based on interstitial Mg donors provides a natural
mechanism to account for the sudden appearance of self-compensation. Indeed,
the amphoteric nature of the Mg impurity leads to Fermi-level pinning and
accounts for the observed dropoff of the hole concentration of GaN samples at
high Mg doping. Our work suggests that current limitations in p-type doping of
GaN could be overcome by extrinsically controlling the Fermi energy during
growth.
