  The semiconducting behaviour and optoelectronic response of gallium nitride
is governed by point defect processes, which, despite many years of research,
remain poorly understood. The key difficulty in the description of the dominant
charged defects is determining a consistent position of the corresponding
defect levels, which is difficult to derive using standard supercell
calculations. In a complementary approach, we take advantage of the embedded
cluster methodology that provides direct access to a common zero of the
electrostatic potential for all point defects in all charge states. Charged
defects polarise a host dielectric material with long-range forces that
strongly affect the outcome of defect simulations; to account for the
polarisation we couple embedding with the hybrid quantum mechanical/molecular
mechanical (QM/MM) approach and investigate the structure, formation and
ionisation energies, and equilibrium concentrations of native point defects in
wurtzite GaN at a chemically accurate hybrid-density-functional-theory level. N
vacancies are the most thermodynamically favourable native defects in GaN,
which contribute to the n-type character of as-grown GaN but are not the main
source, a result that is consistent with experiment. Our calculations show no
native point defects can form thermodynamically stable acceptor states. GaN can
be easily doped n-type, but, in equilibrium conditions at moderate temperatures
acceptor dopants will be compensated by N vacancies and no significant hole
concentrations will be observed, indicating non-equilibrium processes must
dominate in p-type GaN. We identify spectroscopic signatures of native defects
in the infrared, visible and ultraviolet luminescence ranges and complementary
spectroscopies. Crucially, we calculate the effective-mass-like-state levels
associated with electrons and holes bound in diffuse orbitals...
